Effects of texture evolutions and point defects on ultrasonic waves under simple shear and pure shear

In this paper, longitudinal and transverse wave velocities propagating into aluminum alloy A6061 under simple shear and pure shear were studied experimentally. Compared with the same velocity change tendencies of transverse wave under simple shear and pure shear, longitudinal wave velocity shows different change tendencies under both shear states, regardless of the same shear strain states in two cases. Finite element analysis was performed and the analyzed results indicate that the transverse wave velocity depends on texture evolutions mainly, whereas the longitudinal wave velocity is sensitively influenced by point defects induced by cross-slips. Consequently, the longitudinal wave velocity showing a sensitive response to the point defects was examined by measuring longitudinal wave velocity changes propagating into Al single crystal subjected to the combination loads of equi-biaxial tension and compression.     

Ultrasonic nondestructive material evaluation method and study on texture and cross slip effects under simple and pure shear states

Ultrasonic wave velocities propagating in a plastically deformed medium are known to depend upon its microstructural material properties. Therefore, the authors have proposed the theoretical modeling of an ultrasonic nondestructive method to evaluate plastically deformed states. In the present paper, we verify the proposed theoretical modeling of an ultrasonic nondestructive method and examine its accuracy by comparing the experimental results with the simulated subsequent yield surfaces, the longitudinal and transverse wave velocities under combined stress states of an aluminum alloy using internal state variables of an anisotropic distortional yield model which were determined to achieve a good fit for the experimental results of the longitudinal and transverse wave velocity changes under uniaxial tension test. As a special case, the velocity changes of longitudinal wave under pure shear state subjected to the combinations of tension and compression are also studied, it shows a different result compared with that of longitudinal wave velocity under torsional tests of thin thickness cylinders, i.e., simple shear state. The effects on ultrasonic wave velocity changes due to texture and cross slip under simple and pure shear states are studied via a finite element polycrystal model (FEPM).     

压头不同晶向下纳米压痕的多尺度研究

为了研究压头晶体各向异性对纳米压痕的影响,采用多尺度准连续介质(QC)法模拟了不同晶向Ni压头与Ag薄膜的纳米压痕过程。通过对比不同晶向下压头在薄膜上触发的原子滑移,发现压头的晶向引起的界面失配位错在很大程度上决定薄膜开启初始原子滑移系的难易。然后对比了压头在不同晶向下测得的薄膜纳米硬度,发现其计算值是一样的。最后研究压头表面和压痕表面的正应力和切应力的分布,分析了应力分布与原子滑移系的关系。     

Size effects on void growth in single crystals with distributed voids

The effect of void size on void growth in single crystals with uniformly distributed cylindrical voids is studied numerically using a finite deformation strain gradient crystal plasticity theory with an intrinsic length parameter. A plane strain cell model is analyzed for a single crystal with three in-plane slip systems. It is observed that small voids allow much larger overall stress levels than larger voids for all the stress triaxialities considered. The amount of void growth is found to be suppressed for smaller voids at low stress triaxialities. Significant differences are observed in the distribution of slips and on the shape of the deformed voids for different void sizes. Furthermore, the orientation of the crystalline lattice is found to have a pronounced effect on the results, especially for the smaller void sizes.     

On the uniqueness of a rate-independent plasticity model for single crystals

This paper presents the uniqueness and existence conditions for a rate-independent plasticity model for single crystals under a general stress state. The model is based on multiple slips on three-dimensional slip systems. The uniqueness condition for the plastic slips in a single crystal with nonlinear hardening is derived using the implicit function theorem. The uniqueness condition is the non-singularity of a matrix defined by the Schmid tensors, the elasticity, and the hardening rates of the slip systems. When this matrix becomes singular, the limitations on the loading paths that can be accommodated by the active slip systems (i.e., the existence conditions) are also given explicitly. For the compatible loading paths, a particular solution is selected by requiring the solution vector to be orthogonal to the null space of the singular coefficient matrix. The paper also presents a fully implicit algorithm for the plasticity model. Numerical examples of an fcc copper single crystal under cyclic loadings (pure shear and uniaxial strain) are presented to demonstrate the main features of the algorithm.     

Predictive modeling of nanoindentation-induced homogeneous dislocation nucleation in copper

Nanoscale contact of material surfaces provides an opportunity to explore and better understand the elastic limit and incipient plasticity in crystals. Homogeneous nucleation of a dislocation beneath a nanoindenter is a strain localization event triggered by elastic instability of the perfect crystal at finite strain. The finite element calculation, with a hyperelastic constitutive relation based on an interatomic potential, is employed as an efficient method to characterize such instability. This implementation facilitates the study of dislocation nucleation at length scales that are large compared to atomic dimensions, while remaining faithful to the nonlinear interatomic interactions. An instability criterion based on bifurcation analysis is incorporated into the finite element calculation to predict homogeneous dislocation nucleation. This criterion is superior to that based on the critical resolved shear stress in terms of its accuracy of prediction for both the nucleation site and the slip character of the defect. Finite element calculations of nanoindentation of single crystal copper by a cylindrical indenter and predictions of dislocation nucleation are validated by comparing with direct molecular dynamics simulations governed by the same interatomic potential. Analytic 2D and 3D linear elasticity solutions based on the Stroh formalism are used to benchmark the finite element results. The critical configuration of homogeneous dislocation nucleation under a spherical indenter is quantified with full 3D finite element calculations. The prediction of the nucleation site and slip character is verified by direct molecular dynamics simulations. The critical stress state at the nucleation site obtained from the interatomic potential is in quantitative agreement with ab initio density functional theory calculation.     

Rheo-PIV analysis of the slip flow of a metallocene linear low-density polyethylene melt

The continuous extrusion of a metallocene linear low-density polyethylene through a transparent capillary die with and without slip was analyzed in this work by rheometrical measurements and particle image velocimetry (PIV). For this reason, a comparison was made between the rheological behaviors of the pure polymer and blended with a small amount of fluoropolymer polymer processing additive. Very good agreement was found between rheometrical and PIV measurements. The pure polymer exhibited stick-slip instabilities with nonhomogeneous slip at the die wall, whereas the blend showed stable flow. The slip velocity was measured directly from the velocity profiles and was negligible for the pure polymer before the stick-slip but increased monotonously as a function of the shear stress for the blend. The flow curves and the slip velocity as a function of the shear stress deviated from a power law and were well fitted by continuous “kink” functions. Comparison of PIV data with rheometrical ones permitted a direct proof of the basic assumption of the Mooney theory. Finally, the analysis of the velocity profiles showed that there is a maximum in the contribution of slip to the average fluid velocity, which is interpreted as the impossibility for the velocity profile to become plug like in the presence of shear thinning.     

Elastic/crystalline viscoplastic finite element analyses of single- and poly-crystal sheet deformations and their experimental verification

The elastic/crystalline viscoplastic constitutive equation, based on a newly proposed hardening-softening evolution equation, is introduced into the dynamic-explicit finite element code “Itas-Dynamic.” In the softening evolution equation, the effective distance and the angle between each slip system of a crystal are introduced to elucidate the interaction between the slip systems, which causes a decrease of dislocation density. The polycrystal sheet is modeled by Voronoi polygons, which correspond to the crystal grains; and by the selected orientations, which can relate to the texture, they are assigned to the integration points of the finite elements. We propose a direct crystal orientation assignment method, which means that each integration point of finite element has an assigned orientation, and its orientation can be rotated independently. Therefore, this inhomogeneous polycrystal model can consider the plastic induced texture development and subsequent anisotropy evolution. The parameters of the constitutive equation are identified by uni-axial tension tests carried out on single crystal sheets. Numerical results obtained for sheet tensions are compared with experimental ones to confirm the validity of our finite element code. Further, we investigate the following subjects: (1) how the initial orientation of single crystal affects slip band formation and strain localization; (2) how the grain size and particular orientations of the grain affect the strain localization in case of a polycrystal sheet. It is confirmed that the orientation of a single crystal can be related to the primary slip system and the deformation induced activation of that system, which in turn can be related to the slip band formation of the single crystal sheet. Further, in case of a polycrystal sheet, the larger the grain size, the more the strain localizes at a specific crystal, which has the particular orientation. It is confirmed through comparisons with experiments that our finite element code can predict the localization of strain in sheets and consequently can estimate the formability of sheet metals.     

A Dynamic-induced Direct-shear Model for Dynamic Triggering of Frictional Slip on Simulated Granular Gouges

This study presents a dynamic-induced direct-shear model to investigate the dynamic triggering of frictional slip on simulated granular gouges. An incident P-wave is generated as a shear load and a normal stress is constantly applied on the gouge layer. The shear stress accumulates in the incident stage and the frictional slip occurs in the slip stage without the effect of the reflected wave. The experimental results show a non-uniform shear stress distribution along the gouge layer, which may be induced by a shear load induced torque and by normal stress vibration along the layer. The shear stress at the trailing edge strongly affects the frictional slip along the P-wave loading direction, while the rebound stress at the leading edge propagates along the opposite direction. The frictional slip is triggered when the maximum shear stress at the trailing edge reaches a critical value. The normal stress influences the maximum shear stress at the trailing edge, the maximum slip displacement and the slip velocity. The advantages and the limitations of this model are discussed at the end.     

Finite element simulation of PSB macroband nucleation and propagation in single crystal nickel cycled at low plastic strain amplitudes

Substructure models for vein matrix and persistent slip band (PSB) structures are extracted from a uniaxial mixtures model that was developed to simulate cyclic loading experiments on nickel single crystals oriented for single slip. Reverse magnetostriction is included as well. These substructure models are implanted in a single crystal plasticity framework with fully anisotropic elasticity. The resulting constitutive models are incorporated in finite element models to simulate the process of PSB macroband formation and propagation. Perturbation elements (PEs), elements assigned with PSB properties, are used as the loci for PSB macroband nucleation. Transition of elements with vein matrix properties to elements with PSB properties is triggered at integration points by a shear stress criterion applied on slip systems. The resulting finite element models successfully demonstrate the process of PSB formation and propagation, and plastic strain amplitude partitioning between vein matrix and PSB macrobands. The effect of model boundary constraints, strain increment dependence, mesh sensitivity, PE distribution, specimen axis misorientation, and PSB volume fraction generated is examined.     

Characterization of yielding behavior of polycrystalline metals with single crystal plasticity based on representative characteristic length

Single crystal plasticity based on a representative characteristic length is proposed and introduced into a homogenization approach based on finite element analyses, which are applied to characterization of distinctive yielding behaviors of polycrystalline metals, yield-point elongation, and grain size strengthening. The computational manner for an implicit stress update is derived with the framework of a standard multi-surface plasticity at finite strain, where the evolution of the characteristic lengths are numerically converted from the accumulated slips of all of slip systems by exploiting the mathematical feature of the characteristic length as the intermediate function of the plastic internal variables. Furthermore, a constitutive model for a single crystal reproduces the stress–strain curve divided into three parts. Using two-scale finite element analysis, the macroscopic stress–strain response with yield-point elongation under a situation of low dislocation density is reproduced. Finally, the grain size effect on the yield strength is analyzed with modeling of the grain boundary in the context of the proposed constitutive model and is discussed from both macroscopic and microscopic views.     

晶体塑性变形离散滑移模型及有限元分析

基于韧性单晶体实验现象，建立了描述晶体塑性变形的离散滑移模型．该模型的主要特点是：晶体滑移变形在宏观上是不均匀的，滑移带的分布是离散的．利用晶体塑性理论对模型进行了有限变形有限元分析，计算结果揭示了晶体滑移的离散行为，模拟的应力 应变曲线与实验曲线相吻合     

铜三晶体弹性应力场和主滑移系分解切应力的有限元分析

用三维各向异性有限元法,对铜三晶体在拉伸载荷作用下的弹性应力集中特性和各组元晶体主滑移系上的切应力变化进行了计算分析,得到了交为一致的结果;为进一步分析三晶体的循环塑性变形提供了依据。     

用晶体弹塑性有限单元法研究双晶金属拉伸变形

本文从单晶体应力-应变关系的精确实验结果和多晶体滑移特性出发,建立相应的计算模型,并采用微观力学和晶体弹塑性有限单元法,研究双晶金属试样的拉伸变形,得到其应力-应变曲线,晶体内滑移变形和应力分布规律,以及晶界影响区对它们的影响。     

Interface crack between a compressible elastomer and a rigid substrate with finite slippage

We study the deformation of a crack between a soft elastomer and a rigid substrate with finite interfacial slippage. It is assumed that slippage occurs when the interfacial shear traction exceeds a threshold. This leads to a slip zone ahead of the crack tip where the shear traction is assumed to be equal to the constant threshold. We perform asymptotic analysis and determine closed-form solutions describing the near-tip crack opening displacement and the corresponding stress distributions. These solutions are consistent with numerical results based on finite element analysis. Our results reveal that slippage can significantly affect the deformation and stress fields near the tip of the interface crack. Specifically, depending on the direction of slippage, the crack opening profile may appear more blunted or sharpened than the parabola arising from for the case of zero interfacial shear traction or free slippage. The detailed crack opening profile is determined by the constant shear traction in the slip zone. More importantly, we find that the normal stress perpendicular to the interface can increase or decrease when slippage occurs, depending on the direction of slippage and the shear traction in the slip zone.     

Dissipative interface waves and the transient response of a three-dimensional sliding interface with Coulomb friction

We investigate the linearized response of two elastic half-spaces sliding past one another with constant Coulomb friction to small three-dimensional perturbations. Starting with the assumption that friction always opposes slip velocity, we derive a set of linearized boundary conditions relating perturbations of shear traction to slip velocity. Friction introduces an effective viscosity transverse to the direction of the original sliding, but offers no additional resistance to slip aligned with the original sliding direction. The amplitude of transverse slip depends on a nondimensional parameter η=c_sτ₀/μv₀, where τ₀ is the initial shear stress, 2v₀ is the initial slip velocity, μ is the shear modulus, and c_s is the shear wave speed. As η→0, the transverse shear traction becomes negligible, and we find an azimuthally symmetric Rayleigh wave trapped along the interface. As η→∞, the inplane and antiplane wavesystems frictionally couple into an interface wave with a velocity that is directionally dependent, increasing from the Rayleigh speed in the direction of initial sliding up to the shear wave speed in the transverse direction. Except in these frictional limits and the specialization to two-dimensional inplane geometry, the interface waves are dissipative. In addition to forward and backward propagating interface waves, we find that for η>1, a third solution to the dispersion relation appears, corresponding to a damped standing wave mode. For large-amplitude perturbations, the interface becomes isotropically dissipative. The behavior resembles the frictionless response in the extremely strong perturbation limit, except that the waves are damped. We extend the linearized analysis by presenting analytical solutions for the transient response of the medium to both line and point sources on the interface. The resulting self-similar slip pulses consist of the interface waves and head waves, and help explain the transmission of forces across fracture surfaces. Furthermore, we suggest that the η→∞ limit describes the sliding interface behind the crack edge for shear fracture problems in which the absolute level of sliding friction is much larger than any interfacial stress changes.     

Numerical simulation of laminar flow past a circular cylinder with slip conditions

The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.     

单晶体塑性滑移有限变形下的应力计算

为了探讨和发展单晶金属材料的非弹性有限变形分析方法,提出一种单晶体各向异性弹塑性分析的计算格式.该方法是一种以初始构形为变形计算参考构形的描述方法,它对单晶体塑性构形的演化用增量计算以跟随加载路径,而在应力计算时在卸载构形的基础上用Hencky对数弹性应变来计算总量的应力以保证计算的稳定和收敛;通过求解满足瞬时屈服条件和应力与弹性应变关系的广义胡克定律的非线性方程组来搜索激活滑移系.     

Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The resolved shear stress, which drives dislocation in a crystal, is strongly orientation dependent, and therefore, the cyclic plastic deformation of the shear decohesion process is highly anisotropic.The crack planes are often inclined to the loading axis both in the inplane orientation and in the thickness direction. This inclination induces all three modes of the crack tip stress field, K_I, K_II, and K_III.Fatigue crack growth in large-grain Al 7029 aluminum alloy was studied. The crack tip stress fields of the test specimens are calculated with the finite element method. The values of K_I, K_II, and K_III are evaluated. The orientation of the crystal at a crack tip was determined with the Laue X-ray method. The crystal orientation and the calculated crack tip stress fields are used to compute the resolved shear stress intensity of each of the twelve slip systems of the crystal at the crack tip. The resolved shear stress field of a slip system is linearly proportional to the resolved shear stress intensity coefficient, RSSIC.The values of RSSIC thus evaluated are used to analyze the orientations of the crack plane and to correlate with the shear fatigue crack growth rate.