Void coalescence processes quantified through atomistic and multiscale simulation

Simulation of ductile fracture at the atomic scale reveals many aspects of the fracture process including specific mechanisms associated with void nucleation and growth as a precursor to fracture and the plastic deformation of the material surrounding the voids and cracks. Recently we have studied void coalescence in ductile metals using large-scale atomistic and continuum simulations. Here we review that work and present some related investigations. The atomistic simulations involve three-dimensional strain-controlled multi-million atom molecular dynamics simulations of copper. The correlated growth of two voids during the coalescence process leading to fracture is investigated, both in terms of its onset and the ensuing dynamical interactions. Void interactions are quantified through the rate of reduction of the distance between the voids, through the correlated directional growth of the voids, and through correlated shape evolution of the voids. The critical inter-void ligament distance marking the onset of coalescence is shown to be approximately one void radius based on the quantification measurements used, independent of the initial separation distance between the voids and the strain-rate of the expansion of the system. No pronounced shear flow is found in the coalescence process. We also discuss a technique for optimizing the calculation of fine-scale information on the fly for use in a coarse-scale simulation, and discuss the specific case of a fine-scale model that calculates void growth explicitly feeding into a coarse-scale mechanics model to study damage localization. The U.S. Government’s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

TC21钛合金中应变速率拉伸力学行为实验研究

对网篮组织TC21钛合金进行了0.001 s-1～50 s-1的中应变速率室温拉伸试验。试验结果表明,TC21拉伸力学行为在试验应变速率范围内具有明显的应变速率强化效应、应变硬化效应和随应变速率升高而逐渐增大的温升软化效应;屈服应力的应变速率相关性在6 s-1时发生转折;随应变率的升高,应变硬化效应减小,断裂应变和失稳应变增大;试验应变速率范围内TC21的变形机制为位错的热激活机制。SEM和金相观察结果表明,TC21的断裂方式均为韧性断裂,断裂机理为微孔洞的聚集和长大。     

A simple damage-accumulation model for constraint effects on ductile fracture

A simple model is presented to account for the effects of void-type damage on crack initiation and propagation in ductile steels under plane strain conditions by virtue of elementary fracture mechanics solutions. Multiple primary voids from large inclusions are uniformly distributed ahead of the crack tip. The growth of these primary voids is followed by nucleation of a large population of secondary voids from second-phase particles. A critical accumulative damage based on the length ratio of the damage zone to the spacing of primary voids, is employed as a failure criterion, including contributions from two populations of voids. Damage accumulation depends much on the strain and stress states such as stress triaxilities, which are extracted from existing results instead of detailed computation. Results show the dependence of fracture toughness on the size of damage zones associated with constraints. Initiation of crack growth is insensitive to the constraints since nucleation of fine voids is determined by local deformation. The model captures the transition in mechanisms from void-by-void growth to multiple void interactions in terms of a decreasing trend in the slopes of fracture resistance curves. At high constraints and large damage zone, a steady-state crack advance is identified with constant toughness. Damage accumulation from the growth of primary voids determines subsequent crack growth resistance and the study demonstrates its dependences on the crack-tip constraints.     

Growth of a debonded void at a rigid secondary particle in a viscous metal

When a ductile two-phase material is subjected to a high strain-rate deformation, the secondary particles nucleate voids, which will grow and coalesce, in a viscous matrix, leading to a dynamic ductile fracture. If the secondary particle is strong, the void nucleates at the matrix—particle interface and will grow without the shattering of the secondary particle. In this paper the growth of a debonded void at the secondary particle in a viscous metal has been studied theoretically in order to simulate the dynamic ductile fracture of two-phase materials. It has been assumed that the matrix is viscous and that the second-phase consists of randomly-dispersed rigid spherical particles. The analytical technique used in our study is a combination of the equivalent inclusion method of Eshelby and the back stress analysis method of Mori and Tanaka, by which the interaction between debonded voids are accounted for; hence the results presented are valid even for large volume-fractions of debonded voids. The theoretical results obtained in this study are compared with those for the case of complete voids nucleated by the shattering of weak particles.     

Growth and coalescence of penny-shaped voids in metallic alloys

The growth and coalescence of penny-shaped voids resulting from particle fracture is a common damage process for many metallic alloys. A three steps modeling strategy has been followed to investigate this specific failure process. Finite element cell calculations involving very flat voids shielded or not by a particle have been performed in order to enlighten the specific features of a damage mechanism starting with initially flat voids with respect to more rounded voids. An extended Gurson-type constitutive model supplemented by micromechanics-based criteria for both void nucleation and void coalescence is assessed for the limit of very flat voids towards the FE calculations. The constitutive model is then used to generate a parametric study of the effects of the stress state, the microstructure and the mechanical properties on the ductility. Based on these results, a simple closed-form model for the ductility is finally proposed. The main outcomes of this study are that (i) the ductility of metal alloys involving penny-shaped voids is primarily controlled by the relative void spacing; (ii) the definition of an effective porosity in terms of an equivalent population of spherical voids is valid for low particle volume fraction; (iii) the presence of a particle shielding the void does not significantly affect the void growth rates and void aspect evolution; (iv) early fracture by void coalescence can occur under very low stress triaxiality conditions if the particle volume fraction is large enough, explaining that some alloys and composites can fail through a transgranular ductile fracture mode under uniaxial tension condition before the onset of necking; (v) the fracture mechanism moves from void growth controlled to void nucleation controlled when increasing the void nucleation stress, lowering the stress triaxiality, and increasing the initial void aspect ratio.     

Analysis of fracture limit curves and void coalescence in high strength interstitial free steel sheets formed under different stress conditions

Void formation, which is a statistical event, depends on inhomogeneities present in the microstructure. The analysis on void nucleation, their growth and coalescence during the fracture of high strength interstitial free steel sheets of different thicknesses is presented in this article. The analysis shows that the criterion of void coalescence depends on the d-factor, which is the ratio of relative spacing of the ligaments (δd) present between the two consecutive voids to the radius of the voids. The computation of hydrostatic stress (σ_m), the dominant factor in depicting the evolution of void nucleation, growth and coalescence and the dimensional analysis of three different types of voids namely oblate, prolate and spherical type, have been carried out. The ratio of the length to the width (L/W) of the oblate or prolate voids at fracture is correlated with the mechanical properties, microstructure, strains at fracture, Mohr’s circle shear strains and Triaxiality factors. The Lode angle (θ) is determined and correlated with the stress triaxiality factor (T), ratio of mean stress (σ_m) to effective stress (σ_e). In addition, the Void area fraction (V _a), which is the ratio of void area to the representative area, is determined and correlated with the strain triaxiality factor (T_o).     

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are investigated.     

Deformation,diffusion and ductility during creep – continuous void nucleation and creep-fatigue damage

Abstract

It is shown that the assumption of unit (negative) slope in the well known Monkman–Grant plot of time to failure against minimum creep rate is too restrictive. By acknowledging observed slopes in the range 0.8–1, a ductility–strain-rate relation is deduced where ductility decreases with reducing strain rate. This in turn has implications for the ductility exhaustion method as applied during stress relaxation in the dwell period of low cycle fatigue tests of austenitic steels at elevated temperature. The simple method is used to calculate the cyclic creep damage in typical tests on austenitic steels in the region 550–650 °C and is compared to other calculations as employed in the R5 high temperature assessment procedure. The assumption of a uniform nucleation rate of grain boundary voids with creep strain goes some way to predicting the slope of the ductility–strain-rate relation. Both the ‘unconstrained’ and ‘constrained’ (lower shelf) regions of void growth are discussed.     

Copper spall fracture under sub-nanosecond electron irradiation

Ultra-short powerful electron beam is a suitable tool for producing of high rate deformation in substance. In paper we present a new model of high rate fracture and use this model for numerical investigation of fracture of copper target at irradiation by sub-nanosecond electron beam. In this model, fracture is considered as a time-dependent process of nucleation and growth of opening mode cracks. The nucleation and growth rates are controlled by specific free energy of crack surface which is sole fitted parameter. Plastic deformations, both in cracks vicinity and total in substance, are described in frames of dislocation theory. For verification of the model, we performed simulations of spall fracture at plate impact and at irradiation by high-current electron beam with pulse duration of tens of nanoseconds, and reasonable agreement with experimental data has been demonstrated. Simulations of the sub-nanosecond electron beam action on target indicate that spall fracture of the irradiated target surface is possible. This fracture takes place at the enclosed energy density slightly below the value, which is sufficient for melting of irradiated substance. Fracture threshold energy density does not depend on the origin dislocation density and it increases with the increase of pulse duration. As a result, at long pulse durations (more than ten nanoseconds) the substance melts before fracture.     

Multi-scale applications to high strain-rate dynamic fracture

Though the bulk of the Bodega Bay Multi-Scale Modeling workshop was devoted to understanding flow stress within the multi-scale paradigm, a dedicated session was devoted to Dynamic Failure and Fracture. Here, we review recent developments with emphasis on work presented at the workshop in the area of ductile dynamic fracture. The paper begins with a discussion of the relevant experimental observations, followed by an overview of the mechanisms of void nucleation and growth at high strain-rate, including dislocation processes (see the companion review by Bulatov in this issue). While the connection to the continuum is at its infancy, we present some directions that hold promise. Shear localization from the continuum perspective is presented in the companion review by Becker et al. This section finishes with a brief summary of issues that need to be resolved to apply the full apparatus of multi-scale modeling to dynamic fracture. This revised version was published online in June 2006 with corrections to the Cover Date.