Effect of stresses and strains on impurity redistribution in a plate under uniaxial loading

A model for the saturation of the surface layer of a thin metal plate with an impurity from the environment under uniaxial mechanical loading is proposed and investigated. The effect of stresses and strains on the diffusion process is analyzed. It is shown that, first, due to the deformation of the crystal lattice of the base, stresses that occur in local volumes lead to a change in the diffusion activation energy; second, stresses influence impurity transfer (this effect is similar to mass transfer by pressure diffusion in liquids). The joint effect of the two types of influences of stresses and strains on the behavior of the system at various geometrical and physical sample parameters is numerically investigated.     

Effect of loading conditions on regimes of solid-phase transformations in a plate

A two-dimensional mathematical model of propagation of chemical conversion in a plate under mechanical loading is proposed. The problem is numerically studied for three variants of loads and displacements on the plate surfaces: clamped plate, uniaxial tension, and shear. As the fields of temperatures, concentrations, and stresses are coupled, the conversion modes under different loading conditions are found to be different. By means of a parametric study of the model, it is demonstrated that the value of internal stresses may be substantially higher than the external load.     

A GENERALIZED THERMOELASTIC DIFFUSION PROBLEM OF THIN PLATE HEATED BY THE ULTRASHORT LASER PULSES 1)

由于超短激光脉冲具有功率密度高、持续时间短、加工精度高等优势, 近年来被广泛应用于超精细加工、光学储存和微电子器件制造等领域. 本文基于L-S型广义热弹扩散理论, 建立了考虑材料记忆依赖效应和空间非局部效应的记忆依赖型非局部广义热弹扩散耦合理论, 它能够准确预测几何尺寸与内部特征尺寸相近结构的热弹扩散瞬态响应. 推导了所建理论的控制方程, 并基于拉普拉斯积分变换获得了控制方程的解. 作为算例, 利用所建理论和求解方法研究了半无限大薄板受非高斯激光脉冲加热和化学冲击联合作用下的热弹扩散瞬态响应问题, 得到了薄板的温度、化学势、位移、应力和浓度等随非局部参数、热时间迟滞因子和扩散时间迟滞因子等参数变化的分布规律. 结果表明: 传热对传质影响显著, 传质对传热影响甚微; 非局部参数对位移、应力影响显著, 对温度、化学势和浓度几乎没有影响. 该理论及求解方法的建立, 旨在实现材料在机械、热、化学势等冲击作用下传热传质瞬态响应的准确预测.     

超短激光脉冲加热薄板的广义热弹扩散问题

由于超短激光脉冲具有功率密度高、持续时间短、加工精度高等优势, 近年来被广泛应用于超精细加工、光学储存和微电子器件制造等领域. 本文基于L-S型广义热弹扩散理论, 建立了考虑材料记忆依赖效应和空间非局部效应的记忆依赖型非局部广义热弹扩散耦合理论, 它能够准确预测几何尺寸与内部特征尺寸相近结构的热弹扩散瞬态响应. 推导了所建理论的控制方程, 并基于拉普拉斯积分变换获得了控制方程的解. 作为算例, 利用所建理论和求解方法研究了半无限大薄板受非高斯激光脉冲加热和化学冲击联合作用下的热弹扩散瞬态响应问题, 得到了薄板的温度、化学势、位移、应力和浓度等随非局部参数、热时间迟滞因子和扩散时间迟滞因子等参数变化的分布规律. 结果表明: 传热对传质影响显著, 传质对传热影响甚微; 非局部参数对位移、应力影响显著, 对温度、化学势和浓度几乎没有影响. 该理论及求解方法的建立, 旨在实现材料在机械、热、化学势等冲击作用下传热传质瞬态响应的准确预测.      

Coupled model of coating formation on a cylindrical substrate

A coupled model of coating formation on the surface of a part of a cylindrical shape during deposition from the plasma is proposed. This model takes into account the phenomena of thermal diffusion, diffusive thermal conductivity, and mass transfer under the action of the stress gradient, and the formation of chemical compounds. The coating growth rate is considered to be a given function of the particle velocity and particle concentration near the surface of the growing coating. The problem is solved numerically. It is shown that diffusion cross-fluxes, diffusive thermal conductivity, and thermal diffusion during the growth process reduce the width of the transition zone between the substrate and the coating. This effect becomes most essential if the substrate has a low thermal conductivity. Accounting for stresses arising in the coating-substrate system during the deposition process changes the effective transfer coefficients and significantly affects the result of modeling the distribution of chemical elements and their compounds in the coating.     

SOME PROBLEMS FOR DYNAMIC COMPUTATION OF CLOSED CYLINDRICAL SHELL DUE TO AXIAL IMPACT LOAD

The present paper treats some of the problems for dynamic computation of closed cylindrical shell due to an axial impact load, including the calculations of the dynamic stresses and the problems of stability. It analyses the changes of the momentums and the energy in the impact process, takes into account the effect of the mass of the striking object and the system of the closed cylindrical shell to be struck, turns the distributed mass of the total cylindrical shell into an "equivalent mass" being concentrated on only at one end of the shell by using the way of reduced mass, and accordingly derives the dynamic factor of the closed cylindrical shell under the axial impact load, hence resolves the questions of calculation of the dynamic stresses in the loaded case mentioned above and found out the critical loading.     

Nonlocal continuum crystal plasticity with internal residual stresses

We derive a three-dimensional constitutive theory accounting for length-scale dependent internal residual stresses in crystalline materials that develop due to a non-homogeneous spatial distribution of the excess dislocation (edge and screw) density. The second-order internal stress tensor is derived using the Beltrami stress function tensor φ that is related to the Nye dislocation density tensor. The formulation is derived explicitly in a three-dimensional continuum setting for elastically isotropic materials. The internal stresses appear as additional resolved shear stresses in the crystallographic visco-plastic constitutive law for individual slip systems. Using this formulation, we investigate two boundary value problems involving single crystals under symmetric double slip. In the first problem, the response of a geometrically imperfect specimen subjected to monotonic and cyclic loading is investigated. The internal stresses affect the overall strengthening and hardening under monotonic loading, which is mediated by the severity of initial imperfections. Such imperfections are common in miniaturized specimens in the form of tapered surfaces, fillets, fabrication induced damage, etc., which may produce strong gradients in an otherwise nominally homogeneous loading condition. Under cyclic loading the asymmetry in the tensile and compressive strengths due to this internal stress is also strongly influenced by the degree of imperfection. In the second example, we consider simple shear of a single crystalline lamella from a layered specimen. The lamella exhibits strengthening with decreasing thickness and increasing lattice incompatibility with shearing direction. However, as the thickness to internal length-scale ratio becomes small the strengthening saturates due to the saturation of the internal stress.Finally, we present the extension of this approach for crystalline materials exhibiting elastic anisotropy, which essentially depends on the appropriate Green function within φ.     

多圆荷载下刚性道面变形和应力的计算

本文建立多圆荷载作用下弹性半空间体上薄板的挠度与应力的计算式。荷载数量及分布任意,每个圆荷载密度与轮迹半径彼此相异。对计算式中的反常积分及级数的收敛性予以证明。对含振荡函数反常积分建议一种方便的算法。     

A semi-analytic solution of a wellbore in a non-isothermal low-permeability porous medium under non-hydrostatic stresses

The transient stress, displacement, pore pressure and temperature fields around a wellbore in a thermo-poro-elastic (THM) medium subject to non-hydrostatic remote stresses are analyzed under non-isothermal plane-strain conditions. The linear THM model proposed by Coussy (1989) is adopted in the analysis with a focus on thermal effects in low-permeability saturated rocks, characterized by a latent heat associated with local changes of fluid mass content. Non-dimensionalized parameters are identified by reformulating the fully-coupled governing equations and boundary conditions. The wellbore problem is simplified by decomposing it into axisymmetric and deviatoric loading cases. The corresponding analytical solutions are obtained in Laplace space. The inverse Laplace transforms are performed numerically to find the time-dependent distributions of field variables in the rock mass around the wellbore. These numerical results show that although the pore pressure diffusion has little influence on temperature and stress, temperature changes can strongly affect the pore pressure and stress around the wellbore. The temperature change can lead to changes in near-well stresses and the resulting significant change in wellbore breakdown pressure illustrates the importance of considering the THM coupling.     

简支及悬臂箱梁在角隅轴向荷载作用下的翼板纵向应力

基于能量变分原理,拟定轴向荷载作用下箱梁的纵向位移函数,得到关于翼板剪切变形引起的位移差函数的基本微分方程,继而推导出箱梁翼板纵向应力表达式,并首次得出角隅轴向荷载作用下翼板出现应力不均匀分布的荷载及边界条件。通过对一模型箱梁进行计算,并与通用有限元软件ANSYS壳单元计算结果进行比较,验证了该方法和所推导公式的正确性。研究结果表明,当作用于简支箱梁截面角隅处的轴向荷载（合力无偏心）为集中或分布荷载时,翼板不产生纵向应力不均匀现象;当作用于悬臂箱梁截面角隅处的轴向荷载（合力无偏心）为集中荷载时,翼板不产生纵向应力不均匀现象,而当荷载轴向分布时,翼板将产生纵向应力不均匀现象。实际工程中,横力弯曲使悬臂箱梁产生剪力滞效应,这种效应会与轴向分布荷载产生的效应叠加,设计时对此应予以充分考虑。     

Solid-phase combustion in a plane stress state. 2. Stability to small perturbations

Stability of a plane reaction front in the solid phase to small perturbations under conditions of a generalized plane stress state is studied with allowance of the coupled character of heat transfer and deformation processes and possible changes in the reaction rate under the action of internal stresses without external mechanical loading. The problem is solved analytically by the method of perturbations. Conditions of the loss of stability of various conversion regimes in some limiting cases are studied for different technological and physical parameters.     

Some problems for dynamic computation of closed cylindrical shell due to axial impact load

The present paper treats some of the problems for dynamic computation of closed cylindrical shell due to an axial impact load, including the calculations of the dynamic stresses and the problems of stability. It analyses the changes of the momentums and the energy in the impact process, takes into account the effect of the mass of the striking object and the system of the closed cylindrical shell to be struck, turns the distributed mass of the total cylindrical shell into an “equivalent mass” being concentrated on only at one end of the shell by using the way of reduced mass, and accordingly derives the dynamic factor of the closed cylindrical shell under the axial impact load, hence resolves the questions of calculation of the dynamic stresses in the loaded case mentioned above and found out the critical loading.     

Bending-torsional stability analysis of aerodynamically covered pipes with inclined terminal nozzle and concurrent internal and external flows

Stability analysis of a cantilevered pipe with an inclined terminal nozzle as well as simultaneous internal and external fluid flows is investigated in this study. The pipe is embedded in an aerodynamic cover with negligible mass and stiffness simply to streamline the external flow and avoid vortex induced vibrations. The structure of pipe is modeled as an Euler–Bernoulli beam and effects of internal fluid flow including flow-induced inertia, Coriolis and centrifugal forces and the follower force induced by the exhausting jet are taken into account. In addition, neglecting the compressibility effect and using the unsteady Wagner model, aerodynamic loading is determined as a distributed lateral load for any generic structural state. The integral form of coupled equations of motion are obtained using the Hamilton’s principle. Solution to the coupled flexural–torsional equations of motion is realized via the extended Galerkin method. After discretization of the equations of motion, an eigenvalue representation of the problem is obtained. Several parameter studies are then conducted to examine the effects of concurrent fluid flows and other related parameters on the stability margins of the system.     

Complex loading of heterogeneous materials with redistribution of internal mass

The problem of inhomogeneous material with internal friction subjected to complex loading is solved in this paper. Different complex loadings are considered by continuously rotating the principal axes of the strain tensor. A hypoplastic model with internal variables is used to describe the internal structure of the material. The model can describe loading and unloading states. It accounts for essential non-linearity of constitutive equations. The finite element algorithm reduces the problem to a system of nonlinear algebraic equations of high order which are solved by the Newton's method. The results show a good qualitative and quantitative assessment of calculated parameters when compared with data obtained from experiments. Redistribution of internal mass takes place under loading such that a fractal structure is developed in time reflecting the material discontinuities.     

A Prestressed Elastic Strip with Elastic Reinforcements

A contact problem is studied for a prestressed elastic strip with an elastic reinforcement. The integral Fourier transform is used to construct an influence function for an infinite strip with one face fixed. A unit concentrated force is applied to the strip at an arbitrary angle. The contact problem on force transfer from a thin infinite stringer to the prestressed strip is solved. The problem is mathematically formulated as a system of integro-differential equations for the unknown contact stresses on the assumption that the beam bending model and the uniaxial stress model are valid for the stringer, which is subjected to both vertical and horizontal forces. This system is solved in a closed form using the integral Fourier transform. The contact stresses are expressed in terms of Fourier integrals in a quite simple form. The influence of the initial stresses on the contact stress distribution is analyzed, and effects of concentrated load are revealed     

用十字形超细药条离散群同步起爆实现超低比冲量加载

余弦分布载荷的化爆加载技术是高空核爆软X射线辐照下空间结构动态响应考核的主要手段。为适应新型空间飞行器结构考核的复杂构型、高同步性和低比冲量载荷设计要求,提出了一种用十字形超细药条离散群同步起爆实现超低比冲量加载的方法。实验结果验证表明：(1)所制作的十字形超细药条,最小截面尺寸为0.33 mm×0.5 mm,传爆性能稳定,并可通过直径0.5 mm的柔爆索直接起爆;(2)与相同布药密度的条状布药方式相比,布药空间均匀度提高了76.7%;(3)所采用的21点柔爆索同步起爆网络,起爆率达100%,起爆不同步性小于1μs。进一步建立了离散片炸药加载数值计算模型,分析了离散片炸药群同步起爆加载的比冲量空间分布和匀化规律,将匀化过程分为扩散段、叠加段和均匀段3个阶段;对比了方形、十字形、短条形3种形状药片阵列的比冲量演化过程,发现十字形药片所需匀化距离最短、均匀度最高,仅需约0.8倍布药间距即可使比冲量均匀度偏差降至10%以下。     

ANALYTICAL SOLUTIONS FOR THE LAYERED GEO-MATERIALS SUBJECTED TO AN ARBITRARY POINT LOAD IN THE CARTESIAN COORDINATE

This paper presents analytical solutions for the stress and displacement field in elastic layered geo-materials induced by an arbitrary point load in the Cartesian coordinate system. The point load solutions can be obtained by referring to the integral transform and the transfer matrix technique. However, former solutions usually exist in the cylindrical coordinate system subjected to axisymmetric loading. Based on the proposed solutions in the Cartesian coordinate, it is very easy to solve asymmetric problems and consider the condition with internal loads in multi-layered geo-materials. Moreover, point load solutions can be used to construct solutions for analytical examination of elastic problems and incorporated into numerical schemes such as boundary element methods. The results discussed in this paper indicate that there is no problem in the evaluation of the point load solutions with high accuracy and efficiency, and that the material non-homogeneity has a significant effect on the elastic field due to adjacent loading.     

Shear crack propagation in the residual stress field

The problem of propagation of a longitudinal shear crack in a medium with a random field of internal stresses is considered and solved with the use of the theory of quasi-brittle failure. Local criterion of crack propagation under cyclic loading is derived, and its application as a model of fatigue crack propagation is investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 3, pp. 117–119, May–June, 1970.     

Elastic field perturbation by a misfitting ring inclusion

The plane elasticity problem of a circular ring inhomogeneity, with either a hollow or a rigid core, is confronted. A solution is obtained under a wide class of loading conditions, the main limitation being that internal stress sources (if any) are located in the matrix. In order to take into account interfacial residual stresses, misfit between matrix and inhomogeneity is allowed. Loading by misfit alone, by uniform remote stresses, and by an edge dislocation, are explicitly treated as special cases.     

A continuum constitutive model for the mechanical behavior of woven fabrics

We propose a new approach for developing continuum models for the mechanical behavior of woven fabrics in planar deformation. We generate a physically motivated continuum model that can both simulate existing fabrics and predict the behavior of novel fabrics based on the properties of the yarns and the weave. The approach relies on the selection of a geometric model for the fabric weave, coupled with constitutive models for the yarn behaviors. The fabric structural configuration is related to the macroscopic deformation through an energy minimization method, and is used to calculate the internal forces carried by the yarn families. The macroscopic stresses are determined from the internal forces using equilibrium arguments. Using this approach, we develop a model for plain weave ballistic fabrics, such as Kevlar®, based on a pin-joined beam geometry. We implement this model into the finite element code ABAQUS and simulate fabrics under different modes of deformation. We present comparisons between model predictions and experimental findings for quasi-static modes of in-plane loading.