3-D thermal weight function method and multiple virtual crack extension technique for thermal shock problems

An efficient scheme, 3-D thermal weight function (TWF) method, and a novel numerical technique, multiple virtual crack extension (MVCE) technique, were developed for determination of histories of transient stress intensity factor (SIF) distributions along 3-D crack fronts of a body subjected to thermal shock. The TWF is a universal function, which is dependent only on the crack configuration and body geometry. TWF is independent of time during thermal shock, so the whole history of transient SIF distributions along crack fronts can be directly calculated through integration of the products of TWF and transient temperatures and temperature gradients. The repeated determinations of the distributions of stresses (or displacements) fields for individual time instants are thus avoided in the TWF method. An expression of the basic equation for the 3-D universal weight function method for Mode I in an isotropic elastic body is derived. This equation can also be derived from Bueckner-Rice's 3-D WF formulations in the framework of transformation strain. It can be understood from this equation that the so-called thermal WF is in fact coincident with the mechanical WF except for some constants of elasticity. The details and formulations of the MVCE technique are given for elliptical cracks. The MVCE technique possesses several advantages. The specially selected linearly independent VCE modes can directly be used as shape functions for the interpolation of unknown SIFs. As a result, the coefficient matrix of the final system of equations in the MVCE method is a triple-diagonal matrix and the values of the coefficients on the main diagonal are large. The system of equations has good numerical properties. The number of linearly independent VCE modes that can be introduced in a problem is unlimited. Complex situations in which the SIFs vary dramatically along crack fronts can be numerically well simulated by the MVCE technique. An integrated system of programs for solving the thermal shock problems by means of the TWF method was developed. By means of such a system, a series of histories of transient SIF distributions along 3-D crack fronts with different crack depth and crack aspect ratios subjected to different thermal shock conditions were solved. Examples show that the scheme is of high efficiency and of good accuracy. (authors)