Brittle Failure of Nanoscale Notched Silicon Cantilevers: A Finite Fracture Mechanics Approach

The present paper focuses on the Finite Fracture Mechanics (FFM) approach and verifies its applicability at the nanoscale. After the presentation of the analytical frame, the approach is verified against experimental data already published in the literature related to in situ fracture tests of blunt V-notched nano-cantilevers made of single crystal silicon, and loaded under mode I. The results show that the apparent generalized stress intensity factors at failure (i.e., the apparent generalized fracture toughness) predicted by the FFM are in good agreement with those obtained experimentally, with a discrepancy varying between 0 and 5%. All the crack advancements are larger than the fracture process zone and therefore the breakdown of continuum-based linear elastic fracture mechanics is not yet reached. The method reveals to be an efficient and effective tool in assessing the brittle failure of notched components at the nanoscale.

Cutting-out method in the problem of longitudinal shear of anisotropic half-space with a crack

The previously developed direct cutting-out method in application to isotropic materials, in particular to bodies with thin inhomogeneities in the form of cracks and thin deformable inclusions is extended to the case of taking into account the possible anisotropy of the material. The basis of the method is to modulate the original problem of determining the stress state of a limited body with thin inclusions by means of a technically simpler to solve problem of elastic equilibrium of an infinite space with a slightly increased number of thin inhomogeneities, which in turn form the boundaries of the investigated body. By loaded cracks we model the boundary conditions of the first kind, and by absolutely rigid inclusions embedded into a matrix with a certain tension – the boundary conditions of the second kind. Using the method of the jump functions and the interaction conditions of a matrix with inclusion, the problem is reduced to a system of singular integral equations, the solution of which is carried out using the method of collocations. Approbation of the developed approach is carried out on the problem of elastic equilibrium of anisotropic (orthotropic in direction of shear) half-space with a symmetrically loaded very flexible inclusion (a crack) at jammed half-space boundary. The influence of inhomogeneity orientation and the half-space material on the generalized stress intensity factors were studied.

An isogeometric SGBEM for crack problems of magneto-electro-elastic materials

The isogeometric symmetric Galerkin boundary element method is applied for the analysis of crack problems in two-dimensional magneto-electro-elastic domains. In this method, the field variables of the governing integral equations as well as the geometry of the problems are approximated using non-uniform rational B-splines (NURBS) basis functions. The key advantage of this method is that the isogeometric analysis and boundary element method deal only with the boundary of the domain. To verify the accuracy of the proposed method, numerical examples for crack problems in infinite and finite domains are examined. It is observed that the computed generalized stress intensity factors obtained by the proposed method agree well with the exact solutions and other references.

Analytical-Numerical Determination of Stress Distribution around a Tip of Polygon-Like Inclusion

A stress distribution in vicinity of a tip of polygon-like inclusion exhibits a singular stress behaviour. Singular stresses at the tip can be a reason for a crack initiation in composite materials. Knowledge of stress field is necessary condition for reliable assessment of such composites. A stress field near the general singular stress concentrator can be analytically described by means of Muskhelishvili plane elasticity based on complex variable functions. Parameters necessary for the description are the exponents of singularity and Generalized Stress Intensity Factors (GSIFs). The stress field in the closest vicinity of the SMI tip is thus characterized by 1 or 2 singular exponents (1 - λ) where, 0<Re (λ)<1, and corresponding GSIFs that follow from numerical solution. In order to describe stress filed further away from the SMI tip, the non-singular exponents for which 1<Re (λ), and factors corresponding to these non-singular exponents have to be taken into account. Analytical-numerical procedure of determination of stress distribution around a tip of sharp material inclusion is presented. Parameters entering to the procedure are varied and tuned. Thus recommendations are stated in order to gain reliable values of stresses and displacements.