Investigation on in-plane and out-of-plane constraint effects for plates with I-II mixed mode cracks under biaxial compressive loading

Abstract

Crack sizes, geometrical configurations of specimens and structures, as well as loading conditions have significant effect on in-plane and out-of-plane constraint effects. Safety assessment with constraint effects can effectively improve the accuracy. There are prominent discrepancies between compressive fracture and tensile fracture. Most of engineering structures are usually under biaxial loading conditions, so that the influence of biaxial compressive loading on fracture analysis with constraint effects is worth paying attention. The size effect factor (relative crack length a/W, thickness to width ratio t/W and crack inclination angle β) and load factor (lateral pressure coefficient λ) of central cracked plate (CCP) specimens with I-II mixed mode crack on constraint effects under biaxial compressive loading have been investigated through theoretical analysis and finite element analysis. In-plane non-singular T-stress (T11) and its components (Tx, Ty, and Txy), out-of-plane non-singular T-stress (T33), out-of-plane constraint parameter Tz and stress triaxiality factor h have been adopted to quantify constraint effects. It demonstrates that λ has remarkable influence on SIF, T11 and T33 under biaxial compressive loading. The effect of higher a/W (long cracks) on B11 is more noticeable when I-II mixed mode crack is closer to pure mode II crack or pure mode I crack. The proportion of shear fracture increases under biaxial compression with λ. With the increase of β, B33 decreases sharply and then increases rapidly with higher λ. Tz can directly reflect stress states and adequately describe the loss of out-of-plane constraint. The stress state of crack tip is more likely to asymptotic plane-strain condition ahead of crack tip under compression. There are crucial differences in variation range and tendency of Tz subjected to biaxial tensile and biaxial compressive loading. Moreover, Tz is insensitive to λ. Stress triaxiality factor h can illustrate in-plane and out-of-plane constraint effects including size effect and load factor (sensitive to a/W, t/W, β and λ), especially can be adopted as a unified constraint parameter for long cracks under biaxial compressive loading. The in-plane T-stress components can be directly calculated by T11 under biaxial compression. The empirical equations of KII and T11 containing size effect and load factor simultaneously are effective and convenient for applications.