Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical cavity

The thermoelastic interaction for the three-phase-lag (TPL) heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory (2TT). The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace transformation, the fundamental equations are expressed in the form of a vector-matrix differential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the thermal loading (the thermal shock and the ramp-type heating) and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion techniques. The numerical values of the physical quantity are computed for the copper like material. Significant dissimilarities between two models (the two-temperature Green-Naghdi theory with energy dissipation (2TGN-III) and two-temperature TPL model (2T3phase)) are shown graphically. The effects of two-temperature and ramping parameters are also studied.     

Stress field of orthotropic cylinder subjected to axial compression

Based on the constancy hypothesis of material volume, the circumferential and radial stresses of a cylinder specimen are analyzed when the cylinder is subject to a loading along the axial direction. The circumferential and radial stress distribution is a power function of radius parameter when the constitutive relation of specimen material is orthotropic. The stress distribution is a quadratic function of radius parameter for transversely isotropic material. Along the cylinder axial line, the circumferential and radial stresses are maximum and equal to each other. In the circumference boundary surface, the radial stress is zero and the circumferential stress value is minimal. The failure theory of maximum tensile circumferential strain is applied to calculate the critical axial loading. The circumference-boundary-layer failure criterion of orthotropic cylinders is described with the Hill-Tsai strength theory. The obtained strength theory is related to axial stress and mechanical properties of specimen material and to the specimen axialdeformation strain rate and the change rate of strain rate.     

Geometric and material nonlinearities of sandwich beams under static loads

A new theory developed from extended high-order sandwich panel theory(EHSAPT)is set up to assess the static response of sandwich panels by considering the geometrical and material nonlinearities simultaneously.The geometrical nonlinearity is considered by adopting the Green-Lagrange-type strain for the face sheets and core.The material nonlinearity is included as a piecewise function matched to the experimental stress-strain curve using a polynomial fitting technique.A Ritz technique is applied to solve the governing equations.The results show that the stress stiffening feature is well captured in the geometric nonlinear analysis.The effect of the geometric nonlinearity in the face sheets on the displacement response is more significant when the stiffness ratio of the face sheets to the core is large.The geometric nonlinearity decreases the shear stress and increases the normal stress in the sandwich core.By comparison with open literature and finite element simulations,the present nonlinear EHSAPT is shown to be sufficiently precise for estimating the nonlinear static response of sandwich beams by considering the geometric and material nonlinearities simultaneously.     

Deformation due to time harmonic sources in micropolar thermoelastic medium possessing cubic symmetry with two relaxation times

The response of a micropolar thermoelastic medium possessing cubic symmetry with two relaxation times due to time harmonic sources is investigated. Fourier transform is employed and the transform is inverted by using a numerical inversion technique. The components of displacement, stress, microrotation and temperature distribution in the physical domain are obtained numerically. The results of normal displacement, normal force stress, tangential couple stress and temperature distribution are compared for micropolar cubic crystal and micropolar isotropic solid. The numerical results are illustrated graphically for a particular material. Some special cases are also deduced.     

Thermal stresses in infinite circular cylinder subjected to rotation

The present investigation is concerned with the effect of rotation on an infinite circular cylinder subjected to certain boundary conditions.An analytical procedure for evaluation of thermal stresses,displacements,and temperature in rotating cylinder subjected to thermal load along the radius is presented.The dynamic thermal stresses in an infinite elastic cylinder of radius a due to a constant temperature applied to a variable portion of the curved surface while the rest of surface is maintained at zero temperature are discussed.Such situation can arise due to melting of insulating material deposited on the surface cylinder.A solution and numerical results are obtained for the stress components,displacement components,and temperature.The results obtained from the present semi-analytical method are in good agreement with those obtained by using the previously developed methods.     

A unified plasticity methodology for rate-and temperature-sensitive alloys exhibiting a non-linear kinematic hardening behavior

In this paper, a novel unified plasticity methodology is proposed to allow the coupling of rate-and temperature-sensitivity of engineering alloys as well as the non-linear kinematic hardening behavior often observed during cyclic loading. The proposed methodology is general in the sense that an arbitrary constitutive model may be chosen for the viscoplastic part, as well as the cyclic part. We adapt our model with a physically-motivated viscoplasticity flow rule and a nonlinear kinematic hardening model. In contrast with other unified plasticity models, the simplified theory involves few material parameters that can be readily calibrated from standard mechanical tests. The capabilities of the proposed theory are demonstrated for a hot rolled annealed 304 L stainless steel supplied by Vimetal Peckover. The model is tested with stress–strain curves obtained from standard tensile and cyclic uniaxial tests at various strain amplitudes and strain-rates, and good accuracy of the response is obtained for strains up to 15%, within a temperature range of 293–673 K. We note that the cyclic plasticity model in our adapted theory can be readily enhanced with ratchetting, mean stress relaxation, strain amplitude history, Masing effects or other complex capabilities.     

DYNAMICAL FORMATION OF CAVITY FOR COMPOSED THERMAL HYPERELASTIC SPHERES IN NONUNIFORM TEMPERATURE FIELDS

Dynamical formation and growth of cavity in a sphere composed of two incompressible thermal-hyperelastic Gent-Thomas materials were discussed under the case of a non-uniform temperature field and the surface dead loading. The mathematical model was first presented based on the dynamical theory of finite deformations. An exact differential relation between the void radius and surface load was obtained by using the variable transformation method. By numerical computation, critical loads and cavitation growth curves were obtained for different temperatures. The influence of the temperature and material parameters of the composed sphere on the void formation and growth was considered and compared with those for static analysis. The results show that the cavity occurs suddenly with a finite radius and its evolvement with time displays a non-linear periodic vibration and that the critical load decreases with the increase of temperature and also the dynamical critical load is lower than the static critical load under the same conditions.     

A MODEL CONSIDERING HYDROSTATIC STRESS OF POROUS NITI SHAPE MEMORY ALLOY

Based on the micromechanical method and thermodynamic theory,a constitutive model for the macroscopic mechanical behavior of porous NiTi shape memory alloy is presented.The hydrostatic stress is considered for porous NiTi according to the transformation function of dense NiTi.The present model takes account of the tensile-compressive asymmetry of NiTi,and can degenerate to model dense material.Numerical calculations,which only need material parameters of dense NiTi,are conducted to investigate the nonlinear and hysteretic strain of porous NiTi,and the predicted results are in good agreement with the corresponding experiments.     

TEMPERATURE SENSITIVITY AND PREDICTION OF THE MECHANICAL BEHAVIORS OF ULTRAFINE GRAINED ALUMINUM UNDER UNIAXIAL COMPRESSION

In the present work, we explore the strain hardening behaviors as well as the effect of temperature on the plastic deformation of ultrafine grained aluminum. The temperature sensitivity is determined and compared with that of coarse grained material. The results indicate that the flow stress of ultrafine grained aluminum displays enhanced sensitivity to temperature. The reduction in activation volume is suggested to be the major reason for the enhanced temperature sensitivity as grain size is refined into the sub-micrometer regime. Finally, a phenomenological constitutive model is proposed to describe the post-yield response of ultrafine grained aluminum.     

Effect of Stress-Dependent Thermal Conductivity on Thermo-Mechanical Coupling Behavior in GaN-Based Nanofilm Under Pulse Heat Source

The thermal properties of a nanostructured semiconductor are affected by multi-physical fields,such as stress and electromagnetic fields,causing changes in temperature and strain distributions.In this work,the influence of stress-dependent thermal conductivity on the heat transfer behavior of a GaN-based nanofilm is investigated.The finite element method is adopted to simulate the temperature distribution in a prestressed nanofilm under heat pulses.Numerical results demonstrate the effect of stress field on the thermal conductivity of GaN-based nanofilm,namely,the prestress and the thermal stress lead to a change in the heat transfer behavior in the nanofilm.Under the same heat source,the peak temperature of the film with stress-dependent thermal conductivity is significantly lower than that of the film with a constant thermal conductivity and the maximum temperature difference can reach 8.2 K.These results could be useful for designing GaN-based semiconductor devices with higher reliability under multi-physical fields.     

Axisymmetric Thermoelastic Interactions without Energy Dissipation in an Unbounded Body with Cylindrical Cavity

The linear theory of thermoelasticity without energy dissipation is employed to study thermoelastic interactions in a homogeneous and isotropic unbounded body containing a cylindrical cavity. The interactions are supposed to be due to a constant step in radial stress or temperature applied to the boundary of the acvity, which is maintained at a constant temperature or zero radial stress (as the case may be). By using the Laplace transform technique, it is found that the interactions consist of two coupled waves both of which propagate with a finite speed but with no attenuation. The discontinuities that occurs at the wavefronts are computed. Numerical results applicable to a copper-like material are presented.     

Two-phase theory for the superplastic flow

We discuss a theoretical approach to the stress induced motion of vacancies in a polycrystalline material and its connection with superplastic flow, put forward recently by us. After introducing an alternate formulation, the theory is applied to explain the temperature dependent stress-strain rate curves exhibited by some representative alloys. The agreement with experiment is remarkable. We also employ it to study the rate of cavity growth in two superplastic copper alloys that exhibit particularly strong cavitation.     

Analysis of cavitation problem of heated elastic composite ball

The cavitation problem of a composite ball under a uniform temperature is investigated, and the ball is composed of two elastic solid materials. The nonlinear mathematical model of the problem is established with the finite logarithmic strain measure for a large geometric deformation and by the Hooke law for elastic materials. The analytic solutions in a parametric form are derived for the thermal dilatation of the composite ball with a large elastic deformation. Solution curves are given to describe the variations of the critical temperature in the cavitation with the geometric and material parameters. The bifurcation curve is also given to reveal the cavity growth after void nucleation. The numerical results for a computational example indicate that the radius of the cavity will rapidly grow above the critical temperature, and the loop stress will become infinite when void nucleation. This means that the materials near the cavity will produce a plastic deformation leading to local failure and fracture if the material of the internal ball is elastoplastic. In addition, the cavitation of the composite ball appears at a low temperature if the elastic property of the material of the internal ball is nearly uncompressible.     

湿热作用下热超弹性材料在电子封装中的分层失效问题

研究了具有Gent-Thomas特征的热超弹性材料构成的高聚物电子封装件在回流焊过程中由于吸湿所引发的蒸汽压力以及由于材料的热失配引发的热应力共同作用下而导致的“爆米花”式的分层失效问题.利用超弹性材料空穴生成和增长的理论给出了此类封装材料在回流焊过程中孔穴的生成及增长与蒸汽压力和热应力之间的解析关系.分析结果表明,当...     

Multiple scattering of electro-elastic waves from a buried cavity in a functionally graded piezoelectric material layer

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and the dynamic stress around a buried cavity in a functionally graded piezoelectric material layer bonded to a homogeneous piezoelectric material. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the cavity. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. According to the analytical expression of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric property, the position of the cavity in the layer, the incident wave number and the material properties on the dynamic stress around the cavity are analyzed. Analyses show that the piezoelectric property has great effect on the dynamic stress in the region of higher frequencies, and the effect increases with the decrease of the thickness of FGPM layer. If the material properties of the homogeneous piezoelectric material are greater than those at the surface of the structure, the dynamic stress resulting from the piezoelectric property is greater. The effect material properties at the two boundaries of FGPM layer on the distribution of dynamic stress around the cavity is also examined.     

A unified theory for cavity expansion in cohesive-frictional micromorphic media

This paper presents a unified theory for both cylindrical and spherical cavity expansion problems in cohesive-frictional micromorphic media. A phenomenological strain-gradient plasticity model in conjunction with a generalized Mohr–Coulomb criterion is employed to characterize the elasto-plastic behavior of the material. To solve the resultant two-point boundary-value problem (BVP) of fourth-order homogeneous ordinary differential equation (ODE) for the governing equations which is not well-conditioned in certain cases, several numerical methods are developed and are compared in terms of robustness, efficiency and accuracy. Using one of the finite difference methods that shows overall better performance, both cylindrical and spherical cavity expansion problems in micromorphic media are solved. The influences of microstructural properties on the expansion response are clearly demonstrated. Size effect during the cavity expansion is captured. The proposed theory is also applied to a revisit of the classic problem of stress concentration around a cavity in a micromorphic medium subjected to isotropic tension at infinity, for which some conclusions made in early studies are revised. The proposed theory can be useful for the interpretation of indentation tests at small scales.     

Dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity

Introduction Thetheoryofgeneralizedthermoelasticitywithonerelaxationtimebasedonamodified Fourier’slawofheatconductionwasdevelopedbyLordandShulman[1].Thistheoryallowsfor theso_calledsecond_soundeffectsinsolids,hencethermaldisturbancespropagatewithfinite wavespeeds. Themathematicalmodelofthegeneralizedthermoelasticitytheoryisofacomplicatednature thathindersthepossibilityofderivingananalyticalsolution.Mostattemptsdealingwiththese equationsarebasedoneithershort_timesolution[2-4]. Modernstructur…     

黏弹性准饱和土中球空腔动力特性

在频率域内研究了内水压力作用下分数导数型黏弹性准饱和土中球空腔的稳态动力响应. 通 过引入与孔隙率有关的应力系数合理地确定了介质和孔隙水共同承担的内水压力值. 将土骨 架和衬砌分别视为具有分数导数本构模型的黏弹性体和多孔柔性材料, 基于Biot两相介质模 型, 通过引入位移势函数解耦得到了内水压力作用下分数导数型黏弹性准饱和土中半封闭球 形空腔的位移、应力和孔隙水压力解析表达式. 考察了物性和几何各参数对球形空腔动力响 应的影响, 结果表明: 分数导数本构模型更合理地描述了土体的动力学行为; 饱和度对应力 和孔隙水压力影响较大, 而对位移影响较小.     

幂强化材料和超弹性材料组合球体中孔穴的动态生成

在简单加载条件下,研究幂强化材料和超弹性材料组合球体中的动态孔穴生成和增长问题,首先在有限变形动力学的框架下建立了相应的非线性数学模型,得到了应力的表达式,利用变量变换的方法求得了外加载荷和孔穴半径之间的一个精确的微分关系式,证明了当突加载荷超过其临界值时,球体内部有孔穴的突然生成,并随时间呈现非线性的周期振动．通过数值计算,分析了材料参数和球体的半径比对孔穴生成和增长的影响,并与相应的静态结果进行了比较．结果发现,惯性力的影响降低孔穴生成的临界载荷,而且材料的塑性对孔穴生成和增长有明显的影响．     

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress (MCS) theory. Although many models have been incorporated into the literature, there is still room for introducing an improved model in this context. In this work, we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity. The MCS theory is used to investigate the material length scale effects. Using the Laplace transform, the temperature, deflection, displacement, flexure moment, and stress field variables of the micro-beam are derived. The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced. The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.