13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Numerical Solutions of Second Elastic-Plastic Fracture Mechanics Parameter in Test Specimens under Biaxial Loading Ping Ding1, Xin Wang1,* 1 Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, Ontario, K1S 5B6, Canada *Corresponding author: xwang@mae.carleton.ca Abstract Extensive finite elements analyses have been conducted to obtain solutions of constraint parameter A, which is the second parameter in a three-term elastic-plastic asymptotic expansion for crack-tip field, for test specimens under biaxial loading. Three mode I plane-strain test specimens, i.e. single edge cracked plate (SECP), centre cracked plate (CCP) and double edge cracked plate (DECP) were studied. The crack geometries analysed include shallow to deep cracks, and the biaxial loading ratios analysed are 0.5 and 1.0. Solutions of parameter A were obtained for materials following the Ramberg-Osgood power law with hardening exponents of n=3, 4, 5, 7 and 10. Remote tension loading were applied which covers deformation range from small-scale to large-scale yielding. Based on the finite element results of constraint parameter A, crack-tip constraint effect for cracked specimens under biaxial loading is analysed. Using the relationships between A and other two commonly-used second fracture parameters, Q and A2, the present solutions for A can be used to calculate parameters Q and A2. Keywords elastic-plastic fracture, second fracture parameter, biaxial loading, solutions, constraint effect 1. Introduction In classical elastic-plastic fracture mechanics (EPFM), one-parameter approach, which describes the HRR fields [1, 2] based on J-integral [3], usually can work well for high constraint cases. For low constraint cases, under high loading conditions, the dominance of J-integral will be lost, and the one-parameter approach of J-integral will not be appropriate any more. Two-parameter approaches have been developed to overcome the limitation of the EPFM one-parameter approach, in which a second fracture mechanics parameter is introduced to characterize the constraint effect besides the load-related parameter J-integral. Several commonly-used two-parameter approaches are, J-T [4-6], J-Q [7, 8] and J-A2 (J-A) [9-12] approaches, where constraint parameter A is a different normalizing form of A2 [11, 12]. Determination of J-integral and second fracture mechanics parameter, T, Q and A2 (A), is precondition of application of J-T, J-Q and J-A2 (A) approaches. In the early development of EPFM, J-integral solutions have been well established. The solutions of constraint parameter T-stress have also been well established in the literature. Currently, numerical method, such as finite element analysis (FEA) method, is the main method for the determination of constraint parameters Q and A2 (A). For example, Nikishkov et al. [12] suggested an algorithm which determines solutions of A using a least squares procedure based on the finite element analysis results. Although with high accuracy, numerical method is a time-consuming way to obtain solutions of parameters. Correspondingly, understanding of constraint effect near crack-tip is limited because of the scarcity of solutions of constraint parameter A2 (A) and Q. In previous works of authors [13, 14], extensive finite element analyses were conducted to obtain solutions of parameter A for several typical two-dimensional (2D) plane-strain specimens under uniaxial loading conditions. Biaxial loading cases are of equal theoretical and engineering practical significance as uniaxial loading cases. Many researchers have focused their investigations on biaxial loading cases, for example, the results reported by Pop et al. [15] and Méité et al. [16]. In the present work, solutions for A will be obtained for biaxial loading cases for three mode I crack plane-strain specimens, single edge cracked plate (SECP), center cracked plate (CCP) and double edge cracked plate (DECP). In this work, extensive finite element analyses will be carried out for SECP, CCP and DECP cracked specimens under biaxial loading conditions with biaxial loading
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