Papers by A. Amine Benzerga
Journal of The Mechanics and Physics of Solids, Feb 1, 2023
Issues related to the size dependence of the upper shelf energy (USE) and the ductile-to-brittle ... more Issues related to the size dependence of the upper shelf energy (USE) and the ductile-to-brittle transition temperature (DBTT) in the Charpy V-notch test are investigated. Emphasis is placed on the interplay between inertial, strain rate hardening, strain hardening, thermal softening and material length scale effects. Geometrically similar specimens are considered first. For such specimens, the ductile-to-brittle transition temperature is found to increase with specimen size, with the amount of the increase depending on the material properties. To model available experiments, calculations are also carried out for Charpy specimens where only the ligament size is varied and two classes of pipe steels are considered. For a relatively high strength pipe steel, the experimental results exhibit no size dependence of the DBTT. On the other hand, a significant shift in the DBTT is obtained for a low strength steel. The numerical studies are used to understand the difference between these two classes of steels. The extent to which the size effect is material dependent is investigated.
International Journal of Solids and Structures, Oct 1, 2023
Some raw or processed data gathered during the work. Includes all data reported in the paper alon... more Some raw or processed data gathered during the work. Includes all data reported in the paper along with multiple realizations.
Bulletin of the American Physical Society, Mar 21, 2011
Acta Materialia, Jul 1, 2018
Plane strain finite element calculations of mode I crack growth are carried out under small scale... more 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 including a simple model of the embrittling effect of solute (oxygen) diffusion along grain boundaries. Isothermal analyses are carried out for two sets of material and grain boundary parameters: (i) parameter values representative of HASTELLOY R X; and (ii) parameter values representative of P91. For a fixed imposed stress intensity factor range the detrimental environmental effect is found to increase with increased hold time. A stronger detrimental effect of environmentally assisted grain boundary embrittlement is found for HASTELLOY R X than for P91. The variation of the predicted cyclic crack growth rate with imposed stress intensity factor range is found to be in good quantitative agreement with experimental results in the literature for both HASTELLOY R X and P91. Paris law behavior, i.e. the cyclic crack growth rate depending on the imposed stress intensity factor range raised to a power, emerges naturally in the calculations. Parametric studies show that the cyclic crack growth rate and the Paris law exponent are more sensitive to variations in the grain boundary diffusivity, the solute diffusivity and a parameter characterizing the environmental embrittling effect than to parameters characterizing the creep response of the undamaged material. Also, an explicit analytical expression is found that gives a very good fit to the computed dependence of the cyclic crack growth rate on the solute diffusivity.
Journal of The Mechanics and Physics of Solids, Nov 1, 2017
Abstract Plane strain finite deformation finite element calculations of mode I crack growth under... more Abstract 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. The crack growth calculations are based on a micromechanics constitutive relation that couples creep deformation and damage due to grain boundary cavitation. Grain boundary cavitation, with cavity growth due to both creep and diffusion, is taken as the sole failure mechanism contributing to crack growth. The influence on the crack growth rate of loading history parameters, such as the magnitude of the applied stress intensity factor, the ratio of the applied minimum to maximum stress intensity factors, the loading rate, the hold time and the cyclic loading frequency, are explored. The crack growth rate under cyclic loading conditions is found to be greater than under monotonic creep loading with the plateau applied stress intensity factor equal to its maximum value under cyclic loading conditions. Several features of the crack growth behavior observed in creep-fatigue tests naturally emerge, for example, a Paris law type relation is obtained for cyclic loading.
Polymer Degradation and Stability, Oct 1, 2020
In polyethylene, a transient, oxidation-induced strengthening is often observed over a narrow ran... more In polyethylene, a transient, oxidation-induced strengthening is often observed over a narrow range of UV radiation dose. In addition, plastic deformation may not be volume-preserving due to cavitation. Here, we employ a suite of analytical experiments and mechanical testing on pristine and oxidized lowdensity polyethylene films in order to investigate the transient strengthening behavior as well as the propensity for cavitation to fracture. Emphasis is laid on connecting macroscopically observed behavior with microscopic information involving the competition between multi-scale phenomena: chain scission and cross linking at a fine scale, chemi-crystallization, oxidation-induced cracking and mechanical damage at the meso and coarse scales. The results provide an insight into the role of cavitation in the oxidative embrittlement of semicrystalline polymers.
International Journal of Solids and Structures, Oct 1, 2015
Abstract Guided by previous theoretical analyses, an experimental program was designed to probe t... more Abstract Guided by previous theoretical analyses, an experimental program was designed to probe the path-dependence of the fracture locus in ductile materials. The material and loading conditions were chosen so that cavitation-induced failure is the basic damage mechanism. In one set of experiments, round notched specimens of different notch acuities were deformed to complete rupture and a nominal strain to fracture initiation was recorded for each specimen. In another set of experiments, sufficiently large specimens were prestrained in simple tension up to incipient necking, then round notched bars were cut out, again varying the notch acuity, and subsequently deformed to rupture. The latter experiments thus produce a step-jump in stress triaxiality, as opposed to a weakly varying triaxiality in the former. The evolution of stress triaxiality at failure locations was determined by finite-element calculations using an associated flow model and a hardening curve identified experimentally up to a strain of 2.0. The designed program enabled a comparison between the fracture loci with and without load path change. It also allowed qualitative comparisons to be made with previously published theoretical results. A theory of ductile fracture that is posited as a stress-state dependent critical fracture strain model is generally inadequate. The findings here partially illustrate the extent to which this applies.
European Journal of Mechanics A-solids, Jul 1, 2023
Journal of Applied Mechanics, Jul 1, 2015
The minerals, metals & materials series, 2019
The mechanical response of magnesium AZ31 processed using severe plastic deformation is character... more The mechanical response of magnesium AZ31 processed using severe plastic deformation is characterized using a two-surface, pressure-insensitive plasticity model. The model captures the 3D plastic anisotropy and the tension–compression asymmetry as the behavior evolves during straining. The model may be viewed as a reduced-order quasi-crystal plasticity model, whereby the two activation surfaces represent glide- and twinning-dominated flow. The two-surface formulation enables independent, yet coupled, hardening laws in terms of effective plastic strains accumulated on either generic deformation system. Material identification was completed using tension and compression specimens oriented along the principal directions of the processed material, E, L, and F, as well as off-axes specimens that bisected the principal planes E–F, L–F, and L–E. Using the nominal stress–strain and lateral strain data from the experiments, this model can capture the anisotropic behavior of this material.
International Journal of Fracture, May 17, 2021
A three-dimensional finite deformation study of necking and failure in rectangular tensile bars i... more 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 void volume fraction. The constitutive relation takes into account void shape changes and associated void rotations for three-dimensional voids. The constitutive update is carried out using a generalized rate tangent scheme for an elastic-viscoplastic solid. The sensitivity of necking and failure patterns to the aspect ratio of the rectangular bar is investigated with focus on the plane strain limit and a square tensile bar. The calculations predict the well-known slant fracture in plane strain tension and the emergence of a cup-cone like failure region for a square cross-section. Details are provided for the development of porosity in the bar with a square cross-section, including void shape changes and void rotations. The numerical examples show the capability of a constitutive relation for porous plasticity that can model details of void evolution, thus paving the way for advanced analyses of ductile failure under arbitrary loadings.
Modelling and Simulation in Materials Science and Engineering, Mar 24, 2021
A fast Fourier transform (FFT) based method is developed to model the pseudo-elastic behavior and... more A fast Fourier transform (FFT) based method is developed to model the pseudo-elastic behavior and shape-memory effect in phase transforming materials. An infinitesimal strain based variational FFT formulation is adapted and enhanced to enable the solution of nonlinear, stress-controlled and thermo-mechanical problems. The capabilities of the method are illustrated by implementing a computational homogenization approach to modeling the thermo-mechanical response of shape memory alloys with heterogeneities. The accuracy and performance of the method is evaluated by comparison with finite element (FE) solutions for single- and multi-particle cells subjected to various loading schemes. For the class of nonlinear problems of interest, the proposed method is shown to be an order of magnitude faster than the FE method for a given resolution, and possibly for the same accuracy.
Extreme Mechanics Letters, Dec 1, 2016
Plane strain tension analyses of un-notched and notched bars are carried out using discrete shear... more 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 discretely modeled Eshelby inclusions, given analytically for an infinite elastic medium, and an image solution that enforces the prescribed boundary conditions. The image problem is a standard linear elastic boundary value problem that is solved by the finite element method. Potential STZ activation sites are randomly distributed in the bars and constitutive relations are specified for their evolution. Results are presented for un-notched bars, for bars with blunt notches and for bars with sharp notches. The computed stress-strain curves are serrated with the magnitude of the associated stress-drops depending on bar size, notch acuity and STZ evolution. Cooperative deformation bands (shear bands) emerge upon straining and, in some cases, high stress levels occur within the bands. Effects of specimen geometry and size on the stress-strain curves are explored. Depending on STZ kinetics, notch strengthening, notch insensitivity or notch weakening are obtained. The analyses provide a rationale for some conflicting findings regarding notch effects on the mechanical response of metallic glasses.
Mechanics of Materials, Nov 1, 2015
The objective of this paper is to perform numerical assessment of a micromechanical model of poro... more The objective of this paper is to perform numerical assessment of a micromechanical model of porous metal plasticity developed previously by the authors. First, upper bound estimates for the yield loci are computed using homogenization and limit analysis of a spheroidal representative volume element containing a confocal spheroidal void, neglecting elasticity. Unlike in the development of the analytical model, the computational limit analysis is performed without recourse to approximations so that the obtained yield loci are rigorous upper bounds for the true criterion. Next, the model's macroscopic dilatancy at incipient plastic flow is compared against that of the numerical limit analysis approach. Finally, finite-element calculations, with elasticity included, are presented for transversely isotropic porous unit-cells loaded axisymmetrically. The effective stress-strain response as well as evolution of the unit-cell porosity and void aspect ratio are compared with theoretical predictions.
Computer Methods in Applied Mechanics and Engineering, Oct 1, 2016
Finite deformation constitutive relations are developed for a class of plastically anisotropic po... more Finite deformation constitutive relations are developed for a class of plastically anisotropic porous solids with an underlying evolving microstructure. They are based on a model obtained by homogenization for rigid-perfectly plastic materials containing non-spherical voids. To facilitate numerical implementation, heuristic extensions are proposed to incorporate weak elasticity, strain hardening and accurate void shape evolution. A semi-implicit time integration scheme is used along with the Newton-Raphson method to solve the system of equations resulting from the discretization of the constitutive equations. The procedure to calculate the consistent tangent matrix, which is needed to solve the global force-displacement matrix equation is summarized. The framework is used to illustrate the predictive capabilities of the model, first under conditions previously assessed against finite element cell model calculations, then under conditions heretofore not examined. The latter include situations of initial anisotropy as well as situations involving significant void distortions, not only in terms of void enlargement or shape change, but also in terms of void rotations. In particular, various combinations of stress triaxiality, initial void shape, void orientation, matrix orthotropy properties and loading directions are simulated. In addition, the finite element implementation of the model is addressed and illustrated for simple cases.
Journal of The Mechanics and Physics of Solids, Feb 1, 2018
Plane strain tension analyses of un-notched and notched bars are carried out using discrete shear... more 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 discretely modeled Eshelby inclusions, given analytically for an infinite elastic medium, and an image solution that enforces the prescribed boundary conditions. The image problem is a standard linear elastic boundary value problem that is solved by the finite element method. Potential STZ activation sites are randomly distributed in the bars and constitutive relations are specified for their evolution. Results are presented for un-notched bars, for bars with blunt notches and for bars with sharp notches. The computed stress-strain curves are serrated with the magnitude of the associated stress-drops depending on bar size, notch acuity and STZ evolution. Cooperative deformation bands (shear bands) emerge upon straining and, in some cases, high stress levels occur within the bands. Effects of specimen geometry and size on the stress-strain curves are explored. Depending on STZ kinetics, notch strengthening, notch insensitivity or notch weakening are obtained. The analyses provide a rationale for some conflicting findings regarding notch effects on the mechanical response of metallic glasses.
International Journal of Mechanical Sciences, Oct 1, 2016
For general stress states the fracture locus, under strictly proportional loadings, may be viewed... more For general stress states the fracture locus, under strictly proportional loadings, may be viewed as a two dimensional surface. Deviations from that locus under nonproportional loadings have received limited attention in the literature. The general problem is quite complex because of unavoidably intertwined history effects on both damage-free plasticity and plasticity-induced damage. This work first reports on a systematic attempt at quantifying deviations from the proportional fracture locus given a fracture theory. Two generic types of nonproportional loading are considered, which are believed to represent a heuristic integrity basis for an infinity of possible loading histories. In doing so, emphasis is laid on that component of the deviation associated with damage, thus reducing the representation of plastic flow to its simplest form. The predictive capability of the simple theory is then employed to rationalize experimental trends from the literature.
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Papers by A. Amine Benzerga