Some relationships between the peak stresses and the local strain energy density for cracks subjected to mixed-mode (I+II) loading
In this work, a link between the averaged strain energy density (SED) approach and the peak stress method in the case of cracks subjected to mixed mode (I+II) loading has been investigated. Some closed-form expressions of the strain energy density, averaged in a volume of radius R0, as function of the Stress Intensity Factors are provided for plane strain conditions under mixed mode I+II loadings, the material being thought of as isotropic and linear elastic.
On the basis of the peak stress method (PSM) some expressions useful to estimate the mode I and mode II
stress intensity factors (SIFs) have been recently derived. These relationships take advantage of the elastic peak
stresses from FE analyses carried out by using a given mesh pattern where the element size and type are kept
constants. The evaluation of the SIFs from a numerical analysis of the local stress field usually requires very
refined meshes and then large computational effort. The usefulness of the PSM-based expressions is that (i)
only the elastic peak stresses numerically evaluated at the crack tip are needed and not a set of stress–distance
data; (ii) the employed meshes are rather coarse if compared to those necessary for the evaluation of the whole
local stress field.
By substituting the PSM-based relationships in the closed-form expressions of the averaged SED it appears that
the latter can be directly estimated by means of the elastic peak stresses evaluated at the crack tip.
Several FE analyses have been carried out on cracked plates subjected to tension loading considering different
geometrical combinations, varying the length 2a and the inclination ? of the crack (i.e. the mode mixity) as well
as the size d of the adopted finite elements, with the aim to evaluate the local SED and the elastic peak stress
components ?peak and ?peak. In all cases the numerical values of the SED derived from the FE analyses have been compared with those analytically obtained by using the expressions for the SED based on the elastic peak
stresses, in order to verify the range of applicability of the proposed relationships.
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