Void growth and failure in notched bars
TL;DR: In this paper, void growth and ductile failure in the non-uniform multiaxial stress fields of notched bars are studied numerically and experimentally, using an elastic-viscoplastic constitutive relation that accounts for strength degradation resulting from the growth of microvoids.
Abstract: Void growth and ductile failure in the nonuniform multiaxial stress fields of notched bars are studied numerically and experimentally. U-notched bars with different notch acuities are made from partially consolidated and sintered iron powder compacts with various residual porosities. The materials are modelled using an elastic-viscoplastic constitutive relation that accounts for strength degradation resulting from the growth of microvoids. The matrix stress-strain relation and the initial void volume fractions used in the calculations are determined experimentally. The remaining parameters in the constitutive equations are evaluated from micromechanical models. Comparisons of the calculations with experimental results indicate that the constitutive model can provide good estimates of the evolution of the void volume fraction and of the strength reduction induced by void growth under a variety of nonuniform stress histories.
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TL;DR: In this article, a boundary value problem simulating a periodic array of spherical voids in an isotropically hardening elastic-viscoplastic matrix is analyzed, showing a shift from a general axisymmetric deformation state to a mode of uniaxial straining at which point the plastic deformation localizes to the ligament between neighboring voids.
747 citations
TL;DR: In this paper, the first overview of failure of metals is presented, focusing on brittle and ductile failure under monotonic loadings, where the focus is on linking microstructure, physical mechanisms and overall fracture properties.
639 citations
Cites methods or result from "Void growth and failure in notched ..."
...This figure is relatively low compared with [193], yet quite large if one considers...
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...[193] motivating some important choices in micromechanical parameters entering the Gurson model [9] modified by Tvergaard and Needleman [10,194]....
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TL;DR: In this paper, the authors developed constitutive equations for porous ductile solids based on homogenization theory and developed the most widely known model for spherical and cylindrical voids.
Abstract: 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.
540 citations
Cites background or methods from "Void growth and failure in notched ..."
...An early study by Becker et al. (1989) focussed on a plane strain analysis of an elongated void having an elliptical cross-section and representing voids nucleated at MnS stringers in high strength steels....
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...A thorough assessment of the Gurson model against notched bar experiments was made by Becker et al. (1988). Their study centered on a compacted iron powder so that the material contained some initial porosity....
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TL;DR: In this article, the deformation and failure of metal-matrix composites, by the nucleation and growth of voids within the ductile matrix, are studied numerically and experimentally.
Abstract: Deformation and failure of metal-matrix composites, by the nucleation and growth of voids within the ductile matrix, are studied numerically and experimentally. The matrix material is modelled as an elastic-viscoplastic ductile porous solid to characterize the evolution of damage from void formation. The material systems chosen for parametric analyses and for quantitative comparisons between numerical analyses and experiments are aluminum alloys discontinuously reinforced with SiC. The brittle reinforcement phase, in the form of spheres, particulates with sharp corners, or cylindrical whiskers, is modelled as elastic or rigid, with the interfaces between the ductile matrix and the brittle reinforcement assumed to be perfectly bonded. The overall constitutive response of the composite and the evolution of matrix failure are analyzed using finite element models within the context of axisymmetric and plane strain formulations. Detailed parametric analyses of the effects of (i) reinforcement shape, (ii) reinforcement volume fraction, (iii) mechanical properties of the matrix, (iv) nucleation strain and volume fraction of void-nucleating particles, and (v) reinforcement distribution on the overall deformation and ductility of the composite are discussed. The numerical predictions of yield strength, strain hardening exponent and ductility for the composites with different volume fractions of SiC particulates are also compared with experimental measurements.
317 citations
TL;DR: In this article, the effect of stress triaxiality on the onset and evolution of damage in ductile metals is discussed and a series of tests including shear tests and experiments on smooth and pre-notched tension specimens was carried out for a wide range of stress-triaxialities.
280 citations
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TL;DR: In this article, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material.
Abstract: The fracture of ductile solids has frequently been observed to result from the large growth and coalescence of microscopic voids, a process enhanced by the superposition of hydrostatic tensile stresses on a plastic deformation field. The ductile growth of voids is treated here as a problem in continuum plasticity. First, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and subjected to a remotely uniform stress and strain rate field. Then an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material. Growth is studied in some detail for the case of a remote tensile extension field with superposed hydrostatic stresses. The volume changing contribution to void growth is found to overwhelm the shape changing part when the mean remote normal stress is large, so that growth is essentially spherical. Further, it is found that for any remote strain rate field, the void enlargement rate is amplified over the remote strain rate by a factor rising exponentially with the ratio of mean normal stress to yield stress. Some related results are discussed, including the long cylindrical void considered by F.A. McClintock (1968, J. appl. Mech . 35 , 363), and an approximate relation is given to describe growth of a spherical void in a general remote field. The results suggest a rapidly decreasing fracture ductility with increasing hydrostatic tension.
4,156 citations
TL;DR: In this article, a set of elastic-plastic constitutive relations that account for the nucleation and growth of micro-voids is used to model the failure of a round tensile test specimen.
2,962 citations
2,452 citations
TL;DR: In this paper, the authors investigated the hypothesis that localization of deformation into a shear band may be considered a result of an instability in the constitutive description of homogeneous deformation.
Abstract: T his paper investigates the hypothesis that localization of deformation into a shear band may be considered a result of an instability in the constitutive description of homogeneous deformation. General conditions for a bifurcation, corresponding to the localization of deformation into a planar band, are derived. Although the analysis is general and applications to other localization phenomena are noted, the constitutive relations which are examined in application of the criterion for localization are intended to model the behavior of brittle rock masses under compressive principal stresses. These relations are strongly pressure-sensitive since inelasticity results from frictional sliding on an array of fissures; the resulting inelastic response is dilatant, owing to uplift in sliding at asperities and to local tensile cracking from fissure tips. The appropriate constitutive descriptions involve non-normality of plastic strain increments to the yield hyper-surface. Also, it is argued that the subsequent yield surfaces will develop a vertex-like structure. Both of these features are shown to be destabilizing and to strongly influence the resulting predictions for localization by comparison to predictions based on classical plasticity idealizations, involving normality and smooth yield surfaces. These results seem widely applicable to discussions of the inception of rupture as a constitutive instability.
2,411 citations