Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization

Engineering Fracture Mechanics

Volumn 85, Issue , 2012, Pages 1-46

  Zhu, Xian Kui ^a   Joyce, James A ^b  

^a BATTELLE MEMORIAL INSTITUTE   (United States)

^b UNITED STATES NAVAL ACADEMY   (United States)

Author keywords

ASTM standard; CTOA; CTOD; Energy release rate; Fracture test; Fracture toughness; J integral; J R curve; K R curve; Stress intensity factor

Indexed keywords

ASTM STANDARDS; CTOA; CTOD; ENERGY RELEASE; FRACTURE TEST; J INTEGRAL; J-R CURVE; K-R CURVE; STRESS INTENSITY;

BRITTLE FRACTURE; CRACK PROPAGATION; ENERGY RELEASE RATE; FRACTURE TESTING; FRACTURE TOUGHNESS; STANDARDIZATION; STRESS INTENSITY FACTORS;

MATERIALS TESTING;

EID: 84862793390     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engfracmech.2012.02.001     Document Type: Article

References (295)

1. Irwin G.R. Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 1957, 24:361-364.
2. Rice J.R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 1968, 35:379-386.
3. Wells A.A. Application of fracture mechanics at and beyond general yielding. Br Weld J 1963, 10:563-570.
4. Broek D. Elementary engineering fracture mechanics 1974, Noordhoff International Publishing, Leyden.
5. Kanninen M.F., Popelar C.H. Advanced fracture mechanics 1985, Oxford University Press, New York.
6. Hertzberg R.W. Deformation and fracture mechanics of engineering materials 1995, John Wiley & Sons, New York. 4th ed.
7. Anderson T.L. Fracture mechanics - fundamentals and applications 2005, CRC Press, Boca Raton. 3rd ed.
8. Irwin G.R., DeWit R. A summary of fracture mechanics concepts. J Test Evaluat 1983, 11:56-65.
9. Erdogan F. Fracture mechanics. Int J Solids Struct 2000, 37:171-183.
10. Cotterell B. The past, present and future of fracture mechanics. Engng Fract Mech 2002, 69:533-553.
11. Milne I, Ritchie RO, Karihaloo B. Comprehensive structural integrity, vols 1-10 (print version). Elsevier; 2003; or vols. 1-11 (online version), Elsevier; 2007.
12. ASTM E1823-10a. Standard terminology relating to fatigue and fracture testing. American Society for Testing and Materials; 2011.
13. ASTM E399-09e2. Standard test method for linear-elastic plane strain fracture toughness KIc of metallic materials. American Society for Testing and Materials; 2011.
14. ASTM E561-10. Standard test method for K-R curve determination. American Society for Testing and Materials; 2011.
15. ASTM E1820-11. Standard test method for measurement of fracture toughness. American Society for Testing and Materials; 2011.
16. ASTM E1290-08e1. Standard test method for crack-tip opening displacement (CTOD) fracture toughness measurement. American Society for Testing and Materials; 2011.
17. ASTM E2472-06e1. Standard test method for determination of resistance to stable crack extension under low-constraint conditions. American Society for Testing and Materials; 2011.
18. ASTM E1921-11. Standard test method for determining of reference temperature T0 for ferritic steels in the transition range. American Society for Testing and Materials; 2011.
19. Heyer R.H. Crack growth resistance curves (R-curves) - literature review. ASTM STP 527 1973, 3-16. American Society for Testing and Materials.
20. Barsom J.M. Fracture mechanics retrospective - early classic papers (1913 to 1965). ASTM RPS1 1987, American Society for Testing and Materials.
21. Joyce JA. Manual on elastic-plastic fracture: laboratory test procedures. ASTM Manual Series: MNL27; 1996.
22. Landes J.D. Elastic-plastic fracture mechanics: where has it been? Where is it going?. ASTM STP 1360 2000, vol. 30:3-18. American Society for Testing and Materials.
23. Landes J.D. Fracture toughness testing and estimations. Comprehensive structural integrity 2003, vol. Elsevier, [Chapter 7.02].
24. Schwalbe K.H., Landes J.D., Heerens J. Classic fracture mechanics methods. Comprehensive structural integrity 2007, vol. 11. Elsevier.
25. Zhu X.K. J-integral resistance curve testing and evaluation. J Zhejiang Univ Sci A 2009, 10:1541-1560.
26. Zhu XK. Advances in development of J-integral experimental estimation, testing and standardization. In: Proceedings of ASME 2011 pressure vessels and piping conference, Baltimore, Maryland, July 17-21, 2011.
27. Williams M.L. On the stress distribution at the base of a stationary crack. J Appl Mech 1957, 24:109-114.
28. Irwin G.R., Kies J.A., Smith H.L. Fracture strengths relative to onset and arrest of crack propagation. Proc Am Soc Test Mater 1958, 58:640-660.
29. Irwin GR. Plastic zone near a crack and fracture toughness. In: Proceedings of the 7th sagamore ordnance materials conference; 1960. p. 463-78.
30. Dugdale D.S. Yielding of steel sheets containing slits. J Mech Phys Solids 1960, 8:100-108.
31. Griffith A.A. The phenomena of rupture and flow in solids. Philos Trans Roy Soc Lond, Ser A 1920, 221:163-197.
32. Tada H., Paris P.C., Irwin G.R. The stress analysis of cracks handbook 2000, ASME Press, New York. 3rd ed.
33. Murakami Y. Stress intensity factors handbook 1987, Pergamon Press, Oxford.
34. Rooke D.P., Cartwright D.J. Compendium of stress intensity factors 1976, Her Majesty's Stationery Office, London.
35. Gallagher J.P. Damage tolerant design handbook 1983, Air Force Materials Laboratory, Wright-Patterson Air Force Base (OH).
36. Irwin GR. Fracture dynamics. In: Fracturing of metals, symposium of American Society for Metals. Transaction ASM 40A; 1948. p. 147-66.
37. Orowan E. Fracture and strength of solids. Rep Prog Phys 1949, 12:185-232.
38. Irwin GR. Onset of fast crack propagation in high strength steel and aluminum alloys. In: Proceedings of the second sagamore ordnance materials conference, vol. 2; 1956. p. 289-305.
39. Irwin G.R., Kies J.A. Critical energy rate analysis for fracture strength. Weld J Res Suppl. 1954, 19:193-198.
40. Irwin GR. Fracture testing of high-strength sheet materials under conditions appropriate for stress analysis. Report 5486, Naval Research Laboratory, July 27, 1960.
41. Anon. ASTM special committee on fracture testing of high strength materials. ASTM Bulletin, January 1960. p. 29-40.
42. Krafft JM, Sullivan AM, Boyle RW. Effect of dimensions on fast fracture instability of notched sheets. In: Cranfield symposium, vol. I; 1961. p. 8-28.
43. Srawley J.E., Brown W.F. Fracture toughness testing methods. ASTM STP 381 1965, 133-196. American Society for Testing and Materials.
44. Kaufman J.G. Progress in fracture testing of metallic materials. ASTM STP 463 1970, 3-21. American Society for Testing and Materials.
45. Anon. The slow growth and rapid propagation of cracks. Mater Res Stand 1961;1:389-93.
46. Anon. Proposed method of test for plane-strain fracture toughness of metallic materials. ASTM STP 410. American Society for Testing and Materials; 1966. p. 130-45.
47. Brown W.F., Srawley J.E. Plane strain crack toughness testing of high strength metallic materials. ASTM STP 410 1966, 1-65. American Society for Testing and Materials.
48. ASTM E399-70T. Tentative method of test for plane strain fracture toughness of metallic materials. In: Review of developments in plane strain fracture toughness testing, ASTM STP 463. American Society for Testing and Materials; 1970. p. 249-69.
49. Newman J.C. Stress analysis of the compact specimens including the effects of pin loading. ASTM STP 560 1974, 105-121. American Society for Testing and Materials.
50. Srawley J.E. Wide range stress intensity factor expressions for ASTM E399 standard fracture toughness specimens. Int J Fract 1976, 12:475-476.
51. Freese C.E., Baratta F.I. Single edge-crack stress intensity factor solutions. Engng Fract Mech 2006, 73:616-625.
52. Srawley J.E., Jones M.H., Brown W.F. Determination of plane strain fracture toughness. Material research and standards 1967, vol. 7:261-266. American Society for Testing and Materials.
53. Heyer R.H., McCabe D.E. Evaluation of a test method for plane-strain fracture toughness using a bend specimen. ASTM STP 463 1970, 22-41. American Society for Testing and Materials.
54. McCabe D.E. Evaluation of the compact tension specimen for determining plane-strain fracture toughness of high strength materials. J Mater 1972, 7:449-542.
55. Underwood J.H., Kendall D.P. Cooperative plane strain fracture toughness tests with C-shaped specimens. J Test Evaluat 1978, 6:296-300.
56. Wallin K.R.W. Critical assessment of the standard ASTM E399. J ASTM Int 2005, 2:JAI12051.
57. Joyce J.A., Smudz R. Evaluation of elastic intensity using J-integral specimen geometries. J Test Evaluat 1992, 20:1-5.
58. Ic using ASTM E399. J Test Evaluat 1998, 26:455-462.
59. Irwin G.R. Crack toughness testing of strain rate sensitive materials. J Engng Power Transmiss 1964, 86:444-450.
60. Irwin G.R. Basic concepts for dynamic fracture testing. J Basic Engng 1969, 91:519-524.
61. c testing of structural steel. J Struct Div 1974, 7:1331-1349.
62. Ic testing. J Test Evaluat 1983, 11:261-272.
63. Feddersen C.E. Evaluation and prediction of the residual strength of center cracked tension panels. ASTM STP 486 1971, 50-78. American Society for Testing and Materials.
64. Feddersen CE, Simonen FA, Hulbert LE, Hyler WS. An experimental and theoretical investigation of plane-stress fracture of 2024-T351 aluminum alloy. NASA CR-1678. National Aeronautics and Space Administration, Washington, DC, September 1970.
65. Orange TW, Sullivan TL, Calfo FD. Fracture of thin sections containing through and part-through cracks. NASA TN-6305. National Aeronautics and Space Administration, Washington, DC, April 1971.
66. Schwalbe K.H., Newman J.C., Shannon J.L. Fracture mechanics testing on specimens with low constraint - standardisation activities within ISO and ASTM. Engng Fract Mech 2005, 72:557-576.
67. McCabe D.E., Heyer R.H. R-curve determination using a crack-line-wedge-loaded (CLWL) specimen. ASTM STP 527 1973, 17-35. American Society for Testing and Materials.
68. Sullivan A.M., Freed C.N., Stoop J. Comparison of R-curves determined from different specimen types. ASTM STP 527 1973, 85-104. American Society for Testing and Materials.
69. Heyer R.H., McCabe D.E. Plane-stress fracture toughness testing using a crack-line-loaded specimen. Engng Fract Mech 1972, 4:395-412.
70. Heyer R.H., McCabe D.E. Crack growth resistance in plane-stress fracture testing. Engng Fract Mech 1972, 4:413-430.
71. Wang D.Y., McCabe D.E. Investigation of R-curve using comparative tests with center-cracked-tension and crack-line-wedged-loaded specimens. ASTM STP 590 1976, 169-193. American Society for Testing and Materials.
72. Schwalbe K.H., Setz W. R curve and fracture toughness of thin sheet materials. J Test Evaluat 1981, 9:182-194.
73. Hellmann D., Schwalbe K.H. Geometry and size effects on J-R and δ-R curves under plane stress conditions. ASTM STP 833 1984, 557-605. American Society for Testing and Materials.
74. Putatunda S.K., Rigsbee J.M., Corten H.T. Effect of size on elastic-plastic fracture toughness parameters. J Test Evaluat 1985, 13:181-190.
75. Chao Y.J. On a single parameter controlled fracture of solids under plane stress conditions. Int J Fract 1993, 62:R7-R10.
76. Yan C., Mai Y.W. Numerical investigation on stable crack growth in plane stress. Int J Fract 1998, 91:117-130.
77. Feddersen C.E. Discussion. ASTM STP 1966, vol. 410. American Society for Testing and Materials, p. 77-79.
78. Newman J.C., Haines M.J. Verification of stress-intensity factors for various middle-crack tension test specimens. Engng Fract Mech 2005, 72:1113-1118.
79. Dawicke DS, Newman JC, Starnes JH, Rose CA, Young RD, Seshadri BR. Residual strength analysis methodology: laboratory coupons to structural components. In: The third joint FAA/DoD/NASA conference on aging aircraft, Albuquerque, New Mexico, September 20-23, 1999.
80. Pearson H.S., McCabe D.E. R-curve round-robin program for ASTM recommended practice for R-curve determination (E561). J Test Evaluat 1986, 14:191-199.
81. McCabe D.E., Ernst H.A. A perspective on R-curves and instability theory. Theory and analysis, ASTM STP 791 1983, vol. I:I-561-I-584. American Society for Testing and Materials.
82. Newman J.C. An evaluation of fracture analysis methods. ASTM STP 896 1985, 5-96. American Society for Testing and Materials.
83. Reynolds A.P. Comparison of R-curve methodologies for ranking the toughness of aluminum alloys. J Test Evaluat 1996, 24:406-410.
84. Pearson H.S. Evaluation of plane stress fracture testing methods. J Test Evaluat 1986, 14:224-226.
85. R-curve approach. ASTM STP 896 1985, 99-113. American Society for Testing and Materials.
86. McCabe D.E., Landes J.D. J-R curve testing of large compact specimens. ASTM STP 803 1983, vol. II:II-353-II-371. American Society of Testing and Materials.
87. Haynes M.T., Gangloff R.P. High resolution R-curve characterization of the fracture toughness of thin sheet aluminum alloys. J Test Evaluat 1997, 25:82-98.
88. Zhu X.K., Leis B.N. Revisit of ASTM round robin test data for determining R curves of thin sheet materials. J ASTM Int 2009, [paper ID JAI102510].
89. Kobayashi A.S., Chiu S.T., Beeuwkes R. A numerical and experimental investigation on the use of J-integral. Engng Fract Mech 1973, 5:293-305.
90. Hutchinson J.W. Singular behavior at the end of a tensile crack in a hardening material. J Mech Phys Solids 1968, 16:13-31.
91. Rice J.R., Rosengren G.F. Plane Strain deformation near a crack tip in a power law hardening material. J Mech Phys Solids 1968, 16:1-12.
92. McClintock FA. Plasticity aspect of fracture. In: Liebowitz H, editor. Fracture: an advanced treatise, vol. 3. London: Academic press; 1971. p. 47-225.
93. McMeeking R.M., Parks D.M. On criteria for J-dominance of crack-tip fields in large-scale yielding. ASTM STP 668 1979, 175-194. American Society for Testing and Materials.
94. Shih C.F., German M.D. Requirements for a one parameter characterization of crack tip fields by the HRR singularity. Int J Fract 1981, 17:27-43.
95. Rice J.R., McMeeking R.M., Parks D.M., Sorensen E.P. Recent finite element studies in plasticity and fracture mechanics. Comput Meth Appl Mech Engng 1979, 17/18:411-442.
96. Al-Ani A.M., Hancock S.W. J-dominance of short cracks in tension and bending. J Mech Phys Solids 1991, 39:23-43.
97. Parks DM. Three-dimensional aspects of HRR-dominance. In: Proceedings of the conference of european symposium on elastic-plastic fracture mechanics: defect assessment in components-fundamentals and applications, Freiburg, Germany, October 9-12, 1989. p. 205-31.
98. Kumar V, German MD, Shih CF. An engineering approach for elastic-plastic fracture analysis. EPRI report # NP-1931, Electric Power Research Institute; 1981.
99. Begley J.A., Landes J.D. The J-integral as a fracture criterion. ASTM STP 514 1972, 1-23. American Society for Testing and Materials.
100. IC. ASTM STP 514 1972, 24-39. American Society for Testing and Materials.
101. Rice J.R., Paris P.C., Merkle J.G. Some further results of J-integral analysis and estimates. ASTM STP 536 1973, 231-245. American Society for Testing and Materials.
102. Landes J.D., Walker H., Clarke G.A. Evaluation of estimation procedures used in J-integral testing. ASTM STP 668 1979, 266-287. American Society for Testing and Materials.
103. Merkle J.G., Corten H.T. A J integral analysis for the compact specimen considering axial force as well as bending effects. J Press Ves Technol 1974, 96:286-292.
104. I to work done per unit uncracked area: 'total' or component 'due to crack'. Int J Fract 1976, 12:470-474.
105. C (contour integral for fracture analysis). ASTM STP 601 1976, American Society for Testing and Materials.
106. Turner C.E. The ubiquitous η factor. ASTM STP 700 1980, 314-337. American Society for Testing and Materials.
107. Roos E., Eisele U., Silcher H. A procedure for the experimental assessment of the J-integral by means of specimen of different geometries. Int J Press Ves Pip 1986, 23:81-93.
108. Turner C.E. Fracture toughness and specific energy: a reanalysis of results. Mater Sci Engng 1973, 11:275-282.
109. Clarke G.A., Landes J.D. Evaluation of the J-integral for the compact specimen. J Test Evaluat 1979, 7:264-269.
110. C determination for shallow notch welded bend specimens. Fatigue Fract Engng Mater Struct 1987, 10:479-493.
111. Kirk M.T., Dodds R.H. J and CTOD estimation equations for shallow cracks in single edge notched bend specimens. J Test Evaluat 1993, 21:228-238.
112. Nevalainen M., Dodds R.H. Numerical investigation of 3-D constraint effect on brittle fracture in SE(B) and C(T) specimens. Int J Fract 1995, 74:131-161.
113. Paris P.C., Ernst H.A., Turner C.E. A J-integral approach to the development of η factors. ASTM STP 700 1980, 251-338. American Society for Testing and Materials.
114. Ernst H.A., Paris P.C., Rossow M., Hutchinson J.W. Analysis of load-displacement relationships to determine J-R curve and tearing instability material properties. ASTM STP 677 1979, 581-599. American Society for Testing and Materials.
115. Sharobeam M.H., Landes J.D. The load separation criterion and methodology in ductile fracture mechanics. Int J Fract 1991, 47:81-104.
116. pl development in precracked specimen test records. Int J Fract 1993, 59:213-226.
117. Joyce JA. On the mechanisms and mechanics of plastic flow and fracture, Sc.D. thesis, Massachusetts Institute of Technology, May 1974.
118. Towers O.L., Garwood S.J. Maximum load toughness. Int J Fract 1980, 16:R85-R90.
119. Ic testing procedure. ASTM STP 560 1974, 170-186. American Society for Testing and Materials.
120. Hutchinson J.W., Paris P.C. Stability analysis of J-controlled crack growth. ASTM STP 668 1979, 37-64. American Society for Testing and Materials.
121. IC determination. ASTM STP 590 1976, 27-42. American Society for Testing and Materials.
122. Garwood S.J., Robinson J.N., Turner C.E. The measurement of crack growth resistance curves (R-curves) using the J integral. Int J Fract 1975, 11:528-530.
123. Etemad M.R., Turner C.E. An experimental investigation of slow stable crack growth using HY130 steel. J Strain Anal 1985, 20:201-208.
124. Etemad M.R., John S.J., Turner C.E. Elastic-elastic R-curves for large amounts of crack growth. ASTM STP 945 1988, 986-1004. American Society for Testing and Materials.
125. Ernst H.A., Paris P.C., Landes J.D. Estimations on J-integral and tearing modulus T from a single specimen test record. ASTM STP 743 1981, 476-502. American Society for Testing and Materials.
126. Joyce JA. Application of the key curve method to determining J-R curve for A533B steel. Nuclear regulatory commission report, NUREG/CR-1290, February 1980.
127. Zhu X.K., Joyce J.A. More accurate formulation of J-integral equation for evaluating fracture resistance curves. J ASTM Int 2009, 7(1). [paper ID JAI102505].
128. IC testing of navy alloys. ASTM STP 668 1979, 451-468. American Society for Testing and Materials.
129. R curve. Engng Fract Mech 2008, 75:236-252.
130. Kroon M., Faleskog J., Oberg H. A probabilistic model for cleavage fracture with a length scale - parameter estimation and predictions of growing crack experiments. Engng Fract Mech 2008, 75:2398-2417.
131. Johnson H.H. Calibrating the electric potential method for studying slow crack growth. Mater Res Stand 1965, 5:442-445.
132. Schwalbe K.H., Hellmann D. Application of the electrical potential method of crack length measurement using Johnson's formula. J Test Evaluat 1981, 9:218-221.
133. Bakker A. A DC potential drop procedure for crack initiation and R-curve measurements during ductile fracture tests. ASTM STP 586 1985, 394-410. American Society for Testing and Materials.
134. Roos E., Eisele U. Determination of material characteristic values in elastic-plastic fracture mechanics by means of J-integral crack resistance curves. J Test Evaluat 1988, 16:1-11.
135. Eisele U., Roos E. Evaluation of different fracture mechanical J-integral initiation values with regard to their usability in the safety assessment of components. Nucl Engng Des 1991, 130:237-247.
136. Paris P.C., Tada H., Zahoor A., Ernst H. The theory of instability of the tearing mode of elastic-plastic crack growth. ASTM STP 668 1979, 5-36. American Society for Testing and Materials.
137. Morrison J., Karisallen K.J. An experimental comparison of J and CTOD estimation formulas. Engng Fract Mech 1995, 51:145-149.
138. Wang Y.Y., Reemsnyder H.S., Kirk M.T. Inference equations for fracture toughness testing: numerical analysis and experimental verification. ASTM STP 1321 1997, vol. 28:469-484. American Society for Testing and Materials.
139. Wallin K., Laukkanen A. Improved crack growth corrections for J-R curve testing. Engng Fract Mech 2004, 71:1601-1614.
140. Zhu X.K., Leis B.N., Joyce J.A. Experimental estimation of J-R curve from load-CMOD records for SE(B) specimens. J ASTM Int 2008, 5(5). [paper ID JAI101532].
141. Cravero S., Ruggieri C. Further developments in J evaluation procedure for growing cracks based on LLD and CMOD data. Int J Fract 2007, 148:387-400.
142. Zhu X.K., Joyce J.A. Revised incremental J-integral equations for ASTM E1820 using crack mouth opening displacement. J Test Evaluat 2009, 37:205-214.
143. Zhu XK, Leis BN. Experimental determination of J-R curves using SENB specimen and P-CMOD data. In: Proceedings of ASME pressure vessel and piping conference, Chicago, Illinois, USA, July 27-31, 2008.
144. Joyce J.A., Ernst H.A., Paris P.C. Direct J-R curve analysis: a guide to the methodology. ASTM STP 700 1980, 222-236. American Society for Testing and Materials.
145. Herrera R., Landes J.D. Direct J-R curve analysis of fracture toughness test. J Test Evaluat 1988, 16:427-449.
146. Joyce J.A. J-resistance curve testing of short crack bend specimens using unloading compliance. ASTM STP 1131 1992, vol. I:904-924. American Society for Testing and Materials.
147. Herrera R., Landes J.D. Direct J-R curve analysis: a guide to the methodology. ASTM STP 1074 1990, 24-43. American Society for Testing and Materials.
148. Orange T.W. Methods and models for R-curve instability calculations. ASTM STP 1074 1990, 545-559. American Society for Testing and Materials.
149. Landes J.D., Zhou Z., Lee K., Herrera R. Normalization method for developing J-R curves with the LMN function. J Test Evaluat 1991, 19:305-311.
150. Joyce J.A. Analysis of a high rate round robin based on proposed annexes to ASTM E 1820. J Test Evaluat 2001, 29:329-351.
151. Oh Y.J., Hwang I.S., Joyce J.A. Round robin test on normalization method under static loading condition. J Test Evaluat 2006, 34:537-561.
152. Dzugan J., Viehrig H.W. Application of the normalization method for the determination of J-R curves. Mater Sci Engng A 2004, 387-389:307-311.
153. Zhu X.K., Joyce J.A. J-resistance curve testing of HY80 steel using SE(B) specimens and normalization method. Engng Fract Mech 2007, 74:2263-2281.
154. Zhu X.K., Leis B.N. Fracture resistance curve testing of X80 pipeline steel using SENB specimen and normalization method. J Pipeline Engng 2008, 7:126-136.
155. Zhu X.K., Lam P.S., Chao Y.J. Applications of normalization method to experimental measurement of fracture toughness for A285 carbon steel. J Press Ves Pip 2009, 86:669-676.
156. Clarke G.A., Andrews W.R., Begley J.A., Donald J.K., Embley G.T., Landes J.D., et al. A procedure for the determination of ductile fracture toughness values using J integral techniques. J Test Evaluats 1979, 7:49-56.
157. Paris P.C. A written discussion of Begley and Landes (1972). ASTM STP 514 1972, 21-22. American Society for Testing and Materials.
158. Ic testing. ASTM STP 632 1977, 57-81. American Society for Testing and Materials.
159. Ic testing procedure by round robin tests on A533B class 1 pressure vessel steel. J Test Evaluat 1980, 8:213-220.
160. Ic determination of HY130 steel. J Test Evaluat 1980, 8:221-232.
161. ASTM E813-81. Standard test method for JIc, a measure of fracture toughness. American Society for Testing and Materials; 1982.
162. Hiser AL, Loss FJ, Menke BH. J-R Curve characterization of irradiated low upper shelf welds. NUREG/CR-3506; 1984.
163. Jablonski D.A. Computerized single-specimen J-R curve determination for compact tension and three-point bend specimens. ASTM STP 877 1985, 269-297. American Society for Testing and Materials.
164. ASTM E1152-82. Standard test method for determining J-R curves. American Society for Testing and Materials; 1982.
165. I-R curve. J Test Evaluat 1982, 10:245-251.
166. I-R curve testing procedure by round robin tests of HY130 steel. J Test Evaluat 1982, 10:252-262.
167. ASTM E1737-96. Standard test method for J-integral characterization of fracture toughness. American Society for Testing and Materials; 1996.
168. ASTM E1290-90. Standard test method for crack-tip opening displacement (CTOD) fracture toughness measurement. American Society for Testing and Materials; 1998.
169. ASTM E1820-96. Standard test method for measurement of fracture toughness. American Society for Testing and Materials; 1996.
170. Landes J.D., Brown K.H. Results from a round robin on a standard method for measurement of fracture toughness - ASTME1820-96. Filed in the ASTM archives 1997, American Society for Testing and Materials.
171. Landes J.D., Brown K. Results from a round robin on a standard method for measurement of fracture toughness. J Test Evaluat 1998, 26:396-403.
172. Anon. Standard method for measurement of fracture toughness, draft 10. American Society for Testing and Materials, December 1990.
173. Joyce JA, Davis DA, Hackett EM, Hays, application of the J-integral and modified J integral to cases of large crack extension. NUREG/CR-5143, USNRC, 1988.
174. Joyce JA, Hackett EM. Development of an engineering definition of the extent of J singularity controlled crack growth. NUREG/CR-5238, USNRC, 1989.
175. Landes J.D. Evaluation of the ASTM J initiation procedure using the EURO fracture toughness data set. J Test Evaluat 2006, 34:200-210.
176. Wallin K. Specimen size limitation in J-R curve testing - standards versus reality. J ASTM Int 2007, 4(9). [paper ID: JAI100978].
177. Landes J.D., Shaffer D.H. Statistical characterization of fracture in the transition region. ASTM STP 700 1980, 368-382. American Society for Testing and Materials.
178. Ic results. Engng Fract Mech 1984, 19:1085-1093.
179. Anderson T.L., Stienstra D. A model to predict the sources and magnitude of scatter in toughness data in the transition region. J Test Evaluat 1989, 17:46-53.
180. Sorem W.A., Dodds R.H., Rolfe S.T. Effect of crack depth on elastic plastic fracture toughness. Int J Fract 1991, 47:105-126.
181. MacLennan IJ, Hancock JW. The effect of constraint on the ductile-brittle transition. In: in Shallow crack fracture mechanics, toughness tests and applications: TWI international conference. Cambridge, UK, 23-24 September, 2002. p. 21/1-9.
182. Anderson T.L., Dodds R.H. Specimen size requirements for fracture toughness testing in the transition region. J Test Evaluat 1991, 19:123-134.
183. Anderson T.L., Stienstra D., Dodds R.H. A theoretical framework to addressing fracture in the ductile-to-brittle region. ASTM STP 1207 1994, 24:86-214. American Society for Testing and Materials.
184. Weibull W. A statistical distribution function of wide applicability. J Appl Mech 1951, 18:293-297.
185. McCabe D.E., Merkle J.G., Wallin K. An introduction to the development and use of the master curve method. ASTM MNL52 2005, American Society for Testing and Materials.
186. Landes J.D., McCabe D.E. Effect of section size on transition temperature behavior of structural steels. ASTM STP 833 1984, 78-392. American Society for Testing and Materials.
187. Wallin K., Saario T., Torronen K. Statistical model for carbide induced brittle fracture in steel. Metals Sci 1984, 18:13-16.
188. Ic results. Engng Fract Mech 1985, 22:149-163.
189. Anon. PVRC recommendation on toughness requirements for ferritic materials. WRC Bulletin 175, Welding Research Council; August 1972.
190. Wallin K. A simple theoretical Charpy V-KIc correlation for irradiation embrittlement. In: Proceedings of 1989 ASME pressure vessel and piping conference - innovative approaches to irradiation damage and fracture analysis, PVP, vol. 170. American Society for Mechanical Engineers; July 1989.
191. Wallin K. Fracture toughness transition curve shape for ferritic structural steels. Fracture of engineering materials and structures 1991, 3-88. Elsevier, London. S.T. Teoh, K.H. Lee (Eds.).
192. Wallin K. Irradiation damage effects on the fracture toughness transition curve shape for reactor pressure vessel steels. Int J Press Ves Pip 1993, 55:61-79.
193. Merkle JG, Wallin K, McCabe DE. Technical basis for an ASTM standard on determining the characterization temperature, T0, for ferritic steels in the transition range. NUREG/CR-5504, US Nuclear Regulatory Commission, Washington, DC, November 1998.
194. Wallin K. Validity of small specimen fracture toughness estimates neglecting constrain corrections. ASTM STP 1244 1995, vol. 2:519-537. American Society for Testing and Materials.
195. ASTM E1921-97. Standard test method for determining of reference temperature T0 for ferritic steels in the transition range. American Society for Testing and Materials; 1997.
196. Kirk M., Lott R., Kim C., Server W. Empirical validation of the master curve for irradiated and unirradiated reactor pressure vessel steels. Proceedings of 1998 ASME pressure vessels and piping conference, San Diego, CA 1998, American Society of Mechanical Engineers.
197. 0 reference temperature from precracked Charpy specimens. Engng Fract Mech 2001, 68:861-894.
198. Joyce J.A., Tregoning R.L. Determination of constraint limits for cleavage initiated toughness data. Engng Fract Mech 2005, 72:1559-1579.
199. 0 of ASTM E1921. J Test Evaluat 2006, 34(2). [paper ID: JTE14108].
200. 0 for ferritic steels. Recent advances in fracture 1997, 171-182. The Minerals, Metals and Materials Society. R.K. Mahidhara (Ed.).
201. Goodier J.N., Field F.A. Plastic energy dissipation in crack propagation. Fracture of solids 1963, 103-118. Wiley, New York. D.C. Drucker, J.J. Gilman (Eds.).
202. Burdekin F.M., Stone D.E.W. The crack opening displacement approach to fracture mechanics in yielding materials. J Strain Anal 1966, 1:145-153.
203. Harrison J.D., Dawes M.G., Archer G.L., Kamath M.S. The COD approach and its application to welded structures. ASTM STP 668 1979, 606-631. American Society for Testing and Materials.
204. Hollstein T., Blauel J.G. On the relation of the crack opening displacement to the J-integral. Int J Fract 1977, 13:385-390.
205. Daves M.G. Elastic-plastic fracture toughness based on the COD and J-contour integral concepts. ASTM STP 668 1979, 307-333. American Society for Testing and Materials.
206. Kirk M.T., Wang Y.Y. Wide range CTOD estimation formulae for SE(B) specimens. ASTM STP 1256 1995, vol. 26:126-141. American Society for Testing and Materials.
207. Wang Y.Y., Reemsnyder H.S., Kirk M.T. Inference equations for fracture toughness testing: numerical analysis and experimental verification. ASTM STP 1321 1997, vol. 28:469-484. American Society for Testing and Materials.
208. Panontin T.L., Makino A., Williams J.F. Crack tip opening displacement estimation formulae for C(T) specimens. Engng Fract Mech 2000, 67:293-301.
209. Wilson C.D., Landes J.D. Inconsistencies between CTOD and J calculations. J Test Evaluat 1994, 22:505-511.
210. Burdekin MF. Crack opening displacement: a review of principles and methods. In: Proceedings of symposium on fracture toughness concepts for weldable structural steel; 1969. p. C1-12.
211. Hellmann D, Schwalbe KH. On the experimental determination of CTOD based R-curves. In: Schwalbe KH, editor. The crack tip opening displacement in elastic-plastic fracture mechanics (proceedings of the workshop of the CTOD methodology). Berlin: Springer; 1986. p. 115-32.
212. Wu S.X., Mai Y.W., Cotterell B. Plastic rotation factors of three-point bend and compact tension specimens. J Test Evaluat 1988, 16:555-557.
213. Wu S.X., Cotterell B., Mai Y.W. Slip-line field solutions for three-point notch bend specimens. Int J Fract 1988, 37:13-29.
214. Nichols RW, Cowan A, Ingham T, Burdekin MF, Elliot D. The use of critical COD techniques for the selection of fracture resistant materials. In: Proceedings of symposium on fracture toughness concepts for weldable structural steel; 1969. p. F1-113.
215. BS 5762. Methods for crack opening displacement (COD) testing. London: British Standards Institute; 1979.
216. BS 7448: Part 1. Fracture mechanics toughness tests: Part 1 - Method for determining of KIc, critical CTOD and critical J values of metallic materials. London: British Standards Institute; 1991.
217. ASTM E1290-89. Standard test method for crack-tip opening displacement (CTOD) fracture toughness measurement. American Society for Testing and Materials; 1989.
218. Tagawa T., Kayamori Y., Ohata M. Comparison of CTOD standards: BS 7448 - Part 1 and revised ASTM 1290. Engng Fract Mech 2010, 77:327-336.
219. Kanninen M.F., Rybicki E.F., Stonesifer R.B., Broek D., Rosenfied A.R., Marschall C.W., et al. Elastic-plastic fracture mechanics for two-dimensional stable crack growth and instability problems. ASTM STP 668 1979, 121-150. American Society for Testing and Materials.
220. Newman J.C., James M.A., Zerbst U. A review of the CTOA/CTOD fracture criterion. Engng Fract Mech 2003, 70:371-385.
221. Zerbst U., Heinimann M., Donne C.D., Steglich D. Fracture and damage mechanics modeling of thin-walled structures - an overview. Engng Fract Mech 2009, 76:5-43.
222. Horsley D.J. Background to the use of CTOA for prediction of dynamic ductile fracture arrest in pipelines. Engng Fract Mech 2003, 70:547-552.
223. 5 clip guage technique. Engng Fract Mech 2009, 76:101-113.
224. Sakhalkar A., Frink E., Mahmoud S., Lease K. Crack tip opening angle measurement methods and crack tunneling in 2024-T351 aluminum. Strain - Int J Exp Mech 2011, 47:e130-e141.
225. Garwood S.J. Effect of specimen geometry on crack growth resistance. ASTM STP 677 1979, 11-532. American Society for Testing and Materials.
226. R-curve method for fracture toughness characterization. Fracture resistance curves and engineering applications. ASTM STP803 1983, vol. II:I-562-II-581. American Society for Testing and Materials.
227. Towers O.L., Garwood S.J. Influence of crack depth on resistance curves for three-point bend specimens in HY130. ASTM STP 905 1986, vol. 7:454-484. American Society for Testing and Materials.
228. Eisele U., Roos E., Seidenfuss M., Silcher H. Determination of J-integral-based crack resistance curves and initiation values for the assessment of cracked large-scale specimens. ASTM STP 1131 1992, vol. I:37-59. American Society for Testing and Materials.
229. Hancock J.W., Reuter W.G., Parks D.M. Constraint and toughness parameterized by T. ASTM STP 1171 1993, 1-40. American Society for Testing and Materials.
230. Joyce J.A., Hackett E.M., Roe C. Effect of crack depth and mode of loading on the J-R curve behavior of a high-strength steel. ASTM STP 1171 1993, 239-263. American Society for Testing and Materials.
231. Joyce J.A., Link R.E. Effects of constraint on upper shelf fracture toughness. ASTM STP 1256 1995, vol. 26:142-177. American Society for Testing and Materials.
232. Joyce J.A., Link R.E. Application of two parameter elastic-plastic fracture mechanics to analysis of structures. Engng Fract Mech 1997, 57:431-446.
233. Wardle G. A study of specimen size effects on the initiation toughness and tearing resistance of an A533B-1 steel. ASTM STP 1418 2002, 48-66. American Society for Testing and Materials.
234. Lam P.S., Chao Y.J., Zhu X.K., Kim Y., Sindelar R.L. Determination of constraint-modified J-R curves for carbon steel storage tanks. J Press Ves Technol 2003, 125:136-143.
235. Neimitz A., Dzioba I., Galkiewicz J., Molasy R. A study of stable crack growth using experimental methods, finite elements and fractography. Engng Fract Mech 2004, 71:1325-1355.
236. Shen G, Tyson WR, Glover A, Horsley D. Constraint effects on linepipe toughness. In: Proceedings of the 4th international conference on pipeline technology, vol. 2, May 9-13, 2004, Ostend, Belgium. p. 703-20.
237. Zhu X.K., Joyce J.A. J-resistance curve testing of HY80 steel using SE(B) specimens and normalization method. Engng Fract Mech 2007, 74:2263-2281.
238. Ernst H.A. Material resistance and instability beyond J controlled crack growth. ASTM STP 803 1983, vol. I:I-191-I-213. American Society for Testing and Materials.
239. M, resistance curve approach. J Press Ves Technol 1986, 108:50-56.
240. Joyce J.A., Davis D.A., Hackett E.M., Hays R.A. Application of J-integral and modified J-integral to cases of large crack extension. ASTM STP 1074 1990, 85-105. American Society for Testing and Materials.
241. Wilkowski GM, Marschall CM, Landow MP. Extrapolation of C(T) specimen J-R curves. In fracture mechanics: twenty-first symposium, ASTM STP 1074; 1990. p. 56-84.
242. Link RE, Landes JD, Herrera R, Zhou Z. Something new on size and constraint effects for J-R curves. In: defect assessment in components - fundamentals and applications, ESIS/EGF9; 1991. p. 707-21.
243. Hiser AL. Specimen size effects on J-R curves for RPV steels. In: Constraint effects in fracture, ASTM STP 1171; 1993. p. 195-238.
244. Larsson S.G., Carlsson A.J. Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic material. J Mech Phys Solids 1973, 21:263-278.
245. Rice J.R. Limitations to the small scale yielding approximation for crack tip plasticity. J Mech Phys Solids 1974, 22:17-26.
246. Sham T.L. The determination of the elastic T-term using higher order weight functions. Int J Fract 1991, 48:81-102.
247. Fett T. A Green's function for T-stresses in an edge-cracked rectangular plate. Engng Fract Mech 1997, 57:365-373.
248. Yang B., Ravi-Chandar Evaluation of elastic T-stress using the stress difference method. Engng Fract Mech 1999, 64:589-605.
249. Wang X. Elastic T-stress for cracks in test specimens subjected to non-uniform stress distributions. Engng Fract Mech 2002, 69:1339-1352.
250. Wang X. Elastic T-stress solutions for semi-elliptical surface cracks in finite thickness plates. Engng Fract Mech 2003, 70:731-756.
251. Leevers P.S., Radon J.C. Inherent stress biaxiality in various fracture specimen geometries. Int J Fract 1983, 19:311-325.
252. Sherry A.H., France C.C., Goldthorpe M.R. Compendium of T-stress solutions for two and three dimensional geometries. Fatigue Fract Engng Mater Struct 1995, 18:141-155.
253. c). Int J Fract 1991, 48:1-22.
254. Bilby B.A., Cardew G.E., Goldthorpe M.R., Howard I.C. A finite element investigation of the effect of specimen geometry on the fields of stress and strain at the tips of stationary cracks. Size effects in fracture 1986, 37-46. Mechanical Engineering Publications Limited, London.
255. Joyce JA, Tregoning RL. Quantification of specimen geometry effects on the master curve and To reference temperature. In: Proceedings of the 13th European conference on fracture (ECF-13), San Sebastian, Spain, September 6-9, 2000.
256. Betegon C., Hancock J.W. Two-parameter characterization of elastic-plastic crack-tip fields. J Appl Mech 1991, 58:104-110.
257. Du Z.Z., Hancock J.W. The effect of non-singular stresses on crack-tip constraint. J Mech Phys Solids 1991, 39:555-567.
258. Sumpter J.D.G. An experimental investigation of the T-stress approach. ASTM STP 1171 1993, 492-502. American Society for Testing and Materials.
259. Tregoning R.L., Joyce J.A. Application of T-stress based constraint correction to A533B steel fracture toughness data. ASTM STP 1417 2002, Vol. 33:307-327. American Society for Testing and Materials.
260. O'Dowd N.P., Shih C F. Family of crack-tip fields characterized by a triaxiality parameter - I: Structure of fields. J Mech Phys Solids 1991, 39:989-1015.
261. O'Dowd N.P., Shih C.F. Family of crack-tip fields characterized by a triaxiality parameter - II: Fracture applications. J Mech Phys Solids 1992, 40:939-963.
262. O'Dowd N.P., Shih C.F. Two-parameter fracture mechanics: theory and applications. ASTM STP 1207 2002, 24:21-47. American Society for Testing and Materials.
263. O'Dowd N.P. Application of two parameter approaches in elastic-plastic fracture mechanics. Engng Fract Mech 1995, 52:445-465.
264. Faleskog J. Effects of local constraint along three-dimensional crack fronts - a numerical and experimental investigation. J Mech Phys Solids 1995, 43:447-493.
265. Nevalainen M., Dodds R.H. Numerical investigation of 3D constraint effects on brittle fracture in SE(B) and C(T) specimens. Int J Fract 1995, 74:131-161.
266. Gao X., Dodds R.H. An engineering approach to assess constraint effects on cleavage fracture toughness. Engng Fract Mech 2001, 68:263-284.
267. Yang S. Higher order asymptotic crack-tip fields in a power-law hardening material. Ph.D. Dissertation, University of South Carolina, Columbia, South Carolina, 1993.
268. Yang S., Chao Y.J., Sutton M.A. Higher-order asymptotic fields in a power-law hardening material. Engng Fract Mech 1993, 45:1-20.
269. Chao Y.J., Yang S., Sutton M.A. On the fracture of solids characterized by one or two parameters: theory and practice. J Mech Phys Solids 1994, 42:629-647.
270. NIkishkov G.P., Bruckner-Foit A., Munz D. Calculation of the second fracture parameter for finite cracked bodies using a three-term elastic-plastic asymptotic expansion. Engng Fract Mech 1995, 52:685-701.
271. Chao Y.J., Zhu X.K. Constraint-modified J-R curves and its applications to ductile crack growth. Int J Fract 2000, 106:135-160.
272. Cravero S., Ruggieri C. Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens - Part I: Plane strain analyses. Engng Fract Mech 2005, 72:1344-1360.
273. Silva L.A.L., Cravero S., Ruggieri C. Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens - Part II: 3-D effects on constraint. Engng Fract Mech 2006, 73:2123-2138.
274. 2 dominance and size requirements. Int J Fract 1998, 89:285-307.
275. Zhu X.K., Chao Y.J. Characterization of constraint of crack-tip fields in non-hardening materials by the three-term solution. Int J Solids Struct 1999, 36:4497-4517.
276. Kim Y., Chao Y.J., Zhu X.K. Effect of size and crack depth on 3D crack-front constraint for SENB specimens. Int J Solids Struct 2003, 40:6267-6284.
277. Labbe F. Three-term asymptotic stress field expansion for analysis of surface cracked elbows in nuclear pressure vessels. J Mater Engng Perform 2007, 16:220-223.
278. 2. ASTM STP 1244 2002, 2:3-20. American Society for Testing and Materials.
279. Zhu X.K., Leis B.N. Application of constraint-corrected J-R curve to fracture analysis of pipelines. J Press Ves Technol 2006, 128:581-589.
280. Wang Y.Y., Parks D.M. Limits of J-T characterization of elastic-plastic tip fields. ASTM STP 1244 2002, 2:43-67. American Society for Testing and Materials, Philadelphia.
281. Zhu X.K., Leis B.N. Bending modified J-Q theory and crack-tip constraint quantification. Int J Fract 2006, 141:115-134.
282. Chao Y.J., Zhu X.K., Kim Y., Lam P.S., Pechersky M.J., Morgan M.J. Characterization of crack-tip field and constraint for bending specimens under large-scale yielding. Int J Fract 2004, 127:283-302.
283. Zhu X.K., Chao Y.J. Specimen size requirements for two-parameter fracture toughness testing. Int J Fract 2005, 135:117-136.
284. Ritchie R.O., Knott J.F., Rice J.R. On the relationship between critical tensile stress and fracture toughness in mild steel. J Mech Phys Solids 1973, 21:395-410.
285. Shih C.F., O'Dowd N.P., Kirk M.T. A framework for quantifying crack tip constraint. ASTM STP 1171 2002, 2-20. American Society for Testing and Materials.
286. Chao Y.J., Zhang X.H. Constraint effect on brittle fracture. ASTM STP 1296 2002, 41-60. American Society for Testing and Materials.
287. Gao X., Dodds R.H. Constraint effects on the ductile-to-brittle transition temperature of ferritic steels: a Weibull stress model. Int J Fract 2000, 102:43-69.
288. 0. Engng Fract Mech 2001, 68:303-328.
289. Huh N.S., Stumptrack L., Schuler X., Roos E. Quantification of crack-tip constraint effect on master curve reference temperature based on two-parameter approach. Solid State Phenom (Trans Tech Publication, Switzerland) 2006, 110:89-96.
290. Zhu X.K., Jang S.K. J-R curves corrected by load independent parameter in ductile crack growth. Engng Fract Mech 2001, 68:285-301.
291. Zhu X.K., Leis B.N. Constraint corrected J-R curve and its applications for X80 pipeline steel. J ASTM Int 2006, 3(6). [paper ID JAI13209].
292. Zhou DW, Xu WG, Smith SD. R-curve modeling with constraint effect. In: Proceeding of the 12th international conference on fracture, Ottawa, Canada, July 12-17, 2009.
293. Zhou D.W. Measurement and modeling of R-curves for low-constraint specimens. Engng Fract Mech 2011, 78:605-622.
294. Wallin K. Fracture toughness of engineering materials - estimation and application 2011, EMAS Publishing Co., Warrington, UK.
295. Zehnder A.T. Fracture Mechanics 2012, Springer, London.