Ductile fracture in plane stress

A micromechanics-based ductile fracture initiation theory is developed for high-throughput assessment of ductile failure in plane stress. A key concept is that of inhomogeneous yielding such that microscopic failure occurs in bands with the driving force being a combination of band-resolved normal and shear tractions. The new criterion is similar to the much popularized Mohr—Coulomb model, but the sensitivity of fracture initiation to the third stress invariant constitutes an emergent outcome of the formulation. Salient features of a fracture locus in plane stress are parametrically analyzed. In particular, it is shown that a finite shear ductility cannot be rationalized based on an isotropic theory that proceeds from first principles. Thus, the isotropic formulation is supplemented with an anisotropic model accounting for void rotation and shape change in order to complete the prediction of a fracture locus and compare with experiments. A wide body of experimental data from the literature is explored and a simple procedure for calibrating the theory is outlined. Comparisons with experiments are discussed in some detail.

Determination of the stress concentration in the corner point of the wedge-shaped region reinforced by a more rigid thin coating

We analysed the problem of determining the exponents in the asymptotic solution of the isotropic theory of elasticity problem at the top of the wedge-shaped region where its sides (or one of them) are supported by a thin coating and lean without friction on the rigid bases. On the other side of the wedge-shaped region, it is assumed that there are various boundary conditions, including when there is a thin coating. Mathematically, the problem reduces to the problem of determining the roots of transcendental characteristic equations arising from the condition for the existence of a nontrivial solution of a system of the linear homogeneous equations. The characteristics of the stress tensor components have been determined for the various combinations of boundary conditions and physical and geometric parameters. The qualitative conclusions are made. In particular, we have established the combinations of the values of these parameters at which the singular behaviour of stresses arises.

The Trace Theorem for Anisotropic Sobolev — Slobodetskii Spaces with Applications to Nonhomogeneous Elliptic BVPs

In this paper, anisotropic Sobolev — Slobodetskii spaces in poly-cylindrical domains of any dimension N are considered. In the first part of the paper we revisit the well-known Lions — Magenes Trace Theorem (1961) and, naturally, extend regularity results for the trace and lift operators onto the anisotropic case. As a byproduct, we build a generalization of the Kruzhkov — Korolev Trace Theorem for the first-order Sobolev Spaces (1985). In the second part of the paper we observe the nonhomogeneous Dirichlet, Neumann, and Robin problems for p-elliptic equations. The well-posedness theory for these problems can be successfully constructed using isotropic theory, and the corresponding results are outlined in the paper. Clearly, in such a unilateral approach, the anisotropic features are ignored and the results are far beyond the critical regularity. In the paper, the refinement of the trace theorem is done by the constructed extension.DOI 10.14258/izvasu(2018)4-19

Interaction between an edge dislocation near a circular void within the framework of the theory of strain gradient elasticity

The purpose of this paper was to consider an edge dislocation near a circular hole within the isotropic theory of gradient elasticity. The stress field is derived with the help of a stress function method. The gradient stresses possess no singularity at the dislocation line. As a result, the image force exerted on the dislocation due to the presence of the hole remains finite when the dislocation approaches the interface. The gradient solution demonstrates a non-classical size effect.

Micropolar elasticity theory: a survey of linear isotropic equations, representative notations, and experimental investigations

This paper is devoted to a review of the linear isotropic theory of micropolar elasticity and its development with a focus on the notation used to represent the micropolar elastic moduli and the experimental efforts taken to measure them. Notation, not only the selected symbols but also the approaches used for denoting the material elastic constants involved in the model, can play an important role in the micropolar elasticity theory especially in the context of investigating its relationship with the couple-stress and classical elasticity theories. Two categories of notation, one with coupled classical and micropolar elastic moduli and one with decoupled classical and micropolar elastic moduli, are examined and the consequences of each are addressed. The misleading nature of the former category is also discussed. Experimental investigations on the micropolar elasticity and material constants are also reviewed where one can note the questionable nature and limitations of the experimental results reported on the micropolar elasticity theory.

Correction Factor of Surface Deflection for Inverted Asphalt Pavement Based on Linear-Anisotropy

Inverted asphalt pavement has been widely used in practical application. Anisotropy of granular material has been proved by experiment, but the current design specifications are also based on isotropic theory. Based on linear-anisotropic model, on the condition of the high, medium and low strength of soil subgrade, 4 different thickness of asphalt layer and 3 different thickness of granular sandwich are been systematically studied, the results show that, the strength of the soil subgrade has bigger effect on the pavement deflection, the deflection difference of the low to the high subgrade is about 14~23%, with the increase of granular material anisotropy, the deflection correction factor is bigger, with the granular sandwich anisotropic rates from 0.1 to 0.5, the deflection correction factor is within 1.04, the thin asphalt layer and the thick granular sandwich have bigger effect on the deflection correction factor, for the common inverted asphalt pavement structure, the proposed deflection correction factor is 1.02~1.04, it can be used directly in asphalt pavement design.