Tensile response of passivated films with climb-assisted dislocation glide

The tensile response of single crystal films passivated on two sides is analysed using climb enabled discrete dislocation plasticity. Plastic deformation is modelled through the motion of edge dislocations in an elastic solid with a lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The dislocation motion in the films is by glide-only or by climb-assisted glide whereas in the surface passivation layers dislocation motion occurs by glide-only and penalized by a friction stress. For realistic values of the friction stress, the size dependence of the flow strength of the oxidised films was mainly a geometrical effect resulting from the fact that the ratio of the oxide layer thickness to film thickness increases with decreasing film thickness. However, if the passivation layer was modelled as impenetrable, i.e. an infinite friction stress, the plastic hardening rate of the films increases with decreasing film thickness even for geometrically self-similar specimens. This size dependence is an intrinsic material size effect that occurs because the dislocation pile-up lengths become on the order of the film thickness. Counter-intuitively, the films have a higher flow strength when dislocation motion is driven by climb-assisted glide compared to the case when dislocation motion is glide-only. This occurs because dislocation climb breaks up the dislocation pile-ups that aid dislocations to penetrate the passivation layers. The results also show that the Bauschinger effect in passivated thin films is stronger when dislocation motion is climb-assisted compared to films wherein dislocation motion is by glide-only.     

Bauschinger and size effects in thin-film plasticity due to defect-energy of geometrical necessary dislocations

The Bauschinger and size effects in the thinfilm plasticity theory arising from the defect-energy of geometrically necessary dislocations (GNDs) are analytically investigated in this paper. Firstly, this defect-energy is deduced based on the elastic interactions of coupling dislocations (or pile-ups) moving on the closed neighboring slip plane. This energy is a quadratic function of the GNDs density, and includes an elastic interaction coefficient and an energetic length scale L. By incorporating it into the work- conjugate strain gradient plasticity theory of Gurtin, an energetic stress associated with this defect energy is obtained, which just plays the role of back stress in the kinematic hardening model. Then this back-stress hardening model is used to investigate the Bauschinger and size effects in the tension problem of single crystal Al films with passivation layers. The tension stress in the film shows a reverse dependence on the film thickness h. By comparing it with discrete-dislocation simulation results, the length scale L is determined, which is just several slip plane spacing, and accords well with our physical interpretation for the defect- energy. The Bauschinger effect after unloading is analyzed by combining this back-stress hardening model with a friction model. The effects of film thickness and pre-strain on the reversed plastic strain after unloading are quantified and qualitatively compared with experiment results.     

Plasticity size effects in tension and compression of single crystals

The effect of size and loading conditions on the tension and compression stress-strain response of micron-sized planar crystals is investigated using discrete dislocation plasticity. The crystals are taken to have a single active slip system and both small-strain and finite-strain analyses are carried out. When rotation of the tensile axis is constrained, the build-up of geometrically necessary dislocations results in a weak size dependence but a strong Bauschinger effect. On the other hand, when rotation of the tensile axis is unconstrained, there is a strong size dependence, with the flow strength increasing with decreasing specimen size, and a negligible Bauschinger effect. Below a certain specimen size, the flow strength of the crystals is set by the nucleation strength of the initially present Frank-Read sources. The main features of the size dependence are the same for the small-strain and finite-strain analyses. However, the predicted hardening rates differ and the finite-strain analyses give rise to some tension-compression asymmetry.     

非晶碳薄膜固体超滑设计的滚-滑原则

固体超滑是指相互接触的滑动固体表界面间摩擦系数极低(10?3量级或更低)的现象,因此,开展固体超滑理论和超滑技术研究具有重要意义. 目前碳基薄膜固体超滑设计原则是引入杂原子后的表面钝化作用,尤其氢含量起到决定性作用,通常要求氢原子分数高于40%. 然而依据相图,高氢碳薄膜体系仅占碳薄膜种类的小部分,大量无钝化或者少钝化非晶碳薄膜超滑设计缺乏理论指导. 本文作者在前期研究基础上综述了国内外最新进展,面向贫氢非晶碳薄膜体系,提出从滚-滑角度认识无序界面无钝化或者钝化不足情况下摩擦机理,包括滑动机理、滚动机理、滚动-滑动共存,并在此基础上探讨了碳基薄膜的可能发展趋势,以及固体超滑可能的设计原则和方案.      

Distribution of dislocation source length and the size dependent yield strength in freestanding thin films

A method is proposed to estimate the size-dependent yield strength of columnar-grained freestanding thin films. The estimate relies on assuming a distribution of the size of Frank-Read sources, which is then translated into a log-normal distribution of the source strength, depending on film thickness, grain size and theoretical strength of the material, augmented with a single fit parameter. Two-dimensional discrete dislocation plasticity (DDP) simulations are carried out for two sets of Cu films and the fit parameter is determined from independent experiments. Subsequent DDP predictions of the stress-strain curves in comparison with the corresponding experimental data show excellent agreement of initial yield strength and hardening rate for films of varying film thickness and grain size. Having thus demonstrated the power of the proposed strength distribution, it is shown that the mode of this distribution governs the most effective source strength. This is then used to suggest a method to estimate the yield strength of thin films as a function of film thickness and grain size. Simple maps are presented that are in very good agreement with recent experimental results for Cu thin films.     

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. A chief advantage of the present theory is that it is analytically tractable, in the sense that the complexity of the calculations may be reduced, with the aid of closed form analytical solutions, to the determination of the value of the phase field at point-obstacle sites. In particular, no numerical grid is required in calculations. The phase-field representation enables complex geometrical and topological transitions in the dislocation ensemble, including dislocation loop nucleation, bow-out, pinching, and the formation of Orowan loops. The theory also permits the consideration of obstacles of varying strengths and dislocation line-energy anisotropy. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication in single slip under monotonic loading; the Bauschinger effect under reverse loading; the fading memory effect, whereby reverse yielding gradually eliminates the influence of previous loading; the evolution of the dislocation density under cycling loading, leading to characteristic ‘butterfly’ curves; and others.     

Anisotropic strain hardening in polycrystalline copper and aluminium

A new viscoplastic model for the plastic stress-strain behaviour of f.c.c. metals is presented. In this model the strain hardening results from increasing dislocation densities. The observed stagnation of strain hardening after strain reversals is explained by a lowering of the increase in dislocations due to annihilation of dislocations with opposite polarity. The model is applied to Bauschinger and x-y tests on commercial copper and aluminium, and to cyclic tests on copper. The theoretical results are in good agreement with the measurements.     

Dislocation core spreading at interfaces between metal films and amorphous substrates

Experiments with transmission electron microscopy have shown that in a strong electron beam the contrast of dislocations may gradually disappear at an incoherent interface between a metal thin film and an amorphous substrate. There are reasons to believe that this phenomenon is caused by radiation-induced dislocation core spreading at the interface. A quantitative model accounting for this effect will be necessary for a better understanding of dislocation structures and plastic deformation in metal thin films. As a first step toward this objective, we develop a number of mathematical solutions for dislocation core spreading at an incoherent interface. For simplicity, we consider screw dislocations, and consider the interface to be characterized by a shear adhesive strength, τ₀, below which no core spreading occurs, and above which spreading takes place in a viscous manner. We determine the final equilibrium core width and the rate of core spreading for single or planar arrays of dislocations in a homogeneous bulk material or at the interface between a thin film and a semi-infinite substrate where the film and substrate may have the same, or different, elastic constants. Some of our solutions are analytic and others are based on an implicit finite difference method with a Gauss-Chebyshev quadrature scheme. The phenomenon of dislocation core spreading is expected to have a dramatic effect on the strength of crystalline films deposited on amorphous substrates.     

Modeling the Bauschinger effect for sheet metals,part I: theory

It is essential to model the Bauschinger effect correctly for sheet metal forming process simulation and subsequent springback prediction when material points are subjected to cyclic loading conditions. The combined nonlinear hardening model for time independent cyclic plasticity, proposed by Chaboche and co-workers, is examined and a simple modification is suggested for the isotropic part of the hardening rule to utilize the conventional tensile test data directly. This modification is useful for the materials whose reverse loading curves saturate to the monotonic loading curve. In addition, an anisotropic nonlinear kinematic hardening model (ANK model) is proposed in an attempt to represent the Bauschinger effect more realistically. Possible offset in flow stress is modeled by treating the back stress evolution during reverse loading differently from the initial loading. This strategy coupled with the modified isotropic hardening rule seems to provide a way to model the Bauschinger effect consistently over multiple cycles. Two types of auto-body alloys are examined in this paper. Associated material parameters are determined by employing available tension-compression test data and multi-cycle bend test data. A developed finite element formulation is applied to analyze simple validation type of problems. The cyclic stress–strain curves generated from the proposed ANK model match remarkably well with measured data.     

Cyclic stress-strain behaviour of alloy AA6060, part I: Uniaxial experiments and modelling

An experimental and numerical study of the uniaxial cyclic behaviour of the aluminium alloy AA6060 in tempers T4 and T6 is reported. Material characteristics studied through the experimental programme are the monotonic stress-strain curve, the shape of the hysteresis loops, cyclic hardening and softening, mean stress relaxation and memorization of prior strain histories. A model of cyclic plasticity, proposed in the literature, is used to simulate the physical behaviour of the alloy in temper T4. The model utilizes multi-component forms of kinematic and isotropic hardening variables with non-linear evolutionary rules to describe the hysteresis loops and the transient behaviour of the material. The evolution of the Bauschinger effect and the memory of prior strain histories are properly modelled through additional internal variables. Tests and simulations are compared for temper T4, and good agreement is obtained between physical and correlated behaviour.     

Experimental study of the Bauschinger effect for anisotropic metals

The Bauschinger effect is characterized by the Bauschinger and Backhaus functions. The dependence of these functions on the direction of deformation of an initially anisotropic sheet material is studied. The experiments showed that these functions are independent of the direction, which confirms the model of isotropic Bauschinger effect.     

Buckling-induced dislocation emission in thin films on substrates

Atomistic simulations of the evolution of a strained thin film on a substrate has been reported and the formation of dislocations has been observed in the film/substrate interface after the film has buckled. In the framework of the linear elasticity theory, an analytical model has been developed to explain the buckle effect on the formation of the dislocations. A stability diagram with respect to the buckling and dislocation emission phenomena is finally presented for the film as a function of the uniaxial strain and the Burgers vector.     

利用纳米硬度试验法确定Cr/Cu梯度材料的变形特性

利用纳米硬度仪研究了在Cu基底上的Cu／Cr梯度膜的机械性能。梯度膜是通过将Cu靶和Cr靶同时溅射到Cu基底材料上，但两个靶的相对溅射功率随溅射时间变化而制备。利用Oliver and Pharr方法得到了膜随其厚度变化的硬度和弹性模量。然后利用加载／卸载／再加载的方法得到了在不同深度(即膜的厚度)压头平均压力与相对压人深度之间的关系曲线，在此曲线上可以明显反映出材料的屈服特性。     

半共格界面铜镍双层膜力学差异机制纳观探析

为深入了解纳米金属多层膜在沉积法交替制备中, 因晶格失配制备出不同半共格界面的金属多层膜受载诱导的力学特性差异的机制，本文作者基于经典力学的分子动力学法，对半共格Cu基Ni膜和Ni基Cu膜两种界面结构的力学性能展开探析，揭示出多层膜半共格界面失配位错网与压痕诱导产生可动位错的相互作用规律. 研究发现: 铜镍双层膜半共格界面结构可有效提升力学性能，归因于铜镍半共格界面受载产生的柏氏矢量Shockley分位错的差异. Cu基Ni膜半共格界面上的失配位错网对压痕中产生的可动位错表现为排斥，有利于位错穿透半共格区域进入铜基中，对外表现为强化作用；Ni基Cu膜半共格界面上的失配位错网对压痕中产生的可动位错表现为吸引，阻碍位错穿透半共格区域进入镍基中，对外表现为软化作用，增强了材料抵抗变形的能力、耐磨性和韧性. 该性质差异可用Koehler提出的两种不同材料模量间镜像力理论解释. 此研究结果对铜镍多层膜作为涂层应用于微机电系统、海洋装备和航空航天等重大战略领域有着重要理论指导意义与借鉴价值.      

Plane-strain discrete dislocation plasticity incorporating anisotropic elasticity

The increasing application of plane-strain testing at the (sub-) micron length scale of materials that comprise elastically anisotropic cubic crystals has motivated the development of an anisotropic two-dimensional discrete dislocation plasticity (2D DDP) method. The method relies on the observation that plane-strain plastic deformation of cubic crystals is possible in specific orientations when described in terms of edge dislocations on three effective slip systems. The displacement and stress fields of such dislocations in an unbounded anisotropic crystal are recapitulated, and we propose modified constitutive rules for the discrete dislocation dynamics of anisotropic single crystals. Subsequently, to handle polycrystalline problems, we follow an idea of O’Day and Curtin (J. Appl. Mech. 71 (2004) 805–815) and treat each grain as a plastic domain, and adopt superposition to determine the overall response. This method allows for a computationally efficient analysis of micro-scale size effects. As an application, we study freestanding thin copper films under plane-strain tension. First, the computational framework is validated for the special case of isotropic thin films modeled by means of a standard 2D DDP method. Next, predictions of size dependent plastic behavior in anisotropic columnar-grained thin films with varying thickness/grain size are presented and compared with the isotropic results.     

Nucleation of partial dislocations at a crack and its implication on deformation mechanisms of nanostructured metals

Nucleation of partial dislocations at a crack is analyzed based a multiscale model that incorporates atomic information into continuum-mechanics approach. The crack and the slip plane as the extension of the crack are modeled as a surface of displacement discontinuities embedded in an elastic medium. The atomic potential between the adjacent atomic layers along the slip plane is assumed to be the generalized stacking fault energy, which is obtained based on atomic calculations. The relative displacements along the slip plane, corresponding to the configurations of partial dislocations and stacking faults, are solved through the variational boundary integral method. The energetics of partial dislocation nucleation at the crack in FCC metals Al and Cu are comparatively studied for their distinctive difference in the intrinsic stacking fault energy. Compared with nucleation of perfect dislocations in previous studies, several new features have emerged. Among them, the critical stress and activation energy for nucleation of partial dislocations are markedly lowered. Depending on the value of stacking fault energy and crack configuration, the saddle-point configurations of partial dislocations can be vastly different in terms of the nucleation sequence and the size of the stacking fault. These findings have significant implication for identifying the fundamental dislocation and grain-boundary-mediated deformation mechanisms, which may account for the limiting strength and the high strain rate sensitivity of nanostructured metals.     

A discrete dislocation analysis of bending

Bending of a strip in plane strain is analyzed using discrete dislocation plasticity where the dislocations are modeled as line defects in a linear elastic medium. At each stage of loading, superposition is used to represent the solution in terms of the infinite medium solution for the discrete dislocations and a complementary solution that enforces the boundary conditions, which is non-singular and obtained from a linear elastic, finite element solution. The lattice resistance to dislocation motion, dislocation nucleation and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. Solutions for cases with multiple slip systems and with a single slip system are presented. The bending moment versus rotation relation and the evolution of the dislocation structure are outcomes of the boundary value problem solution. The effects of slip geometry, obstacles to dislocation motion and specimen size on the moment versus rotation response are considered. Also, the evolution of the dislocation structure is studied with emphasis on the role of geometrically necessary dislocations. The dislocation structure that develops leads to well-defined slip bands, with the slip band spacing scaling with the specimen height.     

Dislocation pile-ups in bicrystals within continuum dislocation theory

Within continuum dislocation theory the plastic deformation of bicrystals under a mixed deformation of plane constrained uniaxial extension and shear is investigated with regard to the nucleation of dislocations and the dislocation pile-up near the phase boundaries of a model bicrystal with one active slip system within each single crystal. For plane uniaxial extension, we present a closed-form analytical solution for the evolution of the plastic distortion and of the dislocation network in the case of symmetric slip planes (i.e. for twins), which exhibits an energetic as well as a dissipative threshold for the dislocation nucleation. The general solution for non-symmetric slip systems is obtained numerically. For a combined deformation of extension and shear, we analyze the possibility of linearly superposing results obtained for both loading cases independently. All solutions presented in this paper also display the Bauschinger effect of translational work hardening and a size effect typical to problems of crystal plasticity.     

A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales

Plastic flow in crystal at submicron-to-nanometer scales involves many new interesting problems. In this paper, a unified computational model which directly combines 3D discrete dislocation dynamics (DDD) and continuum mechanics is developed to investigate the plastic behaviors at these scales. In this model, the discrete dislocation plasticity in a finite crystal is solved under a completed continuum mechanics framework: (1) an initial internal stress field is introduced to represent the preexisting stationary dislocations in the crystal; (2) the external boundary condition is handled by finite element method spontaneously; and (3) the constitutive relationship is based on the finite deformation theory of crystal plasticity, but the discrete plastic strains induced by the slip of the newly nucleated or propagating dislocations are calculated by dislocation dynamics methodology instead of phenomenological evolution equations used in conventional crystal plasticity. These discrete plastic strains are then localized to the continuum material points by a Burgers vector density function proposed by us. Various processes, such as loop dislocation evolution, dislocation junction formation etc., are simulated to verify the reliability of this computational model. Specifically, a uniaxial compression test for micro-pillars of Cu is simulated by this model to investigate the ‘dislocation starvation hardening’ observed in the recent experiment.