A STUDY OF THE ONSET OF KINK BAND

This paper suggests the asymmetric-plastic theory of crystalline solidsconcerning the plastic rotation of crystal.The deformation of crystalline solidsundergoes three microprocesses:lattice distortion,slip over active crystallographicplanes and the rotation of the crystal.In the asymmetric-plastic theory of crystalsuggested,the corotational rates of symmetric Cauchy stress and moment stresscorrespond to the rates of elastic strain and the gradient of the rotational rate of thecrystal respectively.The Schmid yield condition and Prager's consistency conditionincorporating antisymmetric stress are formulated.Then the asymmetric-plastic modelof crystalline solids is applied for the investigation of the onset of kink band by astandard stability analysis.The orientation of the kink band is perpendicular to theprimary slip system.The width of the kink band is the function of the“characteristiclength”of the microstructure of metal materials.     

Plastic deformation modelled as a self-excited wave process at the meso- and macro-level

A self-excited wave model is developed to describe plastic flow phenomena in crystalline solids. Experimental observations suggest that by plastic flow in single crystals and polycrystalline materials, different underlying mechanisms are responsible for key features of strain localisation corresponding to different stages of the deformation curve. The major autowave (self-excited wave) types manifest themselves in plastically deforming materials. The self-excited wave model could explain plastic flow pattern behaviour corresponding to different physical mechanisms.     

非晶态固体的结构可以决定性能吗?

晶态固体的力学性能与塑性变形主要由结构缺陷, 比如位错的运动决定. 而在非晶态固体中结构如何决定性能, 仍然是固体力学、材料学和凝聚态物理学共同关心但尚未解决的核心问题之一.传统材料学研究的经典范式为"结构决定性能". 遵循这一信条, 已经有大量的实验表征与理论、模拟研究, 尝试将非晶态固体的某种结构特征与性能建立一一对应关系. 但是, 科学界对于非晶固体结构-性能关系成立与否, 以及背后隐藏的规律知之甚少. 本文针对非晶态固体的变形机制以及其微结构特征, 基于分子动力学模拟, 定量评估短程简单结构与中长程复杂结构在决定非晶态固体动力学性能方面的效用. 通过海量抽样每种具体玻璃结构的激活能(标识激发难易程度), 尝试将结构参数与激活能建立定量关系, 从而揭示出非晶态固体结构-性能关系的隐藏主控因素为结构的空间关联, 受限比几何结构本身更关键. 只有某种结构在空间上呈现亚纳米级的空间关联长度, 这种完备结构才有可能有效地决定非晶态固体的力学性能, 而短程简单结构则无效. 进一步, 给出了评价非晶态固体结构预测性能有效性的普适定量方法, 为建立广义无序物质的结构-性能关系提供了筛选准则.      

Flow mechanisms in dense silica-metal oxide-water suspensions

The rheological properties of dense silica in water suspensions (approx. 50% solids by volume) containing additions of metal oxides were examined. Metal oxides used were ferric, zinc and stannic. To prevent settling, testing was performed in a rheometer which was modified to provide for continual stirring of the materials. Relatively small oxide additions had the effect of thickening the mixtures and making them non-Newtonian. Different rate-limiting steps for flow were identified depending on the particular mixture, testing temperature and shear strain rate. Flow could be described using empirical equations which are identical to those often used to describe plastic flow in solid crystalline materials.     

Yielding of magnesium: From single crystal to polycrystalline aggregates

Hexagonal close-packed (hcp) metals show a deformation behavior, which is quite different from that of materials with cubic crystalline structure. As a consequence, rolled or extruded products of magnesium and its alloys exhibit a strong anisotropy and an unlike yielding in tension and compression. In this work, the microstructural mechanisms of deformation in pure magnesium are modeled by visco-plastic constitutive equations of crystal plasticity. Single crystals and textured polycrystals are analyzed numerically. By means of virtual mechanical tests of representative volume elements mesoscopic yield surfaces are generated. The linking of micro- and mesoscale provides a procedure for the simulation of the yielding and hardening behavior of arbitrarily textured solids with hcp structure such as extruded bars or rolled plates.     

Cauchy–Born Rule and the Stability of Crystalline Solids: Static Problems

We study the connection between atomistic and continuum models for the elastic deformation of crystalline solids at zero temperature. We prove, under certain sharp stability conditions, that the correct nonlinear elasticity model is given by the classical Cauchy–Born rule in the sense that elastically deformed states of the atomistic model are closely approximated by solutions of the continuum model with stored energy functionals obtained from the Cauchy–Born rule. The analysis is carried out for both simple and complex lattices, and for this purpose, we develop the necessary tools for performing asymptotic analysis on such lattices. Our results are sharp and they also suggest criteria for the onset of instabilities of crystalline solids.     

Comparison of the geometrically nonlinear and linear theories of martensitic transformation

Over the last few years, a continuum model based on finite or nonlinear thermoelasticity has been developed and successfully used to study crystalline solids that undergo a martensitic phase transformation. A geometrically linear version of this model was developed independently and has been widely used in the materials science literature. This paper presents the two theories and evaluates them by comparing and contrasting the results in various problems. It is established that in analyzing particular microstructures, the linear theory does not offer significant simplifications and misses important details. However, in more general situations where the particular microstructure is unknown and may involve stress, the linear theory can address certain problems which are currently beyond the capabilities of the nonlinear theory. Such analysis can yield valuable qualitative information. Finally, an example where the two theories differ dramatically is presented.     

Determination of the stretch tensor for structural transformations

Structural transformations in crystalline solids are increasingly the basis of the functional behavior of materials. Recently, in diverse alloy systems, both low hysteresis and reversibility of phase transformations have been linked to the satisfaction of the nongeneric conditions of compatibility between phases. According to the Cauchy–Born rule, these conditions are expressed as properties of transformation stretch tensor. The transformation stretch tensor is difficult to measure directly due to the lack of knowledge about the exact transforming pathway during the structural change, and the complicating effects of microstructure. In this paper we give a rigorous algorithmic approach for determining the transformation stretch tensor from X-ray measurements of structure and lattice parameters. For some traditional and emerging phase transformations, the results given by the algorithm suggest unexpected transformation mechanisms.     

固体塑性实验室时间尺度的分子动力学模拟概述

随着超级计算机软硬件的飞速提升,基于经验势函数的分子动力学模拟在解析固体塑性的微观机制方面发挥着关键作用.但是,由于传统分子动力学基于牛顿运动方程数值积分,积分时间步长通常为飞秒量级,其模拟的时间尺度通常限于纳秒量级,从而为模拟长时间尺度固体塑性机制带来了巨大的挑战.本文从分子动力学模拟的时间尺度限制切入,介绍目前国际...     

Self-accommodation in martensite

The shape-memory effect is a phenomenon wherein an apparently plastically deformed specimen recovers all strain when heated above a critical temperature. This is observed in some crystalline solids that undergo martensitic phase transformation. The martensitic transformation is a temperature-induced, diffusionless solid-to-solid phase transformation involving a change in crystalline symmetry. Shape-memory materials are able to transform from the high-temperature austenite to the low-temperature martensite phase without any apparent change in shape. This is known as self-accommodation. Necessary and sufficient conditions that the lattice parameters of a material must satisfy for the material to form a self-accommodating microstructure are derived. The main result states that if the austenite is cubic, the material is self-accommodating if and only if the transformation is volume preserving. On the other hand, if the symmetry of the austenite is not cubic, it is not possible to construct any microstructure that is self-accommodating unless the transformation strain or the Bain strain satisfies additional, rather strict, conditions. These results show good agreement with the available experimental data. The analysis here is significantly different from previous studies because it makes no a priori assumption on the microstructure.     

Acoustic emission and the Portevin-Le Chatelier effect

Many metals and alloys which exhibit repeated discontinuous yielding (Portevin-Le Chatelier effect) also emit rather interesting acoustic energy during work hardening. Both phenomena are dramatic in dead-weight extensions of annealed specimens of brass or aluminum. The acoustic emission from such specimens was monitored and correlated with the features of the Portevin-Le Chatelier effect. It is shown that, when the discontinuous yielding subsides in aluminum, so does the acoustic emission; in fact, smooth continuous flow can occur in these materials with no detectable acoustic emission. Data are presented which are consistent with the hypothesis that, at room temperature, elastic energy released during a yield increment is proportional to the elastic energy stored since the last yield increment. This is not observed at elevated temperatures. It is concluded that additional studies of the acoustic-emission phenomena associated with plastic deformation can aid in achieving a better knowledge of the strain-hardening process for crystalline solids.     

Extension of Bernoulli's theorem on steady flows of inviscid fluids to steady flows of plastic solids

A differential equation is derived which is valid along any streamline in a steady flow of a general continuum where the streamline is also a trajectory of principal stress. For special materials and flow conditions this equation can be integrated to give algebraic relations between variables along the streamline. For inviscid fluids this leads to Bernoulli's famous theorem relating pressure and velocity along any streamline. For three-dimensional ideal flows of Tresca plastic solids and planar ideal flows of general rigid/perfectly plastic solids, it also leads to known results along any streamline. For other special constitutive materials in rigid/plastic solids additional streamline relations are obtained.     

Ultrasonic characterization of point defects induced by cross slip under pure shear

Longitudinal wave velocity is used to characterize the point defects in crystalline solids. High purity Al single crystal was selected for both the finite element analysis and experimental work. Since the jog motions of dislocations caused by intersected slides such as cross slips induce point defects, the total amount of cross slips was calculated instead of calculating directly from the point defects. The effect of crystal orientations on total amount of cross slips under pure shear was also investigated via the finite element method. The result suggest that if the initial shear stress direction is located at the inner side of stereographic triangle, only single slip activities occurred at the beginning of plastic deformation and no effects due to point defects were present. However, as the shear stress direction rotates along the slip direction, point defects are induced by cross slips between primary and secondary slip systems due to work-hardening. This phenomenon was then examined by measuring longitudinal wave velocity changes propagating in Al single crystal subjected to the combination loads of equi-biaxial tension and compression (a pure shear state). Good qualitative agreement between the finite element result and measured data suggest that the longitudinal wave velocity can be used as an index to characterize point defects in crystalline materials.     

A stress-gradient based criterion for dislocation nucleation in crystals

Dislocations are the main lattice defects responsible for the strength and ductility of crystalline solids. The generation of new dislocations is an essential aspect of crystal defect physics, but a fundamental understanding of the mechanical conditions which lead to dislocation nucleation has remained elusive. Here, we present a nucleation criterion motivated from continuum thermomechanical considerations of a crystalline solid undergoing deformation, and demonstrate the criterion's ability to correctly predict dislocation nucleation via direct atomistic simulations. We further demonstrate that the commonly held notion of a nucleation criterion based on the magnitude of local stress components is incorrect.     

Finite strain analysis of crack tip fields in incompressible hyperelastic solids loaded in plane stress

A new method is developed to determine the dominant asymptotic stress and deformation fields near the tip of a Mode-I traction free plane stress crack. The analysis is based on the fully nonlinear equilibrium theory of incompressible hyperelastic solids. We show that the dominant singularity of the near tip stress field is governed by the asymptotic solution of a linear second order ordinary differential equation. Our method is applicable to any hyperelastic material with a smooth work function that depends only on the trace of the Cauchy-Green tensor and is particularly useful for materials that exhibit severe strain hardening. We apply this method to study two types of soft materials: generalized neo-Hookean solids and a solid that hardens exponentially. For the generalized neo-Hookean solids, our method is able to resolve a difficulty in the previous work by Geubelle and Knauss (1994a). Our theoretical results are compared with finite element simulations.     

Wave propagation and critical conditions for energy focusing pattern transformation in anisotropic fluid-filled porous structures

Considering the pore fluid, the energy singular propagation in open-cell anisotropic porous solids is studied with the aim to provide a reference in the energy design and application of porous materials. Firstly, based on Biot’s theory, the perturbed eigenvalue problem that arises when the nearly pure modes are propagated is considered. Then, by using the obtained perturbed eigenvalues, the evolution conditions on the elastic parameters of solid skeleton materials are established for the existence of various systems of folds in the wave front. The emphasis is placed on the slow wave, which is particular for the porous material with the pore fluids. The critical conditions for the pattern transformation in the parameter space are given for the first time. Finally, the special situation (zero porosity) is discussed and the comparison with respect to the results for pure solids is made. The results show that the situation in the pure solids is a degenerated case of the present discussion.     

A sharp interface method for high-speed multi-material flows: strong shocks and arbitrary materialpairs

A general framework is developed for solving high-speed and high-intensity multi-material interaction problems on adaptively refined Cartesian meshes. The framework is applicable for interfaces separating materials with very different properties and in the presence of strong shocks. A sharp interface treatment is maintained through a modified Ghost Fluid Method. The embedded boundaries are tracked and represented with level sets. A tree-based Local Mesh Refinement scheme is employed to efficiently resolve the desired physics. Results are shown for situations that cover varied combination of materials (fluids, rigid solids and deformable solids) with careful benchmarking to establish the validity and the versatility of the approach.