Interaction between a crack and a circular inhomogeneity with interface stiffness and tension

Abstract

The interaction between a straight crack and a circular inhomogeneity with interface stiffness and energy is considered. The Gurtin and Murdoch model is adopted, wherein the interface between the inhomogeneity and the matrix is regarded as a material surface that possesses its own mechanical properties and surface tension. The elastostatics problem is decomposed into two complimentary problems for (1) a circular disk with unknown distributions of traction and displacements along its boundary and (2) a loaded isotropic plane containing a circular hole with unknown distributions of traction and displacements along its boundary. The unknown distributions are determined through the application of the constitutive relations at the material surface. For selected values of the dimensionless parameters that quantify the geometry, material properties and applied loading, the stress field, stress intensity factors and energy release rates are calculated using a complex boundary integral equation approach. Particular attention is paid to crack-tip shielding and anti-shielding that develops as a result of the stresses introduced by the material surface. An illustrative example involving a perforated plate loaded in tension suggests that the material surface produces a modest level of expected effective toughening.

Boundary element analysis of nanoinhomogeneities of arbitrary shapes with surface and interface effects

“…In most of the works cited above, the simplified GurtinMurdoch stress-strain constitutive relation was used where the whole or part of the displacement-gradient term was neglected [25,26]. Using the complex variable method, Mogilevskaya et al [27] recently studied the multiple interactions between the circular nanoinhomogeneities and nanopores using the ''complete'' Gurtin-Murdoch model.…”

Influence of Nanoscale Inhomogeneity Incorporating Interface Effect on Crack Nucleation at Intersection of Twin and Grain Boundary in Nanocomposite

“…Gurtin and his co-workers [34,35] first studied the interface stress of elastic isotropic solids with continuum mechanics and proposed the interface stress model. The interface stress model has been widely utilized to investigate the various mechanical problems in nanostructured materials [36][37][38][39][40][41][42][43][44][45]. Fang and Liu [38,39] studied the interaction of nanoinhomogeneity with screw dislocation and edge dislocation, respectively.…”

“…Fang and Liu [38,39] studied the interaction of nanoinhomogeneity with screw dislocation and edge dislocation, respectively. Mogilevskayaet et al [40] studied the interaction between a circular inclusion and a straight crack with interface elasticity and tension. They discussed the interface effect on the stress intensity factor at the crack tip by using a complex boundary integral equation approach.…”

Boundary element analysis of three dimensional nanoscale inhomogeneities

“…Based on the complex variables boundary element method (CVBEM) in elasticity, Mogilevskaya et al (2008) and Jammes et al (2009) presented some results of multiple interacting circular nano-inhomogeneities or/and nano-pores in one isotropic elastic half-planes as well as in one of two joined, dissimilar isotropic elastic half-planes, respectively. Mogilevskaya et al (2009) used the CVBEM to investigate the interaction between a straight nano-crack and a circular nanoinhomogeneity. In the CVBEM, the unknown displacements and tractions on the inhomogeneity-matrix interfaces as well as the Gurtin-Murdoch equations for the interface of arbitrary shapes are all expanded into Fourier series.…”