Transient Dynamic Analysis of Cracked Multifield Solids with Consideration of Crack-Face Contact and Semi-Permeable Electric/Magnetic Boundary Conditions

Boundary element method (BEM) formulations for transient dynamic crack analysis intwo-dimensional (2D) multifield materials are reviwed in this paper. Both homogeneous and lin-ear piezoelectric as well as magnetoelectroelastic material models are considered. Special attentionis paid to properly modeling the non-linear crack-face contact and semi-permeable electric/magneticboundary conditions. Implementation of the corresponding time-domain BEM(TDBEM) is discussedin detail. The proposed TDBEM uses a Galerkin-method for the spatial discretization, whilst thecollocation method is considered for the temporal discretization. Iterative solution algorithms aredeveloped to compute the non-linear crack-face boundary conditions. Crack-tip elements that ac-count for the square-root local behavior of the crack opening displacements (CODs) at the crack-tipsare implemented. In this way, stress intensity factors (SIF), electric displacement intensity factor(EDIF) and magnetic induction intensity factor (MIIF) may be accurately evaluated from the nu-merically computed CODs at the closest nodes to the crack-tips. Numerical examples involving sta-tionary cracks in piezoelectric and magnetoelectroelastic solids under different combined (mechani-cal/electric/magnetic) impact loadings are investigated, in order to illustrate the effectiveness of theproposed approach and characterize the influence of the semi-permeable crack-face boundary condi-tions on the dynamic field intensity factors.

The Evaluation of Crack Opening Areas for Through-Wall Cracks in the Vicinity of Pipe Branch Connections

A number of papers have been presented at previous ASME PVP conferences, which have evaluated the crack opening areas (COA) and stress intensity factors (K), using elastic finite element analysis techniques, for through-wall cracks in a region where an attachment is welded to a plate. This was a simplified geometry aimed at representing a more complicated geometry of a pipe-branch connection. A number of analyses were considered and conclusions made on the estimation of COA and K using simple handbook solutions. More recently the analyses included the application of nonlinear geometry and the addition of crack face contact when applying bending loads. This paper is a continuation of these previous studies, assessing through-wall cracks in a more realistic pipe-branch connection geometry. The calculated COA and K values for the more complex geometry are compared to values from pipe models with no branch connections, in a similar manner to that applied in the previous work on the simplified plate geometry. Judgments are made on the conservatism, or otherwise, of the estimated COA and K for the more complex geometry solutions compared to the simple geometry solutions.