微压痕尺度效应的理论和实验

对压入深度为亚微米量级的微压痕实验来说,硬度与压入深度的关系将表现出强烈的尺度效应,然而,由传统的弹塑性理论无法预测.采用塑性应变梯度理论对微压痕实验中的尺度效应进行预测;同时对单晶铜和单晶铝进行微压痕实验研究.通过将理论预测结果应用于实验,获得塑性应变梯度理论中的微尺度参量值,该值对于常规金属材料（如铜、铝、银等）来说,取值范围为0.8～1.5　μm.另外,对微压痕边界附近所出现的挤出现象（pile-up）和沉陷现象（sink-in）进行了预测和详细分析.     

金属薄膜沿陶瓷基界面脱胶的微尺度力学研究

采用考虑微尺度效应的塑性应变梯度理论研究弹塑性 (非线性 )脱胶现象 .针对金属 /陶瓷界面非线性脱胶机理 ,分别采用两种断裂过程区模型进行分析 .通过将所得结果应用于铜 /二氧化硅的实验结果中 ,获得对应该体系的微尺度值及无位错核厚度值 .     

轴向冲击下理想塑性直杆动态屈曲的过应力简化分析模型*

本文在理想塑性直杆的动态屈曲分析中引入应变率效应,得到相应的动力学微分方程,求出了屈曲半波长,临界载荷和屈曲时间的表达式.讨论了应变率效应对杆的塑性动态屈曲的影响.并与文[4]的理论和试验结果作了比较.     

Ⅰ型动态扩展裂纹尖端的弹粘-理想塑性场

由于材料在扩展裂纹尖端的粘性效应的存在,考虑粘性效应并假设粘性系数与塑性等效应变率的幂次成反比,对理想塑性材料中平面应变扩展裂纹尖端场进行了弹粘塑性渐近分析,得到了不含间断的连续解,并讨论了Ⅰ型裂纹数值解的性质随各参数的变化规律．分析表明,应力和应变均具有幂奇异性,通过分析使尖端场的弹、粘、塑性可以合理匹配．对于Ⅰ型裂纹,裂尖场不含弹性卸载区．趋于极限情况时,裂纹尖端处于一种超粘性状态,并积聚了大量的能量,在各个受压应力状态下裂纹扩展．     

圆柱正交异性复合厚壁圆筒的弹-塑性分析

本文导出了不可压缩和可压缩材料,平面应变问题的Tsai-Hill屈服准则形式;研究了在均匀径向压力作用下圆柱正交异性复合厚壁圆筒的弹-塑性应力场和位移场.求得了弹性屈服压力、极限载荷和安定载荷的公式.     

利用内聚力模型(CZM)模拟弹粘塑性多晶体的裂纹扩展

采用内聚力模型（CZM）,模拟多晶体中起裂于晶界的二维平面应变裂纹扩展．结果表明,弹粘塑性体中,初始裂纹尖端不会最先开裂．晶体本构的率敏感指数表征了塑性变形和内聚力区耗散两种机制的相互竞争．率敏感指数越大,塑性耗散能越大,内聚力区粘着能越小,使材料的塑性变形越容易,内聚力区诱发的破坏越不易;率敏感指数越小,材料响应越接近弹塑性性质,塑性耗散能减小,粘着能增大,外力功易转化为内聚力区的粘着能,使内聚力单元更易分离．增大内聚力区结合强度或临界张开位移使晶内和晶界的三轴应力度减小,即提高内聚力区韧性也使基体材料抗孔洞损伤能力提高．     

线性硬化材料中稳恒扩展裂纹尖端场的粘塑性解

采用弹粘塑性力学模型,对线性硬化材料中平面应变扩展裂纹尖端场进行了渐近分析．假设人工粘性系数与等效塑性应变率的幂次成反比,通过量级匹配表明应力和应变均具有幂奇异性,奇异性指数由粘性系数中等效塑性应变率的幂指数唯一确定．通过数值计算讨论了Ⅱ型动态扩展裂纹尖端场的分区构造随各材料参数的变化规律．结果表明裂尖场构造由硬化系数所控制而与粘性系数基本无关．弱硬化材料的二次塑性区可以忽略,而较强硬化材料的二次塑性区和二次弹性区对裂尖场均有重要影响．当裂纹扩展速度趋于零时,动态解趋于相应的准静态解;当硬化系数为零时便退化为HR(Hui-Riedel)解．     

率相关晶体塑性模型的塑性各向异性分析

在Sarma和Zacharia的工作基础上,改进了单晶晶体弹粘塑性本构模型的积分算法,并采用改进的欧拉法结合迭代方法求解,特点是稳定性好计算效率较高．然后用上述模型及算法研究了:1）在单向拉伸和平面应变压缩变形下单晶塑性各向异性的特点;2）晶体模型中的主要材料参数（应变率敏感指数m和潜硬化比率q）和加载应变率对单晶塑性各向异性的影响;3）沿不同的晶体方向加载对滑移系启动的影响．     

Ⅲ型弹粘塑性/刚性界面裂纹的定常扩展裂尖场

考虑裂纹尖端的奇异性和粘性效应,建立了双材料界面扩展裂纹尖端的弹粘塑性控制方程．引入界面裂纹尖端的位移势函数和边界条件,对刚性-弹粘塑性界面Ⅲ型界面裂纹进行了数值分析,求得了界面裂纹尖端应力应变场,并讨论了界面裂纹尖端场随各影响参数的变化规律．计算结果表明,粘性效应是研究界面扩展裂纹尖端场时的一个主要因素,界面裂纹尖端为弹粘性场,其场受材料的粘性系数、Mach数和奇异性指数控制．     

一种基于无屈服概念的粘塑性模型

结合位错运动的热激活理论,基于无屈服概念,提出了一组描述金属材料变形规律的弹/粘塑性本构方程.方程从总体上考虑了应变率、应变历史、应率变历史、硬化和温度等效应,具有较强的物理基础.恒温单轴条件下商业纯钛的力学性能的理论预测与实验结果相比较,存在着良好的一致性.     

Strain gradient plasticity solution for an internally pressurized thick-walled cylinder of an elastic linear-hardening material

An elastic-plastic solution is presented for an internally pressurized thick-walled plane strain cylinder of an elastic linear-hardening plastic material. The solution is derived in a closed form using a strain gradient plasticity theory. The inner radius of the cylinder enters the solution not only in non-dimensional forms but also with its own dimensional identity, which differs from that in classical plasticity based solutions and makes it possible to capture the size effect at the micron scale. The classical plasticity solution of the same problem is recovered as a special case of the current solution. To further illustrate the newly derived solution, formulas and numerical results for the plastic limit pressure are provided. These results reveal that the load-carrying capacity of the cylinder increases with decreasing inner radius at the micron scale. It is also seen that the macroscopic behavior of the pressurized cylinder can be well described by using classical plasticity based solutions.     

Strain gradient plasticity solution for an internally pressurized thick-walled cylinder of an elastic linear-hardening material

An elastic-plastic solution is presented for an internally pressurized thick-walled plane strain cylinder of an elastic linear-hardening plastic material. The solution is derived in a closed form using a strain gradient plasticity theory. The inner radius of the cylinder enters the solution not only in non-dimensional forms but also with its own dimensional identity, which differs from that in classical plasticity based solutions and makes it possible to capture the size effect at the micron scale. The classical plasticity solution of the same problem is recovered as a special case of the current solution. To further illustrate the newly derived solution, formulas and numerical results for the plastic limit pressure are provided. These results reveal that the load-carrying capacity of the cylinder increases with decreasing inner radius at the micron scale. It is also seen that the macroscopic behavior of the pressurized cylinder can be well described by using classical plasticity based solutions.     

Strain gradient solutions of half-space and half-plane contact problems

General solutions for the problems of an elastic half-space and an elastic half-plane, respectively, subjected to a symmetrically distributed normal force of arbitrary profile are analytically derived using a simplified strain gradient elasticity theory (SSGET) that contains one material length scale parameter. Mindlin’s potential function method and Fourier transforms are employed in the formulation, and the half-space and half-plane contact problems are solved in a unified manner. The specific solutions for the problems of a half-space/plane subjected to a concentrated normal force or a uniformly distributed normal force are obtained by directly applying the general solutions, which recover the existing classical elasticity-based solutions of the Flamant and Boussinesq problems as special cases. In addition, the indentation problems of an elastic half-space indented by a flat-ended cylindrical punch, a spherical punch, and a conical punch, respectively, are solved using the general solutions, leading to hardness formulas that are indentation size- and material microstructure-dependent. Numerical results reveal that the displacement and stress fields in a half-space/plane given by the current SSGET-based solutions are smoother than those predicted by the classical elasticity-based solutions and do not exhibit the discontinuity and/or singularity displayed by the latter. Also, the indentation hardness values based on the newly obtained half-space solution are found to increase with decreasing indentation radius and increasing material length scale parameter, thereby explaining the microstructure-dependent indentation size effect.     

Stress distribution near a reinforced elliptical hole in a spherical shell at the elastoplastic stage of deformation

On the basis of Lagrange's variational equation the authors obtained nonlinear resolvent equations and coefficients taking into account the effect of a reinforcing element (a rod) on the state of stress and strain of a spherical shell weakened by a curvilinear (elliptical) hole. The article explains the method of numerical investigation of the inelastic state of the shell based on the application of the variational difference method in combination with the method of elastic solutions. The inelastic state of a shell with a reinforced hole was numerically investigated.Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 80–83, 1990.     

Analysis of the structure of the boundary layer in the problem of the torsion of a laminated spherical shell

The structures of the boundary layer in the problem of the torsion of a radially stratified spherical segment (shell) with an arbitrary number of alternating hard and soft layers are investigated. It is shown that weakly attenuating boundary-layer solutions exist. Despite the fact that a stress state, self-balanced in the section, corresponds to these elementary solutions, they may penetrate fairly deeply and considerably change the stress–strain state pattern far from the ends. Using an asymptotic analysis of the problem, an applied theory of torsion is proposed which takes into account weakly attenuating boundary-layer solutions.     

The Axisymmetric Deformation of a Thin,or Moderately Thick,Elastic Spherical Cap

A refined shell theory is developed for the elastostatics of a moderately thick spherical cap in axisymmetric deformation. This is a two-term asymptotic theory, valid as the dimensionless shell thickness tends to zero.The theory is more accurate than “thin shell” theory, but is still much more tractable than the full three-dimensional theory. A fundamental difficulty encountered in the formulation of shell (and plate) theories is the determination of correct two-dimensional boundary conditions, applicable to the shell solution, from edge data prescribed for the three-dimensional problem. A major contribution of this article is the derivation of such boundary conditions for our refined theory of the spherical cap. These conditions are more difficult to obtain than those already known for the semi-infinite cylindrical shell, since they depend on the cap angle as well as the dimensionless thickness. For the stress boundary value problem, we find that a Saint-Venant-type principle does not apply in the refined theory, although it does hold in thin shell theory. We also obtain correct boundary conditions for pure displacement and mixed boundary data. In these cases, conventional formulations do not generally provide even the first approximation solution correctly. As an illustration of the refined theory, we obtain two-term asymptotic solutions to two problems, (i) a complete spherical shell subjected to a normally directed equatorial line loading and (ii) an unloaded spherical cap rotating about its axis of symmetry.     

A flexoelectric spherical microshell model incorporating the strain gradient effect

In this paper, a size-dependent flexoelectric spherical microshell model is proposed considering flexoelectric effect and strain gradient effect. By means of the variation principle, explicit expressions of the governing equations and the boundary conditions are deduced. Solving corresponding governing equations, analytical solutions of both direct and converse flexoelectric responses in static axisymmetric bending problem are obtained. Then, the flexoelectric responses in barium strontium titanate spherical microshells with and without a circular top opening are numerically investigated. Both the direct and converse flexoelectric responses are found to vary non-monotonically as the central angle increases. The converse flexoelectric bending is examined to exist even in clamped spherical microshells, which is different from the case of flat structures. In addition, for all cases, the strain gradient effect will highly reduce the flexoelectric responses, particularly when the thickness approaches the material internal scale constants.     

The steady motion of an elastic cylinder compressed by a fixed shell

The steady mixed problem of the motion of a transversely isotropic elastic circular cylinder, compressed by a finite elastic shell, is solved by the method of piecewise-homogeneous solutions [1]. One of the relations of generalized orthogonality obtained for homogeneous solutions is used. Two special cases are considered: (1) a semi-infinite shell is placed on a movable cylinder with a specified negative allowance the edge of the shell is stress-free, and there is no preloading, and (2) a concentrated encircling load acts on the shell. The solution of the problem of a semi-infinite shell and the system of piecewise-homogeneous solutions are constructed in quadratures by the Wiener-Hopf method. (A similar problem was investigated in [2] in a static formulation. Steady mixed contact problems were investigated previously in [3–10]).     

Two non-holonomic integrable problems tracing back to Chaplygin

The paper considers two new integrable systems which go back to Chaplygin. The systems consist of a spherical shell that rolls on a plane; within the shell there is a ball or Lagrange’s gyroscope. All necessary first integrals and an invariant measure are found. The solutions are shown to be expressed in terms of quadratures.     

圆筒在内外压力作用下的有限位移问题

本文用逐次逼近法求得这个边值问题的一次解和二次解,从而获致位移场,应变场和应力场的二级近似公式,我们的结果还表明:在变形后,(i)圆筒任一截面必位移至另一仍与筒轴垂直的平面上;(ii)应变分量E_RR(2)与E_ΦΦ(2)之和以及应力分量∑_RR(2)与∑_ΦΦ(2)之和在整个圆筒内均不保持恒定。后一效应是经典弹性理论里所没有的,它对∑_ZZ(2)的产生承担责任,此外,∑_ZZ(2)与(∑_RR(2)+∑_ΦΦ(2))之间呈现线性关系,其比例系数仅与圆筒的材料有关。