Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure (KAIST Research Series) 9811680353, 9789811680359

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KAIST Research Series

Ji-Ho Song Chung-Youb Kim

Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure

KAIST Research Series Series Editors Byung Kwan Cho, Department of Biological Sciences, KAIST, Daejeon, Taejon-jikhalsi, Korea (Republic of) Han Lim Choi, Department of Aerospace Engineering, KAIST, Daejeon, Taejon-jikhalsi, Korea (Republic of) Insung S. Choi, Department of Chemistry, KAIST, Daejeon, Korea (Republic of) Sung Yoon Chung, Graduate School of EEWS, KAIST, Daejeon, Korea (Republic of) Jae Seung Jeong, Department of Bio and Brain Engineering, KAIST, Daejeon, Korea (Republic of) Ki Jun Jeong, Dept. of Chemical & Biomolecular Engin., KAIST, Daejeon, Korea (Republic of) Sang Ouk Kim, Dept. of Materials Science & Engineering, KAIST, Daejeon, Korea (Republic of) Chongmin Kyung, School of Electrical Engineering, KAIST, Daejeon, Korea (Republic of) Sung Ju Lee, School of Computing, KAIST, Daejeon, Korea (Republic of) Bumki Min, Department of Mechanical Engineering, KAIST, Daejeon, Korea (Republic of)

More information about this series at https://link.springer.com/bookseries/11753

Ji-Ho Song · Chung-Youb Kim

Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure

Ji-Ho Song Mechanical Engineering Korea Advanced Institute of Science and Technology Daejeon, Korea (Republic of)

Chung-Youb Kim Mechanical Design Engineering Chonnam National University Yosu-city, Korea (Republic of)

ISSN 2214-2541 ISSN 2214-255X (electronic) KAIST Research Series ISBN 978-981-16-8035-9 ISBN 978-981-16-8036-6 (eBook) https://doi.org/10.1007/978-981-16-8036-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Nearly three years ago, namely in 2017, the authors, Song, Kim and Park have published the book “Expert systems for Fatigue Life Predictions” from Nova Science Publishers. Generally, fatigue life consists of fatigue crack initiation period and fatigue growth or propagation period. However, to accurately define fatigue crack initiation life is somewhat difficult but studies on fatigue crack initiation life have been well performed over so long time by many researchers. So many methods to estimate fatigue crack initiation life have been also proposed so far. The word “Fatigue Life” means in the previous book the so-called fatigue crack initiation life and it was estimated by the so-called cumulative fatigue damage rules proposed by many researchers over a long time. Accordingly, a large number of fatigue life data obtained under both constant amplitude loading and variable amplitude one have been accumulated, including random loading, and many accepted fatigue theories on the accumulation of fatigue damage can be found. As have been already referred to in the previous book, an expert system seems to be a good tool for ordinary engineers. When they face complicated engineering problems, they need relevant expertise knowledge of the problems. So, we have published the previous book named Expert systems for Fatigue Life Predictions based on our wide range of researches intended to develop some expert systems for fatigue assessment. On the other hand, the fatigue growth period or life is apparently clear and also defining the fatigue damage for the crack growth period is so easy because the crack length can be identified as fatigue damage. Since fatigue crack growth is essentially a very interesting topic, researches on the topic have been performed worldwide by many researchers. Paris and Erdogan in 1963 have first reported that fatigue crack growth can be well represented by the stress intensity factor, and Elber in 1970 first discovered that crack closure phenomenon appears in fatigue crack. The fatigue crack closure phenomenon is considered to be the most governing factor for fatigue crack growth. Particularly, the fatigue crack closure problem has been investigated for many aspects worldwide for a long time by many researchers and not a few useful results have been obtained. They have been utilized through the use of a computer database v

vi

Preface

and commercial software. However, due to difficulties in accurately measuring the phenomenon, reliable data and results are not so much. We have performed fatigue crack growth researches for about more than 40 years, using a refined method for accurately measuring crack closure behaviour, and as a result, we have a comparatively large amount of reliable data and results. Now we collect and summarize them and have planned to write an expert system for crack growth predictions, particularly based on crack closure, which is the most important governing factor for fatigue crack growth. The expert system for fatigue crack growth predictions based on crack closure is developed using the MATLAB software and consists of six parts: the first part is to define the material classification, and the second part is to describe fatigue crack growth properties in terms of effective stress intensity factor range, that is, the da/dN versus ΔK eff relationship. If the da/dN versus ΔK eff curve data are not available at hand, the user can select relevant da/dN versus ΔK eff curve data from a material database provided in this expert system. The third part is to input the specimen configuration and then to automatically obtain stress intensity factor K expressions proposed by ASTM (American Society for Materials and Testing) International standards, the fourth part is to input or construct load histories to be used and to count load cycles using a most reliable counting method proposed by ASTM and the fifth part is to predict fatigue crack growth for employed load histories and specimen. The last part is to report the obtained results. In the third part, users can select one among eight kinds of through-thickness long crack or a surface crack as a part-through crack. In the fourth part, the system provides users to construct programmed and random loads of 2 degrees of freedom and to select one among five kinds of counting methods, namely peak, level crossing, rain-flow, range-pair and simplified rain-flow method. In the fifth part of the prediction process, users can input also the crack opening data relevant for the load history employed and specify the range of crack length to be predicted. The most important is that the proposed publication will include practically applicable software of the expert system. Users can also use the expert system as an independent software for curve fitting or for the construction of random loads of various history lengths. This book introduces a detailed expert system that is developed and provides the expert system software as a Zip file placed at the end of Chap. 1for the online publication of the book. The software can be also downloaded at URL. The expert system for fatigue crack growth predictions based on the crack closure may be the first, practically applicable fatigue crack growth expert system in the world and the second fatigue assessment expert system followed by the previous expert system developed by the authors. However, we must recognize that the expert system could not be validated sufficiently because sufficient validation data is not available yet. Adversely, there are many parts left to be improved by users. This book and the expert system software may be useful for nearly all engineers, researchers and technologists from the academic, industrial and government sectors who engage in fatigue design and maintenance of structures and also for advanced undergraduate and beginning graduate-level engineering students in universities,

Preface

vii

particularly in the department of mechanical engineering, aerospace engineering, civil engineering and metallurgy. We would like to thank Mr. Smith Ahram Chae, Editor, Ms. Shalini Monica, Project Coordinator and Ms. Manopriya Saravanan, Project Manager, Physical Science and Engineering, Springer, for recommending and arranging to write this book. Seoul, Korea July 2021

Ji-Ho Song Chung-Youb Kim

Contents

1 Important Problems in Fatigue Crack Growth of Materials . . . . . . . . . 1.1 Fatigue Crack Growth Rates in Terms of Stress Intensity Factor Range ΔK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Fatigue Crack Growth Rates in Terms of the Effective Stress Intensity Factor Range ΔK eff Based on the Fatigue Crack Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Fatigue Crack Closure Indispensable for the Fatigue Crack Growth Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Many Issues in Fatigue Crack Closure Measurement . . . . . . . . . . . . . . 1.4.1 The Effect of Stress State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Difficulties in Accurate Determination of the Crack Opening Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Other Expressions of the Effective Stress Intensity Factor Range K eff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Representation of da/dN–K eff Curve . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 The Error Criterion in the da/dN–K eff Curve . . . . . . . . . . . . . . . . . . . 1.7 Relations Between the Effective Crack Opening Ratio U and the Stress Ratio R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 The Error Criterion in Fatigue Crack Growth Predictions . . . . . . . . . . 1.9 Brief Details of Fatigue Crack Growth Predictions in This System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9.1 The Importance of Fatigue Crack Closure Data . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1

4 5 5 5 6 7 8 11 12 13 16 16 17

2 Composition of the Expert System Developed for Fatigue Crack Growth Predictions: FatiCraGro Expert . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3 Part I of the Fatigue Crack Growth Expert System: Material Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

ix

x

Contents

4 Part II of the Fatigue Crack Growth System: Fatigue Crack Growth Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.1 da/dN Versus K eff Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5 Part III of the Fatige Crack Growth Expert System: Specimens and Their Stress Intensity Factor K Expression . . . . . . . . . . . . . . . . . . . . 39 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 6 Part IV of the Fatigue Crack Growth Expert System: Load Histories and Cycle Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 7 Part V of the Fatigue Crack Growth Expert System: Detailed Prediction Methods of Fatigue Crack Growth . . . . . . . . . . . . . . . . . . . . . . 7.1 Crack Growth Prediction of Long Cracks under Constant Amplitude Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Prediction Method by Kikukawa et al. for Long Cracks under Variable Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Prediction Method for Surface Crack Growth . . . . . . . . . . . . . . . . . . . . 7.4 Prediction for Short Fatigue Crack Growth . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51 51 54 58 62 69

8 Part VI of the Fatigue Crack Growth Expert System: Reporting of Results Obtained . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 9 Configuration of the Fatigue Crack Growth Expert System and How to Install and Run the Fatige Crack Growth Expert System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Chapter 1

Important Problems in Fatigue Crack Growth of Materials

Abstract The history of researches on fatigue crack growth is briefly described and some problems in fatigue crack growth are pointed out. Three types of fatigue crack growth rate curves, conventional, tri-linear transitional and multi-linear curves, are defined. Fatigue crack growth rates are influenced by Young’s modulus of material, E. The effect of stress ratio and fatigue crack growth behaviour under variable loading can be explained by the fatigue crack closure. Some important issues in fatigue crack closure measurement are described. The error criteria in da/dN–K eff curve and fatigue crack growth predictions are pointed out and the details of crack growth predictions to be performed are briefly described.

1.1 Fatigue Crack Growth Rates in Terms of Stress Intensity Factor Range ΔK As has already been described in the Preface, it was Paris and Erdogan [1] in 1963 who first expressed fatigue crack growth successfully in terms of the elastic fracture mechanic parameter, stress intensity factor range. They reported that fatigue crack growth data, da/dN, obtained from different sources can be represented in terms of stress intensity factor range ΔK, and da/dN versus ΔK relationship can be expressed as a straight line on a log–log diagram over a wide range of 10–8 –10–2 in./cycle and the slope of the straight line is four. This is called the fourth power law of Paris’ equation represented as da = C(K )4 dN

(1.1)

However, it was somewhat exaggerated. In 1971, Frost et al. [2] rearranged a large number of fatigue growth rate data in National Engineering Laboratory of England, Supplementary Information The online version contains supplementary material available at (https://doi.org/10.1007/978-981-16-8036-6_1).

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6_1

1

2

1 Important Problems in Fatigue Crack Growth of Materials

in terms of stress intensity factor ΔK, along with their equation as da = Cσ 3 a dN

(1.2)

da/dN

They concluded that the data are well represented in terms of ΔK, as well as their equation, and reported that the fatigue crack rate curve should be of sigmoidal form on a logda/dN-logΔK diagram as shown in Fig. 1.1. The straight line between two asymptotic lines corresponds to Paris’equation. The left asymptotic line corresponds to the fatigue crack growth threshold K th and the right asymptotic line corresponds to the fatigue fracture K fc . Usually, people prefer the sigmoidal form for representing the fatigue crack growth rate curve. In 1982, Yoder et al. [3] demonstrated that fatigue crack growth rate curves of 7000 series aluminium alloys have the tri-linear transitional forms influenced by microstructures and Jono et al. [4] have investigated the detail of the tri-linear transitional form on aluminium alloys and expressed the form like as shown in Fig. 1.2. In the growth rate regions, Regions I and III, the growth rate curves may be linear forms, instead of asymptotic forms. In such cases, the fatigue crack growth rate curve will have a multi-linear curve consisting of 5 lines like as shown in Fig. 1.3. It is assumed in the case of a multi-linear crack growth rate curve that neither fatigue crack growth rate threshold nor fatigue fracture exists. It principally means that fatigue crack grows at any stress intensity factor level in Regions I and III. However, it may be reasonable to assume that in Region III, fatigue crack growth in terms of stress

m

I

ΔKth

Region II

ΔK

Fig. 1.1 Sigmoidal form of fatigue crack growth rate curve

III

Kfc

1.1 Fatigue Crack Growth Rates in Terms of Stress Intensity Factor Range ΔK

da/dN

7%

3

IIB

IIA-B 7$

IIA

I

Region II

ΔKth

III Kfc

ΔK

Fig. 1.2 Tri-linear transitional form of fatigue crack growth rate curve

da/dN

7%

IIB

IIA-B 7$

IIA

I ΔKth

Region II

ΔK

III Kfc

Fig. 1.3 Multi-linear form of fatigue crack growth rate curve

intensity factor range ΔK terminates when the stress averaged over the ligament area becomes equal to the stress of 1.25σYS (σYS : 0.2% offset yield strength) or the effective yield strength termed the flow strength σFS = (σYS + σULT )/2 [5]. For convenience, we may replace 1.25σYS or the flow strength with the tensile stress σB .

4

1 Important Problems in Fatigue Crack Growth of Materials

So, we will classify the fatigue crack growth rate curve into three types: first, conventional curve like as shown in Fig. 1.1; secondly, tri-lineartransitional curve, as shown in Fig. 1.2; and lastly, multi-linear curve like as shown in Fig. 1.3. For all materials, fatigue crack growth rate curves are well expressed using material elastic modulus E like as in the following equation [6, 7]:   K n da =C dN E

(1.3)

This result is very important because it means if the materials have the same elastic modulus E, their fatigue crack growth rate curves are similar. For example, among aluminium alloys, there are no large differences in fatigue crack growth rate curves. However, the fatigue crack growth represented by the normal stress intensity factor range ΔK shows the effect of mean load, namely the effect of stress ratio, and also cannot explain the fatigue crack growth under variable loading.

1.2 Fatigue Crack Growth Rates in Terms of the Effective Stress Intensity Factor Range ΔK eff Based on the Fatigue Crack Closure In 1970, Elber [8] discovered that crack closure appears in the fatigue crack growth process and proposed that fatigue crack growth rate should be expressed by the effective stress intensity factor range K eff based on the fatigue crack closure phenomenon as da = C(K e f f )m dN

(1.4)

K e f f = K max − K op = U K

(1.5)

where K max and K op are the maximum and crack opening stress intensity factors, respectively, and U is the effective crack opening ratio defined as U=

K e f f K max − K op = K K max − K min

(1.6)

where K min is the minimum stress intensity factor. He reported that the fatigue crack closure phenomenon can explain the effect of stress ratio and fatigue crack growth behaviour under variable loading. He also proposed the effective opening ratio U versus the stress ratio R relationship for aluminium alloy 2024-T3 as.

1.2 Fatigue Crack Growth Rates in Terms of the Effective Stress Intensity Factor Range …

U = 0.5 + 0.4R, −0.1 < R < 0.7

5

(1.7)

It has been at present well known that the fatigue crack closure phenomenon can explain the effect of stress ratio for almost all materials but the U versus R equation proposed by Elber is questionable. The fatigue crack closure can explain sometimes qualitatively but not quantitatively the fatigue crack growth behaviour under nonstationary variable loading as Hi-Lo or Lo-Hi two-step loading under which crack growth retardation or acceleration abruptly occurs [4, 9]. On the contrary, the fatigue crack closure can explain well the fatigue crack growth behaviour under stationary variable loading as repeated Gaussian random loading of relevant history length [10, 11]. However, there are many problems in fatigue crack closure.

1.3 Fatigue Crack Closure Indispensable for the Fatigue Crack Growth Prediction As has been briefly described in Sect. 1.2, at present it has been well known that the fatigue crack closure phenomenon can explain the effect of stress ratio and fatigue crack growth behaviour under variable loading, particularly under stationary variable loading. It is desirable to employ a method based on the fatigue crack closure, instead of using conventional K, for predicting fatigue crack growth. The da/dN–K eff curve and the effective crack opening ratio data are necessary and the most crucial issue to them is to accurately measure and determine the crack opening or crack closure point.

1.4 Many Issues in Fatigue Crack Closure Measurement 1.4.1 The Effect of Stress State First, fatigue crack closure behaviour is different between the interior and the surface of specimen [6], because the interior of specimen is under plane strain state and the surface of specimen is under plane stress state. This experimental fact means that the results may be different depending on where and how the fatigue crack closure is measured. Most optical methods including the interferometric strain/displacement gage method developed by Sharpe [12, 13] measure the fatigue crack closure on the surface under plane stress which is somewhat higher than that of the interior of specimen under plane strain. Acoustic methods using ultrasonic [14] or Rayleigh waves [15] measure the closure behaviour of interior of specimen but instruments for the methods are high cost and the methods are not easy to use.

6

1 Important Problems in Fatigue Crack Growth of Materials

Kikukawa group of Osaka University, Japan, developed the unloading elastic compliance method using the load-differential displacement hysteresis loop with the strain gage or displacement gage and performed fatigue crack growth experiments using side-grooved specimens in order to measure the fatigue crack closure of the interior of specimen under plane strain [16]. His method seems a good, proper method for measuring fatigue crack closure but employed an electrical subtraction circuit to obtain the differential displacement signal in order to magnify the signal due to fatigue crack closure. As the use of an electrical subtraction circuit for measurement was not familiar to fatigue researchers at that time, the method did not become popular. Instead of an electrical subtraction circuit, it is possible at present to use a computer program, but most fatigue researchers even now prefer to measure fatigue crack closure optically.

1.4.2 Difficulties in Accurate Determination of the Crack Opening Point Commonly the fatigue crack closure or opening point is determined using load– displacement or load-differential displacement hysteresis loop, or other load crack closure signal (e.g., transmitted wave in Rayleigh waves method) hysteresis loop. However, accurately determining the fatigue crack closure or opening point is normally very difficult. As the fatigue crack closure or opening point is generally determined visually by naked eyes, the results are apt to be dependent on observers. This means that the results may be arbitrary. In order to accurately determine the crack opening point without human arbitrariness, Kang and Song [17] developed an automated method using a neural network. They used differential displacement signal curves and employed a backpropagation neural network of three layers. They examined the measurement accuracy and precision of the neural network method, performing computer simulation extensively for various combinations of crack opening levels and signal-to-noise (S/N) ratios. As the neural network method does not depend on the observer, the method is expected to give consistent and unbiased results. They applied the method to constant amplitude loading tests on middle tension (MT) and single-edge-bending (SEB) specimens of aluminium alloy. The crack opening point by the neural network was found to be somewhat lower than that by visual measurement for positive values of stress ratio, while nearly the same or slightly higher for negative values of stress ratio. The validity of the method was not clear for variable loading and it is still laborsome to obtain load-differential displacement hysteresis loop signal for the method. A method was proposed by Donald [18] to calculate the effective stress intensity factor range K eff without determining crack closure or opening point. The method is proposed to explain the crack tip shielding and uses only the compliance ratios obtained simply from the load–displacement curve. Therefore the method was called the compliance ratio technique. The original compliance ratio technique was found

1.4 Many Issues in Fatigue Crack Closure Measurement

7

to be not sufficient for fatigue crack closure measurement, due to signal noise. So, Donald proposed the adjusted compliance ratio technique in 1997 [18]. However, the adjusted technique is not as easy to use as the original compliance ratio technique and it is not clear that the technique provides reliable results. As it is very important to determine the crack opening point accurately without arbitrariness, Chung and Song [20] proposed a method to precisely determine crack opening load based on the ASTM compliance offset method, that is, the normalizedextended ASTM method. The original ASTM compliance offset method has been well established and is easy to use. But it has some drawbacks. Chung and Song discussed the drawbacks in detail and improved the method through computer work. They concluded that a sampling rate of 300 data pairs per load and displacement cycle is desirable and a 1% shift of 10% segment size provides the best results. The relative compliance offset of 8% is recommended rather than the normal compliance offset of 2% in the original ASTM compliance offset method.

1.4.3 Other Expressions of the Effective Stress Intensity Factor Range ΔKeff Normally, the effective stress intensity factor range K eff is defined as in Eq. (1.5), that is K e f f = K max − K op = U K

(1.5)

Paris–Tada–Donald [21] have proposed other expressions of the effective stress intensity factor range based on the partial crack closure. The partial crack closure refers to the phenomenon that the crack closes behind the crack tip, not at the crack tip. They have proposed two methods, 2/π and 2/π0 methods, respectively, expressed as.   2 2 K min (1.8) the 2/π method : K 2/π = K max − K op − 1 − π π the 2/π method : K 2/π0 = K max −

2 K op π

(1.9)

They have reported that the 2/π method gives a slight underestimate of normal K eff , while the 2/π0 method slightly overestimates. Koo–Song–Kang [22] have investigated the validity of 2/π and 2/π0 methods, performing random loading crack growth tests on 2024-T351 aluminium alloy. According to their conclusion, the 2/π and 2/π0 methods improve both the accuracy and precision of crack growth predictions under random loading. However, the above two methods have not been yet confirmed sufficiently. We will here employ the normal expression defined by Eq. (1.5).

8

1 Important Problems in Fatigue Crack Growth of Materials

1.5 Representation of da/dN–K eff Curve The da/dN–K eff curve can also be classified into three types: conventional, tri-linear transitional and multi-linear curves as Fig. 1.4 shows, as well as the da/dN–K curve. Generally, most steel materials show the conventional curves, while non-ferrous materials like aluminium and titanium alloys show tri-linear transitional curve. In Region I of multi-linear curve, theoretically there is no threshold for fatigue crack growth. However, we employ the fatigue crack growth threshold (K eff )th as the K eff value corresponding to a growth rate of 10–10 m/cycle for convenience, likely as

da/dN

7%

da/dN

m

IIB

IIA-B 7$ IIA

I

Region II

(ΔKeff)th

ΔKeff

III

I

a)

Kfc

(ΔKeff)th

a) conventional

Region II

ΔKeff

b) tri-linear-transitional

da/dN

7%

IIB

IIA-B 7$ IIA

I

Region II

(ΔKeff)th

ΔKeff

c) multi-linear Fig. 1.4 da/dN–K eff fatigue growth rate curves.

III Kfc

III Kfc

1.5 Representation of da/dN–K eff Curve

9

ASTM defines K th as the K value corresponding to a growth rate of 10–10 m/cycle [5]. Jono et al. [4] have reported the following equation similar to Eq. (1.3) as da C =√ dN εf



K e f f E

m (1.10)

This means that Young’s modulus E has a large effect on the relationships of da/dN–K eff as well as those of da/dN–K. For various aluminium alloys, Fig. 1.5 shows da/dN–K eff curves obtained on various stress ratios from many different sources. The data are found to be widely dispersed. The data of 6063-T5 by Veers locate somewhat lower than other aluminium alloys, while the data of 2124-T351 by the Ritchie group lie at the highest. We cannot represent all the data by a single da/dN–K eff curve because the data scatter is very large. Fig. 1.6 shows da/dN–K eff curves obtained by two different sources for copper. We can hardly say that they are nearly the same. We cannot represent all the data by a single da/dN–K eff curve because the data scatter is very large. In Fig. 1.7, the da/dN–K eff curves obtained on various stress ratios are plotted for various steel alloys. Except for Welten60 and 15MnVN steel alloys, most of the da/dN–K eff curves seem to lie together.

Fig. 1.5 da/dN–K eff curves for various aluminium alloys.

10

1 Important Problems in Fatigue Crack Growth of Materials

Fig. 1.6 da/dN–ΔK eff curves for copper.

Fig. 1.7 da/dN–K eff curves for various steel alloys

1.5 Representation of da/dN–K eff Curve

11

Fig. 1.8 da/dN–K eff curves for titanium alloys

Figure 1.8 shows da/dN–K eff curves for titanium alloys. The data of Ti-24Al11Nb and Ti-25Al-17Nb alloys show a somewhat different trend from other titanium alloys. All da/dN–(K eff /E) curves for four kinds of materials, aluminium alloys, copper, steel alloys and titanium alloys are shown in Fig. 1.9. Although Eq. (1.10) means that the fracture ductility of the material may influence da/dN–K eff crack growth rate curve of the material, the data scatter seems to be too large beyond the variation of fracture ductility of the material. It is not nearly possible to utilize Eq. (1.10) proposed by Jono et al. [4]. In the expert system developed, all the da/dN–K eff curve data shown in Fig. 1.9 are included in the material database so that the user can utilize them easily.

1.6 The Error Criterion in the da/dN–K eff Curve The da/dN–K eff curve is generally thought to show an almost identical one, irrespective of specimen geometry, stress ratio etc. However, sometimes we may find different da/dN–K eff curves depending on specimen geometry, stress ratio etc. Naturally, the da/dN–K eff curve has a√certain scatter band of error. To authors’ experience, the scatter band of factor of 2 as an error criterion can be obtained for da/dN–K eff curve by performing fatigue crack growth testing carefully [19].

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1 Important Problems in Fatigue Crack Growth of Materials

Fig. 1.9 All da/dN–(K eff /E) curves for four kinds of materials

√ The scatter band of factor of 2 means that the data are falling within √12 ≤ √ ( ddaN )observed ≤ 2. The ratio of the maximum line (representing the maximum ( ddaN )regression line √ data) versus the minimum line (representing the minimum data) is √12 = 2 in this 2 √ case. Generally, the error criterion, the scatter band of factor of 2, seems to be so small that it may be difficult for ordinary researchers to utilize the criterion.

1.7 Relations Between the Effective Crack Opening Ratio U and the Stress Ratio R The fatigue crack closure is known to be influenced by the stress ratio and many kinds of relationship of the effective opening ratio U versus the stress ratio R have been proposed for many materials by many researchers. As has been already described, Elber [4] proposed Eq. (1.7) for aluminium alloy 2024-T3. Schijve [23] proposed the following equation for aluminium alloy 2024-T3: U = 0.55 + 0.33R + 0.12R 2 , − 1 < R < 0.54

(1.11)

Meggiolara et al. [24] proposed other equation for aluminium alloy 2024-T3 as: U = 0.52 + 0.42R + 0.06R 2 , − 1 < R < 0.5

(1.12)

1.7 Relations Between the Effective Crack Opening Ratio U and the Stress Ratio R

13

The above three equations, Eqs. (1.7), (1.11) and (1.12), for aluminium alloy 2024-T3 show similar values but not identical. Katcher and Kaplan [25] proposed the Eqs. (1.13) and (1.14) for aluminium alloy 2219-T851 and recrystallize annealed titanium alloy Ti-6Al-4V, respectively, as: U = 0.68 + 0.91R, 0.08 < R < 0.32 for aluminium alloy 2219 − T851 (1.13) and U = 0.73 + 0.82R, 0.08 < R < 0.35 for recrystallize annealed titanium alloy Ti − 6Al − 4 V

(1.14)

For steels, Madox et al. [26] and Kumar-Singh [27] proposed the following equations, respectively: Madox et al. : U = 0.75 + 0.25R, − 0.5 < R < 0.5

(1.15)

Kumar-Singh:U = 0.7 + 0.15R(2 + R), − 0.5 < R < 0.8

(1.16)

There are some review papers [28–30] on the relationship of U versus R. It has been well known that fatigue crack closure, that is, the effective crack opening ratio U also varies depending on fatigue crack growth rate, even at an identical stress ratio. It means that the U–R relationship is different between high and low growth rate regions. The trend is remarkable, particularly for aluminium alloys and others whose da/dN versus K or da/dN versus K eff curve shows transitional one. Jono et al. [4] reported the typical U–K eff curve, as Fig. 1.10 shows schematically. The transition points in the U–K eff curve nearly correspond to those TA and TB in the da/dN–Keff curve of Fig. 1.4. This means the crack closure behaviour relates closely to the fatigue crack growth mechanism. The expression of U–K eff curve may give a good insight into fatigue crack growth mechanisms but is not practically easy to use. The U–K curve as shown in Fig. 1.11 or K op –K curve is commonly well used .

1.8 The Error Criterion in Fatigue Crack Growth Predictions The error criterion, the scatter band of a factor of 2, is well commonly used in fatigue crack growth predictions [31–33].

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1 Important Problems in Fatigue Crack Growth of Materials

U

R

R

ΔKeff

TA

TB

or da/dn

Fig. 1.10 Typical U–K eff curve

Fig. 1.11 U–K curve

About 40 years ago, a round-robin analysis was conducted by the ASTM task group to predict the fatigue crack growth in 2019-T851 aluminium middle-tension (MT) specimens under random spectrum loadings. Chang [34] has summarized the results. Six kinds of analytical prediction methods used for tests are as follows: Method I: Walker crack growth rate equation; compressive loads set to zero; tensile load retardation not accounted for Method II: Root mean square. Method III: Modified Elber’s equation; load interaction effects accounted for by analytical closure model

1.8 The Error Criterion in Fatigue Crack Growth Predictions

15

Table 1.1 Prediction results of ASTM round-robin tests Method

I

Range (Npred /Nobserved )

0.58~ 1.78 0.82~ 2.13 0.64~ 2.52 0.82~ 1.55 1.24~ 2.65 0.80~ 1.46

II

III

IV

V

VI

Average 0.96 (Npred /Nobserved d)

1.38

1.07

1.11

1.74

1.13

Standard deviation

0.42

0.33

0.20

0.42

0.22

0.36

Method IV: Modified Forman’s equation; load interaction effects accounted for by multiple parameter yield zone model Method V: Walker’s crack growth rate equation; compressive loads set to zero; tensile load retardation effect accounted for by generalized Willenborg model Method VI: Walker’s crack growth rate equation; load interaction effects accounted for by Willenborg/Chang model These methods include almost all effective methods developed to account for load interaction effects by that time. Table 1.1 shows prediction results by each method. The standard deviation in prediction results of Methods I and II which do not account for load interaction effects is relatively high. The prediction results by Method II, root mean square, seems to be not so bad in comparison with Method III based on crack closure or Method V. This means you may predict fatigue crack growth moderately sometimes even without accounting for load interaction effects under spectrum loading where the load interaction effects, acceleration and retardation may occur coincidentally. Method V predicts that the predicted crack growth life N pred is always longer than the test life N observed . This means that Method V always predicts non-conservative estimates. Method IV gives the best results in regard to the range, average and standard deviation of (N pred /N observed ). Method VI gives a similar good result. The following conclusions were obtained by Chang [34]: 1.

2. 3. 4.

Reasonably accurate predictions were achieved for MT specimens subjected to random spectrum loadings using constant amplitude crack growth rate data of MT specimen and the state-of-the-art crack growth prediction methods that account for load interaction effects. The improvement of prediction accuracies seems to depend upon the availability of low-value K crack growth rate data. The trade-off between the computation cost and prediction accuracy should be considered when selecting analytical prediction methods. The extrapolation of the results of the round-robin analysis to other materials and different structural components containing cracks needs to be investigated further.

Referring to Chang’s conclusions, the error criterion, scatter band of a factor of 2, may be said to be reasonable.

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1 Important Problems in Fatigue Crack Growth of Materials

1.9 Brief Details of Fatigue Crack Growth Predictions in This System In fatigue problems, the prediction usually means to predict the fatigue behaviour under variable loading by using the results obtained under constant amplitude loading. In fatigue crack growth problem, it is also very important to predict fatigue crack growth under variable loading by using the constant amplitude crack growth results. Additionally, there are other two great issues in fatigue crack growth problem, i.e. surface cracks and short cracks. Surface cracks are the most well-observed cracks in practical situations. The size of the surface crack is defined by both the crack depth a and crack length c. As the crack length appears on the specimen surface, it can be measured relatively easily. On the other hand, the crack depth is in the interior of specimen difficult to measure its crack growth behaviour. For surface cracks, it is important to predict fatigue crack growth under constant amplitude loading by using the reference constant amplitude crack growth results obtained for the standard long crack specimen. The variation of aspect ratio a/c of the surface crack is very important because the aspect ratio of surface crack influences the value of the stress intensity factor of surface crack. The variation of aspect ratio a/c of the surface crack may be utilized to discuss the validity of the crack growth prediction method used. The short crack is a primary important topic of fatigue crack growth recently. The remarkable characteristic that a short crack grows faster than a long crack at the same K is practically an important and theoretically interesting topic. It is difficult even to predict surface crack growth under constant amplitude loading by using the reference constant amplitude crack growth results obtained for the standard long crack specimen. Many researchers have widely investigated short crack growth behaviour and some methods have been proposed to predict the variation in the crack opening of short cracks with crack growth. The expert system in this work treats these surface and short cracks issues.

1.9.1 The Importance of Fatigue Crack Closure Data Despite difficulties in the measurement of fatigue crack closure, fatigue crack closure is at present considered to be the most governing factor for fatigue crack growth. It is very important to obtain and collect reliable data on fatigue crack closure and further to create a database, if possible. The data on fatigue crack closure are divided into the U–K eff curve data and the effective opening ratio U data. The effective opening ratio U data may be represented by U–R, U–K eff , U–K or K op –K curve. However, there are not so sufficient data, particularly for experimental data. In this system, almost all experimental fatigue closure data obtained so far are collected from the user to utilize.

References

17

References 1. Paris P, Erdogan F (1963) A critical analysis of crack propagation laws. J Basic Engng, Trans ASME D 85:528–534 2. Frost NE, Pook LP, Denton K (1971) A fracture mechanics analysis of fatigue crack growth data for various materials. Engng Fract Mech 3:109–126 3. Yoder GR, Cooley LA, Crooker TW (1982) On microstructural control of near-threshold fatigue crack growth in 7000-series aluminum alloys. Scr Metall 16:1021–1025 4. Jono M, Song J, Mikami S et al (1984) Fatigue crack growth and crack closure behavior of structural materials. J Mat Sci Japan 33:468–474 (in Japanese) 5. Designation: E647–15, (2020) Standard test method for measurement of fatigue crack growth rates. Annual book of ASTM standards. 03(01):707–768 6. Speidel MO (1974) Fatigue crack growth at high temperature. High-temperatures in gas turbines. Elsevier, p207–255 7. Usami S (1982) Applications of threshold cyclic –plastic-zone-size criterion to some fatigue limit problems. EMAS, Fatigue threshold, pp p205-238 8. Elber W (1971) The significance of fatigue crack closure. ASTM STP486:230–242 9. There are many references of such kind. For example, Jono M, Kanaya T, Sugeta A, et al(1983) Retardation of fatigue crack propagation under plane strain condition due to a single overload. J Soc Mat Sci, Japan 32:1383–1389(in Japanese). 10. Kikukawa M, Jono M, Kondo Y (1983) Fatigue crack closure behavior and prediction method of crack growth rate under stationary variable loading including random. Part 2 Extension to high growth rate region. Trans Japan Soc Mech Engnr A 49:278–285(in Japanese). 11. Kim C, Song J (1994) Fatigue crack closure and growth behavior under random loading. Engng Frac Mech 49:105–120 12. Sharpe WN Jr (1968) The interferometric strain gage. Exp Mech 8:164–170 13. Sharpe WN Jr (1982) Application of the interferometric strain/displacement gage. Optical Engng 12:483–488 14. Frandsen JD, Inman RV, Buck O (1975) A comparison of acoustic strain gauge techniques for crack closure. Int J Frac 11:345–348 15. Buck O, Ho CL, Marcus HL et al (1972) Rayleigh waves for continuous monitoring of a propagation crack front. ASTM STP 513:280–291 16. Kikukawa M, M. Jono M, K. Tanaka K (1976) Fatigue crack closure behavior at low stress intensity level. In: Proceedings of second international conference on mechanical behavior of materials, Special Volume:254–277 17. Kang JY, Song JH (1997) Neural network applications in determining the fatigue crack opening load. Int J Fatigue 20:57–69 18. Donald JK (1988) A procedure for standardizing crack closure levels. ASTM STP 982:222–229 19. Donald JK (1997) Introducing the compliance ratio concept for determining effective stress intensity. Int J Fatigue 19:S191–S195 20. Chung YI, Song JH (2009) Improvement of ASTM compliance offset method for precise determination of crack opening load. Int J Fatigue 31:809–819 21. Paris PC, Tada H, Donald JK (1999) Service load fatigue damage-a historical perspective. Int J Fatigue 21:S35–S46 22. Koo JS, Song JH, Kang JY (2004) A quantitative evaluation of K eff estimation methods based on random loading crack growth data. Int J Fatigue 26:192–200 23. Schijve J (1981) Some formulas for the crack opening stress level. Engng Frac Mech 14:461– 465 24. Meggiolaro MA, Tupiassu J, de Castro P (2003) On the dominant role of crack closure on fatigue crack growth modelling. Int J Fatigue 25:843–854 25. Katcher M, Kaplan M (1974) Effects of R-factor and crack closure on fatigue crack growth for aluminium titanium alloys. ASTM STP 559:264–282

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1 Important Problems in Fatigue Crack Growth of Materials

26. Madox SJ, Gurney TR, Mummey AM et al (1978) An investigation of the influence of applied stress ratio on fatigue crack propagation in structural steels. Research report 72 Welding Institute, UK 27. Kumar R, Singh K (1995) Influence of stress ratio on fatigue crack growth in mild steel. Engng Frac Mech 50:377-384 28. Kumar R (1992) Review on crack closure for constant amplitude loading in fatigue. Engng Frac Mech 42:389–400 29. Zhu ML, Xuan FZ, Tu ST (2015) Effect of load ratio on fatigue crack growth in the nearthreshold regime: A literature review, and a combined crack closure and driving force approach. Engng Frac Mech 141:57–77 30. Antunes FV, Chegini AG, Camas D et al (2015) Empirical model for plasticity-induced clack closure based on K max and K. Fatigue Fract Engng Mater Struct 38:983–996 31. Newman JC Jr (1981) A crack-closure model for predicting fatigue crack growth under aircraft spectrum loading. ASTM STP 748:53–84 32. Newman JC Jr (1982) Prediction of fatigue crack growth under variable-amplitude and spectrum loading using a closure model. ASTM STP 761:255–277 33. Kim CY, Choi JM, Song JH (2013) Fatigue crack growth and closure behavior under random loadings in 7475–T7351aluminum alloy. Int J Fatigue 47:196–204 34. Chang JB (1981) Round-robin crack growth predictions on center-cracked tension specimens under random spectrum loading. ASTM STP 748:3–40

Chapter 2

Composition of the Expert System Developed for Fatigue Crack Growth Predictions: FatiCraGro Expert

Abstract The components of the expert system developed for fatigue crack growth predictions are explained. The expert system consists of six parts, namely material details, fatigue crack growth properties, specimen configuration, load histories and cycle counting, fatigue crack growth predictions and reporting results. Each part is briefly described.

In order to predict fatigue crack growth the information on material, specimen, load and crack growth prediction method is necessary. Concretely, the expert system developed for fatigue crack growth predictions in this work, FatiCraGro Expert, is composed of six parts as shown in Fig. 2.1, i.e. material details, fatigue crack growth properties, specimen configuration, load histories and cycle counting, fatigue crack growth predictions and reporting results. Each PART will be briefly described below. PART I is to identify the material to be used for predictions and to input the tensile strength of the material. If you have the tensile strength of material, you may input it. If you have the hardness data, instead of the tensile strength, you can estimate the tensile strength from the hardness of the material using this system. If neither is unavailable, you can select the relevant value from Table I in the Appendix. PART II is to input fatigue crack growth properties. As the expert system to be developed is to predict fatigue crack growth based on fatigue crack closure, the necessary crack growth properties are those related to fatigue crack closure, da/dN– K eff curve and the crack opening point K op data. As the crack opening point K op data is later necessary for PART IV, in PART II you should input only the da/dN–K eff curve. Figure 2.2 shows the procedure of determination of da/dN–K eff curve. The system first asks the user whether da/dN–K eff curve data are available or not. The data are essential for fatigue crack growth prediction. The accuracy of the data is very important to the quality and accuracy of fatigue crack growth prediction. The da/dN–K eff curve data can be inputted through a file saved in the form of equations. If the da/dN–K eff curve data is unavailable, you can input the original da/dN–K eff raw data. It is first necessary for the user to designate the da/dN–K eff © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6_2

19

20

2 Composition of the Expert System Developed for Fatigue Crack Growth …

Fig. 2.1 Composition of the expert system for fatigue crack growth predictions

Fig. 2.2 The procedure of determination of da/dN–K eff curve

curve data type, conventional, trilinear or multi-linear one. The expert system fits the original da/dN–K eff data to relevant curve equations. However, it is common that the da/dN–K eff curve data are unavailable for most users. For the case, the user can select relevant da/dN–K eff curve data from the material data provided in the system. PART III is to input geometrical data of a specimen. Eight kinds of throughthickness long crack and a surface crack as part-through crack are provided. For each

2 Composition of the Expert System Developed for Fatigue Crack Growth …

21

specimen configuration, stress intensity factor K expressions proposed by ASTM (American Society for Materials and Testing) International Standards [1] are given. In addition, we can treat short cracks. PART IV is to input the load history to be tested. The user can input the file of load history saved in advance or can generate various load histories ranging from simple program loading to random loading. The user designates the degree of freedom, 1 or 2 for random loading. In PART IV, we can also count load cycles. Five kinds of counting methods defined by ASTM E1049-85 [2], peak, level crossing, rainflow, range-pair and simplified rain-flow method are prepared and the user can select relevant counting method or compare counting methods. PART V is to predict fatigue crack growth for employed load histories and specimen based on the determined da/dN–K eff curve. The crack opening data at the employed stress ratio should be inputted. The user can input the effective opening ratio U–K data or K op –K data. For the surface crack, you can select the value of U c /U a where U c and U a are the effective crack opening ratio for the crack length and crack depth of the surface crack. If the user designates the range of crack length to be predicted and then presses the Calculate button, the expert system predicts fatigue crack growth and shows the crack length a–number of blocks N b curve. PART VI is to report the prediction results obtained.

References 1. Designation: E647–15 (2020) Standard test method for measurement of fatigue crack growth rates. Annual book of ASTM standards. 03(01):707–768 2. Designation E1049–85 (Reapproved 2017) (2020) Standard Practices for cycle counting in fatigue analysis. Annual Book of ASTM Standards. 03(01):875–884

Chapter 3

Part I of the Fatigue Crack Growth Expert System: Material Details

Abstract The content of the program Part I: Material details are described and explained in detail. The user can predict the tensile strength of the material from the hardness data of the material when necessary.

The program Part I: Material details consists of two steps. Figure 3.1 shows the main page of STEP 1 to specify a material. There are two dialogue boxes: material type and material name. The dialogue box of material type contains a drop-down list as shown in Fig. 3.2. The primary four kinds of alloys: aluminium alloy, copper alloy, steel alloy, and titanium alloy are provided. For aluminium alloy, a drop-down list as shown in Fig. 3.3 is provided. All aluminium alloys included in the material database are listed. As aluminium alloys are used for airplanes, fatigue crack growth researches and data on aluminium alloys are considerably more. Figure 3.4 shows the drop-down list of copper alloy. Fatigue crack growth tests have rarely been performed on copper alloys and the authors have found just only two research results on commercial pure copper by Liaw et al. [1] and Arzaghi et al. [2]. When you select steel alloy as Fig. 3.5, you can find the dialogue box of Steel Alloy Group. You input the material name and should select the corresponding steel alloy group, unalloyed, low alloy or high alloy steel as Fig. 3.6 shows. Figure 3.7 shows the drop-down list of steel alloy. Steel alloy materials have been used for special structures, namely reactors, rails and so on. Figure 3.8 shows the drop-down list of titanium alloy. Data on titanium alloys are frequently found and several popular titanium alloy materials are shown here. The da/dN–K eff curve data of the above alloys are stored in the folder of MaterialData in this expert system. The users can also designate other alloys and other material by selecting the “USER INPUT” option as shown in Figs. 3.9 and 3.10. Clicking the Next button on the page proceeds to the next step. Figure 3.11 shows the main page of Step 2 of PART I: Material details to input © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6_3

23

24

3 Part I of the Fatigue Crack Growth Expert System: Material Details

Fig. 3.1 The main page of STEP I of Material details

Fig. 3.2 The drop-down list of Material Type dialogue box

3 Part I of the Fatigue Crack Growth Expert System: Material Details

Fig. 3.3 The drop-down list of aluminium alloy

Fig. 3.4 The drop-down list of copper alloy

25

26

3 Part I of the Fatigue Crack Growth Expert System: Material Details

Fig. 3.5 The dialogue box of Steel Alloy Group

Fig. 3.6 The drop-down list of Steel Alloy Group

3 Part I of the Fatigue Crack Growth Expert System: Material Details

Fig. 3.7 The drop-down list of steel alloy

Fig. 3.8 The drop-down list of titanium alloy

27

28

3 Part I of the Fatigue Crack Growth Expert System: Material Details

Fig. 3.9 User input for material type

Fig. 3.10 User input for material name

3 Part I of the Fatigue Crack Growth Expert System: Material Details

29

Fig. 3.11 The main page of Step 2 of PART I: Material details to input mechanical properties

mechanical properties. Elastic modulus E data is indispensable. If the user has no data, the system provides well-common values for aluminium, copper, steel and titanium materials, respectively. If you have the tensile strength of material σ B data, you can input it. If otherwise, you can select the relevant value from Table I in the Appendix. If you have the hardness data of the material instead of the tensile strength data, you can estimate the tensile strength from hardness by clicking the Estimate button. The system estimates the tensile strength from hardness as shown in Fig. 3.12. The user can input either Brinnel or Rockwell or Vickers hardness data. The system also shows the equivalent Vickers hardness corresponding to inputted hardness. The fracture ductility εf may be useful if available. Clicking the Next button on the page proceeds to the main page of PART II: Fatigue crack growth properties.

30

3 Part I of the Fatigue Crack Growth Expert System: Material Details

Fig. 3.12 Estimation of the tensile strength from hardness data

References 1. Liaw PK, Leak TR, Williams RS et al (1982) Near-threshold fatigue crack growth behavior in copper. Metal Trans A 13A:1607–1618 2. Arzaghi M, Sarrazin-Baudoux C, Petit J (2014) Fatigue crack growth in ultrafine-grained copper obtained CAP. Adv Mater Res 891–892, 1099–1104

Chapter 4

Part II of the Fatigue Crack Growth System: Fatigue Crack Growth Properties

Abstract In this system fatigue crack growth properties mean da/dN versus K eff curve or da/dN versus K eff original data. How to input or determine da/dN versus K eff curve is described.

4.1 da/dN Versus K eff Curves In this system, the fatigue crack growth prediction is performed based on da/dN versus K eff curves data. Here we determine the da/dN versus K eff curve. Figure 4.1 shows the main page for inputting da/dN–K eff curve data. When da/dN versus K eff curve data is available, first, you designate relevant curve type, either conventional or tri-linear transitional or multi-linear curve data as shown in Fig. 4.2 and then you can input the curve data directly in Fig. 4.3a, or through the file as shown in Fig. 4.3b. If you input the curve data directly in Fig. 4.3a or if you select the file type and click the button Open and then search a file needed, you can obtain the data and graph needed as shown in Fig. 4.4. This da/dN–K eff curve will be used for predictions. Clicking the button Next proceeds Specimen page. If the user has no da/dN versus K eff curves data but the da/dN versus K eff original data, he can input the da/dN versus K eff data through a file as shown in Fig. 4.5a. The file should be saved in Excel file format. If the user obtains da/dN versus K eff data as in Fig. 4.5b, click the button Next to fit the data.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6_4

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32

4 Part II of the Fatigue Crack Growth System …

Fig. 4.1 Main page for inputting da/dN–K eff curve data

Fig. 4.2 Selection of the type of da/dN–K eff curve

4.1 da/dN Versus K eff Curves

33

(a)

(b) Fig. 4.3 Input of da/dN–K eff curve data

34

4 Part II of the Fatigue Crack Growth System …

Fig. 4.4 The da/dN–K eff curve to be used for predictions

The user must select the fitting curve type among conventional, or tri-linear transitional, or multi-linear ones. When the user selects the curve type, the page appears showing the selected type schematically as shown in Fig. 4.5c. The user must wait some moment up to the time that the schematic curve type selected appears. If the user input the fitting range into the No. 4 table as shown in Fig. 4.5d, No. 5 table shows the nearest data values of K eff . Clicking the Fitting button, you obtain the fitted curve as shown in Fig. 4.5e. You can save the fitted da/dN–K eff curve. Clicking the button Next shows the message as in Fig. 4.3f. Clicking the button Yes proceeds to the Specimens page.

4.1 da/dN Versus K eff Curves

35

(a)

(b) Fig. 4.5 Inputting interface when da/dN versus K eff curves raw data are available

36

4 Part II of the Fatigue Crack Growth System …

(c)

(d) Fig. 4.5 (continued)

4.1 da/dN Versus K eff Curves

37

(e)

(f) Fig. 4.5 (continued)

Chapter 5

Part III of the Fatige Crack Growth Expert System: Specimens and Their Stress Intensity Factor K Expression

Abstract Specimen configurations provided in the expert system are explained. Eight kinds of through-thickness cracks and two kinds of part-through cracks are prepared and respective stress intensity factor expressions recommended by ASTM standard are provided.

Figure 5.1 shows the main page of the specimen. The crack geometry can be determined by designating crack type and crack size. Two types of cracks, namely through-thickness or part-through crack, can be selected. Also, two sizes of crack, namely long or short cracks, can be selected as shown in Fig. 5.2. The part-through crack consists of surface crack and corner crack and the user can select a part-through crack either under axial or bending load as Fig. 5.3 shows. For the long through-thickness cracks, eight kinds of specimen configurations proposed by ASTM [1] are provided as Fig. 5.4 shows. For each specimen configuration, the corresponding expression of stress intensity factor recommended by ASTM [1] is provided. Figure 5.5 shows an example of a selected specimen configuration. When the side grooves are attached to the specimen, the effective specimen thickness is determined by using the following equation proposed by Kim and Song [2]: Be f f = B −

(B − Bn ) B

2

(5.1)

After inputting gross and net thicknesses B0 and Bn , press Enter, and the effective thickness Beff will be obtained. The expression of stress intensity factor K is shown in the right lower area. Don’t forget the crack size, long or short. Clicking the button Next on the page proceeds to the main page of load history.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6_5

39

40

Fig. 5.1 The main page of specimen

5 Part III of the Fatige Crack Growth Expert System …

5 Part III of the Fatige Crack Growth Expert System …

Fig. 5.2 Two dialogue boxes for crack type and crack size

41

42 Fig. 5.3 Part-through cracks

5 Part III of the Fatige Crack Growth Expert System …

5 Part III of the Fatige Crack Growth Expert System … Fig. 5.4 Eight kinds of specimen configurations of the long through-thickness crack proposed by ASTM

43

44

5 Part III of the Fatige Crack Growth Expert System …

Fig. 5.5 An example of selected specimen configuration

References 1. Designation: E647–15 (2020) Standard test method for measurement of fatigue crack growth rates. Annual book of ASTM standards. 03(01):707–768 2. Kim J, Song J (1992) Investigation of plane strain fatigue crack growth behavior by using side-grooved specimens. Trans Korean Soc Mech Engnr 16:63–69 (in Korean)

Chapter 6

Part IV of the Fatigue Crack Growth Expert System: Load Histories and Cycle Counting

Abstract How to input a load history is explained. The user can generate either constant amplitude loading or programme loading or random loading. The user can also choose the freedom of degree for random loading. 1 degree of freedom and 2 degrees of freedom are apt to make narrow and wide random load histories, respectively. Cycle counting methods recommended by the ASTM standard are prepared. The user can obtain a range-mean matrix for the used cycle counting. A simplified rain flow method is recommended to use for fatigue crack growth predictions.

Figure 6.1 shows methods to input load histories. The user can input load history either through a file saved in advance or generate various load histories, constant amplitude, programme or random load history which you desire, by the system. The user can change the load magnitude of inputted load history. Figure 6.2 shows the interface to make a constant amplitude load history. The maximum load Pmax , the minimum load Pmin and load unit should be inputted. Figure 6.3 shows the interface to make a programmed load history. The peak and valley loads, Pi and V i , the number of cycles N i of each load block are to be inputted. Figure 6.4 shows the interface to make a random load history. The number of cycles N h , the maximum and minimum loads Pmax and Pmin , respectively, in a unit random load block, and degree of freedom of random load are to be inputted. 1 or 2 degrees of freedom can be selected. 1 degree of freedom and 2 degrees of freedom of random load may cause narrow and wide random histories, respectively. Figure 6.5 shows an example of making a random load history of freedom of 2 and the resulting waveform. When the desired load history is constructed, it will be cycle counted. The cycle counting methods proposed by ASTM [1], peak, level-crossing, rain-flow, range-pair and simplified rain-flow methods are prepared to use and you can obtain a rangemean matrix. Figure 6.6 is the interface for cycle counting and an example of the result. You can designate the numbers of units for load range and load mean for displaying a range-mean matrix diagram. It has been well known that the simplified rain-flow counting method is most relevant to fatigue crack growth predictions [2]. Figure 6.7 shows an example of range-mean matrix obtained. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6_6

45

46

6 Part IV of the Fatigue Crack Growth Expert System …

Fig. 6.1 Interface page for inputting load histories

Fig. 6.2 Interface page for inputting constant load history

6 Part IV of the Fatigue Crack Growth Expert System …

Fig. 6.3 The interface of making a programme loading history

Fig. 6.4 The interface of making a random load history

47

48

6 Part IV of the Fatigue Crack Growth Expert System …

a) An example of inputting for make a random history

b) The obtained load history Fig. 6.5 An example of making a random history

Clicking the button Next proceeds to the PREDICTION page.

6 Part IV of the Fatigue Crack Growth Expert System …

49

Fig. 6.6 The interface for cycle counting and an example of the result

Fig. 6.7 Example of range-mean matrix obtained

References 1. Designation E1049–85(2020) Standard practices for cycle counting in fatigue analysis. Annual Book of ASTM Standards. 03.01:875–884 2. Kikukawa M, Jono M, Kondo Y and Mikami S (1982) Fatigue crack closure behavior and prediction method of crack growth rate under stationary variable loading including random. Trans Japan Soc Mech Engnr A 48:1496–1504 (in Japanese)

Chapter 7

Part V of the Fatigue Crack Growth Expert System: Detailed Prediction Methods of Fatigue Crack Growth

Abstract Primary three kinds of predictions of fatigue crack growth, namely prediction for long crack growth under variable loading, prediction for surface crack growth under constant amplitude loading and prediction for short crack growth under constant amplitude loading are described in detail. The prediction method proposed by Kikukawa et al. is used for long crack growth under random loading and the surface crack growth is predicted by the method proposed by Kim and Song. The short crack growth is predicted by the method of Pang and Song. The process of crack growth prediction in this system is shown.

7.1 Crack Growth Prediction of Long Cracks under Constant Amplitude Loading Figure 7.1 shows the interface for STEP 1 of PREDICTION page. STEP 1 is to input the crack opening data for the selected load history. The user can choose either U–K or K op –K crack opening data. Figure 7.2 is an example of U–K crack opening data obtained for constant amplitude loading at R = 0. R is the stress ratio. Clicking the NEXT button, the STEP 2 window appears to input crack length data as shown in Fig. 7.3. You can choose the minimum crack growth increment per block for the prediction interval and data recording interval in the Options box as Fig. 7.4 shows. Clicking the button Calculate, you can obtain the crack growth prediction result shown in a plot of a–N or K max –N as shown in Fig. 7.5. Clicking the button NEXT proceeds to the REPORT page. Crack growth prediction was made as follows: Using the crack growth rate equation, da/dN–K eff curve, the increment of crack growth for each effective stress intensity factor range, K eff,i was calculated owing to the following Eq. (7.1) ai = C(K e f f,i )n

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6_7

(7.1)

51

52

7 Part V of the Fatigue Crack Growth Expert System …

Fig. 7.1 The interface for STEP 1 of PREDICTION page

Fig. 7.2 An example of U–K data

7.1 Crack Growth Prediction of Long Cracks under Constant Amplitude Loading

Fig. 7.3 The window to input crack length data

Fig. 7.4 Determination of prediction interval and data recording interval

53

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7 Part V of the Fatigue Crack Growth Expert System …

Fig. 7.5 Crack growth prediction result under constant amplitude loading

The crack length after N cycles, aN , can be obtained by a N = a0 + atotal = a0 +

N 

ai

(7.2)

i=1

7.2 Prediction Method by Kikukawa et al. for Long Cracks under Variable Loading It is practically most important to predict fatigue crack growth under variable loading, in particular, under random loading. Not a few software for the prediction of fatigue crack growth under variable loading have been developed based on fatigue crack closure, AFGROW [1], NASGRO [2] and others. The software AFGROW has been developed by Harter [3] and the software NASGRO is developed jointly by Southwest Research Institute® (SwRI® ) and the National Aeronautics and Space Administration (NASA) based on crack closure model originally proposed by Newman [4]. Crack closure models employed in the above two kinds of software are not so easy to understand. In this expert system, the prediction method proposed by Kikukawa

7.2 Prediction Method by Kikukawa et al. for Long Cracks under Variable Loading

55

et al. [5] which is easy to understand and treat has been employed. The outline of the method will be described below. Kikukawa’s research group of Osaka University, Japan, has investigated the effects of crack closure on fatigue crack growth for a long time and proposed a prediction method of fatigue crack growth under random loading [5]. The prediction method is based on the following experimental results: The crack opening point is nearly constant during a random block of a considerable large length. The crack opening point under random loading is governed by the largest load cycle of the random loading and is nearly equal to or slightly higher than the crack opening point of the corresponding load cycle under constant amplitude loading. The relevant method of cycle counting for random loading is the rang-pair method corresponding to the simplified rain-flow method among the cycle counting methods recommended by ASTM [6]. These experimental results give the following prediction procedure: 1. 2.

3.

Perform cycle counting using the simplified rain-flow method and identify the largest load cycle and its range and mean, K max,i . Determine the crack opening point of the corresponding load cycle to the largest cycle from constant amplitude loading data and it will be the crack opening point under random loading, K op,i . Using the determined crack opening point K op,i , calculate the effective stress intensity factor ranges from the random load cycles counted  K e f f,i =

4.

K max,i − K op,i for K op,i ≥ K min,i K max,i − K min,i for K op,i < K min,i

Using the crack growth rate equation, da/dN–K eff curve, calculate the increment of crack growth for each effective stress intensity factor, K eff,i ai = C(K e f f,i )n

5.

(7.3)

(7.4)

. The crack length after N cycles, aN , can be obtained by a N = a0 + atotal = a0 +

N 

ai

(7.5)

i=1

As for nearly all materials the crack opening point of the largest load cycle under random loading is equal to or slightly higher than the crack opening point of the corresponding load cycle under constant amplitude loading, the prediction of Kikukawa et al. is apt to provide a conservative estimate of fatigue crack growth. Their method seems to hold for most materials. However, Jono et al. [7] have obtained the result of ZK141-T7 aluminium alloy that under repeated step loading the crack growth rate in terms of effective stress intensity range, K eff , shows acceleration, compared with constant amplitude loading. They attributed the acceleration to the variation

56

7 Part V of the Fatigue Crack Growth Expert System …

of da/dN–K eff relation due to load interaction and proposed a way to reasonably explain the acceleration. On the other hand, Kim et al. [8] have reported that the crack opening point under random loading is lower than those under constant amplitude loading on aluminium alloy 7475-T7351 to induce acceleration of crack growth under random loading. This means that depending on materials, the crack opening point under random loading may be higher or lower than under constant amplitude loading. For accurate predictions of crack growth under random loading, it is the best way to directly observe the crack opening behaviour under random loading. We have the data of crack opening under random loading on some materials and utilize them for this expert system. If the user chooses random loading in the STEP 1 page of loading histories as shown in Fig. 7.6 or input a file of random loading, the prediction method by Kikukawa will be performed. An example will be shown below. Example: Material 2024-T351, File: 2000cycles narrow band random as shown in Fig. 7.7 Load: Fig. 7.8 Cycle counting: simplified rain-flow method. Figure 7.9 shows the range-mean matrix for the 2000cycles narrow band random when 10 units for range and mean were employed for simplified rain-flow counting. We use the U–K curve as shown in Fig. 7.10 obtained at R = 0 under constant

Fig. 7.6 The main page of STEP 1 of load histories

7.2 Prediction Method by Kikukawa et al. for Long Cracks under Variable Loading

57

Fig. 7.7 2000cycles narrow band random

Fig. 7.8 Load condition

amplitude loading. When the initial crack length ai is 5 mm, the prediction result is obtained as Fig. 7.11. Fatigue crack life is 7.148 × 103 blocks.

58

7 Part V of the Fatigue Crack Growth Expert System …

Fig. 7.9 The range-mean matrix for the 2000cycles narrow band random when 10 units for range and mean were employed for simplified rain-flow counting

Fig. 7.10 The U–K curve at R = 0 under constant amplitude loading

7.3 Prediction Method for Surface Crack Growth The expert system also provides the prediction of fatigue crack growth of surface cracks, particularly under constant amplitude loading. Surface crack growth is practically very important and the prediction method proposed by Kim and Song [9] has been employed. The surface crack growth under random loading may be performed

7.3 Prediction Method for Surface Crack Growth

59

Fig. 7.11 The crack growth prediction result of 2024-T351 for the 2000cycles narrow band random load history

by extending the method used for constant amplitude loading. The outline of the method will be described below. Song’s research group of KAIST, Korea, has proposed a prediction method for surface crack growth through their experiments and detailed literature review of surface crack growth. The detail of prediction by Kim and Song [9] is as follows: Surface crack growth is governed by the crack closure. Therefore, surface crack growth can be represented at crack depth and crack length by the effective stress intensity factor ranges, respectively, as follows: da = Ca (K e f f,a )na dN

(7.6)

dc = Cc (K e f f,c )nc dN

(7.7)

It was assumed that C a = C c = C and na = nc = n. C and n are the coefficients obtained for the through-thickness crack under plane strain state. Therefore da = C(K e f f,a )n = C(Ua K a )n dN

(7.8)

60

7 Part V of the Fatigue Crack Growth Expert System …

dc = C(K e f f,c )n = C(Uc K c )n dN

(7.9)

where U a and U c , K a and K c are the effective opening ratios and the stress intensity factor ranges at crack depth and crack length points, respectively. Equations (7.8) and (7.9) are changed as n  da Ua n · K a = C(Ua K a ) = C Uthr · dN Uthr n  dc Ua U c = C(Uc K c )n = C Uthr · · · K c dN Uthr Ua

(7.10) (7.11)

where U thr is the effective opening ratio of through-thickness crack. Under axial loading, U a /U thr = 1 is considered to be a good estimate. U a /U thr = 1.1 may be better estimate for R = –1. Oh and Song [10] reported that U a /U thr = 1.17 is under bending loading. The value of U c /U a seems to be 0.92 for axial loading and 0.90 for bending loading. If the values of U a /U thr and U c /U a are designated, the user can predict surface crack growth using the through-thickness crack growth data. The assumption that U a /U thr = 1 and U c /U a = 0.91 may correspond to the equation of Newman and Raju [11] as a = c



K a 0.91K c

n (7.12)

The validity of the prediction method has been verified for constant amplitude loading [9, 10], but it may be recommended to try the prediction method for random loading using employing the crack opening ratio of random loading for U thr . In order to predict the growth of a surface crack, the user select the part-through crack as the crack type in the SPECIMENS page. The user should designate the crack size, long or short. Four kinds of specimen type for Part Through Crack appears as shown in Fig. 7.12. For corner cracks, you can set U c = U a , that is, U c /U a = 1 because the situations at the crack depth point A and the crack length point C are nearly the same except that the ligament lengths (B-a) and (W–c) are different. An example will be shown below. Example: Material 7075-T6, surface crack type: surface crack under axial loading, specimen dimension as Fig. 7.13, initial crack depth ai = 2.3 mm, initial crack length ci = 2.4 mm. Load condition: Constant amplitude, stress ratio R = 0, Pmax = 12,000 N. First, the user input data of materials, da/dN–K eff curve and specimen like as shown in Fig. 7.13. Then, if the user finishes inputting load history and clicking the button Next, the STEP 1 (Input crack opening data for the selected load history) page appears. Inputting the crack opening data of R = 0, you obtain Fig. 7.14, showing

7.3 Prediction Method for Surface Crack Growth

Fig. 7.12 Selection of surface crack type

Fig. 7.13 Dimensions of surface crack specimen

61

62

7 Part V of the Fatigue Crack Growth Expert System …

Fig. 7.14 The U–K curve at R = 0 under constant amplitude loading

the U–K curve at R = 0 under constant amplitude loading. On the page the user can change the value of U c /U a . In this system the value of U c /U a = 0.92 is used but you can employ the value of U c /U a = 0.91 proposed by Jolles and Tortoriello [12]. Clicking the button Next in the STEP 1 page and inputting crack depth and length data and then clicking the button Calculate in the STEP 2 page, you can obtain the prediction result as Fig. 7.15a shows. The user can also confirm the variation of aspect ratio a/c of surface crack with crack depth as shown in Fig. 7.15b. If the user selects the surface crack under bending loading, the loading unit will be moment, not force. The prediction process is nearly identical to the case of axial loading.

7.4 Prediction for Short Fatigue Crack Growth Recently the problem of short crack growth became a primary topic of fatigue cracks. We have the aluminium alloy 2024-T351 data of short fatigue crack growth under constant and random loading. The expert system predicts short fatigue crack growth under constant amplitude loading according to the method proposed by Pang and Song [13]. We couldn’t predict fatigue short crack growth under random loading, because fatigue short cracks growth behaviour under random loading is greatly different from the behaviour under constant amplitude loading [14]. The details of the method will be described below.

7.4 Prediction for Short Fatigue Crack Growth

a) Predicted a-N and c-N curves

b) Predicted variation of aspect ratio a/c Fig. 7.15 Growth prediction of surface crack under axial loading

63

64

7 Part V of the Fatigue Crack Growth Expert System …

Researches on short fatigue crack growth have been performed worldwide for many aspects and many useful results have been obtained. One of them is that the crack closure of short cracks is enhanced as the crack length increases. Based on such useful results, Pang and Song [13] have proposed the prediction method of short fatigue crack growth. The crucial issue for the prediction of short fatigue crack growth is to predict the variation in the crack opening of short fatigue crack with crack length. Pang and Song have predicted the effective crack opening ratio of short fatigue crack as follows: Fig. 7.16 shows the opening behaviour of short and long fatigue cracks schematically. The solid lines and dotted lines show the variation in crack opening of short and long cracks, respectively. At the point where the length of the short crack is nearly zero, namely at K eff = 0, the crack hardly closes. If so, the crack opening stress intensity factor K op at K eff = 0 will be as

Fig. 7.16 Schematic behaviour of effective crack opening ratio of short and long fatigue cracks (reprinted with permission of Elsevier)

7.4 Prediction for Short Fatigue Crack Growth

 K op =

K min for R ≥ 0 0 for R < 0

65

(7.13)

Using these values, the effective crack opening ratio at K eff = 0, U 0 will be as follows:  K max −K min = 1 for R ≥ 0 K max −K min (7.14) U0 = K max 1 = for R < 0 K max −K min 1−R The effective crack opening ratio of short fatigue crack decreases linearly from U 0 . At the point of U S=L where the lines of short fatigue crack intersect the dotted lines of long cracks, the crack growth rates are the same for both cracks (da/dN)S=L . Experiments [13] show that the abscissa of U S=L is about (K eff )US=L = 4.3 MPa·m1/2 for aluminium alloy 2024-T351 and it is found to be nearly the same for stress ratios of R ≤ 0. The corresponding crack growth rate (da/dN)S=L is about 4.7 × 10−8 m/cycle. Referring to the data obtained by Jono and Song [14], Pang and Song [13] have found that the abscissa of U S=L is about (K eff )US=L = 5.7 MPa·m1/2 and the corresponding crack growth rate (da/dN)S=L is about 1 × 10−7 m/cycle for aluminium alloy 7075-T6. For the values of (K eff )US=L and (da/dN)S=L of steel materials, you can refer to Table II in the Appendix. If you know the effective stress intensity factor range at U S=L , (K eff )US=L , you can predict the effective crack opening ratio U of short fatigue crack by drawing lines Li Mi in Fig. 7.16. Pang and Song [13] proposed an experimental method for determining (K eff )US=L . For R ≥ 0, the U versus K eff relationship of short fatigue cracks is the line of L0 M0 , L0 A for R = 0.5, L0 B for R = 0.3 and L0 C for R = 0.0. The effective crack opening ratio of short fatigue crack can be determined as U = U0 (R) + g(R)K e f f

(7.15)

where g(R)is the slope of U versus K eff relationship of short fatigue cracks and is defined as g(R) =

U S=L (R) − U0 (K e f f ) S=L

(7.16)

As we can express K eff = UK, the following equation will be obtained: U=

U0 (R) 1 − g(R)K

(7.17)

We can determine U by Eq. (7.17) and in turn, the crack growth rate of short fatigue crack. An example will be shown below.

66

7 Part V of the Fatigue Crack Growth Expert System …

Fig. 7.17 Dimensions of single edge-notched bend specimen

Example: Material 2024-T351, Specimen dimension as in Fig. 7.17, initial crack depth ai  0 mm, final crack length af = 3 mm. Load condition: constant amplitude, stress ratio R = 0, Pmax = 100 N. First, the user inputs the data of materials, da/dN–K eff curve and specimen like as in Fig. 7.17. Then, if the user finishes inputting load history and clicking the button Next, the STEP 1 (Input crack opening data for the selected load history) page appears. Inputting the constant amplitude crack opening data of long crack at R = 0, you obtain the U–K curve of short crack at R = 0 to be used for the prediction like as in Fig. 7.18. On the page the user can change the value of (K eff )US=L . The value of (K eff )US=L is 4.3 MPa·m1/2 for 2024-T351 aluminium alloy and 5.7 MPa·m1/2 for 7075-T6 aluminium alloy. The user may try to assign relevant values of (K eff )US=L for other materials. Figure 7.19a shows the prediction result in the graph and Fig. 7.19b is the result report. As the threshold of K eff , (K eff )th , is nearly 0.479 MPa·m1/2 and the load was so small, the crack grows from the size of a0 = 1.21 mm at which K eff becomes larger than (K eff )th . Lee and Song [15] investigated the crack closure and growth behaviour of short fatigue cracks under random loading. The crack closure behaviour of short fatigue cracks under random loading is different from the behaviour under constant amplitude

7.4 Prediction for Short Fatigue Crack Growth

67

Fig. 7.18 The U–K curve of short crack at R = 0 under constant amplitude loading

loading. The crack opening point under constant amplitude loading follows that of long crack after it reaches minimum value or the value of (K eff )US=L , but the crack opening point under random loading does not follow that of long crack under constant amplitude loading and keep nearly constant value lower than that of long crack under constant amplitude loading. This means the crack growth retardation may occur under random loading after the short crack becomes as large as a long crack. The user may predict the short crack growth as long as the crack is short and does not become a long crack. If we normally predict the short crack growth under random loading by using the method used for constant amplitude loading, the prediction of short crack growth for random loading will be conservative but its degree is not clear because there are few experimental results for it. The user may try it. Defining the short crack region as a region over which the crack opening point decreases with crack growth, the short crack region is wider under random loading than under constant amplitude loading. Any easy prediction method could not be derived under such circumstances different from constant amplitude loading. However, the short crack growth is well expressed by the measured crack opening results. At least, we can say that the crack closure is the primary controlling factor of short fatigue crack growth under random loading as well as under constant amplitude loading. The best way to estimate short crack growth under random loading seems at present to directly measure the crack opening behaviour under random loading.

68

7 Part V of the Fatigue Crack Growth Expert System …

a)

b) Fig. 7.19 The prediction result

References

69

References 1. www.afgrow.net 2. www.swri.org 3. Harter JA (1999) Comparison of contemporary FCG life prediction tools. Int J Fatigue 21:S181– S185 4. Newman JC Jr (1981) A crack-closure model for predicting fatigue growth under aircraft spectrum loading. ASTM STP 748:53–84 5. Kikukawa M et al (1983) Fatigue crack closure behavior and prediction method of crack growth rate under stationary variable loading including random. Trans Japan Soc Mech Engers A 49:278–285 (in Japanese) 6. Designation E1049–85(2020) Standard practices for cycle counting in fatigue analysis. Annual Book of ASTM Standards, Section 3 Metals Test Methods and Analytical Procedures, Vol. 03.01 7. Jono M et al (1985) Fatigue crack growth and crack closure under variable loadings on aluminum alloys(effect of load variation on characteristic form of crack growth rate curve in region II). J Soc Mat Scie, Japan. 34:1193–1199 8. Kim C et al (2013) Fatigue crack growth and closure behavior under random loadings in 7475–T7351 aluminum alloy. Int J Fatigue 47:196–204 9. Kim J, Song J (1992) Prediction of growth behavior of initially semicircular surface cracks under axial loading. Trans Korean Soc Mech Engers 16:1536–1544 (in Korean) 10. Oh C, Song J (2001) Crack growth and closure behavior of surface crack under pure bending loading. Inter J Fatigue. 23:251–258 11. Newman JC, Raju IS (1981) An empirical stress intensity factor equation for the surface cracks. Engng Fract Mech 15:185–192 12. Jolles M, Tortoriello V (1983) Geometry variation during fatigue growth of surface flaw. ASTM STP791:1297–1307. 13. Pang C, Song J (1994) Crack growth and closure behavior of short fatigue cracks. Engng Fract Mech 47:327–343 14. Jono M, Song J (1985) Growth and closure of short fatigue crack. Curr Reseach on Fatigue Cracks. Soc Mat Sci Japan. Mat Res Series 1:35–55 15. Lee S, Song J (2000) Crack closure and growth behavior of physically short fatigue cracks under random loading. Engng Fract Mech 66:321–334

Chapter 8

Part VI of the Fatigue Crack Growth Expert System: Reporting of Results Obtained

Abstract All the used data and all the results obtained so far are reported.

The system provides the report as shown in Fig. 8.1. The user can see the used data. The material data, specimen data, load history data, and the initial crack length a0 and final crack length af are shown. The calculated data of maximum stress intensity factor and effective stress intensity factor range at initial crack length a0 and final crack length af , K max,a0 , K max,af , K eff ,a0 and K eff ,af are shown. The prediction result data N b is also provided. The value of K eff ,a0 may be utilized to compare with the threshold of effective stress intensity factor range (K eff )th . Figure 8.1 is an example of the result obtained under random loading.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6_8

71

72

8 Part VI of the Fatigue Crack Growth Expert System: Reporting of Results Obtained

Fig. 8.1 A report sheet

Chapter 9

Configuration of the Fatigue Crack Growth Expert System and How to Install and Run the Fatige Crack Growth Expert System

Abstract Configuration of the expert system is explained, and a computer specification necessary to install and run the expert system is shown.

Unfortunately, as any good expert system shell is not available at present, the expert system was developed using the software “MATLAB version R2020b” for user interface and executable programs. The free software “MATLAB runtime” provided by MathWorks is necessary. You can download the free software “runtime” at the site https://www.mathworks.com/products/compiler/matlab-runtime.html. Figure 9.1 shows the page of the site. The necessary version is R2020b. Windows 10 is desirable for the OS system of your PC. The software “FatiCraGro” can be downloaded at URL. You can find the following programs in the downloaded Zip file as shown in Fig. 9.2. Clicking the application program “FatiCraGro” opens the expert system for fatigue crack growth predictions. Probably due to the usage of the software “MATLAB” it takes about 2 min at longest for the expert system to begin to run and users must wait patiently meanwhile. The page as shown in Fig. 9.3 appears. If you may happen to face any problem concerning the expert system, please don’t hesitate to contact one of the authors, Professor C. Kim, [email protected] or [email protected].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6_9

73

74

9 Configuration of the Fatigue Crack Growth Expert System …

Fig. 9.1 The page of the site https://www.mathworks.com/products/compiler/matlab-runtime.html Fig. 9.2 Programs included in the Zip file

9 Configuration of the Fatigue Crack Growth Expert System …

Fig. 9.3 The page which first appears

75

Appendix

See Tables A.1 and A.2.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6

77

78 Table A.1 Tensile stress of material

Appendix Material symbol

Tensile strength (MPa)

Representative researcher or Institute

285

Buahombura

Aluminium alloy 6N01 7N01

431

Buahombura

2017-T3

452

Tsukuda

2024-T3

494

Wang

2024-T351

480

KAIST

2124-T351 (Underaged)

488

Ritchie

2524-T3

485.3

Chen

5052

229

Buahombura

5083-O

301

Osaka University

6063-T5

None

Veers

6063-T6

None

Veers

7050-T7451

490

Forth(FAA)

7075-T6

630

KAIST

7075-T6

577

Osaka University

7075-T6

None

Zhu

7075-T6

572

Bu

7075-T651

590

Petit

7249-T76511

578

Newman

7475-T7351

502

KAIST

7475-T761

490

Wang

8090

None

Lee

ZK141-T7

370

Osaka University

Copper(annealed)

263

Liaw

Copper

245

Arzaghi

15MnVN

563

Shen

4340

730

(Agard, FAA)

9Cr-1Mo

558

Bao

A286

1211

Mei

A508

576

Breat

AISI1118

503

Kaynak

AISI316

574

Shin

Cast Iron

None

Uematsu

Fe-3%Si

490

Ohji

Copper alloy

Steel alloy

(continued)

Appendix

79

Table A.1 (continued)

Material symbol

Tensile strength (MPa)

Representative researcher or Institute

HT80

814

Osaka University

Inconel 706

1159

Liaw

Nodular cast iron

450

Clement

S10C

433

Tokaji

S35C

612

Osaka University

SB42-B

None

Osaka University

SM41B

423

Tanaka

SM41C

402

Hoshide

SM50A

510

KAIST

SNCM439

955

Osaka University

SUS304

613

Ogura

SUS329

810

Ogawa

WELTEN60

617

Kitakawa

Titanium alloy Ti-1100

None

Ghonem

Ti-24Al-11Nb

758

Ravichandran

Ti-25Al-17Nb-1Mo

1134

Ravichandran

Ti-6Al-4 V

992, 973

Osaka University

Ti-6Al-4 V

979

Newman

√ Table A.2 The values of (K eff )S=L (MPa m) of steel materials √ Material (K eff )S=L (MPa m) (da/dN)S=L (m/cycle) Representative author or Institute A286

28

5 × 10–8

Mei-very high tensile strength R = 0.05

A508

16

2 × 10–8

Breat R = 0.1

Nodular cast iron 6.8

3×

Clement R = 0.1

S10C

18

4 × 10–8

Tokaji R = 0

S10C

15

3 × 10–8

Tokaji R = −1

SM41B

5.3

10–9

Tanaka R = −1

SNCM439

15

5 × 10–8

10–9

Index

A Acceleration, 5, 15, 55 Acoustic methods, 5 AFGROW, 54 Aluminium, 8 aluminium alloy, 2, 9, 11, 12, 23 Arzaghi et al., 23 Aspect ratio, 16, 62 ASTM, 9, 39, 45 ASTM compliance offset method, 7 ASTM E1049-85, 21 Axial, 39 axial loading, 60

Crack depth, 16, 59, 60 Crack geometry, 39 Crack growth prediction, 51 crack growth prediction result, 51 Crack growth retardation, 67 Crack length, 16, 59, 60 Crack opening data, 51 Crack opening of short and long cracks, 64 Crack opening point, 6, 19, 55, 67 Crack opening stress intensity factor, 64 Crack size, 39, 60 Crack type, 39 Cycle counting, 19 cycle counting methods, 45

B Backpropagation neural network, 6 Bending, 39 bending loading, 60 Brinnel, 29

D Data recording interval, 51 Degree of freedom, 45 Donald, 6

C Chang, 14, 15 Chung, 7 Compliance ratio technique, 6 Constant amplitude, 45, 66 Constant amplitude loading, 51, 58, 62, 67 Conventional, 8 conventional curve, 4, 8 Copper, 9, 11 copper alloy, 23 Corner crack, 39, 60 Crack closure, 4, 54, 59, 64 crack closure model, 54

E Effective crack opening ratio, 4, 5, 13, 64, 65 Effective opening ratio, 4, 12, 16, 60 Effective specimen thickness, 39 Effective stress intensity factor range, 4, 6, 7, 55, 59, 65, 71 Effective thickness, 39 Effective yield strength, 3 Effects of crack closure, 55 Elastic modulus, 4, 29 Elber, 4, 12 Electrical subtraction circuit, 6

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J.-H. Song and C.-Y. Kim, Expert System for Fatigue Crack Growth Predictions Based on Fatigue Crack Closure, KAIST Research Series, https://doi.org/10.1007/978-981-16-8036-6

81

82 Equation of Newman and Raju, 60 Equivalent Vickers hardness, 29 Erdogan, 1 Error criterion, 11, 13

F FatiCraGro, 19, 73 Fatigue crack closure, 5, 6, 12, 16, 19 Fatigue crack growth prediction, 19 Fatigue crack growth properties, 19 Fatigue crack growth rate, 4 fatigue crack growth rate curve, 2, 4 fatigue crack growth rate threshold, 2 Fatigue crack growth threshold, 2, 8 Fatigue fracture, 2 15MnVN, 9 Flow strength, 3 Fourth power law, 1 Fracture ductility, 11, 29 Frost, 1

G Generalized Willenborg model, 15 Gross and net thicknesses, 39

H Hardness, 19, 29 Harter, 54 High alloy, 23 Hi-Lo, 5

I Increment of crack growth, 51, 55 Initial crack length, 57 Interferometric strain/displacement gage method, 5

J Jolles, 62 Jono, 2, 13, 55, 65

K Kang, 6 Kaplan, 13 Katcher, 13 Kikukawa, 55, 56 Kikukawa’s research group, 55 Kikukawa group, 6

Index Kim, 39, 56, 58, 59 Koo–Song–Kang, 7 Kumar-Singh, 13

L Lee, 66 Level crossing, 21, 45 Liaw et al., 23 Ligament lengths, 60 Load-differential displacement hysteresis loop, 6 Load history, 19, 21, 45 Load interaction, 56 load interaction effects, 15 Load unit, 45 Lo-Hi, 5 Long, 39 long crack, 67 Long through-thickness crack, 43 Low alloy, 23

M Madox et al., 13 MaterialData, 23 Material details, 19, 23 Material name, 23 Material type, 23 MathWorks, 73 MATLAB, 73 MATLAB runtime, 73 Maximum load, 45 Maximum stress intensity factor, 71 Meggiolara et al., 12 Minimum crack growth increment per block, 51 Minimum load, 45 Minimum stress intensity factor, 4 Modified Elber’s equation, 14 Modified Forman’s equation, 15 Multi-linear multi-linear curve, 2, 4, 8 Multiple parameter yield zone model, 15

N Narrow and wide random histories, 45 Narrow band random, 56 NASGRO, 54 National Aeronautics and Space Administration (NASA), 54 National Engineering Laboratory, 1 Neural network, 6

Index Newman, 54 Non-ferrous materials, 8 Normalized-extended ASTM method, 7 Number of cycles, 45 Numbers of units for load range and load mean, 45

O Options box, 51 Original ASTM compliance offset method, 7

P Pang, 62, 65 Paris, 1 Paris–Tada–Donald, 7 Paris’ equation, 1 Partial crack closure, 7 Part-through, 39 part-through crack, 20, 39 Part through crack, 60 Peak, 21, 45 Peak and valley loads, 45 Plane strain, 5, 59 Plane stress, 5 PREDICTION, 51 Prediction interval, 51 Program loading, 21 Programme, 45 Programmed load history, 45

R Rain-flow, 21, 45 Random load, 45 random load history, 45 Random loading, 21, 54, 62, 66 Random spectrum loadings, 14 Range-mean matrix, 45, 56, 58 Range-pair, 21, 45 rang-pair method, 55 Rayleigh waves, 5 Reference constant amplitude crack growth results, 16 Repeated Gaussian random loading, 5 Repeated step loading, 55 REPORT, 51 Reporting results, 19 Retardation, 5, 15 Ritchie group, 9 Rockwell, 29 Root mean square, 14

83 Round-robin analysis, 14 S Schijve, 12 7075-T6, 60, 65, 66 7475-T7351, 56 Sharpe, 5 Short crack, 16, 39 short crack growth, 62, 67 short crack region, 67 Short fatigue crack, 65, 66 short fatigue crack growth, 62 Side grooves, 39 Sigmoidal form, 2 Simplified rain-flow, 21, 45 simplified rain-flow counting, 56 simplified rain-flow method, 55, 56 6063-T5, 9 Song, 6, 7, 39, 58, 62, 65, 66 Southwest Research Institute (SwRI), 54 Specimen, 20, 39 specimen configuration, 19 specimen dimension, 60 specimen type, 60 SPECIMENS, 60 Stationary variable loading, 5 Steel, 8 steel alloy, 9, 11, 23 Steel alloy, 23 Stress intensity, 39 Stress intensity factor, 39 stress intensity factor range, 1, 60 Stress ratio, 12 Surface crack, 16, 20, 39, 58 surface crack growth, 59 surface crack under axial loading, 60 T Tensile load retardation, 14 Tensile strength, 19, 29 Threshold, 66 Threshold of effective stress intensity factor range, 71 Through-thickness, 39 through-thickness crack, 39, 59, 60 through-thickness long crack, 20 Ti-6Al-4, 13 Ti-24Al-11Nb, 11 Ti-25Al-17Nb, 11 Titanium alloy, 8, 11, 13, 23 Tortoriello, 62 Transition points, 13

84 Tri-linear transitional, 8 tri-linear transitional curve, 4, 8 tri-linear transitional form, 2 2/π method, 7 2/π0 method, 7 Two-step loading, 5 2019-T851, 14 2024-T3, 4, 12 2024-T351, 7, 56, 62, 65, 66 2124-T351, 9 2219-T851, 13

U Ultrasonic, 5 Unalloyed, 23 Unit random load block, 45 Unloading elastic compliance method, 6 USER INPUT, 23

Index V Variable loading, 54 Veers, 9 Vickers, 29

W Welten60, 9 Willenborg/Chang model, 15

Y Yoder, 2 Young’s modulus, 9

Z ZK141-T7, 55