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.