It is well known that the near-tip displacement eld on a crack surface can be represented in a power series in the variable p r, where r is the distance to the tip. It is shown herein that the coe cients of the linear terms on the two sides of the crack are equal. Equivalently, the linear term in the crack opening displacement vanishes. The proof is a completely general argument, valid for an a...

CRACKS in ductile single crystals are analyzed here for geometries and orientations such that twodimensional states of anti-plane shear constitute possible deformation fields. The crystals are modelled as ideally plastic and yield according to critical resolved shear stresses on their slip systems. Restrictions on the asymptotic forms of stress and deformation fields at crack tips are establish...

Partition of unity enrichment techniques are developed for bimaterial interface cracks. A discontinuous function and the two-dimensional near-tip asymptotic displacement functions are added to the finite element approximation using the framework of partition of unity. This enables the domain to be modelled by finite elements without explicitly meshing the crack surfaces. The crack-tip enrichmen...

Reinforced concrete is a composite material consisting in a rebar embedded in a concrete matrix. The structural equilibrium depends of the quality of bond between the two materials as well as the intrinsic quality of each of the components. When the structure is submitted to heating, cracking can occur due to the difference in thermal expansion properties between the two materials. In the prese...

in this work, the mechanism for fracture of brittle substances such as rocks under a uniform normal tension is considered. the oriented straight micro-cracks are mostly created in all the polycrystalline materials resulting from the stress concentrations. the present work focuses on the interactions of the pre-existing micro-cracks, which can grow and propagate within a rock-like specimen. the ...

In previous studies, enamel showed indications to occlude small cracks in-vivo and exhibited R-curve behaviors for bigger cracks ex-vivo. This study quantifies the crack tip's toughness (K(I0),K(III0)), the crack's closure stress and the cohesive zone size at the crack tip of enamel and investigates the toughening mechanisms near the crack tip down to the length scale of a single enamel crystal...

Recent finite-element results by S. Cl. Larsson and A. J. Carlsson suggest a limited range of validity to the ‘small scale yielding approximation’, whereby small crack tip plastic zones are correlated in terms of the elastic stress intensity factor, It is shown with the help of a model for plane strain yielding that their results may be explained by considering the non-singular stress, acting p...

Crack tip stress and deformation fields are analyzed for tensile-loaded ideally plastic crystals. The specific cases of (0 1 O) cracks growing in the [1 0 1] direction, and (1 0 1) cracks in the [0, 1, O] direction, are considered for both fcc and bcc crystals which flow according to the critical resolved shear stress criterion. Stationary and quasistatically growing crack fields are considered...

A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics simulations. A molecular-dynamics model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat Σ99 [1 1 0] symmetric tilt grain boundary in aluminum. Under hy...