Numerical study on void growth in rate and temperature dependent solids

This paper is concerned about void growth and associated deformation models in porous visco-plastic solids under conditions similar to those found in highly stressed regions ahead of a crack. A plane-strain unit cell containing an initially circular void is examined to simulate the stress states during dynamic fracture of a metal. Two proportional loading rates are prescribed in the two directions of the cell and their ratio is called the “strain biaxiality” expressed in a monotonic relation with stress triaxility. Finite element analysis is performed for the effective stress–strain curves of the porous solids during void growth for a range of initial porosities, strain biaxialities, strain rates and thermal softening coefficients. Numerical results show that the void evolution and the associated non-uniform deformation depend in a complex fashion on these factors. The local zone of high stress concentration which emanates from the void spreads out in the cell to trigger non-uniform deformation and plastic yielding. Subsequently, a small zone with intense plastic strain and heating either expands smoothly near the growing voids or propagates in a specific direction determined by its interaction with the boundary conditions of the cell such as strain biaxility. At low strain biaxiality and for small voids, formation and propagation of zones with intense plastic strain and heating is localized. However, high strain biaxiality leads to rapid uniform expansion of small voids as observed experimentally. It is found that the intense heating zone follows the zone of high plastic strain concentration and diffuses with imposed strain. Thermal softening which reduces the overall stress can be neglected at the early stage of void growth, but it is magnified past the peak stress by accelerating the void growth. But in the long term, the void growth rate is insensitive to thermal softening coefficient. Increasing strain rates can promote void growth and the rate of which tends to be proportional to the eventual strain rate.     

Modeling of hydrogen-assisted ductile crack propagation in metals and alloys

This paper presents a finite element study of the hydrogen effect on ductile crack propagation in metals and alloys by linking effects at the microstructural level (i.e., void growth and coalescence) to effects at the macro-level (i.e., bulk material deformation around a macroscopic crack). The purpose is to devise a mechanics methodology to simulate the conditions under which hydrogen enhanced plasticity induces fracture that macroscopically appears to be brittle. The hydrogen effect on enhanced dislocation mobility is described by a phenomenological constitutive relation in which the local flow stress is taken as a decreasing function of the hydrogen concentration which is determined in equilibrium with local stress and plastic strain. Crack propagation is modeled by cohesive elements whose traction separation law is determined through void cell calculations that address the hydrogen effect on void growth and coalescence. Numerical results for the A533B pressure vessel steel indicate that hydrogen, by accelerating void growth and coalescence, promotes crack propagation by linking simultaneously a finite number of voids with the crack tip. This “multiple-void” fracture mechanism knocks down the initiation fracture toughness of the material and diminishes the tearing resistance to crack propagation.     

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.     

A numerical investigation of ductile fracture initiation in a high-strength low-alloy steel

In this work, static and drop-weight impact experiments, which have been conducted using three-point bend fracture specimens of a high-strength low-alloy steel, are analysed by performing finite-element simulations. The Gurson constitutive model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage and small particles which require large strains to nucleate voids. The most important objective of the work is to assess quantitatively the effects of material inertia, strain rate sensitivity and local adiabatic temperature rise (due to conversion of plastic work into heat) on dynamic ductile crack initiation. This is accomplished by comparing the evolution histories of void volume fraction near the notch tip in the static analysis with the dynamic analyses. The results indicate that increased strain hardening caused by strain rate sensitivity, which becomes important under dynamic loading, plays a benign role in considerably slowing down the void growth rate near the notch tip. This is partially opposed by thermal softening caused by adiabatic heating near the notch tip.     

An analysis of dynamic,ductile crack growth in a double edge cracked specimen

Dynamic crack growth is analysed numerically for a plane strain double edge cracked specimen subject to symmetric impulsive tensile loading at the two ends. The material behavior is described in terms of an elastic-viscoplastic constitutive model that accounts for ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second phase particles are represented, including large inclusions or inclusion colonies with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. The crack growth velocities determined here are entirely based on the ductile failure predictions of the material model, and thus the present study is free from ad hoc assumptions regarding appropriate dynamic crack growth criteria. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses. Different prescribed impact velocities, inclusion spacings and values of the inclusion nucleation stress are considered. Predictions for the dynamic crack growth behavior and for the time variation of crack tip characterizing parameters are obtained for each case analyzed.     

Softening and snap-back instability in cohesive solids

The nature of the crack and the structure behaviour can range from ductile to brittle, depending on material properties, structure geometry, loading condition and external constraints. The influence of variation in fracture toughness, tensile strength and geometrical size scale is investigated on the basis of the π-theorem of dimensional analysis. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must describe energy dissipation per unit of volume and per unit of crack area respectively. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e. the transition from ductile to brittle structure behaviour by increasing the size scale and keeping the geometrical shape unchanged. For extremely brittle cases (e.g. initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap-back instability in the equilibrium path occurs and the load–deflection softening branch assumes a positive slope. Both load and deflection must decrease to obtain a slow and controlled crack propagation (whereas in normal softening only the load must decrease). If the loading process is deflection-controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophic event tends to reproduce the classical LEFM-instability (K_I = K_IC) for small fracture toughnesses and/or for large structure sizes. In these cases, neither the plastic zone develops nor slow crack growth occurs before unstable crack propagation.     

Nature of Microcracks in Ferritic Steels Occurred during Fracture under Conditions of Ductile-Brittle Transition Temperature Region

It has been shown by means of EBSD techique that fracture of ferritic steel in ductile-brittle transition temperature region, along with the formation of previously discribed cleavage microcracks, results in the formation of ductile microcracks. It has also been shown that microstructure of plastic zones under brittle and ductile fracture components produced by the main crack propagation differ significantly. Better developed plastic zone under ductile fracture component protects steel from overstress. The plastic zone under brittle fracture surface, apparently, has a reduced local plasticity. Consequently, the cleavage microcracks formation precedes the fracture process. During the main crack formation such microcracks occur in steel microvolumes located both in front of its tip and in adjacent to its edges microvolumes. Further propagation of the main crack is realized in steel which already contains scattered cavities and reduces to ductile fracture of the connections between them.     

A modeling approach for the complete ductile–brittle transition region: cohesive zone in combination with a non-local Gurson-model

The present study deals with the simulation of crack propagation in the ductile–brittle transition region on the macro-scale. In contrast to most studies in the literature, not only the ductile softening by void growth and coalescence is incorporated but also the particular material degradation by cleavage. A non-local Gurson-type model is employed together with a cohesive zone to simulate both failure mechanisms simultaneously. This consistent formulation of a boundary value problem allows arbitrary high mesh resolutions. The results show that the model captures qualitative effects of corresponding experiments such as the cleavage initiation in front of a stretch zone, the formation of secondary cracks and possible crack arrest. The influence of the temperature on the predicted toughness is reproduced in the whole ductile–brittle transition region without introducing temperature-dependent fit parameters. A comparison with experimental data shows that the shift of the ductile–brittle transition temperature associated with a lower crack-tip constraint can be predicted quantitatively.     

Cavity growth in ductile particles bridging a brittle matrix crack

The addition of a dispersed ductile phase in a brittle ceramic can result in an increased fracture toughness, mainly due to plastic dissipation during crack bridging. The large elastic-plastic deformations of a ductile particle intercepted by a brittle matrix crack are here analysed numerically with main focus on the effect of the growth of a single void in the particle centre, as has been observed experimentally. Particle-matrix debonding is incorporated in the numerical model, represented in terms of a cohesive zone formulation, and so is the effect of initial residual stresses induced by the thermal contraction mismatch during cooling from the processing temperature. The bridging behaviour is studied for different combinations of material parameters, and the void growth behaviour is related to previous results for cavitation instabilities in elastic-plastic solids.     

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.     

基于微孔贯通细观损伤模型的金属韧性断裂分析

韧性材料断裂过程通常可看作是材料内部微孔洞的形核、扩展及相互贯通的积累。经典的Gurson- Tvergaard (GT)模型能够很好地模拟具有变形均匀、各向同性的孔洞的萌生及扩展过程;但无法模拟由孔洞贯通而引起的局部变形过程,因此需要对其修正,引入相应的孔洞贯通准则。该文采用两种贯通准则对经典GT模型进行修正,即Thomason的塑性极限载荷准则和临界等效塑性应变准则。借助用户自定义程序UMAT将采用这两种贯通准则修正的GT本构关系嵌入至商用有限元软件ABAQUS中,从而可通过对金属材料应力状态和断裂机理的分析控制孔洞的贯通。以一组含有不同缺口根半径的圆棒拉伸试验件为例,分析了该类金属构件自孔洞萌生至最终断裂的整个损伤演化过程,并与试验数据进行了对比,验证了该模型的有效性。该文还讨论了金属断裂过程中应力三轴度对微裂纹萌生与扩展的影响。     

A numerical analysis of failure characteristics of ductile layers in laminated composites

In this study, the failure of the ductile layers from collinear, multiple and delaminating cracks that occur in laminated composite systems was studied using a constitutive relationship that accounts for strength degradation resulting from the nucleation and growth of voids. The results indicate that, in laminated composites, void nucleation and growth ahead of the cracks occur at a much faster rate because of evolution of much higher stress values in the interface region. Except for short crack extensions, collinear and multiple cracks develop crack resistance curves similar to that seen for a crack in the ductile layer material as a homogenous isotropic cases. For delaminating crack cases, the fracture behaviour is strongly influenced by the delamination length. The resistance of the ductile layers to crack extension can be significantly reduced by short delamination lengths; however, for large delamination lengths the resistance to crack extension becomes greater than that seen for the ductile material. The results also show that, if the crack tip is at the interface, similar maximum stress values develop in the ductile layers as in the fracture test of the same ductile material, suggesting that ductile–brittle fracture transition behaviour of the ductile layers is dependent upon the extent of the cracks in the brittle layers and fracture characteristics of the brittle layers.     

Ductile rupture in thin sheets of two grades of 2024 aluminum alloy

The damage and rupture mechanisms of thin sheets of 2024 aluminum alloy (Al containing Cu, Mn, and Mg elements) are investigated. Two grades are studied: a standard alloy and a high damage tolerance alloy. The microstructure of each material is characterized to obtain the second phase volume content, the dimensions of particles and the initial void volume fraction. The largest particles consist of intermetallics. Mechanical tests are carried out on flat specimens including U-notched (with various notch radii), sharply V-notched and smooth tensile samples. Stable crack growth was studied using “Kahn samples” and pre-cracked large center-cracked tension panels M(T). The macroscopic fracture surface of the different specimens is observed using scanning electron microscopy. Smooth and moderately notched samples exhibit a slant fracture surface, which has an angle of about 45° with respect to the loading direction. With increasing notch severity, the fracture mode changes significantly. Failure initiates at the notch root in a small triangular region perpendicular to the loading direction. Outside this zone, slant fracture is observed. Microscopic observations show two failure micromechanisms. Primary voids are first initiated at intermetallic particles in both cases. In flat regions, i.e. near the notch root of severely notched samples, void growth is promoted and final rupture is caused by “internal necking” between the large cavities. In slanted regions these voids tend to coalesce rapidly according to a “void sheet mechanism” which leads to the formation of smaller secondary voids in the ligaments between the primary voids. These observations can be interpreted using finite element simulations. In particular, it is shown that crack growth occurs under plane strain conditions along the propagation direction.     

Some contribution to process zone fracture mechanics

The mechanism of the ductile fracture is studied theoretically for the Al Alloy 7075-T6 specimens. A model for the interaction of a crack tip with a void nearby is analyzed by using the Modified Gurson's Model. Taking fracture criterion into consideration, the analysis of a crack propagation is carried out and besides the distribution of the equivalent plastic strain, the void volume fraction f and the localization are obtained. Microcracks nucleate on the ligament between crack and void, and grow and coalesce each other, and at last the main crack thus formed coalesces with the void and the coalescence of the crack and void is completed. And these phenomenon occurs in the localized region.The initiation of the microcrack of 7075 occurs at small J and the microcrack penetration between crack and void occurs at larger J, and the propagation does not occur smoothly. These results coincide with the results of the experiments by FRASTA (FRActure Surface Topographic Analysis) and Fractography.     

Dynamic ductile crack growth and transition to cleavage – a cell model approach

The fracture behavior of ferritic steel in the transition regime is controlled by the competition between ductile tearing and cleavage. Many test specimens that failed by catastrophic cleavage showed significant amounts of ductile tearing prior to cleavage fracture. The transition from ductile tearing to cleavage has been attributed to the increase in constraint and sampling volume associated with ductile crack growth. This work examines the role of dynamic ductile crack growth on the fracture mode transition by way of a cell model of the material. The cell model incorporates the effects of stress triaxiality and strain rate on material failure characteristics of hole growth and coalescence. Loading rate and microstructure effects on the stress fields that evolve with rapid (ductile) crack growth are systematically studied. The stress fields are employed to compute the Weibull stress which provides probability estimates for the susceptibility to cleavage fracture. A center-cracked panel subjected to remote tension is the model problem under study. The computational model uses an elastic-viscoplastic constitutive relation which incorporates enhanced strain rate hardening at high strain rates. Adiabatic heating due to plastic dissipation and the resulting thermal softening are also accounted for. Under dynamically high loading rate, our model shows the crack speed achieves its peak value soon after crack initiation and quickly falls off to slower speeds with further crack growth. Remarkably, the Weibull stress follows a similar pattern which suggests that the transition to the cleavage fracture is most likely to occur, if at all, at the peak speed of ductile crack growth. Key words: Dynamic fracture, ductile tearing, crack growth, transition regime, cleavage fracture, cell model, finite element.     

Fatigue voids and their significance

ABSTRACT Fractures from tests on 2014‐T6511 and 2024‐T3 test coupons under specially designed programmed loading reveal voids with distinct fatigue markings. These ‘fatigue voids’ appear to form as a consequence of the separation of noncoherent secondary particulates from the matrix in early fatigue. The process of their formation is through the initiation, growth and coalescence of multiple interfacial cracks around the particulate. Such voids become visible on the fatigue fracture surface if and when the crack front advances through them. In vacuum, each fatigue void is the potential initiator of an embedded penny‐shaped crack. The one closest to the specimen surface is likely to become the dominant crack, indicating that fatigue voids appear to be the likely origins of the dominant crack in vacuum. In air, the dominant crack forms at the notch surface and grows much faster, giving less opportunity for multiple internal cracks to spawn off from the innumerable internal fatigue‐voids. Thus in air, fatigue voids do not appear to affect the fatigue process at low and intermediate growth rates. At high crack growth rates involving considerable crack tip shear, slip planes with particulate concentration offer the path of least resistance. This explains the increasing density of fatigue voids with growth rate. Very high growth rates signal the onset of a quasi‐static crack growth component that manifests itself through growing clusters of microvoid coalescence associated with static fracture. Fatigue voids are likely to form in other Al‐alloys with secondary noncoherent particulates. They have nothing in common with microvoids associated with ductile fracture.     

An FEM study on crack tip blunting in ductile fracture initiation

Ductile fracture is initiated by void nucleation at a characteristic distance (I_c) from the crack tip and propagated by void growth followed by coalescence with the tip. The earlier concepts expressed I_c in terms of grain size or inter-particle distance because grain and particle boundaries form potential sites for void nucleation. However, Srinivas et al. (1994) observed nucleation of such voids even inside the crack tip grains in a nominally particle free Armco iron. In an attempt to achieve a unified understanding of these observations, typical crack-tip blunting prior to ductile fracture in a standard C(T) specimen (Mode I) was studied using a finite element method (FEM) supporting large elasto-plastic deformation and material rotation. Using a set of experimental data on Armco iron specimens of different grain sizes, it is shown that none of the locations of the maxima of the parameters stress, strain and strain energy density correspond to I_c. Nevertheless, the size of the zone of intense plastic deformation, as calculated from the strain energy density distribution ahead of the crack tip in the crack plane, compares well with the experimentally measured I_c. The integral of the strain energy density variation from the crack tip to the location of void nucleation is found to be linearly proportional to J_IC. Using this result, an expression is arrived at relating I_c to J_IC and further extended to CTOD_c.     

Microstructural effects on ductile fracture in heterogeneous materials. Part I: Sensitivity analysis with LE-VCFEM

Ductile failure of heterogeneous materials, such as cast aluminum alloys and discretely reinforced aluminums or DRA’s, initiates with cracking, fragmentation or interface separation of inclusions, that is followed by propagation in the matrix by a ductile mechanism of void nucleation and growth. Damage localizes in bands of intense plastic deformation between inclusions and coalesces into a macroscopic crack leading to overall failure. Ductile fracture is very sensitive to the local variations of the microstructure morphology. This is the first of a two part paper on the effect of microstructural morphology and properties on the ductile fracture in heterogeneous ductile materials. In this paper the locally enhanced Voronoi cell finite element method (LE-VCFEM) for rate-dependent porous elastic–viscoplastic materials is used to investigate the sensitivity of strain to failure to loading rates, microstructural morphology and material properties. A model is also proposed for strain to failure, incorporating the effects of important morphological parameters.     

MODELLING FOR TRANSCRYSTALLINE AND INTERCRYSTALLINE FRACTURE BY VOID NUCLEATION AND GROWTH

A criterion has been formulated for transcrystalline and intercrystalline fracture caused by the evolution of voids located both in a grain and on grain boundaries. The criterion is based on the idea of plastic collapse for a unit cell that is a regular structural mezovolume of polycrystalline material. The criterion does not require the introduction of any empirical parameters, such as critical void size, critical size of ligament between voids and critical void volume fraction, which are used in most models.
Modelling has been performed for void nucleation and growth in a grain and on grain boundaries for elastic–plastic deformation and under creep conditions. A scheme is proposed to describe the transition from transcrystalline to intercrystalline cavitation fracture as a function of strain rate and temperature.
The effect of stress triaxiality on the critical strain and the lifetime for both transcrystalline and intercrystalline fracture has been investigated. A comparison of the results predicted by the suggested criterion with available empirical data has been performed.