Prediction of the Durability of a Plate with a Through Crack Taking into Account Biaxial Constraints of Deformations along the Front of a Normal Rupture Crack

Abstract

A methodology for evaluating the durability of plate elements of structures taking into account biaxial constraints of deformations along the front of a normal rupture crack (mode I crack) is presented. The absence of the available published data in which the prediction of the crack growth is carried out using T_xx and T_zz stresses which are nonsingular terms in the Williams expansion for stresses at the crack tip is noted. The calculation of the fatigue crack growth rate is based on the Paris equation in which the range of the effective SIF is used instead of the range of the usual stress intensity factor (SIF). In this case, the expression for the effective SIF includes T_xx and T_zz stresses in addition to the usual SIF. This approach provides taking into account, for example, the thickness of the plate for predicting the durability, which is impossible when only the SIF and T_xx stresses are used. The formula for the effective SIF is derived on the basis of the assumption that tangential stresses in the pre-fracture zone are equal to the local strength of the material. In this case, the size of the pre-fracture zone and the local strength of the material are determined taking into account T_xx and T_zz stresses. The numerical simulation is based on a proprietary finite element program which allows calculating T_xx and T_zz stresses at the front of a through crack in a plate subjected to cyclic uniaxial and biaxial tension. It is shown that nonsingular T_xx stresses primarily describe the effect of biaxial loading on the survivability, whereas T_zz stresses describe the effect of the plate thickness on the survivability. It is shown that, with increasing thickness of the plate, the value of the effective SIF increases owing to the increased constraint along the crack front, thus increasing the crack growth rate and decreasing the survivability. With an increase in the stress ratio R, under the condition of a constant stress range, the maximum effective SIF reaches the critical value equal to the fracture toughness much faster, thus reducing the durability. It is shown that, for uniaxial cyclic tension, the durability predicted by the proposed methodology is higher than that in the classical approach, when the conventional SIF is used in the Paris equation. For biaxial cyclic tension of a plate, an increase in stresses directed parallel to the crack banks leads to an increase in crack front constraints and therefore to a decrease in the durability compared to the classical approach. In other words, the classical theory does not always provide a conservative estimate of the durability, which indicates the expediency of using the developed method for calculating the durability taking into account biaxial constraints of deformations along the crack front.