Triangular quarter‐point elements as elastic and perfectly‐plastic crack tip elements

TLDR

Triangular and prismatic quadratic isoparametric elements that collapse one side and place the mid‑side node at the crack‑tip quarter point capture the (1/√r) elastic and (1/r) perfect‑plastic singularities of fracture mechanics. The authors perform small‑scale‑yielding fracture analyses and compare finite‑element results with theoretical predictions. These elements enable determination of crack‑tip field parameters, loading, and geometry relationships, and allow fracture prediction in ductile structures such as pressure vessels under service conditions.

Abstract

Abstract Triangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid‐side node near the crack tip at the quarter point, are shown to embody the (1/√ r ) singularity of elastic fracture mechanics and the (1/ r ) singularity of perfect plasticity. The procedure of performing the fracture analysis for the case of small scale yielding is discussed, and the finite element results are compared with theoretical results. The proposed elements have wide application in the fracture analysis of structures where ductile fracture is investigated. They permit a determination of the relationship between crack tip field parameters, loading, and geometry. And for a given fracture criterion can be applied to the prediction of fracture in structures such as pressure vessels under in service conditions.