A.A. Benzerga

Ductile Fracture by Void Growth to Coalescence

Publisher Summary An important failure mechanism in ductile metals and their alloys is by growth and coalescence of microscopic voids. In structural materials, the voids nucleate at inclusions and second-phase particles by decohesion of the particle–matrix interface or by particle cracking. Void growth is driven by plastic deformation of the surrounding matrix. Early micromechanical treatments of this phenomenon considered the growth of isolated voids. Later, constitutive equations for porous ductile solids were developed based on homogenization theory. Among these, the most widely known model was developed by Gurson for spherical and cylindrical voids.

Micromechanics of coalescence in ductile fracture

Significant progress has been recently made in modelling the onset of void coalescence by internal necking in ductile materials. The aim of this paper is to develop a micro-mechanical framework for the whole coalescence regime, suitable for finite-element implementation. The model is defined by a set of constitutive equations including a closed form of the yield surface along with appropriate evolution laws for void shape and ligament size. Normality is still obeyed during coalescence. The derivation of the evolution laws is carefully guided by coalescence phenomenology inferred from micromechanical unit-cell calculations. The major implication of the model is that the stress carrying capacity of the elementary volume vanishes as a natural outcome of ligament size reduction. Moreover, the drop in the macroscopic stress accompanying coalescence can be quantified for many initial microstructures provided that the microstructure state is known at incipient coalescence. The second part of the paper addresses a more practical issue, that is the prediction of the acceleration rate δ in the Tvergaard–Needleman phenomenological approach to coalescence. For that purpose, a Gurson-like model including void shape effects is used. Results are presented and discussed in the limiting case of a non-hardening material for different initial microstructures and various stress states. Predicted values of δ are extremely sensitive to stress triaxiality and initial spacing ratio. The effect of initial porosity is significant at low triaxiality whereas the effect of initial void shape is emphasized at high triaxiality.

Coalescence-Controlled Anisotropic Ductile Fracture

The anisotropic ductile fracture of rolled plates containing elongated inclusions is promoted by both the dilational growth of voids and the coalescence process. In the present article, the emphasis is laid on the latter process. The effects of void shape and mainly of inter-particle spacings are investigated. Two types of coalescence models are compared: a localization-based model and plastic limit-load models. The capabilities of both approaches to incorporate shape change and spacing effects are discussed. These models are used to predict the fracture properties of two low alloy steels containing mainly manganese sulfide inclusions. Both materials are characterized in different loading directions. Microstructural data inferred from quantitative metallography are used to derive theoretical values of critical void volume fractions at incipient coalescence. These values are used in FE-calculations of axisymmetrically notched specimens with different notch radii and loading directions.

Synergistic effects of plastic anisotropy and void coalescence on fracture mode in plane strain

The macroscopic fracture in plane strain is known to be shear-like in ductile materials. In most structural materials, fracture starts after diffuse necking, at the centre of the specimen, by micro-void coalescence giving rise afterwards to the macroscopic shear fracture mode. In this paper, the effect of coalescence on shear band development and on associated fracture mode in plane strain is analysed numerically. The calculations are performed using a recent elastic-viscoplastic Gurson-like model that accounts for void shape evolution, coalescence and post-coalescence micromechanics along with isotropic hardening and orthotropic plasticity for the matrix behaviour. The latter is introduced to represent the actual flow properties of hot-worked materials. No kinematic hardening or nucleation formulation is used in order to focus attention on coalescence effects and to discuss, with respect to experiments, published results based on kinematic hardening and nucleation effects. The most important finding is the synergistic effect of plastic anisotropy and post-coalescence yield surface curvature upon the onset of a shear band after the fracture sets in at the centre of the specimen.

Effect of Stress Triaxiality on the Flow and Fracture of Mg Alloy AZ31

The microscopic damage mechanisms operating in a hot-rolled magnesium alloy AZ31B are investigated under both uniaxial and controlled triaxial loadings. Their connection to macroscopic fracture strains and fracture mode (normal vs shear) is elucidated using postmortem fractography, interrupted tests, and microscopic analysis. The fracture locus (strain-to-failure vs stress triaxiality) exhibits a maximum at moderate triaxiality, and the strain-to-failure is found to be greater in notched specimens than in initially smooth ones. A transition from twinning-induced fracture under uniaxial loading to microvoid coalescence fracture under triaxial loading is evidenced. It is argued that this transition accounts in part for the observed greater ductility in notched bars. The evolution of plastic anisotropy with stress triaxiality is also investigated. It is inferred that anisotropic plasticity at a macroscopic scale suffices to account for the observed transition in the fracture mode from flat (triaxial loading) to shear-like (uniaxial loading). Damage is found to initiate at second-phase particles and deformation twins. Fracture surfaces of broken specimens exhibit granular morphology, coarse splits, twin-sized crack traces, as well as shallow and deep dimples, in proportions that depend on the overall stress triaxiality and fracture mode. An important finding is that AZ31B has a greater tolerance to ductile damage accumulation than has been believed thus far, based on the fracture behavior in uniaxial specimens. Another finding, common to both tension and compression, is the increase in volumetric strain, the microscopic origins of which remain to be elucidated.

Ductile failure modeling

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 void shapes and for shape changes during growth. This includes cases of very low stress triaxiality, where the voids can close up to micro-cracks during the failure process. The void growth models have also been extended to consider the effect of plastic anisotropy, or the influence of nonlocal effects that bring a material size scale into the models. Often the voids are not present in the material from the beginning, and realistic nucleation models are important. The final failure process by coalescence of neighboring voids is an issue that has been given much attention recently. At ductile fracture, localization of plastic flow is often important, leading to failure by a void-sheet mechanism. Various applications are presented to illustrate the models, including welded specimens, shear tests on butterfly specimens, and analyses of crack growth.

Effective Yield Criterion Accounting for Microvoid Coalescence

An effective yield function is derived for a porous ductile solid near a state of failure by microvoid coalescence. Homogenization theory combined with limit analysis are used to that end. A cylindrical cell is taken to contain a coaxial cylindrical void of finite height. Plastic flow in the intervoid matrix is described by J2 theory while regions above and below the void remain rigid. Velocity boundary conditions are employed which are compatible with an overall uniaxial straining for the cell, a postlocalization kinematics that is ubiquitous during the coalescence of neighboring microvoids in rate-independent solids. Such boundary conditions are not of the uniform strain rate kind, as is the case for Gursonlike models. A similar limit analysis problem for a square-prismatic cell containing a square-prismatic void was posed long ago (Thomason, P. F., 1985, “Three-Dimensional Models for the Plastic Limit–Loads at Incipient Failure of the Intervoid Matrix in Ductile Porous Solids,” Acta Metallurgica, 33, pp. 1079–1085). However, to date a closed-form solution to this problem has been lacking. Instead, an empirical expression of the yield function proposed therein has been widely used in the literature. The fully analytical expression derived here is intended to be used concurrently with a Gursonlike yield function in numerical simulations of ductile fracture.

Smaller is Softer : An Inverse Size Effect in a Cast Aluminum Alloy

Abstract The stress–strain curves of A356 cast aluminum alloys exhibit an unusual size effect on flow properties: the finer the microstructure, the lower the tensile flow strength. Tensile tests were carried out on specimens made of an A356 alloy with 7% Si as the main alloying element. The specimens were cast at two cooling rates. For both processing conditions the microstructure within each grain consists of pro-eutectic aluminum dendrites separated by a boundary eutectic region of segregated silicon particles of ≈2–3 μm diameter. The fast cooling rate gives rise to a secondary dendrite arm spacing of approximately 20–30 μm, while the secondary dendrite arm spacing obtained with the slow cooling rate is about 80–100 μm. Discrete dislocation plasticity is used to model the inverse size effect in this alloy. The dislocations are represented as line defects in an elastic solid and dislocation nucleation, annihilation and drag are incorporated through a set of constitutive rules. Obstacles to dislocation motion are randomly distributed in the dendrite and the eutectic regions, but with different densities and strengths. The thickness of the eutectic region is found to be a key parameter in determining the inverse size effect. In addition, the size effect is found to depend on the extent to which dislocation nucleation takes place in the eutectic region.

Effects of Manufacturing-Induced Voids on Local Failure in Polymer-Based Composites

This paper presents results of a computational study focused on examining the role of manufacturing-induced voids in the initiation and growth of damage at the microstructural level in polymer matrix composites loaded in tension normal to fibers. The polymer deformation is described by an improved macromolecular constitutive model accounting for strain-rate-, pressure-, and temperature-sensitive yielding, isotropic hardening before peak yield, intrinsic postyield softening, and rapid anisotropic hardening at large strains. A new craze model that accounts for craze initiation, growth, and breakdown mechanisms is employed. An energy-based criterion is used for cavitation induced cracking that can lead to fiber/matrix debonding. The role of voids is clarified by conducting a comparative study of unit cells with and without voids. The effects of strain rate and temperature are investigated by a parametric study. The overall composite stress-strain response is also depicted to indicate manifestation of microlevel failure on macroscopic behavior.

Size Effects in the Charpy V-Notch Test

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.