13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- CMOD-Based J Integral Measurement for Surface Cracked Specimens Xudong Qian1,*, Ya Li1 1 Department of Civil and Environmental Engineering, National University of Singapore, Singapore 117576, Singapore * Corresponding author: qianxudong@nus.edu.sg Abstract This paper proposes an experimental approach based on the measured crack-mouth opening displacement (CMOD) to determine the mode I energy release rate for surface cracks in plate specimens subjected to four-point bending. The proposed experimental scheme measures the load versus CMOD relationships in a surface cracked specimen under four-point bending, and computes the relative rotation, θ, between the two crack planes based on the measured CMOD, and the bending moment (M) applied on the cracked cross section based on the measured load. The energy release rate, measured by the J-integral value, computes from the area under the M-θ curve, similar to the eta-approach originally proposed by Rice and co-workers for single-edge-notched bend, SE(B), specimens. This study examines the above approach for four plate specimens with fatigue pre-cracked, machined surface notches. The measured J value shows close agreement with the energy release rate computed using the domain integral approach. Keywords surface crack, crack-mouth opening displacement, energy release rate, domain integral, compliance. 1. Introduction The standard procedure to derive the fracture resistance curve, namely the J-R curve restricts to small-scale planar specimens with a straight, through-thickness crack front [1-2] under high-constraint, small-scale yielding conditions. The fracture resistance thus measured characterizes the capabilities of the material in resisting fracture failure in an idealized, plane-strain condition. In contrast, realistic cracks in structural details often entail a complex topology with a curved crack-front, sometimes resembling a semi-elliptical shape. The varying crack-extensions along the curved crack fronts impinge inevitably on the resistance against crack growth at individual crack-front locations, due to the stress redistribution caused by the non-uniform crack extensions along the curved crack front. The plane-strain fracture resistance obtained using the conventional through-thickness fracture specimens may not, therefore, represent the fracture resistance reserved at different crack-front locations in curved surface cracks. The fracture resistance measured from the through-thickness specimens may thus not provide an accurate description of the evolving fracture resistance as the surface crack grows in the integrity assessment for engineering structures, e.g., the level 3C ductile tearing assessment. An experimental method to measure the J-integral values for surface crack specimens becomes much-needed to overcome the transferability of the J-R curve from the material level to the specimen/structural level. This study proposes such an experimental approach to determine the energy release rate for surface cracked plate specimens. The calculation of the energy release rate utilizes the CMOD-based approach, frequently used in the conventional through-thickness fracture specimens in evaluating the energy release rate. The experimental procedure determines the gross energy release rate along the entire crack front using the area under the moment-rotation curve of the crack plane, similar to the η-approach originally proposed by Rice et al. [3]. The rotation of the crack plane derives from a numerically determined center of rotation. The dimensionless η-value is, on the other hand, determined by coupling the numerical strain energy (the area under the M-θ curve computed from finite element [FE] models with a stationary crack) and the domain-integral values. The energy release rate determined from the compliance method agrees closely with the energy release computed using the domain-integral approach implemented in WARP3D [4].
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