K-dominance and size effect in mode I fracture of brittle materials with low to medium porosity

Abstract

Linear Elastic Fracture Mechanics usually only considers the singular stresses when describing the conditions under which fracture would occur in a brittle material. However, it is becoming more widely recognised that non-singular stresses can become significant depending on the geometry and configuration of the specimen. This study investigates the impact of non-singular stresses on the stress intensity of low to medium porosity brittle materials. To address this, discrete finite element models of Double Cantilever Beam (DCB) samples were created and the full near-tip stress field in mode I loading was numerically evaluated. A parametric study was conducted, examining the influence of overall specimen size, material porosity and crack tip location relative to the nearest void. Results indicate a prominent size effect on the stress intensity at the crack tip of porous materials, with smaller specimen exhibiting tougher behaviour than their respective larger counterparts. This size effect, which is amplified with increasing porosity, is closely correlated with the variation of non-singular stresses, both parallel and normal to the crack plane. A model to predict the behaviour of porous specimen for different sizes is suggested based on the findings.

Experimental and numerical analysis of size effects on stress intensity in anisotropic porous materials

“…Experimental findings also show a strong size effect, with smaller specimen exhibiting lower normalised stress concentration at the crack tip than their larger counter-parts, which are then seemingly converging to a constant value for increasing size. This behaviour is consistent with the numerically predicted results for both, the exact representation of the tested specimens, and specimens of similar configuration, where the voids were placed in a triangular array and the specimen's aspect ratio was large enough to assume the existence of a long crack [30].…”

“…Using laser-cutting, a horizontal crack was created in the midplane of each specimen, with a crack length to total specimen length ratio approaching α/W = 0.5, where α is the crack length. It has been shown [30] that the local stress intensity oscillates greatly for varying locations of the crack tip with respect to the nearest void. In order to produce comparable results, in all cases the crack tip was designed to be directly below the void, thus producing small variations in the value of the α/W ratio.…”

“…For each model the locations of all nodes in the extension of the crack tip were exported, along with the y-direction nodal stresses at each node. The stress intensity and amplitude of non-singular stresses at each location was then estimated by using the projection method (previously used by the authors in [30], originally presented in [33]), which is briefly described below.…”

“…The significance of non-singular stresses on the size effect observed in porous materials has been previously investigated by the authors numerically [30], where a two-dimensional, quasi-isotropic material with circular pores arranged in an equilateral triangular array was studied in mode I fracture. The results showed that the existence of porosity can significantly reduce the size of the K-dominant zone, causing variations in the estimated stress distribution at the crack tip for different specimen sizes and porosity levels.…”

Fracture toughness of rigid polymeric foams: A review

“…Touliatou and Wheel 101 observed also a prominent size effect on brittle materials with low and medium porosity. As the specimen size increases, the material becomes less tough, until it converges to a specific value.…”