Features of evolution of wedge-shaped twins in bismuth single crystals subjected to polysynthetic twinning

Features of evolution of wedge-shaped twins in bismuth single crystals with polysynthetic twins are examined. Polysynthetic twins are found to promote an increase in number, and a decrease in length, of indentation-induced wedge-shaped twins. The latter quantities depend on the density of twins in a polysynthetic twin. Based on the dislocation model, stress fields in the vicinity of wedge-shaped and polysynthetic twins are calculated at a mesoscopic level. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 208–216, May–June, 2008.     

Dislocation Model of Polysynthetic Shear Bands in Amorphous Materials

A dislocation model for a polysynthetic shear band in an amorphous material is proposed. The stress fields near the polysynthetic shear band are calculated. The distribution of impurities in an amorphous binary Fe–B medium containing a polysynthetic shear band is determined.     

考虑拉压强度差效应的厚壁圆筒承载能力分析

应用双剪统一强度理论，考虑材料的拉压异性和同性，推导了在内压力和轴力联合作用下的厚壁圆筒的塑性极限载荷表达式．在该表达式中，当反映中间主应力效应的系数取不同的值时，就能得到按Tresca屈服准则、线性逼近的Mises屈服准则和双剪应力屈服准则的计算结果，并且绘制了在相应准则下的极限应力线图．从而可知：在三维应力状态下，应用该理论，可以获得极限载荷分析的精确解；极限载荷线图与三种屈服准则的屈服曲线是相吻合的；计算的结果可以用于拉压异性和同性的材料，为工程应用提供了理论依据．     

Influence of the boundary conditions on the stress state of a flexible cylindrical shell of variable stiffness in a magnetic field

The effect of the boundary conditions on the stress state of a circular cylindrical shell of variable thickness (stiffness) is analyzed using a geometrically nonlinear problem statement. The cylindrical shell is subject to a magnetic field, external electric current, and nonstationary mechanical load. Numerical results are presented and analyzed     

Static and dynamic buckling modes of a cylindrical shell under external pressure

We consider the problem of static and dynamic buckling modes of thin shells under external hydrostatic pressure. If the statement of the problem uses the linearized equations of motion obtained in the moderately large bending theory of shells according to the classical or refined model, then part of terms related to the external load in these equations are assumed to be conservative, and the other terms are assumed to be nonconservative. In this connection, we study four statements of the elastic stability problem for a cylindrical shell with hinged faces. The first of them is the statement of the static boundary value problem in the sense of Euler, where the action of external pressure is assumed to be conservative. The second statement is used to study small vibrations near the static equilibrium by a dynamic method for the same conservative load. The third and fourth statements of the problem correspond to the action of a nonconservative load and are similar to the first and second statements, respectively. They use the linearized equations of equilibrium and motion constructed earlier in a consistent version on the basis of a Timoshenko type model and allowing one to reveal all classical and nonclassical shell buckling modes.     

Flexural Stress Concentration Near a Hyperboloidal Neck in a Transversely Isotropic Piezoceramic Cylinder

The general solution of the electroelastic problem for a transversely isotropic hyperboloid of revolution is used to find the stress concentration near a hyperboloidal neck in a piezoceramic body subjected to bending. The solution is a sum of four partial solutions for the case where the forces and the normal component of the induction vector on the neck surface are equal to zero. Numerical examples are given for specific external loads and properties of the body. The stress components and normal component of the induction vector near the neck vertex are plotted as a function of the external load and neck curvature     

用双剪应力屈服准则求轴对称球扁壳的极限荷载

本文导出轴对称球面扁壳在双剪应力屈服下的极限条件，并求出周边固定简支情况下的极限载荷。     

A crystal plasticity theory for latent hardening by glide twinning through dislocation transmutation and twin accommodation effects

Imagine a residual glide twin interface advancing in a grain under the action of a monotonic stress. Close to the grain boundary, the shape change caused by the twin is partly accommodated by kinks and partly by slip emissions in the parent; the process is known as accommodation effects. When reached by the twin interface, slip dislocations in the parent undergo twinning shear. The twinning shear extracts from the parent dislocation a twinning disconnection, and thereby releases a transmuted dislocation in the twin. Transmutation populates the twin with dislocations of diverse modes. If the twin deforms by double twinning, double-transmutation occurs even if the twin retwins by the same mode or detwins by a stress reversal. If the twin deforms only by slip, transmutation is single. Whether single or double, dislocation transmutation is irreversible. The multiplicity of dislocation modes increases upon strain, since the twin finds more dislocations to transmute upon further slip of the parent and further growth of the twin. Thus, the process induces an increasing latent hardening rate in the twin. Under profuse twinning conditions, typical of double-lattice structures, this rate-increasing latent hardening combined with crystal rotation to hard orientations by twinning is consistent with a regime of increasing hardening rate, known as Regime II or Regime B. In this paper, we formulate governing equation of the above transmutation and accommodation effects in a crystal plasticity framework. We use the dislocation density based model originally proposed by Beyerlein and Tomé (2008) to derive the effect of latent hardening in a transmuting twin. The theory is expected to contribute to surmounting the difficulty that current models have to simultaneously predict under profuse twinning, the stress-strain curves, intermediate deformation textures, and intermediate twin volume fractions.     

Study of possible void nucleation and growth in solids in the framework of the Davis-Nadai deformation theory

In the framework of the Davis-Nadai deformation theory, we study the problem of a ball with a central cavity subjected to internal and external pressure. The solution is constructed in the reference configuration for the polynomial material deformation law with possible regard to matter conservation inside the cavity. The obtained solution is analyzed; it is mathematically proved that the limit load exists in the case of uniform compression, and a method for determining this load is given. It is also proved that a new void can be formed in a solid ball in the case of its extension, and the critical load of void formation is estimated. It is shown that the already existing spherical void cannot completely disappear under the action of external pressure (assuming that its shape is preserved and remaining in the framework of the continuity hypothesis).     

Finding the elastic strain limit at the tip region of a physical cut with arbitrarily loaded faces

A model describing the stress-strain state in the neighborhood of a physical cut with an arbitrary distribution of external load along its faces is presented. The stress-strain state of a material layer bounded by the continuations of the cut faces is considered. The interaction between the layer and the external half-planes leads to a closed system of integrodifferential equations for the mean stress components in the layer, which splits into two equations for the mean normal stresses and an equation for the mean shear stress. Numerical solutions of the system for the cases of symmetric and antisymmetric loading of the faces by concentrated forces are given. Conditions for the transition of the tip region of the cut to the state of plasticity and fracture are considered.     

Transient response of a cracked piezoelectric strip under arbitrary electro-mechanical impact

By using the well-developed integral transform methodology, the dynamic response of stress and electric displacement around a finite crack in an infinite piezoelectric strip are investigated under arbitrary dynamic anti-plane loads. The dynamic stress intensity factors and electric displacement are obtained analytically. It is shown that the dynamic crack-tip stress and electric field still have a square-root singularity. Numerical computations for the dynamic stress intensity factor show that the electric load has a significant influence on the dynamic response of stress field. The higher the ratio of the crack length to the width of the strip, the higher the peak value of the dynamic stress intensity factor is. On the other hand, the dynamic response of the electric field is determined solely by the applied electric load. The electric field will promote or retard the propagation of the crack depending on the time elapse since the application of the external electro-mechanical loads. The project supported by the National Natural Science Foundation of China and the Post-Doctor Science Foundation of China     

Mechanics of adhesive joints

Summary Taking into consideration both the pulling and bending actions of the external force, the differential equations for bending of a partly attached tape in a peeling test have been derived. The equations relating the peeling load to the adhesive force were derived under the assumption that the peeling may proceed step by step from the attached end when the adhesive force is overcome by either the tensile stress along the interface (shearing peeling) or that which is perpendicular to the interface (tensile peeling). To verify the validity of the obtained equations, the dependence of the peeling load P on the angle between the direction of the action of the load and the adhering surface has been investigated using plasticized polymer films. In view of the elementary mechanics, the results were satisfactory, while a modification was attempted by introducing the stress concentration factor.     

用切比雪夫多项式研究短梁的弯曲计算

考虑剪切效应,利用切比雪夫多项式构造严格满足表面切应力边界条件的轴向位移表达式,建立了短梁弯曲问题的新理论．利用奇异函数把作用在短梁上的复杂外载荷表示为分布载荷,推导出了短梁弯曲时的截面正应力公式及挠曲线表达式．把采用切比雪夫多项式推导出短梁的弯曲计算公式计算结果与弹性理论计算结果进行比较,可知该方法的计算精度较高．研究结果表明：在复杂外载荷作用下,当长高比小于等于6时,剪切变形对梁的弯曲挠度影响较大,而当长高比小于3时,剪切变形对梁的弯曲应力影响较大;因此建议采用切比雪夫多项式方法给出的挠度表达式、弯曲应力进行计算,因为切比雪夫多项式方法不但给出了复杂外载荷作用下梁截面挠度、弯曲应力的计算通式,而且该方法具有计算过程简便、精度高的优点．     

Effects of vertical exciting force of a tracked vehicle on the dynamic compaction of a high lifted decomposed granite

The main purpose of this paper is to evaluate the effects of a jumping action of a tracked vehicle mounted with a vertical oscillator on vibro-compaction of a high lifted decomposed granite. A vibro-compaction test was executed using a model tracked vehicle of 4.9 kN weight under a condition of frequency of 16 Hz and load ratio of maximum vertical exciting force to vehicle weight of 0.2–2.0. As a result, it was observed that both the amount of sinkage of terrain surface and the dry density of soil increased hyperbolically with increment of the load ratio and the dry density distribution with depth became uniform for the whole depth of the soil stratum. It was confirmed that the volume shrinkage of soil was succeeded by the propagation of acceleration to deep stratum due to the jumping action and the dilatancy phenomenon due to an alternative shear stress. The optimum load ratio obtaining a maximum dry density at the frequency of 16 Hz was judged to be 2.0 within this experiment. In the application of these test results to an actual prototype tracked vehicle of 39.2 kN weight, it was estimated that the degree of compaction of a high lifted soil stratum of 90 cm became over 90% at the load ratio of 2.0.     

An analytical solution of an axisymmetric problem of deforming an isotropic half-space with an elastic fixed boundary under the action of a distributed load

An analytical solution to the axisymmetric problem on the action of a distributed load on an isotropic half-space when the load is given by a function dependent on the radial coordinate is obtained. The surface of the half-space is elastically fixed outside the circular domain of load application, the shear stresses are absent along the entire boundary, and the stresses vanish at infinity. At the boundary and inside the elastic half-space, the solutions are represented by the formulas for the stress tensor components and for the displacement vector components.     

基于新型广义位移的箱形梁扭转单元及应用

为了改进变截面连续箱梁桥的扭转分析理论,将截面总扭转角分解为自由翘曲扭转角和约束剪切扭转角,选取自由翘曲转角扭率作为广义位移,提出一个2节点8自由度的扭转梁段单元。从约束扭转控制微分方程出发,推导单元刚度矩阵及等效节点荷载列阵。引入应力增大系数,以反映约束扭转对初等梁应力的增大效应。数值算例验证了本文梁段单元的可靠性。最后对一个三跨变截面连续箱梁桥进行分析,结果表明,双力矩影响线与弯矩影响线较为类似,按双力矩影响线进行最不利荷载加载时最大应力值偏小;应力增大系数在集中荷载作用截面出现极值,均发生在腹板与顶板交点处;利用偏载放大系数来考虑扭转附加效应时,不宜考虑弯曲正应力较小及翘曲正应力出现极值的梁段区域。     

用双剪屈服准则对钢筋混凝土板进行塑性铰线的极限分析

利用双剪屈服准则建立了用机动法计算钢筋混凝土薄板极限载荷的新的塑性铰线理论，并导出了双向布置钢筋的钢筋混凝土板的屈服条件，实例计算表明其更符合实验结果。     

Saturation of a plate with an environmental impurity under mechanical loading conditions

We analyze a model of saturation of a thin plate with an alloying element under uniform loading with a distributed constant load. The appearance of internal stresses accompanying the diffusion processes is taken into account as well as the effect of the stresses on the mass transfer. The exact solution of the mechanical equilibrium problem has allowed us to reduce the model to a nonlinear diffusion problem with a convective term responsible for mass transfer under the action of stresses. We have found that the external loading significantly affects the process if the magnitude of the distributed load is greater than that of the internal stresses, which, in turn, depends on the material properties and the diffusant type. The time-dependence curves of the average strains in the direction of the acting load are typical of the phenomena of diffusion creep.     

Propagation of thin plastic zones in the vicinity of a normally separating crack

A problem of the development of a plastic zone in the vicinity of a physical cut in the plain strain and stress states is posed and solved on the basis of a discrete deformation model under the assumption of an ideal elastoplastic medium. The Tresca yield condition and the ultimate plasticity condition are used in studying the plane stress state. The dependence of the plastic zone length on the external load is compared with a similar dependence obtained on the basis of the Leonov-Panasyuk-Dugdale model. In contrast to the Leonov-Panasyuk-Dugdale model, the distributions of stresses and lengths of plastic zones in the plane strain and stress states are found to be substantially different if elastic compressibility and compressive-tensile stresses along the cut direction are taken into account.     

陶瓷基复合材料基体唇形裂纹失效规律研究

建立横向拉伸载荷下的唇形裂纹数学模型,采用复变函数的方法,通过保角映射,推导了唇形裂纹尖端应力场和位移场的解析解,建立了唇形裂纹的应力强度因子准则和最大能量释放率准则,结合算例分析陶瓷基复合材料基体唇形裂纹的几何参数、外载荷和纤维分布对失效准则的影响规律.结果 表明,(1)裂纹尖端应力场和位移场的解析解与有限元计算结果...