Path-independent integral for the sharp V-notch in longitudinal shear problem

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:48

Article

Shi Weichen

关键词: Sharp V-notch;    Notch stress intensity factor;    Conserved quantity;    Path-independent integral;    Noether's theorem;   

DOI  :  10.1016/j.ijsolstr.2010.10.019

来源: Elsevier

【 摘 要 】

By applying Noether's theorem to the elastic energy density in longitudinal shear problem, it is shown that its symmetry-transformations of material space can be expressed by the real and imaginary parts of an analyt ic function. This kind of the symmetry-transformations leads to the existence of a conservation law in material space, which does not belong to trivial conservation laws and whose divergence-free expression gives a path-independent integral. It is found that by adjusting the analytic function, a finite value can be obtained from this path-independent integral calculated around the material point with any order singularity. For a sharp V-notch placed on the edge of homogenous materials and/or the interface of bi-materials, application shows that the finite value obtained from this path-independent integral is directly related to the notch stress intensity factor (NSIF) and does not depend on the location of integral endpoints chosen respectively along two traction-free surfaces of which form a notch opening angle. Usability is presented in an example to estimate the NSIF of a bi-material plate. (C) 2010 Elsevier Ltd. All rights reserved.

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