# Showing papers in "Journal of The Mechanics and Physics of Solids in 1999"

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TL;DR: In this paper, a mechanism-based theory of strain gradient plasticity is proposed based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient.

Abstract: A mechanism-based theory of strain gradient plasticity (MSG) is proposed based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on strain gradient. While such linear dependence is predicted by the Taylor hardening model relating the flow stress to dislocation density, existing theories of strain gradient plasticity have failed to explain such behavior. We believe that a mesoscale theory of plasticity should not only be based on stress–strain behavior obtained from macroscopic mechanical tests, but should also draw information from micromechanical, gradient-dominant tests such as micro-indentation or nano-indentation. According to this viewpoint, we explore an alternative formulation of strain gradient plasticity in which the Taylor model is adopted as a founding principle. We distinguish the microscale at which dislocation interaction is considered from the mesoscale at which the plasticity theory is formulated. On the microscale, we assume that higher order stresses do not exist, that the square of flow stress increases linearly with the density of geometrically necessary dislocations, strictly following the Taylor model, and that the plastic flow retains the associative structure of conventional plasticity. On the mesoscale, the constitutive equations are constructed by averaging microscale plasticity laws over a representative cell. An expression for the effective strain gradient is obtained by considering models of geometrically necessary dislocations associated with bending, torsion and 2-D axisymmetric void growth. The new theory differs from all existing phenomenological theories in its mechanism-based guiding principles, although the mathematical structure is quite similar to the theory proposed by Fleck and Hutchinson. A detailed analysis of the new theory is presented in Part II of this paper.

1,679 citations

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TL;DR: The quasicontinuum method as discussed by the authors links atomistic and continuum models through the device of the finite element method which permits a reduction of the full set of atomistic degrees of freedom.

Abstract: Mixed atomistic and continuum methods offer the possibility of carrying out simulations of material properties at both larger length scales and longer times than direct atomistic calculations. The quasicontinuum method links atomistic and continuum models through the device of the finite element method which permits a reduction of the full set of atomistic degrees of freedom. The present paper gives a full description of the quasicontinuum method, with special reference to the ways in which the method may be used to model crystals with more than a single grain. The formulation is validated in terms of a series of calculations on grain boundary structure and energetics. The method is then illustrated in terms of the motion of a stepped twin boundary where a critical stress for the boundary motion is calculated and nanoindentation into a solid containing a subsurface grain boundary to study the interaction of dislocations with grain boundaries.

661 citations

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TL;DR: In this paper, the authors formulate the theory in terms of deformation fields and regard the dislocations as manifestations of the incompatibility of the plastic deformation gradient field, and show that the incremental displacements of inelastic solids follow as minimizers of a suitably defined pseudoelastic energy function.

Abstract: Plastically deformed crystals are often observed to develop intricate dislocation patterns such as the labyrinth, mosaic, fence and carpet structures. In this paper, such dislocation structures are given an energetic interpretation with the aid of direct methods of the calculus of variations. We formulate the theory in terms of deformation fields and regard the dislocations as manifestations of the incompatibility of the plastic deformation gradient field. Within this framework, we show that the incremental displacements of inelastic solids follow as minimizers of a suitably defined pseudoelastic energy function. In crystals exhibiting latent hardening, the energy function is nonconvex and has wells corresponding to single-slip deformations. This favors microstructures consisting locally of single slip. Deformation microstructures constructed in accordance with this prescription are shown to be in correspondence with several commonly observed dislocation structures. Finally, we show that a characteristic length scale can be built into the theory by taking into account the self energy of the dislocations. The extended theory leads to scaling laws which appear to be in good qualitative and quantitative agreement with observation.

512 citations

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TL;DR: In this article, the authors studied the influence of six morphological imperfections on the yielding of 2D cellular solids for biaxial loading and quantified the knock-down effect of these defects on the hydrostatic yield strength.

Abstract: The influence of each of the six diAerent types of morphological imperfection—waviness, non-uniform cell wall thickness, cell-size variations, fractured cell walls, cell-wall misalignments, and missing cells—on the yielding of 2D cellular solids has been studied systematically for biaxial loading. Emphasis is placed on quantifying the knock-down eAect of these defects on the hydrostatic yield strength and upon understanding the associated deformation mechanisms. The simulations in the present study indicate that the high hydrostatic strength, characteristic of ideal honeycombs, is reduced to a level comparable with the deviatoric strength by several types of defect. The common source of this large knock-down is a switch in deformation mode from cell wall stretching to cell wall bending under hydrostatic loading. Fractured cell edges produce the largest knock-down eAect on the yield strength of 2D foams, followed in order by missing cells, wavy cell edges, cell edge misalignments, G Voronoi cells, d Voronoi cells, and non-uniform wall thickness. A simple elliptical yield function with two adjustable material parameters successfully fits the numerically predicted yield surfaces for the imperfect 2D foams, and shows potential as a phenomenological constitutive law to guide the design of structural components made from metallic foams. # 1999 Elsevier Science Ltd. All rights reserved.

420 citations

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TL;DR: In this paper, a constitutive model for the non-linear switching of ferroelectric polycrystals under a combination of mechanical stress and electric field is developed for nonlinear switching, where the switching event, which converts one crystal variant into another, gives rise to a progressive change in remanent strain and polarisation.

Abstract: A constitutive model is developed for the non-linear switching of ferroelectric polycrystals under a combination of mechanical stress and electric field. It is envisaged that the polycrystal consists of a set of bonded crystals and that each crystal comprises a set of distinct crystal variants. Within each crystal the switching event, which converts one crystal variant into another, gives rise to a progressive change in remanent strain and polarisation and to a change in the average linear electromechanical properties. It is further assumed that switching is resisted by the dissipative motion of domain walls. The constitutive model for the progressive switching of each crystal draws upon elastic–plastic crystal plasticity theory, and a prescription is given for the tangent moduli of the crystal, for any assumed set of potentially active transformation systems. A self-consistent analysis is used to estimate the macroscopic response of tetragonal crystals (representative of lead titanate) under a variety of loading paths. Also, the evolution of the switching surface in stress-electric field space is calculated. Many of the qualitative features of ferroelectric switching, such as butterfly hysteresis loops, are predicted by the analysis.

388 citations

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TL;DR: In this paper, a modified hydrogen transport model was used to simulate the effect of the hydrostatic stress and trapping on the hydrogen distribution in a plastically deforming steel, where hydrogen atoms diffuse through lattice sites and trap sites are filled by lattice diffusion.

Abstract: The hydrogen transport model of Sofronis and McMeeking was used in order to simulate the effect of the hydrostatic stress and trapping on the hydrogen distribution in a plastically deforming steel. In this model it is assumed that hydrogen atoms diffuse through lattice sites and that trap sites are filled by lattice diffusion. These trap sites are formed due to plastic deformations. Coupled diffusion elastic–plastic finite element analyses were carried out in order to investigate the hydrogen concentration in lattice and trap sites near a blunting crack tip under small-scale yielding conditions. The numerical results of Sofronis and McMeeking were reproduced and it was found that in their model hydrogen is created. The hydrogen balance is satisfied by including a strain rate factor in the hydrogen transport equation. As a consequence no differences were found at steady state, i.e. at low strain rates. The strain rate factor decreases the hydrogen concentration in lattice sites due to the filling of trap sites. When the strain rate is sufficiently high, the lattice sites can be almost depleted of hydrogen while trap sites remain saturated. The modified hydrogen transport model predicts strong dependence of the hydrogen concentration in lattice sites on the strain rate, while the hydrogen concentration in trap sites is not affected significantly. The modified hydrogen transport model provides greater insight into the strain rate dependence of hydrogen embrittlement as observed in tensile tests.

267 citations

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TL;DR: In this article, an embedded process zone (EPZ) model was used to study the coupling between fracture of the interface and plastic deformation of the adherends in an adhesively-bonded joint.

Abstract: An embedded-process-zone (EPZ) model was used to study the coupling between fracture of the interface and plastic deformation of the adherends in an adhesively-bonded joint. In this model, it was assumed that the primary role of the adhesive layer is to provide a traction-separation law for the interface. A series of experiments were performed in which thin, adhesively-bonded, symmetrical, double-cantilever beams made of an aluminum alloy were split by inserting different sizes of wedges along the interface. The parameters for the interfacial traction-separation law were determined by comparing the results of these experiments with numerical simulations using the EPZ model. It was found that once these parameters had been established for one thickness of specimen, the EPZ model could be used without further modification to predict the effect of the wedges on specimens made with different thicknesses of aluminum. These predictions showed excellent agreement with experimental observations. A subsequent series of tests involved monitoring the load, displacement and deformed shapes of a series of T-peel specimens made with the same combination of adhesives and adherends. Without changing any of the parameters determined from the wedge tests, the EPZ model gave excellent quantitative predictions for the results of these T-peel tests.

244 citations

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TL;DR: In this paper, a theory for single crystal thin films, starting from three dimensional nonlinear elasticity theory augmented by a term for interfacial energy, is given, which predicts the existence of exact, untwined austenite/martensite interfaces.

Abstract: A direct derivation is given of a theory for single crystal thin films, starting from three dimensional nonlinear elasticity theory augmented by a term for interfacial energy. The derivation involves no a priori choice of asymptotic expansion or ansatz. It yields a frame-indifferent Cosserat membrane theory with one Cosserat vector field. The theory is applied to multi-well energy functions appropriate to martensitic materials. It is found that, unlike in bulk materials, which generally only support finely twinned austenite/martensite interfaces as energy minimizing states, the thin film theory predicts the existence of exact, untwined austenite/martensite interfaces. These are used to construct some simple energy minimizing deformations—”tents” and “tunnels”—that could possibly be the basis of simple large-deformation microactuators. Explicit results are given for martensitic materials in the systems NiMnGa, NiTi,NiTiCu, and NiAl. A certain alloy of precise composition Ni_(30.5) Ti_(49.5) Cu_(20.0) is predicted to support a four-sided “tent” on an (001) film, which furthermore is predicted to collapse to the substrate upon heating. A formal derivation is given of higher order theories, which yields two additional Cosserat vectors and an explicit form of the bending energy. The derivation indicates an approach to plate-shell-thin film theories that is rather different from the ones usually followed.

224 citations

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TL;DR: In this article, the role of the grain boundary in influencing the deformation of a bicrystal is explored using a rate-dependent crystal formulation of the Fleck-Hutchinson strain gradientplasticity theory.

Abstract: The role of the grain boundary in influencing the deformation of a bicrystal isexplored using a rate-dependent crystal formulation of the Fleck–Hutchinson strain gradientplasticity theory. The physical basis of the theory is the elevated strengthening of a slip systemdue to geometrically necessary dislocations, associated with spatial gradients of slip. The theoryis implemented within the finite element framework and is used to study the deformation of abicrystal under in-plane shear loading. Contrary to classical scale-independent crystal plasticitytheories, the strain gradient theory predicts that the deformation state depends strongly upongrain size. Strain gradient effects are pronounced within a narrow layer at the grain boundary of abicrystal, and a significant grain-size dependence of the yield strength is predicted.

213 citations

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TL;DR: In this article, a new Hill-type approach is proposed for rate-dependent elastoplastic heterogeneous materials, which relies on an affine formulation instead of Hills incremental one and on the use of the correspondence principle to solve the concentration problem; this problem is proved to reduce to a linear viscoelastic one with eigenstrain.

Abstract: This paper aims at proving that, contrary to previous contributions to the subject, Hillsconception of the nonlinear self-consistent scheme, which has been applied in the past toelastoplasticity and to viscoplasticity, can still be adopted with success for elastoviscoplasticity.After a qualitative presentation of the main arguments for this statement, a new Hill-typeapproach is proposed for rate-dependent elastoplastic heterogeneous materials. The associatedlinearization procedure relies on an affine formulation instead of Hills incremental one and onthe use of the correspondence principle to solve the concentration problem; this problem isproved to reduce to a linear viscoelastic one with eigenstrain, i.e. to a linear thermoviscoelasticproblem. The full set of equations is reported for the case of the self-consistent scheme andillustrative applications are given for polycrystals: they are shown to be, as expected, alwayssofter than Kroner-type predictions and to take better into account the viscoelastic coupling andthe associated long range memory effect. In conclusion, the connection and differences betweenthe present approach and other ones already proposed for viscoplastic materials is emphasizedand the limits of Hills conception itself are acknowledged and discussed.

168 citations

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TL;DR: In this article, a model for the densification of spherical powders is developed for the early stages of cold and hot compaction under general loading, and a general prescription is given for computing the macroscopic stress as a function of strain rate and accumulated strain.

Abstract: A model for the densification of spherical powders is developed for the early stages of cold and hot compaction under general loading. General viscoplastic properties are adopted which reduce to strain hardening plasticity at ambient temperature and to power law creep at elevated temperature. A large strain analysis is carried out to determine the macroscopic compaction behaviour, based on the affine motion of particles with viscoplastic dissipation occurring at the contacts between particles. Random packing is assumed and the model includes the increase in the number of contacts per particle with densification. A general prescription is given for computing the macroscopic stress as a function of strain rate and accumulated strain. Detailed results are presented for yield surfaces and creep dissipation surfaces after isostatic and closed die compaction. A scalar constraint factor is derived for a random mixture of two populations of particles with different sizes and strengths. The predictions include the limiting case of deformable spheres reinforced with rigid spheres of different size.

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TL;DR: In this paper, a compressed closed-cell polymer foam was modelled using a BBC lattice model of tetrakaidecahedral cells, loaded in the [001] direction, assuming that the faces act as membranes, for a linearly elastic, or a yielding material.

Abstract: A compressed closed-cell polymer foam was modelled using a BBC lattice model of tetrakaidecahedral cells, loaded in the [001] direction. The contributions of cell face tensions and edge bending were analysed, assuming that the faces act as membranes, for a linearly-elastic, or a yielding material. The moduli and tensile yield stresses of highly oriented polymer films were measured to provide data for modelling, and the amount of polymer in the foam cell faces found to be high. Tensile face strains are predicted to reach 40% of the foam compressive strain. The predicted Youngs moduli are slightly low, because compressive face stresses are ignored, but Poissons ratio is correctly predicted. The compressive foam yield stress is predicted to depend on tensile yielding of the cell faces. Predicted values are close to experimental values for polyethylene foams, but half those of polystyrene extruded foams. The latter foam may collapse in compression when face yielding commences, rather than by the collapse mechanism of the model.

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TL;DR: In this paper, the role of the hydrostatic stress on failure of mild steel axisymmetric notched specimens is investigated, and the failure site for specimens having a small notch radius is found in regions of low triaxiality.

Abstract: To investigate the role of the hydrostatic stress on failure, some static and dynamic tensile tests on mild steel axisymmetric notched specimens are described in this paper. Finite–Element results and experimental data indicate that the failure site, for specimens having a small notch radius, occurs in regions of low triaxiality. Comparisons are made between Finite–Element and Bridgman analyses. The influence of some material parameters on the triaxiality levels is explored.

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TL;DR: In this paper, the power of neural networks in identifying material parameters from data obtained by spherical indentation is demonstrated for an academic problem (pure kinematichardening, given Youngs modulus).

Abstract: In this paper the power of neural networks in identifying material parameters fromdata obtained by spherical indentation is demonstrated for an academic problem (pure kinematichardening, given Youngs modulus) . To obtain a data basis for the training and validation of theneural network, numerous finite element simulations were carried out for various sets of materialparameters. The constitutive model describing finite deformation plasticity is formulated withnonlinear kinematic hardening of Armstrong–Frederick type. It was shown by Huber and Tsakmakis, 1998a that the depth–load response of a cyclic indentation process, consisting ofloading, unloading and reloading of the indenter displays a typical hysteresis loop for givenmaterial parameters. The inverse problem of leading the depth–load response back to the relatedparameters in the constitutive equations is solved using a neutral network.

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TL;DR: In this paper, the effects of the mechanical properties of the laminate and the reinforcement, notch length, and plate thickness on the transition between the two limiting configurations, notch sensitivity and mechanical behavior are analyzed.

Abstract: Limiting cases and length scales are detailed for Mode II delamination cracks bridged by through-thickness reinforcement. Analytical results are found for two limits: a steady-state configuration indicative of noncatastrophic failure and a small-scale bridging configuration indicative of catastrophic failure. General large-scale bridging conditions are studied numerically using bending theory for anisotropic plates. The effects of the mechanical properties of the laminate and the reinforcement, notch length, and plate thickness on the transition between the two limiting configurations, notch sensitivity and mechanical behavior are analyzed. All of these effects can be expressed succinctly in terms of a few length scales which are material-structure parameters involving the plate thickness.

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TL;DR: In this paper, the authors analyzed dynamic crack growth along a bimaterial interface under impact shear loading, and the resistance to crack initiation and the crack speed history were predicted without invoking any additional failure criterion.

Abstract: Dynamic crack growth along a bimaterial interface under impact shear loading is analyzed numerically. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any additional failure criterion. Full finite strain transient analyses are carried out. A plane strain model of the configuration used in experiments of Rosakis and co-workers is analyzed. Calculations are carried out for parameters characterizing a steel-PMMA bimaterial. For a sufficiently low impact velocity, the crack speed increases smoothly to the PMMA Rayleigh wave speed, whereas above a sharply defined transition impact velocity, the crack speed reaches a value somewhat less than the PMMA dilational wave speed. This high speed crack growth is associated with multiple crack face contact, separated by discrete micro-crack like openings behind the main shear crack. The calculations reproduce, at least qualitatively, the type of crack speed histories and crack tip fields seen in the experiments. They are also consistent with optical observations of finite multi-site contact occurring at intersonic crack speeds.

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TL;DR: In this article, the authors consider materials which can be described by plasticity laws exhibiting nonlinearkinematic and nonlinear isotropic hardening effects and show that the material parameters governing the constitutive behavior may be determined from data obtained by spherical indentation.

Abstract: We consider materials which can be described by plasticity laws exhibiting nonlinearkinematic and nonlinear isotropic hardening effects. The aim is to show that the materialparameters governing the constitutive behavior may be determined from data obtained byspherical indentation. Note that only the measurable global quantities (load and indentationdepth) should be utilized, which are available, e.g. from depth-sensing indentation tests. For thisgoal use is made of the method of neural networks. The developed neural networks apply also tothe case of pure kinematic as well as pure isotropic hardening. Moreover it is shown how amonotonic strain–stress curve can be assigned to the spherical indentation test.

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TL;DR: In this article, the apparent stiffness tensors of two-dimensional elastic composite samples smaller than the representative volume element (RVE) are studied as a function of system size, and the results show that the difference between the Dirichlet, Neumann and the effective stiffensors depends strongly on the phase stiffness contrast ratio.

Abstract: The apparent stiffness tensors of two-dimensional elastic composite samples smaller thanthe representative volume element (RVE) are studied as a function of system size. Numericalexperiments are used to investigate how the apparent properties of the composite converge withincreasing scale factor n, defined to be the ratio between the linear size of the composite and thelinear size of the unit cell. Under affine (Dirichlet-type) or homogeneous stress (Neumann-type) boundary conditions, the apparent elastic moduli overestimate orunderestimate, respectively, the effective elastic moduli of the infinitely periodic system. Theresults show that the difference between the Dirichlet, Neumann and the effective stiffnesstensors depends strongly on the phase stiffness contrast ratio. Dirichlet boundary conditionsprovide a more accurate estimate of the effective elastic properties of stiff matrix composites,whereas Neumann boundary conditions provide a more accurate estimate for compliant matrixstructures. It is shown that the apparent bulk and shear moduli may lie outside of theHashin–Shtrikman bounds. However, these bounds provide good upper and lower estimates forthe apparent bulk and shear moduli of structures with a scale factor n ⩾ 2. A similar approach isused to study hierarchical composites containing two distinct structural levels with a finiteseparation of length scales. It is shown, numerically, that the error associated with replacing thesmallest-scale regions by an equivalent homogeneous medium is very small, even when the ratiobetween the length scales is as low as three.

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TL;DR: In this article, the influence of thickness on the fracture toughness of aluminum 6082T0 thin plates of 1-6 mm thicknesses was investigated experimentally and numerically from tensile testing of cracked DENT specimens.

Abstract: The influence of thickness on the fracture toughness of aluminium 6082T0 thin plates of 1-6 mm thicknesses was investigated experimentally and numerically from tensile testing of cracked DENT specimens. The critical J-integral, J(c), critical CTOD, delta(CTODc), and essential work of fracture, w(e), are found to increase with thickness and to constitute equivalent measures of fracture toughness at small thickness. For larger thickness, J(c) and delta(CTODc) increase non-linearly with thickness and reach a maximum for 5-6 mm thickness Whereas iv, keeps increasing linearly with thickness. This difference is related to a more progressive development of the necking zone in front of the crack tip when thickness increases: at large thickness, cracking initiates well before the neck has developed to its stationary value during propagation, w(e) is more directly related to the steady-state crack growth resistance. A linear regression on the fracture toughness/thickness curve allows further separation of the two contributions of the essential work of fracture: the necking work and the fracture work spent for damaging. The maximum of the stress triaxiality ratio is shown to constitute a pertinent parameter for characterising how constraint affects cracking initiation in the present context where out-of-plane constraint dominates in-plane constraint. It allows justifying the shape of the J(c)/thickness relationship and results in the proposal of a 3D J(c)/thickness/triaxiality fracture locus. As fracture profiles are macroscopically flat with microscopic dimples and with only very small shear lips along the edges, a local criterion based on the growth and coalescence of voids has been used in order to predict fracture initiation. (C) 1999 Elsevier Science Ltd. All rights reserved.

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TL;DR: In this article, a specially developed infrared radiometer has been used to measure the rise in specimen surface temperature during the high strain rate tests where the deformation process is essentially adiabatic.

Abstract: Shear stress-strain curves have been obtained for thin-walled tubular specimens of Ti6Al4V alloy at strain rates from ∼7×10−4/s to ∼1000/s. A specially developed infrared radiometer has been used to measure the rise in specimen surface temperature during the high strain rate tests where the deformation process is essentially adiabatic. The data obtained were used to obtain material constants for a Zerilli–Armstrong type constitutive relation giving the best fit with the observed mechanical response. This relation was incorporated in the ABAQUS/explicit FE code and shown to predict the experimentally measured flow stress in the impact tests with reasonable accuracy. A failure criterion, based on a critical value of effective plastic strain, is also incorporated, the critical condition being chosen to give agreement between the predicted and the measured overall failure strains. The validity of the constitutive relation and associated failure criterion is then assessed in terms of their ability to predict the observed mechanical response in tensile impact tests on specimens of both cylindrical and rectangular cross-section where the early onset of localised plastic flow and significant temperature rises in this region provide a more rigorous test of the proposed model. High-speed photography was used to monitor the changing specimen cross-section and the infrared radiometer was used to determine the specimen surface temperature in the region of localised deformation. Reasonable agreement was obtained between the experimental results and the numerical predictions using the ABAQUS/explicit FE code.

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TL;DR: In this paper, a general three-dimensional analysis of a penny-shaped crack subjected to normal mechanical loads and free surface electric charges symmetrically applied on its upper and lower surfaces is presented.

Abstract: This paper intends to present a general three-dimensional analysis of a penny-shapedcrack subjected to normal mechanical loads and free surface electric charges symmetricallyapplied on its upper and lower surfaces. To this end, the potential theory method is employed andgeneralized to analyze the piezoelectric crack problem under consideration. In particular, anotherpotential of a simple layer, corresponding to the electric effect, is introduced. As a typicalexample, a closed-form solution is first obtained for a penny-shaped crack subjected to a pair ofconcentrated forces acting in opposite directions and a pair of point charges on crack surfaces.Exact expressions for stress and electric displacement intensity factors are also presented.

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Brown University

^{1}TL;DR: In this article, three dimensional finite element computations are used to predict the formation of quantum dot arrays in a strained epitaxial thin film system, where a small, doubly sinusoidal variation in film thickness is introduced to trigger island formation.

Abstract: Three dimensional finite element computations are used to predict the formation of quantum dot arrays in a strained epitaxial thin film system. The film is idealized as an initially planar, isotropic elastic layer with isotropic surface energy, which is coherently bonded to an elastic, lattice mismatched substrate. A small, doubly sinusoidal variation in film thickness, intended to represent the dominant wavelength of surface roughness, is introduced to trigger island formation. The film continues to roughen due to strain induced surface diffusion and eventually breaks up into arrays of discrete islands. The conditions necessary for island formation are identified, and are shown to differ significantly from the conditions necessary for spontaneous roughening of a strained layer. A detailed parametric study is conducted to determine the influence of the properties of film and substrate, film thickness, and surface roughness on the resulting island morphologies. In particular, our simulations show that there exists a critical range of surface roughness wavelength which leads to the formation of perfectly periodic island arrays. Finally, our predictions are compared with existing experimental measurements.

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TL;DR: In this article, a phenomenological continuum model of film growth is presented based on a series expansion of the deposition flux in powers of the profile gradient, consideration of the energetics of the film-substrate interface and the enforcement of Onsagers reciprocity relations.

Abstract: We present a phenomenological continuum model of film growth based on a series expansion of the deposition flux in powers of the profile gradient, consideration of the energetics of the film–substrate interface and the enforcement of Onsagers reciprocity relations. The interfacial term, which operates at very small thicknesses, is nonconservative and breaks the ±h symmetry of the remaining terms in the kinetic equation. By virtue of this term, very thin flat films are predicted to be stable within an appropriate range of parameters, and to loose stability and become rough at a well-defined critical thickness. This instability effectively provides an island nucleation mechanism. For thick films, the rate processes envisioned in the model favor a characteristic slope for the film profile, a feature which is in keeping with observation for a number of systems including YBCO films. The enforcement of reciprocity ensures the existance of a kinetic potential and enables the use of direct methods of the calculus of variations. Within this framework, we provide an explicit construction for the coarsening of the film profile based on a sharp interface approximation. The construction predicts characteristic exponents for the evolution of grain size and film roughness which are in close agreement with the observational evidence for YBCO. The predictions of the construction are also born out by numerical tests.

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TL;DR: In this article, the intrinsic toughness of glass/epoxy interfaces of sandwich specimens was calculated via finite element analysis and subtracted from the steady-state fracture toughness to obtain the intrinsic hardness of the interface.

Abstract: Glass/epoxy interfaces of sandwich specimens were fractured under steady-state conditions over a wide range of in-plane mode-mix. The plastic dissipation was calculated via finite element analysis and subtracted from the steady-state fracture toughness to obtain the intrinsic toughness of the interface. Mechanisms which contribute to the intrinsic toughness were found to include the thermodynamic work of adhesion, local inelastic deformations and polymer chain pull-out, but their combined energy was only approximately 15% of the intrinsic toughness. Angular dependent x-ray photoelectron spectroscopy of the glass surfaces after fracture revealed epoxy adsorbed to a depth of approximately 3 nm. Cleavage of epoxy strands was found to be the most significant mechanism contributing approximately 40% to the intrinsic toughness of the interface.

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TL;DR: In this paper, a detailed finite element model of the microstructure and an accurate elasto-viscoplastic model for the glassy polymeric matrix material was used to predict the mechanical behavior of voided polycarbonate.

Abstract: The mechanical behaviour of voided polycarbonate has been predicted by using a detailed finite element model of the microstructure and an accurate elasto–viscoplastic model for the glassy polymeric matrix material. On the microstructural level a spatially periodic plane strain matrix with irregularly distributed voids has been considered. The voids represent low-modulus non-adhering rubbery particles under negative pressure. The constitutive model for the homogeneous parts of the material reflects the typical yield and post-yield behaviour of glassy polymers: strain rate and history dependent yield, intrinsic strain softening and subsequent strain hardening. The finite element simulations show that the irregular void distribution causes a radical change in deformation behaviour. In particular the macroscopic strain softening disappears. This transformation in macroscopic behaviour originates from the arbitrary order in which local shear bands between the randomly distributed voids are formed and subsequently harden. In the averaged overall mechanical response the individual unstable yield and post-yield behaviour of the local shear bands is evened out, resulting in an overall stable macroscopic deformation behaviour. This mechanism is believed to be primarily responsible for the toughness enhancement of heterogeneous polymer systems through the addition of easily cavitating rubbery particles.

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TL;DR: In this paper, the stability of quasi-static frictional slip of a single degree of freedom elastic system is studied for a Dieterich-Ruina rate and state dependent friction law, showing steady state velocity weakening, and following the ageing (or slowness) version of the state evolution law.

Abstract: The stability of quasi-static frictional slip of a single degree of freedom elastic system is studied for a Dieterich–Ruina rate and state dependent friction law, showing steady-state velocity weakening, and following the ageing (or slowness) version of the state evolution law. Previous studies have been done for the slip version. Analytically determined phase plane trajectories and Liapunov function methods are used in this work. The stability results have an extremely simple form: (1) When a constant velocity is imposed at the load point, slip motion is always periodic when the elastic stiffness, K, has a critical value, Kcr. Slip is always stable when K > Kcr > 0, with rate approaching the load-point velocity, and unstable (slip rates within the quasi-static model become unbounded) when K Kcr. An implication of this result for slip instabilities in continuum systems is that a critical nucleation size of coherent slip has to be attained before unstable slip can ensue. (2) When the load point is stationary, the system stably evolves towards slip at a monotonically decreasing rate whenever K ⩾ Kcr > 0. However, when K

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Brown University

^{1}TL;DR: In this paper, the authors investigated dynamic necking bifurcations which occur during rapid plane strain extension of a block of strain hardening plastic material and found that the number of necks formed per unit length is proportional to the square root of the mean extensional strain rate of the block.

Abstract: Dynamic necking bifurcations which occur during rapid plane strain extension of a block of strain hardening plastic material are investigated. The block is presumed to be a portion of a plate or thin-walled shell deforming at high strain rate. It is found that the rates of growth of both very long and very short wavelength modes of nonuniform deformation are suppressed by inertia, thus promoting a necking pattern at an intermediate wavelength. The analysis indicates that, for blocks of small aspect ratio, the number of necks formed per unit length is proportional to the square root of the mean extensional strain rate of the block. The results of the analysis agree with necking patterns observed in high velocity ring expansion experiments and in detailed numerical simulations.

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TL;DR: In this paper, the internal stress state of a three-phase elliptic inclusion which is bonded to an infinite matrix through an intermediate elastic layer is studied. But the authors focus on the interphase layer.

Abstract: For an elastic inclusion embedded within an elastic matrix, it is the interfacialstresses that control mechanical integrity of the inclusion/matrix system. To eliminate the stresspeaks at the interface, the uniform hydrostatic stress state within the inclusion is of particularinterest because it achieves both uniform normal stress and vanishing tangential stress along theentire interface. Motivated by practical significance of interphase layer, the present paper studiesthe internal stress state of a three-phase elliptic inclusion which is bonded to an infinite matrixthrough an intermediate elastic layer. What is essential is that the interfaces of the three-phaseelliptic inclusion considered are two confocal ellipses. A simple condition is found that ensuresthat the internal stress state within the elliptic inclusion is uniform and hydrostatic. For givenremote stresses and material parameters, this condition gives a simple relationship between thethickness of the interphase layer and the aspect ratio of the elliptic inclusion. The exact stressfield is obtained in elementary form when this condition is met. In particular, the hoop stress inthe interphase layer is found to be uniform along the entire interphase/inclusion interface. It isbelieved that the availability of this condition relies on the confocal character of the ellipticinterfaces.

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TL;DR: In this paper, a three-dimensional model of a tungsten-silver composite is statistically constructed from an experimental two-dimensional image, and the effective Young's modulus (E) of the model is computed in the temperature range 25-1060 degrees C using a finite element method.

Abstract: A three-dimensional model of a tungsten-silver composite is statistically constructed from an experimental two-dimensional image. The effective Young's modulus (E) of the model is computed in the temperature range 25-1060 degrees C using a finite element method. The results are in good agreement with experimental data. The reconstructed and overlapping sphere models are examples of bi-continuous (non-particulate) media. The computed moduli of the models are not generally in good agreement with the predictions of the self-consistent method. It has also been possible to evaluate the three-point variational bounds on the Young's moduli of the models using the results of Beran, Molyneux, Milton and Phan-Thien. The measured data were close to the upper bound if the properties of the two phases were similar (1/6 < E-1/E-2 < 6). (C) 1999 Elsevier Science Ltd. All rights reserved.

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TL;DR: In this paper, the deformation behavior of amorphous polymer-rubber blends is investigated in terms of an axisymmetric unit cell model containing an initially spherical rubber particle.

Abstract: The deformation behaviour of amorphous polymer–rubber blends is investigated in terms of an axisymmetric unit cell model containing an initially spherical rubber particle. The behaviour of the rubber is described by an incompressible non-Gaussian network theory, while for the matrix we adopt a recent large strain elastic–viscoplasticity model that incorporates the intrinsic softening upon yield and the subsequent progressive orientation hardening typical for amorphous glassy polymers. Guided by simple analytical estimates, cavitation of the rubber particle is interpreted in terms of the unstable growth of a pre-existing small void. It is shown that cavitation and yield are essentially coupled processes. On the macroscopic scale, both are softening mechanisms : If macroscopic yield takes place before the limit stress for cavitation is reached, cavitation is prohibited. Furthermore, and contrary to common belief, it is found from the interfacial stress history that, using realistic material parameters, the rubber particle continues to significantly affect plasticity in the matrix in the post-cavitation regime, i.e. after it has cavitated, so that cavitated particles cannot always be considered to be equivalent to particle-sized voids.