The comparison between three different elements within a center crack plate considering elastic-plastic action

Abstract

Stress near a crack tip in plasticity was analyzed using three different finite element modelings; a constant strain triangle, eight-noded quadrilaterial, and a crack tip singularity element all considering viscoplasticity. The specimen under consideration was a center cracked plate made from IN-100, a nickel-base superalloy containing a half-crack length equal to 0.1367 in. (3.472 mm). An elastic solution was formulated in conjunction with two different loadings to generate plasticity. Fine mesh and coarse mesh solutions for the higher order elements were generated and compared considering equal number of degrees of freedom in two specific regions referred to as the near field and the far field regions. The authors determined that the elements whose elastic solutions conformed best to linear elastic fracture mechanics predictions were the constant strain triangle and the eight-noded quadrilateral in a fine mesh. The crack tip element did not perform as well as expected. For the plastic analysis, the constant strain triangle exhibited the largest plastic region. The eight-noded isoparametric element came within 15% of the stress levels generated from the constant strain triangle. The stress singularity that is characteristic of the crack tip element forced that element to behave unnaturally stiff immediately adjacent to the crack tip. Because it is not as stiff as either the crack tip element or the eight-noded element, the constant strain triangle offered the most promising solutions as verified through experimentation. It was therefore determined that the constant strain triangle offered the best solution to elastic-plastic finite element problems for the center cracked plate.