A CRITICAL REVIEW ON CRITERIA OF FRACTURE MECHANICS

doi:10.6052/0459-1879-16-069

Abstract

Abstract:

In this paper, the K criterion for linear fracture mechanics, the G criterion for interfacial fracture mechanics, and the J criterion for elastoplastic fracture mechanics has been briefly reviewed, from the preliminary works of Inglis and Griffith to the foundation contributions of Irwin and Rice. Recently, on the basis of the G criterion for interfacial fracture mechanics, the K criterion for interfacial fracture mechanics was derived. This shows that the criteria of fracture mechanics need to be further improved. Thereupon, some debatable issues in the criteria of fracture mechanics are raised. Then, the strain discontinuity at the crack tip is assumed as the source of the stress singularity at a crack tip, and the physical meaning of the stress intensity factor is discussed. At the end, it is concluded that an improved and reliable analysis for the elastoplastic stress field near a crack tip is the key for the establishment of a criterion of elastoplastic fracture mechanics, and an improved and reliable analysis for the elastoplastic stress field near a crack tip depends on the determination of the magnitude of the stress at the crack tip, which caused the strain discontinuity at the crack tip.

Key words:

stress singularity|stress intensity factor|crack extension criterion|fracture mechanics

CLC Number:

O346.1

Ji Xing. A CRITICAL REVIEW ON CRITERIA OF FRACTURE MECHANICS[J]. Chinese Journal of Theoretical and Applied Mechani, 2016, 48(4): 741-753.

References

1 Rossmanith HP. The struggle for recognition of engineering fracture mechanics. In: Rossmanith HP, ed. Fracture Research in Retrospect, An Anniversary Volume in honour of Professor George R. Irwin's 90th Birthday. Rotterdam: Balkema Publishers, 1997
2 Anderson Ted L. Fracture Mechanics-fundamentals and Applications. 3rd Edition. Taylor & Francis Group, 2005
3 范天佑. 断裂理论基础. 北京:科学出版社,2003 (Fan Tianyou. Foundation of Fracture Theory. Beijing: Sicience Press, 2003 (in Chinese))
4 Kirsch G. Verein Deutscher Ingenieure (VDI) (English: Association of German Engineers), 42, 1898
5 Inglis CE. Stresses in a plate due to the presence of cracks and sharp corners. Proc Inst Naval Arch, 1913, 55: 219-241
6 Westergaard HM. Bearing pressures and cracks. ASME J Appl Mech, 1939, 61: A-49-53
7 Williams ML. On the stress distribution at the base of a stationary crack. ASME J Appl Mech, 1957, 24: 109-114
8 Muskhelishvili NI. Some Basic Problems in the Theory of Elasticity. Netherlands: Noordho, Ltd., 1953
9 杜庆华,余寿文,姚振汉. 弹性理论. 北京:科学出版社,1986 (Du Qinghua, Yu Shouwen, Yao Zhenhan. Theory of Elasticity. Beijing: Science Press, 1986 (in Chinese))
10 Sih GC. Mechanics of Fracture I. Methods of Analysis and Solutions of Crack Problems. Leyden: Noordhoof, 1973
11 Williams ML. The stresses around a fault or crack indissimilar media. Bulletin of the Seismological Society of America, 1959, 49 (2): 199-204
12 England AH. Stress distribution in bonded dissimilar materials with cracks. ASME J Appl Mech, 1965, 32: 400-402
13 Griffith AA. The phenomena of rupture and flow in solids. Phil Trans Roy Soc London A, 1920, 221: 163-198
14 Timoshenko S. Theory of Elasticity. McGraw-Hill, 1933
15 Irwin GR. Fracture Dynamics. Fracturing of Metals. Cleveland, OH: ASM, 1948
16 Orowan E. Fracture and strength of solids. Reports on Progress in Physics, 1949, 12: 185-232
17 Post D. Photoelastic stress analysis for an edge crack in a tensile field. Proc Soc Exp Stress Anal, 1954, 12(1): 99-116
18 Irwin GR. Analysis of stresses and strains near the end of a crack traversing a plate. ASME J Appl Mech, 24: 361-364
19 Irwin GR, Fracture. In: Flügge S, ed. Encyclopedia of Physics. Vol. VI -Elasticity and Plasticity. Berlin: Springer-Verlag, 1958
20 Sih GC. Handbook of Stress Intensity Factors, Vol 1. Inst of Fracture and Solid Mechanics, Lehigh Univ, Bethlehem PA. 1973
21 中国航空研究院. 应力强度因子手册. 北京: 科学出版社, 1993 (China Aviation Academy. Handbook of Stress Intensity Factors. Beijing: Science Press, 1993 (in Chinese))
22 Rice JR. Elastic fracture mechanics concepts for interfacial cracks. ASME J Appl Mech, 1988, 55: 98-103
23 Rice JR, Sih GC. Plane problems of cracks in dissimilar media. ASME J Appl Mech, 1965, 32: 418-423
24 Suo ZG. Mechanics of interface fracture. [PhD Thesis]. Harvard University, 1989
25 Hutchinson JW, Suo ZG. Mixed mode cracking in layered materials. Adv Appl Mech, 1991, 29: 63-191
26 Ji X. SIF-based fracture criterion for interface cracks. Acta Mech Sin, 2016. (Accepted. DOI 10.1007/s10409-015-0551-1)
27 Liechti XM, Chai YS. Asymmetric shielding in interfacial fracture under in-plane shear. ASME J Appl Mech, 1992, 59: 296-304
28 Banks-Sills L. Interface fracture mechanics: theory and experiment. Int J Fract, 2015, 191: 131-146
29 Wells AA. Application of fracture mechanics at and beyond general yielding. British Welding Journal, 1963, 10: 563-570
30 Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. ASME J Appl Mech, 1968, 35: 379-386
31 Hutchinson JW. Singular behavior at the end of a tensile crack tip in a hardening material. J Mech Phys Solids, 1968, 16: 13-31
32 Rice JR, Rosegren GF. Plain strain deformation near a crack tip in a power law hardening material. J Mech Phys Solids, 1968, 16: 1-12
33 Sipes JD. Elastic-plastic fracture mechanics, a critical review. Ship Structure Committee, December 17, 1990, SSC-345, SR-1321
34 ASTM E1820-11. Standard test method for measurement of fracture Toughness. American Society for Testing and Materials, 2011
35 ASTM E399-09e2. Standard test method for linear-elastic plane strain fracture toughness K_Ic of metallic materials. American Society for Testing and Materials, 2011
36 Zhu XK, Joyce JA. Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization. Engineering Fracture Mechanics, 2012, 85: 1-46
37 Erdogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear. ASME, J Basic Engng, 1963, 85: 519-527
38 Palaniswamy K, Knauss WG. Propagation of a crack under general, in-plane tension. Int J Fracture Mech, 1972, 8: 114-117
39 Sih GC. Strain-energy-density factor applied to mixed mode crack problems. International Journal of Fracture, 1974, 10: 305-321
40 赵怡枢. 复合型裂纹扩展的应变能准则. 固体力学学报,1987, 21: 65-69 (Zhao Yishu. Strain energy criterion for crack extension of coupled modes. Acta Mechanica Solida Sinica, 1987, 21: 65-69 (in Chinese))
41 Dempsey JP, Sinclair GB. On the singular behavior at the vertex of a bi-material wedge. Journal of Elasticity, 1981, 11(3): 318-327
42 Sinclair GB. On the stress singularity at an interface crack. Int J Fract, 1980, 16: 111-119
43 Sinclair GB. Stress singularities in classical elasticity–I: Removal, interpretation and analysis. Appl Mech Rev, 2004, 57(4): 251-297
44 Sinclair GB. Stress singularities in classical elasticity—II: Asymptotic Identification. Appl Mech Rev, 2004, 57 (5): 385-439
45 Sinclair GB. On the source of singularities in mechanics. XXI International Congress of Theoretical and Applied Mechanics, Warsaw, Poland, 2004, August 15-21
46 Barenblatt GI. The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech, 1962, 7: 55-129
47 Sinclair GB. On the influence of cohesive stress-separation laws on elastic stress singularities. J Elast, 1996, 44: 203-221
48 陈篪. 论裂纹扩展判据. 新金属材料,1977,(3-4): 1-14 (Chen Chi. On the criteria for crack extension. New Metallic Materials, 1977, (3-4): 1-14 (in Chinese))
49 Dundurs J. Discussion of “Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading”. ASME J Appl Mech, 1969, 36: 650-652
50 Bogy DB. Edge-bonded dissimilar orthogonal elastic wedge under normal and shear loading. ASME J Appl Mech, 1968, 35: 460-466
51 Bogy DB. Two edge bonded elastic wedges of different materials and wedge angles under surface tractions. ASME J Appl Mech, 1971, 38: 377-389
52 Hein VL, Erdogan F. Stress singularity in a two-material wedges. Int J Fract, 1971, 7: 317-330
53 Gradin PA. A fracture criterion for edge-bonded bi-material bodies. Journal of Composite Materials, 1982, 16: 448-456
54 Akisanya AR, Fleck NA. Interfacial cracking from the free-edge of a long bi-material strip. International Journal of Solids and Structures, 1997, 34: 1645-1665
55 Reedy ED. Connection between interface corner and interfacial fracture analyses of an adhesively-bonded butt joint. International Journal of Solids and Structures, 2000, 37: 2429-2442
56 Labossiere PEW, Dunn ML, Cunningham SJ. Application of bimaterial interface corner failure mechanics to silicon/glass anodic bonds. Journal of the Mechanics and Physics of Solids, 2002, 50: 405-433
57 Nied HF. Mechanics of interface fracture with applications in electronic packaging, IEEE Transaction on Device and Materials Reliability, 2003, 3: 129-143
58 Ji X. On fracture criteria for bi-material corners. International Journal of Applied Mechanics, 2014, 6 (5): 1450062-1-12
59 Bogy DB. On the problem of edge-bonded elastic quarter-planes loaded at boundary. International Journal of Solids and Structures, 1970, 6: 1287-1313
60 嵇醒. 半平面双材料角界面应力奇异性分布规律的研究. 固体力学学报,2011, 35(5): 446-458 (Ji Xing. Study on singular interfacial stresses in bimaterial corners of edge-bonded quarter-planes. Acta Mechanica Solida Sinica, 2011, 35(5): 446-458 (in Chinese))