Three-parameter Theory Of Three-dimensional Fracture For Power Law Materials

In aeronautic and astronautic fields, it is important to accurately assessing the structure's capacity for bearing load. However, the damage tolerance method currently used in engineering application is based on the two-dimensional (2D) fracture theory, then we can not accurately predict the damage behaviors of three-dimensional (3D) structures from experimental data. Based on the 3D fracture theory and finite element analyses, we make a deep analysis of the 3D mode I through-thickness crack tip stress fields for the power law plasticity and creeping solids, propose simplified formulations for the two-parameter solution and three-parameter solution for convienent for engineering application, and bring up an idea to further develop criteria for 3D fracture problems. The main contents are as follows:1. Based on the 3D facture theory for creeping solids built by our group, we proceed to investigate the relations between crack tip strain fields and time, crack tip displacement fields and time, crack tip opening displacements and time. We draw conclusions from finite element analyses that the C(t)-T_z two-parameter solution can provide efficient prediction for the tensile stress on the ligament ahead of the crack under small scale creep conditions, while under extensive creep conditions, a third parameter, Q*, is necessary to be introduced. Besides, we prove the out-of-plane shear stresses being ignored in the derivation is reasonable.2. From the 3D fracture theory, we can see that the actual 3D state is a transition state from plane strain in the crack tip to plane stress far away from the tip. But it's too complicated to be applied in the engineering problems. Here, we propose a"linear transition"form for the power law plasticity and creeping solids to simplify the theoretical calculation, which is verified by the finite element methods, and fit the varying parameters in appendix. Based on the simplified 3D fracture theory, we compare the J-T_z two-parameter solution and J-T_z-QT three-parameter solution for the power law plasticity solids in detailed finite element analysis, and give the mode I fracture criteria for power law plasticity solids and creep crack growth in a simplified form.