Extensive finite element analyses are performed to obtain numerical solutions of constraint parameter A for two-dimensional (2D) and three-dimensional (3D) crack geometries under both uniaxial and biaxial loading condition through a least-square fitting method. Based on the determined numerical solutions of constraint parameter A, constraint effect at crack-tip (-front) of 2D and 3D cracked specimens are analyzed under both uniaxial and biaxial loading condition. Three sets of methodologies for estimating constraint parameter A of elastic-plastic fracture mechanics are developed in the present research. They are: (1) estimating constraint parameter A by curve shape similarity, (2) predicting A values directly from the T-stress, and (3) determining parameter A based on the fully plastic solutions of A. With the obtained numerical solutions of constraint parameter A, estimate formulas for A values corresponding to the three sets of newly-developed estimate methodologies are developed for 2D and 3D cracked structures under both uniaxial and biaxial loading. It is shown that all three sets of methods can be used to predict A values with good accuracy. In the present research, it has been validated that, the obtained solutions of constraint parameter A (whether estimate methods / formulas or numerical solutions) can be utilized to predict other two commonly-used constraint parameters Q and A2 (a different normalized form of A) through the relationships between A and Q as well as A and A2.
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