Abstract
A boundary element formulation using augmented kernels, for planar time-dependent inelastic deformation problems for bodies with cutouts, has been presented in a companion paper[l]. The primary advantage of this formulation is that the effect of the cutout is incorporated in the kernels and the cutout boundary need not be modelled in a numerical solution procedure. In this paper, the specific kernels for plates with elliptic cutouts are first derived. These kernels are then used to obtain numerical solutions for time-dependent stress fields near stationary crack tips in finite plates. A crack is modelled as a very narrow ellipse and both remote tensile (mode one) and remote shear (mode two) loadings are considered. The deformation of the plate material is assumed to be described either by the equations of power law creep or the combined creep-plasticity constitutive model of Hart.
Highlights
A boundary element formulation for planar time-dependent inelastic deformation of plates with cutouts has been presented in a companion paper [I]
This differential equation is transformed into an integral equation for certain concentrations on the boundary, using, as kernels, augmented versions of the usual singular fundamental solutions of the . biharmonic equation in an'infinite plane. '"l'heseaugmented kernels guarantee that the cutout boundary remains traction free for all time
The effect of the cutout on the stress field is incorporated into the kernelsanddiscrete modelling of the cutout boundary is not necessary
Summary
A boundary element formulation for planar time-dependent inelastic deformation of plates with cutouts has been presented in a companion paper [I]. A nonhomogeneous biharmonic equation for the rate of the stress function is obtained. It is imperative that stresses in the near field of the cracks be obtained very accurately if the redistribution of stres,seswith time is to be determined . That formulation requires discrete;~modell%ngof the cutout boundary and a very large number of boundary elements are usually needed near crack tips in order to obtain the stresses accurately in these regions. As stated earlier, the crack boundary need not be modelled in the numerical calculations and an accurate and efficient determination df stresses near the crack is possible.
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