On the use of quarter-point tetrahedral finite elements in linear elastic fracture mechanics

•Quarter point tetrahedra (QPT) can reproduce the inverse square root singularity.•QPTs improve the displacement field significantly in the region near the crack front.•Displacement correlation method computes accurate SIFs on unstructured meshes.•A mesh dependent optimal sampling distance is defined for SIF computation.•Unstructured tetrahedral meshes are efficient and accurate for analyzing fractures.

This paper discusses the reproduction of the square root singularity in quarter-point tetrahedral (QPT) finite elements. Numerical results confirm that the stress singularity is modeled accurately in a fully unstructured mesh by using QPTs. A displacement correlation (DC) scheme is proposed in combination with QPTs to compute stress intensity factors (SIF) from arbitrary meshes, yielding an average error of 2–3%. This straightforward method is computationally cheap and easy to implement. The results of an extensive parametric study also suggest the existence of an optimum mesh-dependent distance from the crack front at which the DC method computes the most accurate SIFs.