Elastic Waves in an Inhomogeneous Austenite Plate in the Model of a Transversely Isotropic Medium

The effect of the elasticity modulus and density inhomogeneities on the elastic wave transmissivity through an austenitic steel plate has been investigated. The elastic properties of austenitic steel have been simulated by a transversely isotropic medium. The mutual action of the elastic anisotropy and spatial inhomogeneity has been considered. It has been shown that the main factors determining the interference pattern in the plate are the plate thickness, absolute value of the modulus (density) variation, and spatial derivative of the modulus. Properties of both inhomogeneous and homogeneous transversely isotropic plates have been compared with those of an isotropic plate. Studies of the elastic properties of austenitic steel using the model of transversely isotropic medium have been reviewed.     

Elastic analysis of unbounded solids using volume integral equation method

A volume integral equation method (VIEM) is used to calculate the plane elastostatic field in an unbounded isotropic elastic medium containing isotropic or anisotropic inclusions subject to remote loading. It should be noted that this newly developed numerical method does not require the Green’s function for anisotropic inclusions to solve this class of problems, since only the Green’s function for the unbounded isotropic matrix is involved in their formulation for the analysis. A detailed analysis of displacement and stress fields is carried out for isotropic or anisotropic inclusions. The method is shown to be very accurate and effective for investigating the local stresses in composites containing isotropic or anisotropic fibers.     

Analysis of elastic wave scattering problems using volume integral equation method

A volume integral equation method (VIEM) is applied for the effective analysis of elastic wave scattering problems in unbounded solids containing isotropic or anisotropic inclusions. It should be noted that this newly developed numerical method does not require Green’s function for anisotropic inclusions to solve this class of problems since only Green’s function for the unbounded isotropic matrix is involved in their formulation for the analysis. Through the analysis of plane wave scattering problems in unbounded isotropic matrix with isotropic or anisotropic inclusions, it will be established that this new method is very accurate and effective for solving plane wave scattering problems in unbounded solids containing isotropic or anisotropic inclusions.     

Numerical simulation of the effects of elastic anisotropy and grain size upon the machining of AA2024

Turning modeling and simulation of different metallic materials using the commercially available Finite Element (FE) softwares is getting prime importance because of saving of time and money in comparison to the costly experiments. Mostly, the numerical analysis of machining process considers a purely isotropic behavior of metallic materials; however, the literature shows that the elastic crystal anisotropy is present in most of the ‘so-called’ isotropic materials. In the present work, the elastic anisotropy is incorporated in the FE simulations along with the effect of grain size. A modified Johnson-Cook ductile material model based on coupled plasticity and damage evolution has been proposed to model the cutting process. The simulation results were compared with experimental data on the turning process of Aluminum alloy (AA2024). It was found that the elastic anisotropy influences the average cutting force up to 5% as compared to the isotropic models while the effect of grain size was more pronounced up to 20%.     

A new strength criterion for isotropic materials,taking account of their elastic or deformational properties

A new strength criterion for isotropic materials is proposed, taking account of their elastic or deformational properties.     

On the experimental solution of plane elasticity problems by the method of caustics

The optical method of caustics is used for the complete experimental determination of the stress field inside a plane isotropic elastic medium. Two experiments are required for this determination.     

An elastic-plastic constitutive equation for transversely isotropic materials and its application to the bending of perforated circular plates

Extending Hencky's interpretation for Mises' yield condition to anisotropic materials, it is first assumed that the plastic deformation occurs when the elastic distortion energy attains to a certain constant value. Then, the shearing stress and the shearing strain intensities are defined in terms of the elastic and the plastic distortion energy. By assuming the deformation theory of plasticity along with the hydrostatic pressure insensitivity of material response, trigonometric representations of stress and strain are derived in order to formulate an elastic-plastic constitutive equation for transversely isotropic materials. Yield conditions and the corresponding yield loci for the relevant materials are also discussed. As an application of the resulting constitutive equation, elastic-plastic bending of perforated circular plates is analysed by modelling them by equivalent homogeneous transversely isotropic plates.     

A generalized self-consistent estimate for the effective elastic moduli of fiber-reinforced composite materials with multiple transversely isotropic inclusions

The effective elastic properties of a fiber-reinforced composite material with multiple transversely isotropic inclusions are estimated by the use of a generalized self-consistent method, which considers strong interactions between the inclusion and matrix as well as among inclusions. The accuracy of this method is established by comparing to the closed-form analytic solutions by Christensen when the matrix and inclusion are isotropic. Furthermore, current predictions from the generalized self-consistent method for a composite with multiple inclusions correspond well with the numerical results from finite element analysis. The generalized self-consistent method can be particularly useful in establishing micromechanics models of natural biological composite materials such as cortical bone to examine the dependence of the elastic properties of cortical bone on its porosity.     

含固有缺陷复合材料有效弹性性能预报

根据缺陷在复合陶瓷中分布特点,将缺陷简化为刚度为0的椭球夹杂,嵌入到横观各向同性基体中,建立含缺陷复合材料的细观结构模型。应用相互作用直推估计法推导含缺陷胞元的有效刚度,结合刚度体平均化方法,假设胞元空间随机分布,得到复合材料的等效刚度表达式,分析横观各向同性基体中缺陷体积分数、取向和形状对材料等效刚度的影响,并进一步讨论缺陷周围基体各向异性的影响。结果表明,缺陷存在导致材料弹性性能明显降低,在缺陷体积分数较小时,弹性常数对缺陷体积分数更加敏感;缺陷形状对弹性常数有较大影响,当缺陷接近于薄片状时,缺陷厚度对弹性常数影响明显,而缺陷平面形状对弹性常数基本没有影响;当片状缺陷垂直于基体中弹性模量较大的轴时,缺陷对材料有效性能的降低作用更显著,考虑缺陷周围基体各向异性是很有必要的。     

Effective elastic properties of damaged isotropic solids

In continuum damage mechanics, damaged solids have been represented by the effective elastic stiffness into which local damage is smoothly smeared. Similarly, damaged solids may be represented in terms of effective elastic compliances. By virtue of the effective elastic compliance representation, it may become easier to derive the effective engineering constants of damaged solids from the effective elastic compliances, all in closed form. Thus, in this paper, by using a continuum modeling approach based on both the principle of strain energy equivalence and the equivalent elliptical micro-crack representation of local damage, the effective elastic compliance and effective engineering constants are derived in terms of the undamaged (virgin) elastic properties and a scalar damage variable for both damaged two- and three-dimensional isotropic solids.     

Strain energy density in fiber composites based on high-epoxy binders

The energy of the elastic field in unidirectional composites based on high-epoxy resins is calculated. The influence of the composition and concentration of isotropic components and the type of external mechanical loading on that elastic energy is considered.     

复杂多孔板有效弹性常数的结构分析方法

基于弹性薄板理论给出了基于模态分析、最大挠度等效和总应变能等效确定复杂孔板有效弹性常数的方法,提出了具有普适性的多孔板有效弹性常数与有效质量比或有效承载分数之间的关联式,根据有限元结构分析结果,评价了3种方法与ASME规范方法的一致性。结果表明,这些方法可用于分析各种复杂孔形和各种排布方式下的多孔板强度评价和振动控制问题。     

Use of Spectra of Normal and Tangential Displacement Components in Lamb Waves for Separating Single-Mode Components

The paper considers one of simple engineering models--an isotropic elastic layer lying on a rigid base where a wave is driven by a vertical periodic load applied to the surface. Using the Hankel transformation and the method of loop integration, formulas have been obtained for the elastic field due to propagating modes generated by an axially symmetrical surface source in a zone where the effect of inhomogeneous waves is insignificant. Calculations of displacement amplitudes and their ratios versus frequency for propagating modes are given.     

Asymptotic solutions for axisymmetric contact of a thin,transversely isotropic elastic layer

The problem of a rigid sphere in normal contact with a thin, transversely isotropic elastic layer is investigated. The thin elastic layer rests on a rigid foundation and both the limiting cases, wherein the interface is either ideally bonded or unbonded and frictionless, are considered. Approximate analytical solutions for the contact pressure beneath the spherical indenter and for the contact patch radius are presented. By comparing these with those predicted by the finite element method, the accuracy of the solution methods is determined.     

Investigating elastic stability of cylindrical shell with an elastic core under axial compression by energy method

In this paper, the elastic axisymmetric buckling of a thin, isotropic and simply supported cylindrical shell with an elastic core under axial compression has been analyzed using energy method. The nonlinear strain-displacement relations in general cylindrical coordinates are simplified using Sanders kinematic relations (Sanders, 1963) for axial compression. Equilibrium equations are obtained by using minimum potential energy together with Euler equations applied for potential energy function in cylindrical shell. To acquire stability equation of cylindrical shell with an elastic core, minimum potential energy theory and Trefftz criteria are implemented. Stability and compatibility equations for an imperfect cylindrical shell with an elastic core are also obtained by the energy method, and the buckling analysis of shell is carried out using Galerkin method. Critical load curves versus the aspect ratio are obtained and analyzed for a cylindrical shell with an elastic core. It is concluded that the application of an elastic core increases elastic stability and significantly reduces the weight of cylindrical shells.     

Analysis of contact between transversely isotropic coated surfaces: development of stress and displacement relationships using FEM

The problem of an elastic cylinder in normal contact between transversely isotropic layered substrate surfaces is investigated using the finite element method (FEM). A two-dimensional finite element model is developed which accurately determines the normal stress, contact length, and approach distance of layered surfaces. Numerical results, which are initially verified using Hertzian theory, are obtained at 756 distinct conditions by varying coating material, coating thickness, normal load, cylinder radius, and cylinder material. The numerical results are normalized with respect to Hertzian contact theory and a dimensionless anisotropic coating material parameter, ζ, is introduced. Numerical expressions for the normalized maximum normal stress, contact length, and approach distance are subsequently determined by curve-fitting the results of the 756 simulations performed. The relevance of such expressions are ascertained and discussed by comparing predicted results to isotropic layer theory presented by Gupta and Walowit [P.K. Gupta, J.A. Walowit. Contact stresses between an elastic cylinder and a layered elastic solid, ASME J. Lubrication Technol., Vol. 94 (1974) pp. 250–274.]     

集中载荷作用下双模量圆板弯曲计算

双模量圆板在集中载荷作用下发生弯曲变形时,会形成各向同性的拉伸和压缩区。因此,可把双模量圆板看成两种各向同性材料组成的层合板,采用弹性理论建立了双模量圆板在集中载荷作用下的静力平衡方程,利用此静力平衡方程确定了双模量圆板的中性面位置。在此基础上,建立了集中载荷作用下双模量圆板的弯曲微分方程,求得了圆板的挠度表达式。通过算例讨论分析了双模量对圆板弯曲变形的影响,得到了圆板材料拉压弹性模量相差较大时,其挠度计算不宜采用相同弹性模量经典薄板理论,而应该采用双模量薄板理论的结论。     

Volume integral equation method for multiple isotropic inclusion problems in an infinite solid under tension or in-plane shear

A volume integral equation method (VIEM) is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solid containing interacting multiple isotropic inclusions subject to uniform remote tension or in-plane shear. This method is applied to two-dimensional problems involving long parallel cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix, and the central inclusion is carried out for square and hexagonal packing of the inclusions. The effects of the number of isotropic inclusions and various fiber volume fractions on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy and efficiency of the method are examined in comparison with results obtained from analytical and finite element methods.     

On the Effect of Isotropic Hardening on the Coefficient of Restitution for Single or Repeated Impacts Using a Semi-Analytical Method

A semi-analytical method is proposed for the simulation of moderately high-speed impacts of a relatively hard particle on an elastic–plastic substrate. Potential applications of the current modeling approach include shot-peening and ultrasonic peening as well as impacts on functional surfaces such as mechanical seals or bearings. The coefficients of restitution for single impacts on an elastic–perfectly plastic semi-infinite body or one with isotropic hardening have been computed for various impact velocities. The current approach is three dimensional and numerically efficient in terms of CPU time and memory space required. Numerical results are in good agreement with those obtained by other authors for elastic–perfectly plastic behavior. Coefficients of restitution resulting from repeated impacts at a constant initial velocity are also studied. Finally, equations fitting these numerical results are proposed.     

The equivalent elastic compliances of an elastic solid with interface cracks

A periodic array of interface cracks was considered earlier as a simple model to study the effect of crack interaction on the elastic fields of a solid composed of two dissimilar isotropic elastic materials. This paper focuses on the perturbation of the elastic compliances of the solid due to the interacting interface cracks. The problem is formulated using Betti's reciprocal theorem. The analysis provides the equivalent elastic compliances in terms of the geometric parameters of the interface cracks for various levels of loadings and material combinations. The results show that the interaction between cracks is significant only when the crack spacing is less than four times the crack length. Also, contact between crack faces introduces coupling between applied shear stress and normal displacement, but it is significant only when the ratio of the magnitudes of the shear and normal stresses exceeds two.