Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation

Nanoindentation experiments have shown that microstructural inhomogeneities across the surface of gold thin films lead to position-dependent nanoindentation behavior [Phys. Rev. B (2002), to be submitted]. The rationale for such behavior was based on the availability of dislocation sources at the grain boundary for initiating plasticity. In order to verify or refute this theory, a computational approach has been pursued. Here, a simulation study of the initial stages of indentation using the embedded atom method (EAM) is presented. First, the principles of the EAM are given, and a comparison is made between atomistic simulations and continuum models for elastic deformation. Then, the mechanism of dislocation nucleation in single crystalline gold is analyzed, and the effects of elastic anisotropy are considered. Finally, a systematic study of the indentation response in the proximity of a high angle, high sigma (low symmetry) grain boundary is presented; indentation behavior is simulated for varying indenter positions relative to the boundary. The results indicate that high angle grain boundaries are a ready source of dislocations in indentation-induced deformation.     

Influence of uniaxial plastic deformation on surface magnetic field in steel

Under geomagnetic field, surface magnetization measurements were made on 1045 and a3 steels samples uniaxially deformed to differing magnitudes of plastic strain, to study the dependence of surface magnetic field and its distribution on plastic deformation. The results indicated initial increase in surface magnetic field with increasing plastic strain followed by a decrease at higher plastic deformation. At still higher plastic deformation, the surface magnetic field was found to be almost independent of plastic strain. In the middle part of the sample, the uneven plastic deformation interrupted the linear distribution of surface magnetic field. The behavior of surface magnetic field and its distribution with plastic deformation were largely controlled by the different mechanisms of interaction of domain walls with isolated dislocation, dislocation tangles and dislocation cellular structures.     

An evaluation for several kinematic hardening rules on prediction of multiaxial stress-controlled ratchetting

This study evaluates the performance of several non-linear kinematic hardening rules in predicting the various biaxial ratchetting experiments of stainless steel (SS) 304L under various stress-controlled histories performed by Hassan et al. (2008). The non-linear kinematic hardening rules proposed by 9, 32, 33 and 160, 19, 12 and 13 and the different rules of Abdel-Karim (2009) are examined and carefully scrutinized. The considered kinematic hardening rules range from the simple classical ones to more detailed rules, which incorporate additional terms and/or parameters to simulate different factors that affect ratchetting. It is shown that none of the examined kinematic hardening rules is general enough to simulate all of the ratchetting responses for the experiments under consideration.     

Effect of the relationship between the elastic modulus and plastic strain on residual stresses and strains in a tube

A semi-analytical solution of the problem of compression of a tube by an outer pressure with subsequent unloading is obtained. The effect of the relationship between the shear modulus and plastic strain on the residual stress and strain was evaluated using experimental data, according to which at an accumulated plastic strain of 0.25, the shear modulus decreases by 20%. It is found that despite the significant decrease in the shear modulus, its dependence on the accumulated strain has no significant effect on the residual strain. The effect of this dependence is manifested mainly in the distribution of the residual radial stress, but, in this case, too, it is extremely weak. The obtained general solution can be used to evaluate the effect of the relationship between the shear modulus and the accumulated plastic strain on the residual stress and strain for other materials.     

Micromechanical deformation analysis of beta alloy titanium in elastic and elastic/plastic tension

An experimental analysis was conducted to document micromechanical behavior of a large grain beta alloy titanium in elastic and elastic/plastic tension. The deformation associated with individual grains was measured by microscopic moiré interferometry. After subtracting uniform strains, the multiplied fringe patterns revealed strong anomalies. The anomalous deformation was documented even at the early stage of loading. Slip along grain boundaries was not observed, but strong shear strains developed within the grains near grain boundaries. Paper was presented at the 1994 SEM spring conference on Experimental Mechanics held in Baltimore, MD, on June 6–8.     

Accounting for the frequency-dependent dynamic elastic modulus of Duralumin in deformation problems

The flexural vibrations of D16AT Duralumin specimens have been investigated, showing that the dynamic elastic modulus of D16AT Duralumin is significantly dependent on frequency. It has been found that the dynamic elastic modulus significantly reduces in the frequency range 0–20 Hz, and at high frequencies, it is practically constant. A general method has been developed to determine the modes and frequency of free vibrations of a structure taking into account the dependence of the dynamic elastic modulus of the material on its deformation frequency. Numerical experiments on impulsive loading of an elongated plate have been performed, showing that the frequency dependence of the dynamic elastic modulus of Duralumin should be taken into account in structural analysis.     

On the hyperbolic variation of elastic modulus in a non-homogeneous stratum

An exact formulation is presented for the governing dual integral equations representing the mixed boundary-value problem of the static stress distribution under a long rigid rectangular body lying on the free surface of a non-homogeneous stratum. The shear modulus of the stratum increases in the depth direction y from a value G₀ at the surface according to the hyperbolic variation.

$G\left(y\right)=\frac{G_{o}h}{h?y}$

It, therefore, simulates a practical soil, of arbitrary Poisson's ratio, which smoothly merges into a rigid bed at a depth h below the surface. The work shows that the problem is governed by both kinds of exponential integral function and that the effect of surface elastic properties is dominant in the solution of the governing equations. The limiting case of a homogeneous half-space is easily recovered from the general formulation as h tends to infinity.     

Effect of creep prestrain on subsequent plastic deformation

The effect of creep prestrain on subsequent plastic deformation is experimentally investigated. The experiments are performed by subjecting thin-walled tubular specimens of stainless steel SUS 304 after creep prestraining to combined axial load and torsion at room temperature to 600°C. The stress-strain relations subsequent to creep prestrain are determined under combined stress state with and without temperature changes in prestraining and subsequent plastic straining. On the experimental results, the plastic hardening effects by creep prestrain are discussed under various temperature conditions. The subsequent stress-strain relations are compared with the calculated results on the equi-plastic strain surfaces.     

考虑初始缺陷与弹性模量的岩石变形破坏过程模拟方法

针对扰动作用下岩石存在初始缺陷的特点,通过探讨含初始缺陷岩石变形力学特征,根据含初始缺陷岩石弹性模量的变化情况,建立了初始损伤的确定方法。然后,引入几何损伤理论,通过分析三轴压缩条件下岩石损伤演化规律,建立了含初始缺陷岩石损伤模型,进而建立了考虑初始缺陷与弹性模量的岩石统计损伤本构模型,并给出了参数的确定方法。最后,通过砂岩三轴压缩试验资料分析得出:本文理论模型能够反映不同围压作用下含初始缺陷岩石的变形破坏全过程,与试验曲线较为接近;且常见损伤模型是本文理论模型的特例,表明本文模型和方法具有一定的合理性与可行性。     

Analysis of elastic and plastic deformation associated with indentation testing of thin films on substrates

A study has been made of the elastic and plastic deformation associated with submicrometer indentation of thin films on substrates using the finite element method. The effects of the elastic and plastic properties of both the film and substrate on the hardness of the film/substrate composite are studied by determining the average pressure under the indenter as a function of the indentation depth. Calculations have been made for film/substrate combinations for which the substrate is either harder or softer than the film and for combinations for which the substrate is either stiffer or more compliant than the film. It is found, as expected, that the hardness increases with indentation depth when either the yield strength or the elastic modulus of the substrate is higher than that of the film. Correspondingly, the hardness decreases with indentation depth when the yield strength or elastic modulus of the substrate is lower than that of the film. Functional equations have been developed to predict the hardness variation with depth under these different conditions. Finite element simulation of the unloading portion of the load displacement curve permits a determination of the elastic compliance of the film/substrate composite as a function of indentation depth. The elastic properties of the film can be separated from those of the substrate using this information. The results are in good agreement with King's analytical treatment of this problem.     

Effect of interface stresses on the elastic deformation of an elastic half-plane containing an elastic inclusion

The effect of the interface stresses is studied upon the size-dependent elastic deformation of an elastic half-plane having a cylindrical inclusion with distinct elastic properties. The elastic half-plane is subjected to either a uniaxial loading at infinity or a uniform non-shear eigenstrain in the inclusion. The straight edge of the half-plane is either traction-free, or rigid-slip, or motionless, which represents three practical situations of mechanical structures. Using two-dimensional Papkovich–Neuber potentials and the theory of surface/interface elasticity, the elastic field in the elastic half-plane is obtained. Comparable with classical result, the new formulation renders the significant effect of the interface stresses on the stress distribution in the half-plane when the radius of the inclusion is reduced to the nanometer scale. Numerical results show that the intensity of the influence depends on the surface/interface moduli, the stiffness ratio of the inclusion to the surrounding material, the boundary condition on the edge of the half-plane and the proximity of the inclusion to the edge.     

Effect of rising elastic modulus in surface layer on stress intensity and gradient

The relaxation element method is applied to obtain the stress field around a crack under normal tension. A surface layer is assumed to surround the crack periphery taken to be in the shape of a narrow ellipse. The elastic modulus within this layer increases from zero to the bulk value of the medium outside. Calculations show that the stresses are finite at the crack tip; they reach a maximum in the layer and then decay to the well known solution of Griffith outside the layer. The influence of plastic deformation on the crack front stresses can also be simulated by the surface layer model. Stress concentration at the crack front is found to be lower when plastic deformation takes place. Sharp decay of stress next to the crack is accompanied by increase of local stress gradients. Severity of the local stress fluctuation depends on the width of the crack surface layer.     

Evolution of the E structural unit during uniaxial and constrained tensile deformation

Molecular dynamics simulations are used to study the mechanisms by which Shockley partial dislocations are nucleated from 1 1 0 copper grain boundaries which contain the E structural unit. Simulations in this work indicate that the natural conformation of the interface porosity with respect to the primary dislocation slip systems is responsible for the easy emission of Shockley partial dislocations during a tensile deformation. Furthermore, it is found that tensile stresses parallel to the interface plane can diminish the severity of the E structural unit on the dislocation nucleation process.     

Effect of pore concentration on localized plastic deformation in polycrystals

Presented is a mesomechanical model that simulates the behavior of localized plastic deformation in polycrystal subjected to uniaxial load. Edge effect and pore concentration are analyzed. Predicted results between the mechanical properties of polycrystal and pore concentration are inconclusive as porosity alone could not explain the increase or decrease of polycrystal strength. The model applies to low pore concentration of less than 5% and hence coalescence of pores is also neglected.     

Dislocation dynamics and acoustic emission during plastic deformation of crystals

A soliton approach to acoustic emission during plastic deformation of crystals is presented. The approach is based on a microscopic Frenkel-Kontorova model where the rigidity of the substrate is removed in order to establish the interaction mechanism between a dislocation and both longitudinal and transverse acoustic waves. It is shown that this interaction is described by a sine-Gordon-d' Alembert system. Within the framework of this system, two basic mechanisms of acoustic emission are investigated both analytically and numerically. One mechanism is related to nonstationary dislocation motion and the other one to the annihilation of dislocation kink-antikink pairs during Frank-Read source operation. In both cases, computer simulations are obtained which illustrate graphically the analytical considerations and model the acoustic radiation. The obtained results are in agreement with existing experimental data and may provide a better physical insight to the acoustic emission mechanisms during plastic deformation of crystals.     

Torsion of an elastic solid cylinder with a radial variation in the shear modulus

A Green's function approach is used to formulate and obtain the stress field, under torsional loads in a radially finite solid cylinder with radially variable elastic modulus. With this approach a certain dual static-geometric analogy in the solution is readily proved and applied to generate the solution with stress boundary conditions from that with displacement boundary conditions and vice-versa.The problem is solved using both boundary conditions and for an exponentially varying shear modulus. In particular, under displacement boundary conditions, the stress field in the solid with a generalised Reissner-Sagoci boundary condition is easily deduced. With stress boundary conditions, the criteria for crack propagation in such elastic models are also obtained using the Griffith-Irwin condition of rupture.     

Effect of plastic deformation on the acoustoelastic response of some materials

Acoustoelastic birefringence is measured with the acoustic polarimeter by transmitting ultrasonic shear waves at two perpendicular polarizations through the thickness of several uniaxial test specimens. The results are availablefor the following materials: SAE 1010 and SAE 4118 steel, pure titanium, 2024 aluminum and 60\2-40 brass, but are only presented here for SAE 4118 steel and pure titanium. The uniaxial test specimens have been subjected to plastic deformation followed by complete unloading. It is shown that the assumption that the plastic flow leading to the residual-stress state does not change the acoustic response of the material, does not hold for all materials and that further characterization development is required for general quantitative residual-stress determination.     

Effect of sample dimensions,lubrication and deformation rate on uniaxial compression of gelatin gels

The response of 10% gelatin gels to uniaxial compression is determined in part by frictional effects at the gel-platen interface. By using teflon-coated plates, lubricated with paraffin or silicone oil, these frictional effects are effectively eliminated. The stress-strain response can then be described by the two-constant Mooney-Rivlin relation, the sum of the two parameters (C ₁ +C ₂ ) being about 25% lower in lubricated compression than the value obtained in simple shear and torsion. Cross-head speed (for total testing times of 0.2–3 min) had no effect on material response, but long-term stress relaxation does occur over periods of about 30 min and longer. Sample radius did not affect the response in lubricated compression but had a major effect under unlubricated conditions. No systematic change in response was seen with sample diameter to height (aspect) ratios between 9.6 and 3.1 in lubricated compression, but data scatter for a given sample diameter was worst at the lowest heights (highest aspect ratio). Agreement of all true stress versus strain data was within about ± 7% regardless of sample height or deformation rate.