Alan Needleman

Texas A&M University | TAMU · Materials Science & Engineering

A method for solving three dimensional discrete dislocation plasticity boundary-value problems using a monopole representation of the dislocations is presented. At each time step, the displacement, strain and stress fields in a finite body are obtained by superposition of infinite body dislocation fields and an image field that enforces the boundar...

The requirement of a non-negative dissipation rate for all possible deformation histories is generally imposed on plastic constitutive relations. This is a constraint analogous to the Coleman-Noll [1] postulate that the Clausius-Duhem inequality needs to be satisfied for all possible deformation histories. The physical basis for the Clausius-Duhem...

A previously proposed strain gradient plasticity theory is extended to incorporate a non-quadratic power law function of the plastic strain gradient in the free energy expression with an exponent of N + 1. The values of N are taken to vary from N = 1 to N = 0. A simple shear problem of a metal layer between rigid boundaries is analyzed. Two stages...

The focus is on discrete defects that can be modeled by continuum mechanics, but where the discreteness of the carriers of plastic deformation plays a significant role. The formulations are restricted to small deformation kinematics and the defects considered, dislocations and discrete shear transformation zones (STZs), are described by their linea...

The most widely used phenomenological constitutive relation to model ductile failure of structural metals at room temperature is based on the work of Gurson (1977) and has the advantage of having both a micromechanics basis and sufficient simplicity to enable complex engineering calculations to be carried out. The predictions of this framework have...

Load and hold conical indentation responses calculated for materials having creep stress exponents of 1.15, 3.59 and 6.60 are regarded as input ‘experimental’ responses. A Bayesian-type statistical approach (Zhang et al. 2019 J. Appl. Mech. 86 , 011002 ( doi:10.1115/1.4041352 )) is used to infer power-law creep parameters, the creep exponent and th...

Dynamic frictional slip along an interface between plastically compressible solids is analyzed. The plane strain, small deformation initial/boundary value problem formulation and the numerical method are identical to those in Shi et al. (Int J Fract 162:51, 2010) except that here the material constitutive relation allows for plastic compressibility...

The response in constrained shear of materials characterized by discrete Shear Transformation Zone (STZ) plasticity is investigated. A plane strain strip of finite thickness is analyzed within a small deformation framework and with the STZs modeled as Eshelby inclusions in an isotropic elastic solid. The strip is unbounded and consists of periodic...

A three-dimensional finite deformation study of necking and failure in rectangular tensile bars is carried out using a constitutive relation for porous material plasticity. The fully dynamic formulation accounts for void nucleation and growth along with thermal and rate effects, but here focus is on quasi-static response with a specified initial vo...

The response in spherical indentation is used to identify material properties for plastically compressible materials with presumed known elastic properties. The materials are assumed to be characterized by a Deshpande–Fleck constitutive relation (Deshpande and Fleck, 2000). The indentation force versus indentation depth responses and the residual s...

Plane strain finite element analyses are used to model the experiments of Mu et al. (2014, 2016) for a thin metal layer confined between elastic solids. The thin metal layer undergoes elastic-plastic deformations, here modelled by strain gradient plasticity, while the rest of the solid deforms only elastically. Plane strain is assumed and finite st...

We develop a continuum mechanics model of blastocyst hatching. The blastocyst and the zona pellucida are modeled as concentric thick-walled initially spherical shells embedded in a viscous medium. Each shell is characterized by a nonlinear elastic–viscous–constitutive relation. The stiffer outer shell (the zona pellucida) contains an opening. The s...

The influence of grain size distribution on ductile intergranular crack growth resistance is investigated using full-field microstructure-based finite element calculations and a simpler model based on discrete unit events and graph search. The finite element calculations are carried out for a plane strain slice with planar grains subjected to mode...

Plastic deformation of crystalline metals mainly takes place by the nucleation and motion of dislocations, line defects in the atomic lattice. At a length scales of micrometers, dislocations can conveniently be idealized as discrete line defects in an elastic continuum and plastic deformation can be represented by the evolution of the dislocation s...

Instrumented indentation tests provide an attractive means for obtaining data to characterize the plastic response of engineering materials. One difficulty in doing this is that the relation between the measured indentation force versus indentation depth response and the plastic stress-strain response is not unique. Materials with very different un...

Preface: Proceedings of the Century Fracture Mechanics Summit

The influence of grain size distribution on ductile intergranular crack growth resistance is investigated using full field microstructure-based finite element calculations and a simpler model based on discrete unit events and graph search. The finite element calculations are carried out for a plane strain sheet with planar grains subjected to mode...

Simple shear of a ductile layer constrained between two rigid solids is analyzed using a conventional one dimensional strain gradient plasticity formulation. The aim of the analyses is to gain insight into the scaling relations and size effects seen in the experiments of Mu et al. (Extreme Mech. Lett. 1 (2014) 62-69; MRS Commun. 6 (2016) 289-294; J...

Vasoya et al. (J. Appl. Mech., 86, 051005, 2019) gave a general expression for the dissipation associated with a single transforming Eshelby inclusion in a linear elastic solid and showed that requiring the dissipation to be non-negative provides a strong limit on the maximum value of the transformation strain magnitude. Non-negative dissipation is...

A model based on discrete unit events coupled with a graph search algorithm is developed to predict intergranular fracture. The model is based on two hypotheses: (i) the key unit event associated with intergranular crack propagation is the interaction of a grain boundary crack with a grain boundary segment located at an angle with the initial crack...

We consider the maximum value of the magnitude of trans- formation strain for an Eshelby inclusion set by the requirement of non-negative dissipation. The general formulation for a linear elastic solid shows that the dissipation associated with a strain transformation can be calculated as an integral over the transformed inclusion. Closed-form expr...

Nonuniform and localized deformation in planar single crystals subjected to dynamic tensile loading is investigated using finite element method. An idealized planar double-slip model is used to represent the crystal geometry. A size-dependent higher-order gradient crystal plasticity theory accounting for finite strains is adopted to characterize th...

Dynamic crack growth is analyzed numerically for a planar bimaterial block with an initial edge crack subject to mode II impact loading along the side of the block. The crack is constrained to grow along a weak interface directly ahead of the initial crack tip. A cohesive constitutive relation, that relates tractions and displacement jumps, is spec...

The plastic properties that characterize the uniaxial stress–strain response of a plastically isotropic material are not uniquely related to the indentation force versus indentation depth response. We consider results for three sets of plastic material properties that give rise to essentially identical curves of indentation force versus indentation...

Plane strain finite element calculations of mode I crack growth are carried out under small scale creep conditions with an imposed stress intensity factor that is a prescribed cyclic function of time. The finite deformation analyses are based on a constitutive relation that couples creep deformation and damage due to grain boundary cavitation inclu...

The indentation of plant cells by a conical indenter is modeled. The cell wall is represented as a spherical shell consisting of a relatively stiff thin outer layer and a softer thicker inner layer. The state of the interior of the cell is idealized as a specified turgor pressure. Attention is restricted to axisymmetric deformations, and the wall m...

Plane strain tension analyses of un-notched and notched bars are carried out using discrete shear transformation zone plasticity. In this framework, the carriers of plastic deformation are shear transformation zones (STZs) which are modeled as Eshelby inclusions. Superposition is used to represent a boundary value problem solution in terms of discr...

Plane strain finite deformation finite element calculations of mode I crack growth under small scale creep conditions are carried out. Attention is confined to isothermal conditions and two time histories of the applied stress intensity factor: (i) a monononic increase to a plateau value subsequently held fixed; and (ii) a cyclic time variation. Th...

The effect of taper on the plastic response of micropillars with a relatively high density of dislocation sources ( ) is analyzed. The large number of dislocation sources and dislocations in the simulations rule out many of the mechanisms that govern size effects in pillars with a low dislocation source density. The mechanical response of compresse...

A model for description of the creep response of porous cubic single crystal is presented. The plastic potential is obtained by specializing the orthotropic potential of Stewart and Cazacu (Int. J. Solids Struct., 48, 357, 2011) to cubic symmetry. The crystal matrix material response is characterized by power law creep. The predictions of this poro...

We explore the possibility of engineering the crack path by controlling a material's microstructure in order to increase its crack growth resistance. Attention is confined to a specific type of microstructure that is encountered in a variety of structural metals and alloys - second phase particles distributed in a ductile matrix. The type of contro...

Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic-viscoplastic constitutive relation with various hardening-softening-hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding...

Ductile fracture of structural metals occurs mainly by the nucleation, growth and coalescence of voids. Here an overview of continuum models for this type of failure is given. The most widely used current framework is described and its limitations discussed. Much work has focused on extending void growth models to account for non-spherical initial...

The influence of material inertia on neck development in a notched round bar is analyzed numerically. Dynamic axisymmetric calculations are carried out for isotropically hardening elastic-viscoplastic solids so that both material strain rate sensitivity and material inertia are accounted for. The focus is on the effect of bar size on whether the no...

The indentation response of polymer spherical shells is investigated. Finite deformation analyses are carried out with the polymer characterized as a viscoelastic/viscoplastic solid. Both pressurized and unpressurized shells are considered. Attention is restricted to axisymmetric deformations with a conical indenter. The response is analyzed for va...

The effect of soft elasticity, i.e., a relatively small value of the ratio of Young’s modulus to yield strength and plastic compressibility on the indentation of isotropically hardening elastic–viscoplastic solids is investigated. Calculations are carried out for indentation of a perfectly sticking rigid sharp indenter into a cylinder modeling inde...

Localization of deformation and failure, a complete loss of stress carrying capacity, is studied for two rate dependent constitutive relations: (i) a Kelvin-Voigt solid and (ii) a viscoplastic solid. A planar block infinite in one direction is subjected to monotonically increasing shear displacements at a fixed rate. Geometry changes are neglected...

Ductile crack growth in a grain boundary layer is modeled under mode I plane-strain, small-scale yielding conditions. The calculations are carried out for planar polycrystals using an elastic–viscoplastic constitutive relation for a progressively cavitating solid with two populations of void nucleating second-phase particles. The material propertie...

A cohesive surface theory of fracture is a phenomenological continuum framework that is closely related to classical fracture mechanics. As such it shares the advantages and disadvantages of any phenomenological continuum frame- work. The continuum is characterized by two constitutive relations: (1) a volumetric constitutive law that relates stress...

The effect of material parameters on the statistics of fracture surfaces is analyzed under small scale yielding conditions. Three dimensional calculations of ductile crack growth under mode I plane strain, small scale yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progressively cavitating plastic solid...

Isothermal creep tests on single-crystal Ni-based superalloy sheet specimens show a thickness-dependent creep response that is known as the thickness debit effect. A size-dependent creep response at similar length scales has also been observed in a wide variety of other materials. We focus on Ni-based single-crystal superalloys and present a phenom...

Micro-mechanical experiments, image analysis, and theoretical modeling revealed that local failure events and compressive stresses of vertically aligned carbon nanotubes (VACNTs) were uniquely linked to relative density gradients. Edge detection analysis of systematically obtained scanning electron micrographs was used to quantify a microstructural...

Three dimensional calculations of ductile crack growth under mode I plane strain, small scale yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progres- sively cavitating plastic solid with two populations of void nucleating second phase particles. Full field solutions are obtained for three dimensional m...

Motivated by a model that qualitatively captured the response of vertically aligned carbond nanotube (VACNT) pillars in uniaxial compression, we consider the uniaxial tensile response of a class of compressible elastic-viscoplastic solids. In Hutchens et al. ["Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes," J. Mech. Phys....

In the cohesive surface model cohesive tractions are transmitted across a two-dimensional surface, which is embedded in a three-dimensional continuum. The relevant kinematic quantities are the local crack opening displacement and the crack sliding displacement, but there is no kinematic quantity that represents the stretching of the fracture plane....

'Metal-Matrix Composites are being used or considered for use in a variety of applications in the automotive, aerospace and sporting goods industries. This book contains sixteen chapters, all written by leading experts in the filed, which focus on the processing, microstructure and characterization, mechanics and micromechanics of deformation, mech...

Creep tests on Ni-based single-crystal superalloy sheet specimens typically show greater creep strain rates and/or reduced strain or time to creep rupture for thinner specimens than predicted by current theories, which predict a size-independent creep strain rate and creep rupture strain. This size-dependent creep response is termed the thickness d...

The effect of material parameters characterizing viscoplastic flow on the indentation response of polymers is investigated using three-dimensional finite element analyses and a one-dimensional expanding spherical cavity model. The polymer is characterized by a finite strain elastic–viscoplastic constitutive relation and two indenter shapes are cons...

Motivated by a model of the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we consider the deformation of a class of compressible elastic-viscoplastic solids with a hardeningsoftening-hardening variation of flow strength with plastic strain. In previous work (Hutchens et al. 2011) a constitutive relation was...

Experimental observations have shown that the roughness of fracture surfaces exhibit certain characteristic scaling properties. Here, calculations are carried out to explore the extent to which a ductile damage/fracture constitutive relation can be used to model fracture surface roughness scaling. Ductile crack growth in a thin strip under mode I,...

Numerical studies of the ductile-brittle transition are described that are based on incorporating physically based models of the competing fracture mechanisms into the material's constitutive relation. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth o...

Vertically aligned carbon nanotube’s extreme compliance and mechanical energy absorption/dissipation capabilities are potentially promising aspects of their multi-functionality. Mathematical models have revealed that a hardening-softening-hardening material relation can capture the unique sequential, periodic buckling behavior displayed by vertical...

Experimental observations on tensile specimens in Srivastava et al (2012 in preparation) indicated that the growth of initially present processing induced voids in a nickel-based single crystal superalloy played a significant role in limiting creep life. Also, creep tests on single crystal superalloy specimens typically show greater creep strain ra...

Indentation of spherical shells by a rigid conical indenter is analyzed. Because the shape change associated with overall bending provides a main deviation from the corresponding indentation behavior of a half-space, finite deformation analyses are carried out. The shell material is characterized by a hypoelastic relation that reduces to isotropic...

A discrete dislocation simulation of plastic deformation in metallic interconnects caused by thermal stress is carried out. The calculations are carried out using a two dimensional plane strain formulation with only edge dislocations. A boundary value problem is formulated and solved for the evolution of the thermal stress field and the evolution o...

Small scale yielding around a plane strain mode I crack is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic material. At each stage of loading, superposition is used to represent the solution in terms of solutions for edge dislocations in a half-space and a...

The effect on stiffness and debonding of an interphase zone of altered polymer properties surrounding each carbon nanotube (CNT) in a CNT reinforced polymer composite is investigated. The interphase zone has position dependent material properties that merge with those of the polymer at a sufficiently large distance from the inclusion. There is evid...

A framework for accurately modeling fatigue crack growth in ductile crystalline solids is necessarily multiscale. The creation of new free surface occurs at the atomistic scale, where the material’s cohesive strength is controlled by the local chemistry. On the other hand, significant dissipation during fatigue crack growth takes place at a size sc...

A finding by Benzerga et al. (Acta Mater 2001; 49:3071) that the yield strength of Al–7Si–0.3Mg castings is smaller for castings with a fine secondary dendrite arm spacing (SDAS) than for those with a coarse SDAS is revisited. Previous experimental data for Al–Si–Mg castings are reviewed, and new experiments carried out, both on the original castin...

The effect of plasticity on dynamic frictional sliding along an interface between two identical elastic–viscoplastic solids is analyzed. The configuration considered is the same as that in Coker etal. (J Mech Phys Solids 53:884–992, 2005) except that here plane strain analyses are carried out and bulk material plasticity is accounted for. The speci...

We present a finite element method with a finite thickness embedded weak discontinuity to analyze ductile fracture problems. The formulation is restricted to small geometry changes. The material response is characterized by a constitutive relation for a progressively cavitating elastic–plastic solid. As voids nucleate, grow and coalesce, the stiffn...

Convergent beam electron diffraction patterns of silicon from blanket wafers of ∼50 nm Si _0.85 Ge _0.15 on Si and ∼126 nm Si _0.79 Ge _0.21 on Si and from a complementary metal-oxide-semiconductor transistor with recessed Si _0.82 Ge _0.18 stressors were analyzed at zone axes slightly off...

The grain size dependence of the flow strength of polycrystals is analyzed using plane strain, discrete dislocation plasticity. Dislocations are modeled as line singularities in a linear elastic solid and plasticity occurs through the collective motion of large numbers of dislocations. Constitutive rules are used to model lattice resistance to disl...

A hierarchical multi-scale model that couples a region of material described by discrete dislocation plasticity to a surrounding region described by conventional crystal plasticity is presented. The coupled model is aimed at capturing non-classical plasticity effects such as the long-range stresses associated with a density of geometrically necessa...

The monotonic and cyclic crack growth rate of cracks is strongly influenced by the microstructure. Here, the growth of cracks emanating from pre-cracked micron-scale elastic particles and growing into single crystals is investigated, with a focus on the effects of (i) plastic confinement due to the elastic particle and (ii) elastic modulus mismatch...

Plane strain indentation of single crystals by a periodic array of flat rigid contacts is analyzed. The calculations are carried out, with the mechanical response of the crystal characterized by conventional continuum crystal plasticity or by discrete dislocation plasticity. The properties used in the conventional crystal plasticity description are...

Bulging and necking in long thin polymer tubes subjected to increasing internal pressure are analysed numerically. The polymer is characterized by a finite strain elastic–viscoplastic constitutive relation and the calculations are carried out using a dynamic finite element program. Two types of imposed loading are prescribed: (i) a pressure that in...

The effect of a reduced section thickness leading to creep strain greater than that observed in the creep response of thicker sections is termed the thickness debit effect. We carry out three-dimensional analyses of the creep response of specimens with rectangular cross sections under uniaxial tensile loading having a boundary damage layer and expl...

of a paper presented at Microscopy and Microanalysis 2008 in Albuquerque, New Mexico, USA, August 3 – August 7, 2008

The Izod impact test is analyzed numerically using a polymer constitutive relation with material parameters qualitatively representative of a polycarbonate. The computations are full 3D transient analyses using explicit time integration and accounting for finite strains. The main purpose of the analyses is a comparison of the stress and strain fiel...

The cohesive segments method is a finite element framework that allows for the simulation of the nucleation, growth and coalescence of multiple cracks in solids. In this framework, cracks are introduced as jumps in the displacement field by employing the partition of unity property of finite element shape functions. The magnitude of these jumps are...

We study properties of dynamic ruptures and the partition of energy between radiation and dissipative mechanisms using two-dimensional in-plane calculations with the finite element method. The model consists of two identical isotropic elastic media separated by an interface governed by rate- and state-dependent friction. Rupture is initiated by gra...

The initiation and growth of necks in polymer tubes subjected to rapidly increasing internal pressure is analyzed numerically. Plane strain conditions are assumed to prevail in the axial direction. The polymer is characterized by a finite strain elastic–viscoplastic constitutive relation and the calculations are carried out using a dynamic finite e...

Numerical analyses of the Izod impact test for polymers are used to compare the effect of different sets of material parameters. Full 3D finite strain transient analyses are carried out using a nonlinear polymer constitutive relation. The predicted differences in the overall load-deflection response and in the evolution of the field quantities in t...

Contact and frictional sliding of a surface between two solids governs a range of technologically important mechanical behaviors and failure mechanisms. Frictional dissipation significantly contributes to the energy needed for material processing and to that used by rotating machinery. Wear and surface fracture limit the lifetime of machines and co...

We study properties of dynamic ruptures and the partition of energy between radiation and dissipative mechanisms using two-dimensional in-plane calculations with the finite element method. The model consists of two identical isotropic elastic media separated by an interface governed by rate- and state-dependent friction. Rupture is initiated by gra...

This paper reports a study of the indentation of a model polycrystal using two-dimensional discrete dislocation plasticity. The polycrystal consists of square grains having the same orientation. Grain boundaries are modelled as being impenetrable to dislocations. Every grain has three slip systems, with a random distribution of initial sources and...

Numerical and experimental investigation of frictional sliding under dynamic loading conditions is dis- cussed. The configuration analyzed consists of two plates of Homalite (an elastic birefringent polymer material) connected along a planar interface. The plates are characterized as isotropic elastic materials and the interface is characterized by...

There is considerable experimental evidence that over length scales of the order of microns and smaller the plastic response of crystalline metals differs from the predictions of conventional continuum plasticity. In particular, the plastic response of crystalline metals is often size dependent over this length scale. The size dependence arises in...