单晶铜中的类层错四面体稳定性

层错四面体作为受核辐照作用金属材料中一类常见的三维缺陷,会极大的改变材料塑性变形行为.论文借助分子静力学和分子动力学方法,针对不同构型、不同尺寸的类层错四面体,考察了不同形状空位团簇演化为类层错四面体的位错反应机理和形成能变化趋势,研究了类层错四面体附近空位形成能分布特征和最小空位形成能随类层错四面体尺寸增大的变化规律,分析了含不同构型、不同尺寸的类层错四面体铜单晶体的微观变形机理和单晶体屈服应力随类层错四面体尺寸增大的变化规律.研究发现:类层错四面体通过Silcox-Hirsch机制形成,且经历了空位团簇坍塌、Frank位错环分解和Shockley位错交汇形成层错四面体棱边三个过程;类层错四面体附近最小空位形成能随着类层错四面体尺寸变化而变化,且变化趋势与类层错四面体构型在稳态、亚稳态和非稳态之间过渡相关,稳态无尖端类层错四面体的最小空位形成能变化趋势表现出明显的尺寸效应;剪切会导致含类层错四面体铜单晶体产生两类层错四面体位错开动模式,即:斜面Shockley偏位错滑移和层错四面体底面压杆位错分解,且含类层错四面体的单晶体屈服应力基本上随着类层错四面体尺寸增大而逐渐减小.     

离散罚函数法在层合板稳定性计算中的应用

为保证复合材料夹层板稳定性计算中层间变形的协调性,本文采用了离散罚函数方法。     

Orientation effects in nanoindentation of single crystal copper

Numerical simulations and experimental results of nanoindentation on single crystal copper in three crystallographic orientations [(1 0 0), (0 1 1) and (1 1 1)] using a spherical indenter (3.4 μm radius) were reported. The simulations were conducted using a commercial finite element code (ABAQUS) with a user-defined subroutine (VUMAT) that incorporates large deformation crystal plasticity constitutive model. This model can take full account of the crystallographic slip as well as the orientation effects during nanoindentation. Distributions of the out-of-plane displacements and shear stresses as well as shear strains were obtained for indentation depths of up to 310 nm. The experimental studies were conducted using an MTS Nano Indenter (XP) system from which the load–displacement relationships were obtained while the surface topography as well as the surface profile along a line scan of indents were obtained using a Digital Instruments (Dimension 3100) atomic force microscope (AFM). The top views of the indent pile-up patterns under the spherical indenter show two-fold, three-fold, and four-fold symmetries for the (0 1 1), (1 1 1), and (1 0 0) orientations, respectively. Attempt was made to relate the anisotropic nature of the surface topographies around the indents in different crystallographic orientations of the single crystal copper specimens with the active slip systems and local texture variations. A reasonably good agreement had been obtained on several aspects of nanoindentation between the experimental and numerical results reported in this investigation as well as similar results reported in the literature. Thus, material properties of single crystal copper can be determined based on an appropriate numerical modeling of the nanoindentation on three crystallographic orientations.     

Multiscale dislocation dynamics simulations of shock compression in copper single crystal

Ultra short pulse shock wave propagation, plastic deformation and evolution of dislocations in copper single crystals with (0 0 1), (0 1 1) and (1 1 1) orientations are investigated using multiscale dislocation dynamics plasticity analyses. The effects of peak pressure, pulse duration, crystal anisotropy and the nonlinear elastic properties on the interaction between shock wave and dislocations are investigated. The results of our calculations show that the dislocation density has a power law dependence on pressure with a power of 1.70 and that the dislocation density is proportional to pulse duration and sensitive to crystal orientation. These results are in very good agreement with the analytical predications of Meyers et al. [Meyers, M.A., Gregori, F., Kad, B.K., Schneider, M.S., Kalantar, D.H., Remington, B.A., Ravichandran G., Boehly, T., Wark, J., 2003. Laser-induced shock compression of monocrystalline copper: characterization and analysis. Acta Materialia 51, 1211–1228] and the experimental results of Murr [Murr, L.E., 1981. Residual microstructure-mechanical property relationships in shock loaded metals and alloys. In: Meyers, M.A., Murr, L.E. (Eds.), Shock Waves and High Strain Rate Phenomena in Metals. Plenum, New York, pp. 607–673]. It is shown also that incorporating the effect of crystal anisotropy in the elastic properties results in orientation dependent wave speed and peak pressure. The relaxed configurations of dislocation microstructures show the formation of microbands coincident with the slip planes.     

PMN-PT夹层弹性半空间结构中SH波的传播Propagation of SH waves in sandwich structures consisting of PMN-PT single crystal layer and elastic half-spaces

分析了弹性上下半空间和PMN‐PT单晶层组成的夹层结构中SH波的传播性质,PMN‐PT单晶沿[011]c方向极化,宏观上呈mm2对称,且晶体沿角度θ方向切割。基于正交各向异性压电材料和各向同性弹性材料的基本方程,得到了夹层结构中SH波传播时行列式形式的频散方程。通过对数值算例进行分析可以看出,PMN‐PT单晶的切割角度和弹性材料属性对结构中的相速度有很大影响,因此波的某些传播性能可以通过材料的设计以及晶体切割的方向来实现,这些结论为声表面波器件的开发和应用提供了理论依据。     

Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper at mesoscale

Constitutive laws are critical in the investigation of mechanical behavior of single crystal or polycrystalline materials in applications spanning from microscale to macroscale. In this investigation, a combined FEM simulation and experimental nanoindentation approach was taken to determine the mechanical behavior of single crystal copper incorporating the mesoplastic constitutive model. This model was implemented in a user-defined subroutine in 3D ABAQUS/Explicit code. Nanoindentation was modeled using the multiscale modeling technique involving mesoplasticity and elasticity, i.e., mesoplastic constitutive model was used near the local nanoindentation region (where the dislocations are generated) while elastic constitutive model was used in rest of the region in the workmaterial. The meso-mechanical behavior of the crystalline structure and the effect of the mesoplastic parameters on the nanoindentation load-displacement relationships were investigated in the FEM analysis. Nanoindentation tests were conducted on single crystal copper to determine load-displacement relationships. Appropriate mesoplastic parameters were determined by fitting the simulated load-displacement curves to the experimental data. The mesoplastic model, with appropriate parameters, was then used to determine the stress-strain relationship of a single crystal copper at meso-scale. The effect of indenter radius (3.4-) on material hardness under nanoindentation was simulated and found to match the experimental data for several indenter radii (3.4, 10 and ). A comparison of the topographies of nanoindentation impressions in the experiments with FEM results showed a reasonably good agreement.     

Fracture in single crystal NiTi

This paper presents an investigation of the pseudoelastic transformation of two crystallographic orientations of a single crystal NiTi shape memory alloy (SMA). Both uniaxial tension and notched tension samples are considered with the tensile axes along the [1 0 0] and [1 1 1] directions. The phase transformation is observed using optical techniques in situ. For the uniaxial tension samples, martensite plates and Lüders-band structures are observed. For the notched samples, transformation structures in the [1 0 0] sample appeared predominantly on the sides of the notch and crack tip with stable crack propagation. In the [1 1 1] notched samples transformation occurs directly ahead of the notch and unstable crack propagation is observed. An available work criterion is used to predict the location of the transformation, with good agreement to the experimental observations. The different fracture behavior of the two notched sample orientations is explained utilizing the available work calculations.     

Reverse plasticity in single crystal silicon nanospheres

Nanoparticles in the range of 20 to 100 nm in size can be deposited, isolated, and individually probed for their mechanical properties. With a hypersonic plasma particle deposition technique, this has been successfully accomplished for silicon and titanium. We have already shown that silicon nanoparticles are superhard in the 30 to 50 GPa range after work hardening (Gerberich, W.W., Mook, W.M., Perrey, C.R., Carter, C.B., Baskes, M.I., Mukherjee, R., Gidwani, A., Heberlein, J., McMurry, P.H., Girshick, S.L., 2003a. Superhard silicon nanospheres. J. Mech. Phys. Solids 51, 979). At the same time when small nanospheres are compressed, a fraction of the plastic strain is reversed after unloading. Initially, the amount of reverse dislocation motion was small but appeared to accelerate once a threshold strain was reached. The cumulative reverse plastic strain from repeated loading of the same nanosphere appeared to increase from less than 0.04 to approximately 0.4 as cumulative strain increased from 0.2 to 0.6. For large strains then, it appears that a greater amount of plastic strain is recovered after unloading. This can at least partially be understood in terms of the enormous back stress developed at the small scale when dislocations are only a few nm apart. As the ramifications to nanoscopic features on MEMS, micromachines and magnetic recording devices is considerable, it is desirable to understand if a length scale can be developed for such phenomena. In terms of classic dislocation theory an attempt is made. Problems and prospects are discussed with regards to predictive models for hardness and reverse plasticity.     

Stability conditions for tensegrity structures

Stability conditions for tensegrity structures are derived based on positive definiteness of the tangent stiffness matrix, which is the sum of the linear and geometrical stiffness matrices. A necessary stability condition is presented by considering the affine motions that lie in the null-space of the geometrical stiffness matrix. The condition is demonstrated to be equivalent to that derived from the mathematical rigidity theory so as to resolve the discrepancy between the stability theories in the fields of engineering and mathematics. Furthermore, it is shown that the structure is guaranteed to be stable, if the structure satisfies the necessary stability condition and the geometrical stiffness matrix is positive semidefinite with the minimum rank deficiency for non-degeneracy.     

Stability conditions of prestressed pin-jointed structures

Pin-jointed structures are first classified to trusses, tensile structures, and tensegrity structures in view of their respective stability properties. A sufficient condition for stability of an equilibrium state is derived for tensegrity structures. The condition is based on the bilinear forms of the linear and geometrical stiffness matrices considering the flexibility of members. The stability is defined by the positive definiteness of the tangent stiffness matrix, whereas the definition of prestress-stability is based on the geometrical stiffness matrix and the infinitesimal mechanisms. Numerical examples verify that the so-called super-stability condition might not be satisfied by a stable tensegrity structure, and that a prestress-stable structure can be unstable if the prestresses are moderately large.