Search

Abstract In this work, the exact solution for the stress fields ahead of cracks initiated at sharp notch tips under antiplane shear and torsion loadings is derived in close form, leveraging conformal mapping and the complex potential method for antiplane elasticity. Based on the stress field distributions, relevant expressions for the mode III crack stress intensity factors are derived and their accuracy is discussed in detail taking advantage of a bulk of results from FE analyses. Highlights • General approach closed-form solution for the stress field in anti-plane shear and torsion. • Closed-form solution for V-notches weakened by a crack. • Closed-form solution for Stress Intensity Factor (SIF) and discussion on effect of notch opening, notch depth and crack. [ABSTRACT FROM AUTHOR]

In this work, a unified solution approach is proposed for the analytical evaluation of the stress fields close to notches under antiplane shear and torsion loadings, which allows a large variety of notch problems to be tackled. The method is based on the complex potential approach for antiplane elasticity combined with the use of proper conformal mappings. In particular, it is shown that a well defined analytical link does exist between the complex potential to be used to determine stresses and the first derivative of the conformal mapping used to mathematically describe the notch profile. This makes some methodologies such as Schwarz-Christoffel transformation, which allows describing any polygonal domain automatically, very attractive for the direct solution of notch problems. A bulk of solutions are provided to support this finding, from cracks and pointed notches, to radiused notches. In addition, the accuracy of each proposed solution is discussed in detail taking advantage of a bulk of results from FE analyses. [ABSTRACT FROM AUTHOR]

This study investigates how the insertion of multimaterial circular regions embracing the tip of a finite V-notch can be used to reduce the Notch Stress Intensity Factors (NSIFs) in structures subjected to antiplane shear or torsion. Towards this goal, this work presents a novel theoretical framework to calculate stress distributions and NSIFs in closed-form. Thanks to the new solution, it is shown that by tuning multimaterial region radii and elastic properties it is possible to significantly reduce the NSIFs and stress concentrations at the material interfaces. To investigate whether the proposed multimaterial system translates into increased structural capacity even in the presence of significant nonlinear deformations, computational simulations were conducted using nonlinear hyperelastic-damage and elasto-plastic-damage models. The preliminary results show increases of structural capacity up to 46% and of nominal strain at failure of up to 86% at the expenses of only a 8% reduction in structural stiffness. It is expected that a similar approach can be extended to other loading conditions (e.g. mode I and mode II, and fatigue) and that even larger gains can be obtained by performing thorough optimization studies. [Display omitted] [ABSTRACT FROM AUTHOR]

In this paper, antiplane piezoelectricity problems with multiple inclusions are studied by the generalized finite difference method (GFDM). Developed from the Taylor series and the Moving Least Squares, the GFDM expresses the derivatives of variables as the combination of values of surrounding nodes where the sparse matrix will be obtained considering the boundary conditions and interface conditions. Stress concentration and electric field concentration are analyzed in three numerical examples, which contain circular and elliptical piezoelectric inclusions in various sizes, locations, and material parameters. The applicability and validity of the proposed method are verified through the comparison with reference results. • The GFDM is applied with DDM for antiplane piezoelectricity problems. • Inclusions in various sizes, locations and material parameters are analyzed. • The proposed method maintains high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Abstract: An oblique edge crack in an anisotropic material under antiplane shear loadings is investigated. The antiplane problems are formulated based on a linear transformation method. An anisotropic solid containing an edge crack subjected to concentrated forces is first considered. The stress intensity factor for the edge crack with concentrated forces is obtained from the solution of the transformed edge crack in an isotropic material which is solved by using conformal mapping technique and complex function theory. The solution of the edge crack under concentrated loads is used to construct the stress intensity factor for the oblique edge crack in the anisotropic material subjected to antiplane distributed loads. Some numerical computations are carried out to calculate the stress intensity factors for the edge crack in inclined orthotropic materials subjected to point forces as well as distributed tractions. [Copyright &y& Elsevier]

Abstract: An eigenfuntion expansion method is employed for obtaining three-dimensional asymptotic displacement and stress fields in the vicinity of the front of a crack/anticrack type discontinuity weakening/reinforcing an infinite pie-shaped trimaterial plate, of finite thickness, formed as a result of bimaterial (matrix/semiconductor/ARC plus reaction product/scatterer) deposit over a substrate (fiber/ARC/semiconductor). The wedge is of general (unsymmetric) geometrical configuration, and is subjected to antiplane shear (mode III) far field loading. Each material is isotropic and elastic, but with different material properties. The material 2 or the substrate is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying composition of the bimaterial deposit. Numerical results pertaining to the variation of the mode III eigenvalues (or stress singularities) with various wedge aperture angles of the material 1 (reaction product/scatterer), are also presented. Hitherto generally unavailable results, pertaining to the through-thickness variations of stress intensity factors for symmetric parabolic load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the trimaterial plates under investigation, form also an important part of the present investigation. [Copyright &y& Elsevier]

Abstract: We consider a mathematical model which describes the antiplane shear deformations of a piezoelectric cylinder in frictional contact with a foundation. The process is mechanically dynamic and electrically static, the material behavior is described with a linearly electro-viscoelastic constitutive law, the contact is frictional and the foundation is assumed to be electrically conductive. Both the friction and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is of the form of a system coupling a second order hemivariational inequality for the displacement field with a time-dependent hemivariational inequality for the electric potential field. Then we prove the existence of a unique weak solution to the model. The proof is based on abstract results for second order evolutionary inclusions in Banach spaces. Finally, we present concrete examples of friction laws and electrical conductivity conditions for which our result is valid. [Copyright &y& Elsevier]

Abstract: We study a mathematical model which describes the antiplane shear deformations of a cylinder in frictional contact with a rigid foundation. The process is dynamic, the material behavior is described with a linearly viscoelastic constitutive law and friction is modeled with a general subdifferential boundary condition. We derive a variational formulation of the model which is in a form of an evolutionary hemivariational inequality for the displacement field. Then we prove the existence of a weak solution to the model. The proof is based on an abstract result for second order evolutionary inclusions in Banach spaces. Also, we prove that, under additional assumptions, the weak solution to the model is unique. We complete our results with concrete examples of friction laws for which our results are valid. [Copyright &y& Elsevier]

Abstract: A mode III crack with a cohesive zone in a power-law hardening material is studied under small scale yielding conditions. The cohesive law follows a softening path with the peak traction at the start of separation process. The stress and strain fields in the plastic zone, and the cohesive traction and separation displacement in the cohesive zone are obtained. The results show that for a modest hardening material (with a hardening exponent N =0.3), the stress distribution in a large portion of the plastic zone is significantly altered with the introduction of the cohesive zone if the peak cohesive traction is less than two times yield stress, which implies the disparity in terms of the fracture prediction between the classical approach of elastic–plastic fracture mechanics and the cohesive zone approach. The stress distributions with and without the cohesive zone converge when the peak cohesive traction becomes infinitely large. A qualitative study on the equivalency between the cohesive zone approach and the classical linear elastic fracture mechanics indicates that smaller cracks require a higher peak cohesive traction than that for longer cracks if similar fracture initiations are to be predicted by the two approaches. [Copyright &y& Elsevier]

Abstract: We derive a general expression for an interface parameter which makes possible the design of a neutral elliptic inhomogeneity when the stress field in the surrounding matrix is a polynomial function of order and the composite is subjected to antiplane shear deformations. [Copyright &y& Elsevier]

Abstract: The effective behavior and the distribution of local mechanical fields of linearly viscous 2-D polycrystals under antiplane shear is investigated. Several microstructures are considered, and a full-field approach based on the Fast Fourier Transform technique is applied. First, the accuracy of this technique is evaluated on a strictly isotropic 2-phase microstructure. Voronoi tessellation is then used to generate artificial microstructures, and a real (fully recrystallized) polycrystalline microstructure is obtained by electron back-scattering diffraction. Ensemble averages over several configurations using eight crystalline orientations (phases) are performed. Although a slight anisotropy is obtained for the effective behavior of each individual configuration, statistically, the results are in very good agreement with the available analytical isotropic solution. At phase level, a marked asymmetry is obtained for the distribution of local stresses. The intraphase first- and second-order moments of the stress field, calculated for both microstructures are compared with corresponding self-consistent predictions. [Copyright &y& Elsevier]

The solution of appropriate elasticity problems involving the interaction between inclusions and dislocations plays a fundamental role in many practical and theoretical applications, namely, it increases the understanding of material defects thereby providing valuable insight into the mechanical behavior of composite materials.Although the problem of a three-phase circular inclusion interacting with a dislocation in antiplane shear has been presented [Xiao and Chen, Mech. Mater. 32 (2000) 485], the analysis is limited to the classical perfect bonding condition. The current paper considers the solution for a homogeneous circular inclusion interacting with a dislocation under thermal loadings in antiplane shear. The bonding along the inhomogeneity–matrix interface is considered to be imperfect with the assumption that the interface imperfections are constant. It is found that when the inhomogeneity is soft, regardless of the level of interface imperfection, the inhomogeneity will always attract the dislocation. As a result, no equilibrium positions are available. Alternatively, when the inhomogeneity is hard, an unstable equilibrium position is found which depends on the imperfect interface condition and the shear moduli ratio μ2/μ1. [Copyright &y& Elsevier]

Three-dimensional asymptotic stress field in the vicinity of the front of a bimaterial pie-shaped wedge of general (unsymmetric) geometry is obtained by a recently developed eigenfunction expansion method. The bimaterial pie-shaped wedge is subjected to four combinations of wedge-side boundary conditions – free–free, clamped–clamped, free–clamped and clamped–free. Each material is isotropic and elastic, but with different material properties. Additionally, numerical results pertaining to the variation of the lowest eigenvalues (or stress singularities) with respect to the wedge opening angle of the bimaterial wedge, subjected to the aforementioned wedge-side boundary conditions, are also presented. Dependence of the same on the material properties of the component material phases is also an important part of the present investigation. [Copyright &y& Elsevier]