Research Progress on Evaluation Methods of Fracture Toughness and Fatigue Crack Growth in High-strength Steel

doi:10.3901/JME.2023.16.018

Abstract

Abstract: The issue of fatigue and fracture in high-strength steel has always been a hot research direction due to long time service under cyclic loading. Accurately evaluating the fatigue life and monitoring the service status of high-strength steel are crucial to ensure the safe operation of large equipment. With the development of fracture mechanics, damage tolerance design has become a significant fatigue fracture control method in industrial fields such as aviation, aerospace, nuclear power and high-speed railway. As the key parameters in damage tolerance design, accurately understanding of evaluation methods for fracture toughness and fatigue crack growth plays a significant connecting role in solving the bottleneck problem of integrity and reliability research on large components. In this study, the classification and failure of high-strength steels are firstly reviewed. Then, the characterization forms of fracture toughness and fatigue crack growth are analyzed. The small-sample methods for estimating fracture toughness are systematically elaborated from the size effect and energy criterion. The research progress on the quantitative relationship between tensile properties, impact toughness and fracture toughness are discussed. The models and methods of fatigue crack growth in the near-threshold region, steady-state region and whole-stage region are illustrated respectively. Additionally, the stress ratio and size effect on the fatigue crack growth of high-strength steel are emphasized. Finally, several open problems in the field of fracture toughness and fatigue crack growth are addressed for future studies.

Key words: high-strength steel, tensile strength, fracture toughness, impact toughness, fatigue crack growth

CLC Number:

TG142

LI Hefei, ZHANG Peng, ZHANG Zhefeng. Research Progress on Evaluation Methods of Fracture Toughness and Fatigue Crack Growth in High-strength Steel[J]. Journal of Mechanical Engineering, 2023, 59(16): 18-31.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://www.cjmenet.com.cn/EN/10.3901/JME.2023.16.018

http://www.cjmenet.com.cn/EN/Y2023/V59/I16/18

References

[1] MATLOCK D, SPEER J. Design considerations for the next generation of advanced high strength sheet steels[C]//Proceedings of 3rd International Conference on Structural Steels, 2006:774-781.
[2] 邵琛玮. Fe-Mn-C系孪生诱发塑性钢的低周疲劳行为研究[D]. 北京:中国科学院大学, 2017. SHAO Chenwei. Investigations on the low-cycle fatigue behaviors of Fe-Mn-C twinning-induced plasticity steels[D]. Beijing:University of Chinese Academy of Sciences, 2017.
[3] ZHAO J, JIANG Z. Thermomechanical processing of advanced high strength steels[J]. Progress in Materials Science, 2018, 94:174-242.
[4] 张志勤,黄维,高真凤. 汽车用第3 代先进高强度钢的研发进展[J]. 特殊钢, 2013, 34:16-21. ZHANG Zhiqin, HUANG Wei, GAO Zhenfeng. Research progress of the 3rd generation advanced high strength steel for automobile[J]. Special Steel, 2013, 34:16-21.
[5] 徐祖耀. 自主创新发展超高强度钢[J]. 上海金属, 2009, 31:1-6. XU Zuyao. Independent innovation to develop ultra-high strength steel[J]. Shanghai Steel, 2009, 31:1-6.
[6] YU A, HUANG H, LI Y, et al. Fatigue life prediction of rolling bearings based on modified SWT mean stress correction[J]. Chinese Journal of Mechanical Engineering, 2021, 34(6):258-269.
[7] 陈林,戴宇恒,崔健伟,等. 微合金化钢轨淬火工艺的优化及其疲劳裂纹扩展行为研究[J]. 机械工程学报, 2022, 58(14):233-240. CHEN Lin, DAI Yuheng, CUI Jianwei, et al. Optimization of quenching process and fatigue crack growth behavior of microalloyed rail[J]. Journal of Mechanical Engineering, 2022, 58(14):233-240.
[8] 胡华彦,温建锋,吴蔚峰,等. 高温蠕变条件下表面裂纹扩展行为分析[J]. 机械工程学报, 2020, 56(24):40-50. HU Huayan, WEN Jianfeng, WU Weifeng, et al. Analysis of surface creep crack growth behavior under high temperature creep condition[J]. Journal of Mechanical Engineering, 2020, 56(24):40-50.
[9] JIANG S, WANG H, WU Y, et al. Ultrastrong steel via minimal lattice misfit and high-density nanoprecipitation[J]. Nature, 2017, 544(7651):460-464.
[10] WANG Y, SUN J, JIANG T, et al. A low-alloy high-carbon martensite steel with 2.6 GPa tensile strength and good ductility[J]. Acta Materialia, 2018, 158:247-256.
[11] WANG Z, FAN Z, CHEN X, et al. Modeling and experimental analysis of roughness effect on ultrasonic nondestructive evaluation of micro-crack[J]. Chinese Journal of Mechanical Engineering, 2021, 34(6):144-155.
[12] 周素霞,卢俊霖,吴毅,等. 基于直流电位降的高铁车轴裂纹检测研究[J]. 机械工程学报, 2022, 58(14):288-295. ZHOU Suxia, LU Junlin, WU Yi, et al. Research on crack detection of high-speed railway axle based on direct current potential drop[J]. Journal of Mechanical Engineering, 2022, 58(14):288-295.
[13] 周长江,王豪野,靳广虎,等. 考虑残余应力的螺旋锥齿轮接触疲劳裂纹萌生-扩展寿命计算方法研究[J]. 机械工程学报, 2022, 58(23):28-38. ZHOU Changjiang, WANG Haoye, JIN Guanghu, et al. Calculation method of contact fatigue life of spiral bevel gears considering residual stress[J]. Journal of Mechanical Engineering, 2022, 58(23):28-38.
[14] 尹敏轩,朱涛,杨冰,等. 基于可靠性的重载货车钩舌疲劳断裂寿命[J]. 机械工程学报, 2021, 57(4):210-218. YIN Minxuan, ZHU Tao, YANG Bing, et al. Fatigue fracture life of heavy-haul wagon's coupler knuckle based on reliability[J]. Journal of Mechanical Engineering, 2021, 57(4):210-218.
[15] YANG B, WEI Z, LIAO Z, et al. Optimisation method for determination of crack tip position based on gauss-newton iterative technique[J]. Chinese Journal of Mechanical Engineering, 2021, 34(4):207-218.
[16] YANG B, DUAN H, WU S, et al. Damage tolerance assessment of a brake unit bracket for high-speed railway welded bogie frames[J]. Chinese Journal of Mechanical Engineering, 2019, 32(4):194-204.
[17] ZHU X, JOYCE J. Review of fracture toughness (G, K,J, CTOD, CTOA) testing and standardization[J]. Engineering Fracture Mechanics, 2012, 85:1-46.
[18] RITCHIE R. The conflicts between strength and toughness[J]. Nature Materials, 2011, 10(11):817-822.
[19] SURESH S, RITCHIE R. Propagation of short fatigue cracks[J]. International Metals Reviews, 1984, 29(1):445-475.
[20] WANG C, MILLER K. Short fatigue crack growth under mean stress, uniaxial loading[J]. Fatigue & Fracture of Engineering Materials & Structures, 1993, 16(2):181-198.
[21] 姚卫星. 结构疲劳寿命分析[M]. 北京:国防工业出版社, 2003. YAO Weixing. Structural fatigue life analysis[M]. Beijing:National Defense Industry Press, 2003.
[22] PUGNO N, CIAVARELLA M, CORNETTI P, et al. A generalized Paris' law for fatigue crack growth[J]. Journal of the Mechanics and Physics of Solids, 2006, 54(7):1333-1349.
[23] SURESH S. Fatigue of materials[M]. Cambridge:Cambridge University Press, 1998.
[24] RITCHIE R. Mechanisms of fatigue-crack propagation in ductile and brittle solids[J]. International Journal of Fracture, 1999, 100(1):55-83.
[25] 郑修麟. 材料疲劳理论与工程应用[M]. 北京:科学出版社, 2013. ZHENG Xiulin. Material fatigue theory and engineering application[M]. Beijing:Science Press, 2013.
[26] CHAWLA K, METERS M. Mechanical behavior of materials[M]. Englewood:Prentice Hall, 1999.
[27] LANDERS J. Evaluation of the KIc size criterion[J]. International Journal of Fracture, 1981, 17:R47-R51.
[28] 肖怀荣,蔡力勋,于思淼,等. 基于能量密度等效和三维尺寸的Ⅰ型裂纹试样弹塑性问题的半解析求解[J]. 机械工程学报, 2022, 58(14):241-251. XIAO Huairong, CAI Lixun, YU Simiao, et al. Semi-analytical elastoplastic solutions for mode-I-crack specimens based on energy density equivalence and three-dimensional sizes[J]. Journal of Mechanical Engineering, 2022, 58(14):241-251.
[29] READ D, REED R. Effects of specimen thickness on fracture toughness of an aluminum alloy[J]. International Journal of Fracture, 1977, 13(2):201-213.
[30] LAI M, FERGUSON W. Fracture toughness of aluminium alloy 7075-T6 in the as-cast condition[J]. Materials Science and Engineering, 1985, 74(2):133-138.
[31] WALLIN K. Size effect in KIC results[J]. Engineering Fracture Mechanics, 1985, 22:149-163.
[32] LI Hefei, DUAN Qiqiang, ZHANG Peng, et al. A new method to estimate the plane strain fracture toughness of materials[J]. Fatigue & Fracture of Engineering Materials & Structures, 2019, 42(2):415-424.
[33] STARK H, IBRAHIM R. Estimating fracture toughness from small specimens[J]. Engineering Fracture Mechanics, 1986, 25(4):395-401.
[34] MERLE B, GOKEN M. Fracture toughness of silicon nitride thin films of different thicknesses as measured by bulge tests[J]. Acta Materialia, 2011, 59(4):1772-1779.
[35] GREEN G, KNOTT J. On effects of thickness on ductile crack growth in mild steel[J]. Journal of the Mechanics and Physics of Solids, 1975, 23(3):167-183.
[36] MATTHEWS J, HYATT C, PORTER J, et al. Effect of thickness on the relationship between shear lip and energy in dynamic tear specimens[J]. Engineering Fracture Mechanics, 1998, 60(5-6):529-542.
[37] PRASAD N, KUMAR N, NARASIMHAN R, et al. Fracture behavior of magnesium alloys-role of tensile twinning[J]. Acta Materialia, 2015, 94:281-293.
[38] SHI X, ZENG W, ZHAO Q. The effect of surface oxidation behavior on the fracture toughness of Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy[J]. Journal of Alloys and Compounds, 2015, 647:740-749.
[39] LAI M, FERGUSON W. Relationship between the shear lip size and the fracture toughness[J]. Materials Science and Engineering, 1980, 45(2):183-188.
[40] LI Hefei, ZHANG Peng, QU Ruitao, et al. The minimum energy density criterion for the competition between shear and flat fracture[J]. Advanced Engineering Materials, 2018, 20(8):1800150.
[41] RITCHIE R, SERVER W, WULLAERT R. Critical fracture stress and fracture strain models for the prediction of lower and upper shelf toughness in nuclear pressure vessel steels[J]. Metallurgical Transactions A, 1979, 10(10):1557-1570.
[42] KAMP N, SINCLAIR I, STARINK M. Toughness-strength relations in the overaged 7449 Al-based alloy[J]. Metallurgical and Materials Transactions A, 2002, 33(4):1125-1136.
[43] ALEXOPOULOS N, TIRYAKIOGLU M. Relationship between fracture toughness and tensile properties of A357 cast aluminum alloy[J]. Metallurgical and Materials Transactions A, 2009, 40(3):702-716.
[44] SCHWALBE K. On the influence of microstructure on crack propagation mechanisms and fracture toughness of metallic materials[J]. Engineering Fracture Mechanics, 1977, 9(4):795-832.
[45] BARSOM J, ROLFE S. Fracture and fatigue control in structures:Applications of fracture mechanics[M]. West Conshohocken:ASTM International, 1977.
[46] ROBERTS R. Interpretive report on small scale test correlations with KIC data[J]. WRC Bulletin, 1981, 265:1-17.
[47] RONALD T, HALL J, PIERCE C. Usefulness of precracked charpy specimens for fracture toughness screening tests of titanium alloys[J]. Metallurgical and Materials Transactions B, 1972, 3(4):813-818.
[48] DUAN Qiqiang, QU Ruitao, ZHANG Peng, et al. Intrinsic impact toughness of relatively high strength alloys[J]. Acta Materialia, 2018, 142:226-235.
[49] LI Hefei, DUAN Qiqiang, ZHANG Peng, et al. The relationship between strength and toughness in tempered steel:Trade- off or invariable?[J]. Advanced Engineering Materials, 2019, 21(4):1801116.
[50] LI Hefei, DUAN Qiqiang, ZHANG Peng, et al. The quantitative relationship between fracture toughness and impact toughness in high-strength steels[J]. Engineering Fracture Mechanics, 2019, 211:362-370.
[51] LARDNER R. A dislocation model for fatigue crack growth in metals[J]. The Philosophical Magazine:A Journal of Theoretical Experimental and Applied Physics, 1968, 17(145):71-82.
[52] DESHPANDE V, NEEDLEMAN A, VAN DER GIESSEN E. A discrete dislocation analysis of near-threshold fatigue crack growth[J]. Acta Materialia, 2001, 49(16):3189-3203.
[53] SHYAM A, ALLISON J, SZCZEPANSKI C, et al. Small fatigue crack growth in metallic materials:A model and its application to engineering alloys[J]. Acta Materialia, 2007, 55(19):6606-6616.
[54] PIPPAN R, WEINHANDL H. Discrete dislocation modelling of near threshold fatigue crack propagation[J]. International Journal of Fatigue, 2010, 32(9):1503-1510.
[55] MCCLINTOCK F. On the plasticity of the growth of fatigue cracks[J]. Fracture of Solids, 1963, 20:65-102.
[56] DONAHUE R, CLARK H, ATANMO P, et al. Crack opening displacement and the rate of fatigue crack growth[J]. International Journal of Fracture Mechanics, 1972, 8(2):209-219.
[57] SADANANDA K, SHAHINIAN P. Prediction of threshold stress intensity for fatigue crack growth using a dislocation model[J]. International Journal of Fracture, 1977, 13(5):585-594.
[58] 沈学成,黄毓晖,朱明亮,等. 疲劳门槛值统一理论模型的比较及验证[J]. 机械工程学报, 2020, 56(24):81-87. SHEN Xuecheng, HUANG Liuhui, ZHU Mingliang, et al. Comparison and verification of unified fatigue threshold models[J]. Journal of Mechanical Engineering, 2020, 56(24):81-87.
[59] JIANG Y. A fatigue criterion for general multiaxial loading[J]. Fatigue & Fracture of Engineering Materials & Structures, 2000, 23(1):19-32.
[60] PARIS P, ERDOGAN F. A critical analysis of crack propagation laws[J]. Journal of Basic Engineering, 1963, 85:528-533.
[61] XU T, FENG Y, SONG S, et al. Fatigue crack propagation behaviour of steels with different microstructures[J]. Materials Science and Engineering:A, 2012, 551:110-115.
[62] ROE K, SIEGMIND T. An irreversible cohesive zone model for interface fatigue crack growth simulation[J]. Engineering Fracture Mechanics, 2003, 70(2):209-232.
[63] LI Hefei, ZHANG Peng, WANG Bin, et al. Predictive fatigue crack growth law of high-strength steels[J]. Journal of Materials Science & Technology, 2022, 100:46-50.
[64] LAIRD C. The influence of metallurgical structure on the mechanisms of fatigue crack propagation[M]//Fatigue crack propagation. ASTM International, 1967.
[65] SURESH S. Fatigue crack deflection and fracture surface contact:micromechanical models[J]. Metallurgical Transactions A, 1985, 16(2):249-260.
[66] TVERGAARD V. On fatigue crack growth in ductile materials by crack-tip blunting[J]. Journal of the Mechanics and Physics of Solids, 2004, 52(9):2149-2166.
[67] GU I, RITCHIE R. On the crack-tip blunting model for fatigue crack propagation in ductile materials[M]//Fatigue and Fracture Mechanics:29th Volume. ASTM International, 1999.
[68] NGUYEN O, REPETTO E, ORTIZ M, et al. A cohesive model of fatigue crack growth[J]. International Journal of Fracture, 2001, 110(4):351-369.
[69] ROE K, SIEGMUND T. An irreversible cohesive zone model for interface fatigue crack growth simulation[J]. Engineering Fracture Mechanics, 2003, 70(2):209-232.
[70] CHEW H. Cohesive zone laws for fatigue crack growth:Numerical field projection of the micromechanical damage process in an elasto-plastic medium[J]. International Journal of Solids and Structures, 2014, 51(6):1410-1420.
[71] PANWAR S, SUNDARARAGHAVAN V. Dislocation theory-based cohesive model for microstructurally short fatigue crack growth[J]. Materials Science and Engineering:A, 2017, 708:395-404.
[72] ALLEGRI G. A unified formulation for fatigue crack onset and growth via cohesive zone modelling[J]. Journal of the Mechanics and Physics of Solids, 2020, 138:103900.
[73] LO Y, BORDEN M, RAVI-CHANDAR K, et al. A phase-field model for fatigue crack growth[J]. Journal of the Mechanics and Physics of Solids, 2019, 132:103684.
[74] SCHREIBER C, KUHN C, MULLER R, et al. A phase field modeling approach of cyclic fatigue crack growth[J]. International Journal of Fracture, 2020, 225(1):89-100.
[75] YAN S, SCHREIBER C, MULLER R. An efficient implementation of a phase field model for fatigue crack growth[J]. International Journal of Fracture, 2022, 237:47-60.
[76] WANG X, RAN H, JIANG C, et al. An energy dissipation-based fatigue crack growth model[J]. International Journal of Fatigue, 2018, 114:167-176.
[77] CHANDRAN K. Mechanics of fatigue crack growth under large-scale plasticity:A direct physical approach for single-valued correlation of fatigue crack growth data[J]. International Journal of Fatigue, 2018, 117:299-313.
[78] CHENG A, CHEN N, PU Y. An energy principles based model for fatigue crack growth prediction[J]. International Journal of Fatigue, 2019, 128:105198.
[79] 李鹤飞. 高强钢断裂韧性与裂纹扩展机制研究[D]. 合肥:中国科学技术大学, 2019. LI Hefei. Study on fracture toughness and crack propagation mechanism of high strength steel[D]. Hefei:University of Science and Technology of China, 2019.
[80] WU S, LI C, LUO Y, et al. A uniaxial tensile behavior based fatigue crack growth model[J]. International Journal of Fatigue, 2020, 131:105324.
[81] HOSSEINI Z, DADFARNIA M, SOMERDAY B, et al. On the theoretical modeling of fatigue crack growth[J]. Journal of the Mechanics and Physics of Solids, 2018, 121:341-362.
[82] HUANG X, MOAN T. Improved modeling of the effect of R-ratio on crack growth rate[J]. International Journal of Fatigue, 2007, 29(4):591-602.
[83] KANG G, LUO H. Review on fatigue life prediction models of welded joint[J]. Acta Mechanica Sinica, 2020, 36(3):701-726.
[84] HU Xuteng, ZHU Lei, JIANG Rong, et al. Small fatigue crack growth behavior of titanium alloy TC4 at different stress ratios[J]. Fatigue & Fracture of Engineering Materials and Structures, 2018, 42:339-351.
[85] WALKER K. The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum[J]. ASTM International, 1970:1-14.
[86] CHAI M, HOU X, ZHANG Z, et al. Identification and prediction of fatigue crack growth under different stress ratios using acoustic emission data[J]. International Journal of Fatigue, 2022, 160:106860.
[87] KUJAWSKI D. A fatigue crack driving force parameter with load ratio effects[J]. International Journal of Fatigue, 2001, 23:239-246.
[88] ZHAN W, LU N, ZHANG C. A new approximate model for the R-ratio effect on fatigue crack growth rate[J]. Engineering Fracture Mechanics, 2014, 119:85-96.
[89] CHANDRAN K. New approach for the correlation of fatigue crack growth in metals on the basis of the change in net-section strain energy[J]. Acta Materialia, 2017, 129:439-449.
[90] VENKATESAN K, LIU Y. Subcycle fatigue crack growth formulation under positive and negative stress ratios[J]. Engineering Fracture Mechanics, 2017, 189:390-404.
[91] ELBER W. The significance of fatigue crack closure, Damage tolerance in aircraft structures[J]. ASTM International, 1971, 486:230-242.
[92] NOROOZI A, GLINKA G, LANMBERT S. A two parameter driving force for fatigue crack growth analysis[J]. International Journal of Fatigue, 2005, 27:1277-1296.
[93] LI Hefei, YANG Shaopu, ZHANG Peng, et al. Material-independent stress ratio effect on the fatigue crack growth behavior[J]. Engineering Fracture Mechanics, 2022, 259:108116.
[94] PUTATUNDA S, RIGSBEE J. Effect of specimen size on fatigue crack growth rate in AISI 4340 steel[J]. Engineering Fracture Mechanics, 1985, 22:335-345.
[95] GUO Wanlin. Fatigue crack closure under triaxial stress constraint-I. experimental investigation[J]. Engineering Fracture Mechanics, 1994, 49:265-275.
[96] SHIN C, LIN S. Evaluating fatigue crack propagation properties using miniature specimens[J]. International Journal of Fatigue, 2012, 43:105-110.
[97] COSTA J, FERREIRA J. Effect of stress ratio and specimen thickness on fatigue crack growth of CK45 steel[J]. Theoretical and Applied Fracture Mechanics, 1998, 30:65-73.
[98] KORDA A, MUTOH Y, MIYASHITA Y, et al. Effects of pearlite morphology and specimen thickness on fatigue crack growth resistance in ferritic-pearlitic steels[J]. Materials Science & Engineering A, 2006, 428:262-269.
[99] WANG Q, YAN Z, LIU X, et al. Understanding of fatigue crack growth behavior in welded joint of a new generation Ni-Cr-Mo-V high strength steel[J]. Engineering Fracture Mechanics, 2018, 194:224-239.
[100] PARK H, LEE B. Effect of specimen thickness on fatigue crack growth rate[J]. Nuclear Engineering and Design, 2000, 197:197-203.
[101] CLARH J, TROUT J. Influence of temperature and section size on fatigue crack growth behavior in Ni-Mo-V alloy steel[J]. Engineering Fracture Mechanics, 1970, 2:107-123.
[102] JACK A, PRICE A. Effects of thickness on fatigue crack initiation and growth in notched mild steel specimens[J]. Acta Metallurgica, 1972, 20:857-866.
[103] MATOS P, NOWELL D. Experimental and numerical investigation of thickness effects in plasticity-induced fatigue crack closure[J]. International Journal of Fatigue, 2009, 31:1795-1804.
[104] PARIS P, TADA H, KEITH J. Service load fatigue damage-a historical perspective[J]. International Journal of Fatigue, 1999, 21:S35-S46.
[105] CODRINGTON J, KOTOUSOV A. A crack closure model of fatigue crack growth in plates of finite thickness under small-scale yielding conditions[J]. Mechanics of Materials, 2009, 41:165-173.
[106] SADANANDA K, MATCHA N, VASUDEVAN A. A review of fatigue crack growth resistance in the short crack growth regime[J]. Materials Science and Engineering A, 2019, 754:674-701.
[107] CHANG T, GUO W. A model for the through-thickness fatigue crack closure[J]. Engineering Fracture Mechanics, 1999, 64:59-65.
[108] VOORWALD H, TORRES M, JUNINOR C. Modelling of fatigue crack growth following overloads[J]. International Journal of Fatigue, 1991, 13:423-427.
[109] HUANG X, TORGEIR M, CUI W. An engineering model of fatigue crack growth under variable amplitude loading[J]. International Journal of Fatigue, 2018, 30:2-10.
[110] SHE C, ZHAO J, GUO W. Three-dimensional stress fields near notches and cracks[J]. International Journal of Fracture, 2008, 151:151-160.
[111] YU P, SHE C, GUO W. Equivalent thickness conception for corner cracks[J]. International Journal of Solids and Structures, 2010, 47:2123-2130.
[112] YU P, GUO W. An equivalent thickness conception for evaluation of corner and surface fatigue crack closure[J]. Engineering Fracture Mechanics, 2013, 99:202-213.
[113] GUO W, ZHU J, GUO W. Equivalent thickness-based three dimensional stress fields and fatigue growth of part-through cracks emanating from a circular hole[J]. Engineering Fracture Mechanics, 2020, 228:106927.
[114] 于培师,赵军华,郭万林. 三维损伤容限设计:离面约束理论与疲劳断裂准则[J]. 机械工程学报, 2021, 57(16):87-105. YU Peishi, ZHAO Junhua, GUO Wanlin. Three-dimensional damage tolerance design:Out-of-plane constraint theory and fatigue fracture criteria[J]. Journal of Mechanical Engineering, 2021, 57(16):87-105.
[115] SHUTER D, GEARY W. The influence of specimen thickness on fatigue crack growth retardation following an overload[J]. International Journal of Fatigue, 1995, 17:111-119.
[116] CHANDRAN K, DORMAN S. The nature of specimen-size-effect on fatigue crack growth and net-section fracture mechanics approach to extract the size-independent behavior[J]. International Journal of Fatigue, 2021, 145:106088.
[117] MEIROM R, CLARK T, MUHLSTEEIN C. The role of specimen thickness in the fracture toughness and fatigue crack growth resistance of nanocrystalline platinum films[J]. Acta Materialia, 2012, 60:1408-1417.
[118] LI Hefei, CUI Zhaojia, PENG Linkai, et al. A new strategy to clarify the thickness effect on the fatigue crack growth rate in high-strength steels[J]. Fatigue and Fracture of Engineering Materials and Structures, 2022, 45:2845-2853.
[119] JIANG Y, LI X, JIANG W, et al. Thickness effect in laser shock processing for test specimens with a small hole under smaller laser power density[J]. Optics & Laser Technology, 2019, 114:127-134.
[120] MATOS P, NOWELL D. Experimental and numerical investigation of thickness effects in plasticity-induced fatigue crack closure[J]. International Journal of Fatigue, 2009, 31:1795-1804.
[121] ZHANG S, XIE J, JIANG Q, et al. Fatigue crack growth behavior in gradient microstructure of hardened surface layer for an axle steel[J]. Materials Science & Engineering A, 2017, 700:66-74.
[122] GRANADOS-ALEJO V, RUBIO-GONZALEZ C, VAZQUEZ-JIMENEZ C, et al. Influence of specimen thickness on the fatigue behavior of notched steel plates subjected to laser shock peening[J]. Optics & Laser Technology, 2018, 101:531-544.
[123] RAY S, KISHEN J. Fatigue crack propagation model and size effect in concrete using dimensional analysis[J]. Mechanics of Materials, 2011, 43:75-86.