13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- experimental energy release rate to a small deformation level, at which the amount of ductile crack extension remains small. For both specimens, the numerically computed energy release rate agrees closely with those measured from the experiments. Figure 10. Comparison of the energy release rate for the surface cracked plate specimen SP4. 4. Summary and Conclusions This study describes a compliance-based procedure to measure the energy release rate for surface cracks in plate specimens subjected to four-point bending. The average energy release rate along the crack front derives from the η-approach using the area under the M-θ curve for the cracked section. The center of rotation for the crack plane remains at about 18% of the remaining ligament measured from the crack tip at the deepest crack-front location, for the four surface cracked specimens considered in this study. This value, however, requires further validation when the η-approach is extended to other types of surface cracked specimens under different loading conditions. The energy release rate calculated using the η-approach based on the area under the numerical moment-rotation curves of the cracked section matches closely with the average energy release rate based on the domain-integral values computed in the large-deformation, elastic-plastic analyses. The energy release rate estimated using the η-approach from the experimental M-θ curves agrees well with that estimated using the numerical M-θ curve, before substantial crack extensions occur in the experimental specimen. Together with a compliance based method to determine the crack size in the surface cracked plate specimen, the approach proposed here provides a basis to determine the J-R curve for surface cracked specimens [8]. References [1] American Society for Testing and Materials, Standard test method for measurement of fracture toughness. ASTM E1820-11. West Conshohocken, PA, United States, 2011. [2] X. K. Zhu, J. A. Joyce, Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization. Eng Fract Mech 85 (2012) 1-46. [3] J. R. Rice, P. C. Paris, J. G. Merkle, Some further results of J-integral analysis and estimates. ASTM STP 536, American Society for Testing and Materials, Philidelphia, PA, (1973) 23-245. [4] A. Gullerud, K. Koppenhoefer, A. Roy, S. RoyChowdhury, M. Walters, B. Bichon, K. Cochran, A. Carlyle, R. H. Jr. Dodds. WARP3D: 3-D dynamic nonlinear fracture analysis of solids using parallel computers and workstations. Structural Research Series (SRS) 607 UILU-ENG-95-2012 University of Illinois at Urbana Champaign.
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