Dear All
I'm working on my thesis and in a part of it, I have to determine the stress around a sharp v-notch specially on the tip of it. the model is so simple(a rectangular plate with a v-notch on on the left side of it) and the load is tensile. But after solving the problem with both ANSYS & ABAQUS I realized the finer meshes,the greater stress on the tip of notch. I tried p-element method,but by using maximum level of p-element(that is 8) and fine meshes I couldn't reach to convergence again. I'm so confused and I really need help.
thanx.
Hi Ali The stress at a
Hi Ali
The stress at a stress concentration like a crack tip is related to 1/r, where r is the crack tip radius. If the radius is zero, then the stress is infinite; in other words there's a singularity. In real materials, nature steps in and, for example, plastic flow of the material mimics a larger crack tip radius. However, in a finite element model, you probably have a geometrically sharp crack tip and hence a theoretically infinite stress. Therefore the stress will never converge, no matter how fine your mesh.
There are analytical expressions for the stress around simple geometric shapes with notches, such as the one you describe - you probably don't need to do an FE analysis.
Hope this helps,
Cheers,
Tony
Convergence of stress at crack tip
Ali:
To be more precise, the dominant term in the convergent asymptotic expansion that Williams proposed is 1/sqrt(r), not 1/r. There is a very fine paper by Williams, On the stress distribution at the base of a stationary crack. J. Appl. Mech., 24, 11-114 (1957) that discusses the derivation of this asymptotic expansion. The first term is 1/sqrt(r) and its coefficient is the Mode I Stress Intensity Factor, commonly called KI. The second term is the T-stress whose importance I have yet to discover.
Your post brings up a very important issue, I think. One of your first tasks when formulating the finite element model, before you've made even one node is to understand problem type--is the problem smooth? If smooth, where are the strong stress gradients (for instance at holes or notches)? If not smooth, where are the singularities and what is the strength of those singularities? For instance, cracks typically are 1/sqrt(r); however, you have milder singularities at interfaces of two different materials.