Detailed un-standard experiments of fracture toughness in which SENB specimens of five different thicknesses were included, were carried out to investigate the size effect on the ductile and brittle fracture. It is found that the fracture toughness on the upper shelf increases with the size of the specimens, which have the similar geometry and then decreases gradually to the plane strain fracture toughness. The ductile fracture toughness increases with the size in the range of 4—16 mm for the increment of the plastic deformation zone size and plastic fracture strain under general yielding conditions, and then drops down from 16—22 mm for the increase of the high-stress triaxiality zone and the plastic deformation zone size not changing much which is less than the residual ligament width. While the fracture toughness of the lower shelf increases with the thickness in the range of 4—8 mm for the plastic deformation zone size increasing under small-scale yielding conditions, and then drops down from 8 to 22 mm for the increase of the high out-of-plane constraint. Theoretical analysis with the primary definition of the fracture toughness J integral, the constraint level and the plastic deformation volume was performed to investigate the different size effects for different temperatures. Finite Element Analysis simulations with continuum damage model to get the distribution and variety of the stress triaxiality as an important factor of fracture strain and fracture toughness.
Anderson, T.L., Steinstra, D. and Dodds, R.H. ( 1994). A Theoretical Framework for Addressing Fracture in the Ductile-brittle Transition Region, Fracture Mechanics , Vol. 24, pp. 185-214, ASTM STP 1207, ASTM, Philadelphia.
2.
Bertolino, G., Perez Ipina, J. and Meyer, G. ( 2006). Influence of the Crack-tip Hydride Concentration on the Fracture Toughness of Zircaloy-4, Journal of Nuclear Materials , 348(1-2): 205-212.
3.
Bezensek, B. and Hancock, J.W. ( 2004). The Re-characterisation of Complex Defects: Part I: Fatigue and Ductile Tearing, Engineering Fracture Mechanics , 71(7-8): 981-1000.
4.
Bluhm, J.I. ( 1961). A Model for the Effect of Thickness on Fracture Toughness , ASTM Proceedings, 61: 1324-1331.
5.
Bonora, N. ( 2005). Ductile Damage Evolution Under Triaxial State of Stress: Theory and Experiments, International Journal of Plasticity , 21(5): 981-1007.
6.
Byun, T.S., Kim, S.H., Lee, B.S. and Kim, I.S. ( 2000). Estimation of Fracture Toughness Transition Curves of Rpv Steels from Ball Indentation and Tensile Test Data, Journal of Nuclear Materials, 277(2-3): 263-273.
7.
Chae, D. and Koss, D.A. ( 2004). Damage Accumulation and Failure of Hsla-100 Steel , Materials Science and Engineering, A366(2): 299-309.
8.
Chandrakanth, S. and Pandey, P.C. ( 1995). An Isotropic Damage Model for Ductile Material , Engineering Fracture Mechanics, 50(4): 457-465.
9.
Chao, Y.J. and Lam, P.S. ( 1996). Effects of Crack Depth, Specimen Size, and Out-of-plane Stress on the Fracture Toughness of Reactor Vessel Steels, ASME Journal of Pressure Vessel Technology, 118(4): 415-423.
10.
Chao, Y.J. and Zhu, X.K. ( 2000). Constraint-Modifed J-R Curves and its Application to Ductile Crack Growth, International Journal of Fractures , 106(22): 135-160.
11.
Chao, Y.J., Liu, S. and Broviak, B. ( 2001). Brittle Fracture: Constraint Effect and Crack Curving under Mode I Conditions, Experimental Mechanics, 41(3): 232-241.
12.
Chen, Z.-A., Zeng, Z. and Chao, Y.J. ( 2007). Effect of Crack Depth on the Shift of the Ductile- Brittle Transition Curve of Steels, Engineering Fracture Mechanics , 74(15): 2437-2448.
13.
Chow, C.K. and Nho, K.H. ( 1997). Effect of Thickness on the Fracture Toughness of Irradiated Zr-2.5nb Pressure Tubes, Journal of Nuclear Materials, 246(1): 84-87.
14.
Cotterell, B., Li, Q.-F., Zhang, D.-Z. and Mai, Y.-W. ( 1985). On the Effect of Plastic Constraint on Ductile Tearing in a Structural Steel, Engineering Fracture Mechanics , 21(1-2): 239-244.
15.
Demofonti, G. and Hadlay, I. ( 1922). Review of Fracture Parameters for Laboratory Measurement of the Resistance to Ductile Crack Propagation in Line Pipe Steels, In: The International Conference on Pipeline Reliability, pp. 1-13, Calgary, Canada.
16.
Du, Z.-Z. and Hancock, J.W. ( 1991). The Effect of Non-singular Stresses on Crack-tip Constraint , Journal of the Mechanics and Physics of Solids , 39(4): 555-567.
17.
Gao X.S. and Dodds Jr R.H. ( 2000). Constraint Effects on the Ductile-to-Brittle Transition Temperature of Ferritic Steels: A Weibull Stress Model, International Journal of Fractures, 102(11): 43-69.
18.
Gao X.S. and Dodds Jr R.H. ( 2000). An Engineering Approach to Assess Constraint Effects on Cleavage Fracture Toughness, Engineering Fracture Mechanics , 68(3): 263-283.
19.
Geary, W., Dutton, J. and Shuter, D.M. ( 2000). The Influence of Size Effects and Dynamic Loading on the Fracture Toughness of Commercial Grp Materials, Composites Science and Technology, 60(4): 633-638.
20.
Gurson, A.L. ( 1977). Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I-Yeild Criteria and Flow Rules for Porous Ductile Media , Journal of Engineering Material and Technology, 99(1): 2-15.
21.
Hancock, J.W. and Nekkal, A. ( 1998). The Application of Constraint Based Fracture Mechanics to Engineering Structures, Nuclear Engineering and Design , 184(11): 77-88.
22.
Hu, X.Z. ( 2004). Influence of Fracture Process Zone Height on Fracture Energy of Concrete, Cement and Concrete Research, 34(8): 1321-1330.
23.
Kang, Y.L., Zhang, Z.F., Wang, H.W. and Qin, Q.H. ( 2005). Experimental Investigations of the Effect of Thickness on Fracture Toughness of Metallic Foils, Material Science and Engineering, A394(1-2): 312-319.
24.
Kim, S.H., Byun, T.S., Lee, B.S., Hong, J.H. and Kim, L.S. ( 1998). Proceeding of the 12th Conference on Mechanical Behaviors of Materials, Chang-won, South Korea, p. 203.
25.
Kim, Y., Chao, Y.J. and Zhu, X.K. ( 2003). Efeect of Specimen Size and Crack Depth on 3D Crack-front Constraint for SENB Specimens, International Journal of Solids Structures, 40(23): 6267-6284.
26.
Kulkarni, D.M., Prakash, R., Talan, P. and Kumar, A.N. ( 2004). The Effect of Specimen Thickness on the Experimental and Finite Element Characterization of Ctod in Extra Deep Drawn Steel Sheets , Sadhana, 29(4): 365-380.
27.
Landes, J.D. and McCabe, D.E. ( 1984). Effect of Section Size on Transition Temperature Behavior of Structural Steels, In: Fracture Mechanics: 15th Symposium, ASTM STP 833, ASTM, Philadelphia, pp. 378-392.
28.
MacLennan, I. and Hancock, J.W. ( 1995). Constraint-based Failure Assessment Diagrams, International Journal of Pressure Vessels and Piping, 64(33): 287-298.
29.
Needleman, A. and Tvergaard, V. ( 1984). An Analysis of Ductile Rupture in Notched Bars , Journal of Mechanics and Physis of Solids, 32(6): 461-490.
30.
Odette, G.R., Edsinger, K., Lucas, G.E. and Donahue, E. ( 1998). Small Specimen Test Techniques, ASTM STP 1329, Vol. 3 , p. 298, American Society for Testing and Materials, Philadelphia, PA.
31.
Odette, G.R., Yamamoto, T., Rathbun, H.J., He, M.Y., Hribernik, M.L. and Rensman, J.W. ( 2003). Cleavage Fracture and Irradiation Embrittlement of Fusion Reactor Alloys: Mechanisms, Multiscale Models, Toughness Measurements and Implications to Structural Integrity Assessment, Journal of Nuclear Materials, 323(2-3): 313-340.
32.
Ono, H., Kasada, R. and Kimura, A. ( 2004). Specimen Size Effects on Fracture Toughness of JLF-1 Reduced-activation Ferric Steel, Journal of Nuclear Materials , 329-333(2): 1117-1121.
33.
Pandey, A.B., Majumdar, B.S. and Miracle, D.B. ( 1998). Effect of Thickness and Precracking on the Fracture Toughness of Particle-reinforced Al-Alloy Composites, Metallurgical and Materials Transactions, 29A(4): 1237-1243.
34.
Priest, A.H. and Holmes, B. ( 1981). A Multi-test Piece Approach to the Fracture Characterization of Pipeline Steels, International Journal of Fractures, 17(3): 277-99.
35.
Rivalin, F., Pineau, A., Fant, M.Di. and Besson, J. ( 2001). Ductile Tearing of Pipeline-steel Wide Plates I. Dynamic and Quasi-static Experiments, Engineering Fracture Mechanics , 68(3): 329-345.
36.
Rivalin, F., Besson, J., Pineau, A. and Fant, M.Di. ( 2001). Ductile Tearing of Pipeline-steel Wide Plates II. Modeling of In-plane Crack Propagation, Engineering Fracture Mechanics , 68(3): 347-364.
37.
Rathbun, H.J., Odette, G.R., He, M.Y., Lucas, G.E. and Sheckherd, J.W. ( 1999). Pressure Vessels and Piping, Fracture, Fatigue and Weld Residual Stress, Vol. 393, p. 17, ASME, New York .
38.
Rice, J.R. and Tracey, D.M. ( 1969). On the Ductile Enlargement of Voids in Triaxial Stress Fields, Journal of Mechanics and Physics of Solids , 17(3): 201-217.
39.
Shiro, J., Akira, N. and Jun, S. ( 1999). Effect of Size and Configuration of 3-point Bend Bar Specimens, Journal of Nuclear Materials, 271-272(1): 87-91.
40.
Sumpter, J.D.G. and Forbes, A.T. ( 1992). Constraint Based Analysis of Shallow Cracks in Mild Steel , In: TWI/EWI/IS International Conference on Shallow Crack Fracture Mechanics, Toughness Tests and Applications, Woodhead Publishing Ltd, Cambridge, England.
41.
Wallin, K. ( 1985). The Size Effect in KIC Results, Engineering Fracture Mechanics, 22(1): 149-163.
42.
Yan, C. and Mai, Y.W. ( 1997). Effect of Constraint on Ductile Crack Growth and DuctileBrittle Fracture Transition of a Carbon Steel, International Journal of Pressure Vessels and Piping, 73(3): 167-173.
43.
Yan, C., Mai, Y.W. and Ye, L. ( 2000). Effects of Constraint on Crack Tip Stress Fields and Fracture Toughness in Adhesive Joints, European Structural Integrity Society, 27: 307-316.
