Abstract
Using a single parameter fracture mechanics theory, a minimum specimen size requirement of min(a, b, B) >200J/σ0 in tension and min(a, b, B) >25J/σ0 in bending, where B is the thickness, b the remaining ligament and a is the crack length of the specimen, were derived [Shih and German (1981), International Journal of fracture 17, 27–43] which have provided the basis for modern fracture toughness testing procedures. Two-parameter fracture toughness testing including the constraint, on the other hand, is desirable since it offers a solution to the transferability issue. A size requirement for a valid two-parameter fracture toughness testing based on the J-A2 three-term solution was determined as min(a, b, B) > 11J/σ0 [Chao and Zhu (1998), International Journal of fracture 89, 285–307] in which the limiting case is bend specimens under large scale yielding (LSY). Recent work by Chao et al. (2004, International Journal of fracture, 27, 283–302) has shown that the J-A2 dominance at a crack tip can be significantly enhanced for bending specimens under LSY if a modified J-A2 solution is adopted. This current paper further studies the size of the J-A2 dominant zone using the modified J-A2 solution for deep bend specimens with hardening from low to high and loading from SSY to LSY using finite element analysis. Based on the results, a rather relaxed specimen size requirement min(a, b, B) >6J/σ0 is developed and recommended for a valid two-parameter fracture toughness testing using the J-A2 fracture criterion. Validity of the size requirement is demonstrated by using the experimental J-R curves from non-standard bending specimens for A285 steel.
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References
A.M. Al-Ani S.W. Hancock (1991) ArticleTitleJ-dominance of short cracks in tension and bending Journal of the Mechanics of Physics and Solids 39 23–43
InstitutionalAuthorNameASTM E 1820-01 (2001) Standard Test Method for Measurement of Fracture Toughness American Society of Testing and Materials West Conshohocken PA
C. Betegon J.W. Hancock (1991) ArticleTitleTwo parameter characterization of elastic-plastic crack-tip fields Journal of Applied Mechanics 58 104–110
Y.J. Chao S. Yang M.A. Sutton (1994) ArticleTitleOn the fracture of solids characterized by one or two parameters: theory and practice Journal of the Mechanics of Physics and Solids 42 629–647
Chao, Y.J. and Zhang, L. (1997). Tables of plane strain crack tip fields: HRR and higher order terms, Me-Report, 97-1, Department of Mechanical Engineering, University of South Carolina.
Y.J. Chao X.K. Zhu (1998) ArticleTitleJ-A2 characterization of crack-tip fields: extent of J-A2 dominance and size requirements International Journal of Fracture 89 285–307 Occurrence Handle10.1023/A:1007487911376
Y.J. Chao X.K. Zhu Y. Kim P.S. Lam M.J. Pechersky M.J. Morgan (2004) ArticleTitleCharacterization of crack-tip fields and constraints for bending specimens under large-scale yielding International Journal of Fracture 127 283–302 Occurrence Handle10.1023/B:FRAC.0000036849.12397.6c
J.W. Hutchinson (1968) ArticleTitleSingular behavior at the end of a tensile crack in a hardening material Journal of the Mechanics of Physics and Solids 16 13–31 Occurrence Handle0166.20704
J.W. Hutchinson (1983) ArticleTitleFundamentals of the phenomenological theory of nonlinear fracture mechanics Journal of Applied Mechanics 50 1042–1051 Occurrence Handle1983nyap.book.....H
Y. Kim X.K. Zhu Y.J. Chao (2001) ArticleTitleQuantification of constraint on elastic-plastic 3D crack front by the J-A2 three-term solution Engineering Fracture Mechanics 68 895–914
Y. Kim Y.J. Chao X.K. Zhu (2003) ArticleTitleEffect of specimen size and crack depth on 3D crack-front constraint for SENB specimens International Journal of Solids and Structures 40 6267–6284
P.S Lam Y.J. Chao X.K. Zhu Y. Kim R.L. Sindelar (2003) ArticleTitleDetermination of constraint-modified J-R curves for carbon steel storage tanks Journal of Pressure Vessel Technology 123 111–222
R.M. McMeeking (1977) ArticleTitleFinite deformation analysis of crack-tip opining in elastic-plastic materials and applications for fracture Journal of the Mechanics of Physics and Solids 25 357–381
R.M. McMeeking D.M. Parks (1979) On the criteria for J-dominance of crack-tip fields in large-scale yielding, Elastic-Plastic Fracture ASTM STP 668, American Society for Testing and Materials Philadelphia 175–194
G.P. Nikishkov A. Brucker-Foit D. Munz (1995) ArticleTitleCalculation of the second fracture parameter for finite cracked bodies using a three-term elastic-plastic asymptotic expansion Engineering Fracture Mechanics 52 685–701 Occurrence Handle10.1016/0013-7944(95)00024-P
N.P. O’Dowd C.F. Shih (1991) ArticleTitleFamily of crack-tip fields characterized by a triaxiality parameter – I. structure of fields Journal of the Mechanics of Physics and Solids 39 989–1015
N.P. O’Dowd C.F. Shih (1992) ArticleTitleFamily of crack-tip fields characterized by a triaxiality parameter – II. fracture applications Journal of the Mechanics of Physics and Solids 40 939–963
D.M. Parks (1992) Advances in characterization of elastic-plastic crack-tip fields A.S. Argon (Eds) Fracture and Fatigue Springer-Verlag New York 59–98
J.R. Rice G.F. Rosengren (1968) ArticleTitlePlane strain deformation near a crack tip in a power law hardening material Journal of the Mechanics of Physics and Solids 16 1–12
J.R. Rice (1968) ArticleTitleA path independent integral and the approximate analysis of strain concentration by notches and cracks Journal of Applied Mechanics 35 379–386
R.O. Ritchie J.F. Knott J.R. Rice (1973) ArticleTitleOn the relationship between tensile stress and fracture toughness in mild steel Journal of the Mechanics of Physics and Solids 21 395–410
C.F. Shih (1981) ArticleTitleRelationships between the J-integral and the crack opening displacement for stationary and extending cracks Journal of the Mechanics of Physics and Solids 29 305–326 Occurrence Handle0464.73122
C.F. Shih (1985) ArticleTitleJ-dominance under plane strain fully plastic conditions: the edge crack panel subject to combined tension and bending International Journal of Fracture 29 73–84
C.F. Shih M.D. German (1981) ArticleTitleRequirements for a one parameter characterization of crack tip fields by HRR singularity International Journal of Fracture 17 27–43
Y.Y. Wang D.M. Parks (1995) Limit of J-T characterization of elastic-plastic crack tip fields M. Kirk A. Bakker (Eds) Constraint Effects in Fracture – Theory and Applications: Second Volume, ASTM STP 1244 American Society of Testing Materials Philadelphia 43–67
S. Yang Y.J. Chao M.A. Sutton (1993a) ArticleTitleHigher-order asymptotic fields in a power-law hardening material Engineering Fracture Mechanics 45 1–20 Occurrence Handle10.1016/0013-7944(93)90002-A
S. Yang Y.J. Chao M.A. Sutton (1993) ArticleTitleComplete theoretical analysis for higher order asymptotic terms and the HRR zone at a crack tip for mode I and mode II loading of a hardening materials Acta Mechanica 98 IssueID1–4 99–106
X.K. Zhu Y.J. Chao (2001) ArticleTitleConstraint effects on crack-tip fields in elastic-perfectly plastic materials Journal of the Mechanics and Physics of Solids 49 363–399
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Zhu, X.K., Chao, Y.J. Specimen Size Requirements for Two-parameter Fracture Toughness Testing. Int J Fract 135, 117–136 (2005). https://doi.org/10.1007/s10704-005-3946-3
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DOI: https://doi.org/10.1007/s10704-005-3946-3