13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 3.0E+07 3.5E+07 4.0E+07 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 J б/бL a/W=0.1,Prediction a/W=0.1,FEA a/W=0.5,Prediction a/W=0.5,FEA CCP,n=10,λ=0.5 Figure 3. Comparisons of J-integral, CCP Material properties used for all the analyses are specified as follows, yield stress σ0=4.0×10 8 Pa, elasticity modulus E=2.0×1011 Pa, Poisson ratio υ=0.3, material coefficient α=1.0, and hardening exponent n=3, 4, 5, 7 and 10. The used material properties cover a wide range of both high and low strain hardening behaviors. 3.2. 2D cracked models and FEA procedure Three typical cracked specimens under biaxial loading (shown in Figure 1), i.e. single edge cracked plate (SECP), center cracked plate (CCP) and double edge cracked plate (DECP), are studied through finite element analysis method. Due to the symmetry of the specimens, only a half of the SECP or a quarter of the CCP or DECP structure is modeled in the finite element analyses. A typical three-dimensional (3D) finite element mesh used for all three specimen models is illustrated in Figure 2. Total 1196 elements are included in the mesh and element type is assigned as 20-node quadratic hybrid brick with linear pressure, reduced integration [18]. Element radial sizes of finite element mesh are varied according to a geometric progression. The value for geometry size ratio of height over width, H/W, is 3.0. This 3D mesh is utilized to simulate 2D plane strain conditions with an additional boundary condition, the displacement in the model thickness direction uz=0. Finite element analyses for all three specimens (SECP, CCP and DECP) are carried out with two values of biaxial loading ratio, λ=σx/σy=0.5, and 1.0 (see Figure 1). The external loads applied on the remote end of the specimens are normalized by yield stress σ0, i.e. σ/σ0. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 A б/б0 SECP,a/W=0.3 λ=0.5 ◆ FEM,n=3 ◇ FEM,n=4 ■ FEM,n=5 □ FEM,n=7 ▲ FEM,n=10 Figure 4. FEA solutions of constraint parameter A for SECP, a/W=0.3, λ=0.5 The fitting area to calculate the values of parameter A from FEA results by a least square fitting method suggested by Nikishkov et al. (see [12, 14]) is set as 3 1.5≤ ≤ r and 0 0 45 0 ≤ ≤θ , and the opening stress, σθ, is set as the stress component used for the least square fitting process. Verifications of the used finite element model (mesh) and succedent fitting process for A values determination are carried out through comparison of solutions for two fracture parameters, load-related parameter J-integral and constraint parameter Q (J-Q approach). The comparison is based on J-integral estimation formulas and solutions of parameter Q for CCP specimen under
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