SYMPOSIA PAPER Published: 01 January 1990

Treatment of Singularities in a Middle-Crack Tension Specimen


A three-dimensional finite-element analysis of a middle-crack tension (M-T) specimen subjected to Mode I loading was performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements with collapsed non-singular elements at the crack front. The displacements and stresses from the analysis were used to estimate the power of singularities, by a log-log regression analysis, along the crack front. Analyses showed that finite-sized cracked bodies have two singular stress fields of the form σ = C0(θ,z)r + D0(θ,ϕ)Rλσ. The first term is the cylindrical singularity with the power -½ and is dominant over the middle 96% of the crack front and becomes nearly zero at the free surface. The second term is a vertex singularity that exists at the intersection of the crack front and the free surface. Because of two singular stress fields near the free surface and the classical square root singularity elsewhere, the strain energy release rate (G) appears to be an appropriate parameter all along the crack front.

Author Information

Shivakumar, KN
Analytical Services and Materials Inc., Hampton, VA
Raju, IS
Analytical Services and Materials Inc., Hampton, VA
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Developed by Committee: E08
Pages: 470–489
DOI: 10.1520/STP19009S
ISBN-EB: 978-0-8031-5134-5
ISBN-13: 978-0-8031-1299-5