Void nucleation effects on shear localization in porous plastic solids

The influence of void nucleation occurring during the deformation history on shear localization is investigated by employing a constitutive model of a rate independent porous plastic solid. Both plastic strain controlled and stress controlled nucleation processes are simulated. Two deformation histories are considered, one corresponding to uniaxial tension and the other to plane strain tension. The enhanced triaxiality at the center of a neck is simulated by application of Bridgman's solution for the stress and deformation state at the minimum section of a necked bar. The destabilizing effect that arises when void nucleation is stress controlled and nucleation occurs over a narrow range of stress is illustrated. Results are also presented employing parameter values representative of spheroidized carbon steels employed in a recent experimental study carried out by Fisher [23] and the predictions of the model are discussed in light of the experimental observations.

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Résumé On étudie l'influence de la nucléation de lacunes qui survient au cours de la déformation dans les zones où se produit un cisaillement, en recourant à un modèle constitutif représentant un solide plastique poreux dont les caractéristiques sont indépendantes de la vitesse. On simule à la fois les processus de nucléation sous déformation plastique contrôlée et sous contrainte contrôlée. On considère deux histoires de déformations, l'une correspondant à une contrainte uniaxiale et l'autre à une contrainte appliquée en état plan de déformation. La triaxialité créée au centre d'un rétrécissement est simulée par l'application d'une solution de Bridgman pour déterminer la contrainte et l'état de déformation à la section minimum d'une barre rétrécie. On illustre l'effet déstabilisant qui se produit lorsque la nucléation de lacunes se trouve contrôlée par la tension et qu'elle survient sur une bande étroite de contraintes. Les résultats sont également présentés en recourant à des valeurs paramétriques représentatives pour les aciers au carbone utilisés dans une étude expérimentale récente effectuée par Fisher (23), et l'on discute les prédictions du modèle à la lumière des observations expérimentales.

     

Finite element analyses of shear localization in rate and temperature dependent solids

The effects of strain hardening, strain rate sensitivity, thermal softening, heat conduction and the imposed strain rate on the shear localization process in plane strain compression are examined. The deformation, stress and temperature fields are computed in an infinite solid which contains a periodic rectangular array of inhomogeneities. The inhomogeneities give rise to non-uniform deformation fields which, under certain conditions, may localize in the form of a shear band. Boundary conditions are prescribed such that the resulting fields possess periodicity with respect to the inhomogeneity distribution. In this manner, attention may be confined to a rectangular region of the solid which surrounds a single inhomogeneity. Full two-dimensional analyses are performed within the context of a viscoplasticity theory which, in the rate independent limit, corresponds to flow theory with combined isotropic and kinematic hardening. Full account is taken of finite strain and rotation effects, but attention is confined to quasi-static loading. The initiation and propagation of shear bands is examined for the bounding theories of isotropic and kinematic hardening. The predicted response depends significantly on the multi-axial hardening characterization of the solid.     

On some simple steady forming process of viscoplastic solids

Summary Steady drawing and extrusion processes of conventional viscoplastic materials, through wedge-shaped and conical dies, are analyzed. The basic material model assumes that the Eulerian strain rate is the sum of a plastic part and a viscous part. The investigation is restricted to relatively long and tapered dies with small wall friction. Within these limitations it is permissible to treat the flow patterns as being nearly radial. The problem is thus reduced to a single non-linear differential equation. A few exact solutions are obtained and a further analysis is given for purely viscous solids. For the latter case we demonstrate the existence of optimum die angles where the required drawing tension attains a minimum.With 5 FiguresDedicated to Prof. James F. Bell on the occasion of his 70th birthday.     

A theoretical description of large viscoplastic shear deformation in metals

In this work, a new 3-dimensional viscoplastic model based on a previous plasticity theory is presented. The proposed constitutive model anticipates the contribution of the main features of plastic behavior, such as yielding, rate effect, isotropic and kinematic hardening, through a new approximation of the constitutive equation with a viscoplastic term, as well as a new consideration of the functional form of the rate of plastic deformation. A high accuracy simulation of shear experimental data at various rates and temperatures for a variety of materials, as well as the sign inversion of normal stress has been postulated.     

Adiabatic shear failure in brittle solids

Recent studies have revealed microscopic amorphous lamella resulting from inelastic deformation in the ballistic impact of boron carbide ceramic. The possibility that these deformation features are a consequence of adiabatic shear deformation in the impact event is explored. An early theory of adiabatic shear that was limited to the response of rigid-plastic deformation is expanded to include elastic strain energy. The study reveals that elastic strain energy is commonly a small, but not negligible, contribution to impact-induced adiabatic shear in metals. Elastic strain energy is paramount in brittle solids. Relations are developed from the theory to predict the nominal width and spacing of adiabatic shear-bands in brittle solids. Comparisons of the theoretical predictions are consistent with observations of impact-induced deformation features in boron carbide.     

Modes of dynamic shear failure in solids

The technique of loading edge cracks by edge impact (LECEI) for generating high rates of crack tip shear (mode-II) loading is presented. The LECEI-technique in combination with a gas gun for accelerating the impactor is used to study the high rate shear failure behaviour of three types of materials. Epoxy resin (Araldite B) shows failure by tensile cracks up to the highest experimentally achievable loading rate; steel (high strength maraging steel X2 NiCoMo 18 9 5) shows a failure mode transition: at low rates failure occurs by tensile cracks, at higher rates, above a certain limit velocity, failure by adiabatic shear bands is observed; aluminum alloy (Al 7075) shows failure due to shear band processes in the high rate regime, but this failure mode is observed over the entire range of lower loading rates, even down to quasi-static conditions. Characteristics of the failure modes are presented. When transitions are observed in the failure process from tensile cracks to shear bands the limit velocity for failure mode transition depends on the bluntness of the starter crack the failure is initiated from: The larger the bluntness of the starter crack the higher the critical limit velocity for failure mode transition. The data indicate that adiabatic shear bands require and absorb more energy for propagation than tensile cracks. Aspects of the energy balance controlling mode-II instability processes in general are considered. Effects very different than for the mode-I instability process are observed: When failure by a tensile crack occurs under mode-II initiation conditions, a notch is formed between the initiated kinked crack and the original starter crack, and, at this notch a compressive stress concentration builds up. The energy for building up this stress concentration field is not available for propagation of the initiated kinked crack. The energy density of a mode-II crack tip stress field, however, when compared to an equivalent mode-I crack tip field, is considerably larger, and, consequently, the remaining driving energy for any mode-II initiated failure process, nevertheless, is higher than for the case of equivalent mode-I initiation conditions. Furthermore, mode-II crack tip plastic zones are considerably larger than equivalent mode-I crack tip plastic zones. Consequently, validity conditions for linear-elastic or small scale yielding failure behaviour are harder to fulfill and possibilities for the activation of nonlinear high energy ductile type failure processes are enhanced. Speculations on how these effects might favour failure by high energy processes in general and by shear bands processes in particular for conditions of high rate shear mode-II loading are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Wave propagation and localization problems in saturated viscoplastic geomaterials

This paper presents an improved algorithm to deal with wave propagation and localization problems in saturated viscoplastic geomaterials. It consists of a mixed formulation in terms of effective stress, velocity and pore pressure that uses a fractional step algorithm allowing the use of equal order of interpolation for the three variables and the simplest element such as the linear triangle. The viscoplastic model used is of modified cam‐clay type. Viscoplasticity results in a strong source term that deteriorates the accuracy of the two‐step Taylor–Galerkin algorithm. Therefore a Runge–Kutta splitting scheme has been used to deal with the source terms, resulting in a better accuracy of the method. Copyright © 2006 John Wiley & Sons, Ltd.     

Quantum localization of hydrogen atoms in solids

Quantum distributions of hydrogen-like atoms in solids were investigated theoretically by the first-principles path-integral molecular dynamics (FP-PIMD) method, in which interatomic forces are calculated precisely based on the density functional theory. Some distributions are qualitatively different from those obtained by conventional simulations with classical treatment of protons. Interestingly, quantum fluctuations sometimes cause localization of the nuclei. The mechanism of this ‘quantum localization’ is intuitively explained by considering characteristic potential energy surfaces.     

Review of shear surface acoustic waves in solids

General considerations about physical reasons for the existence of surface acoustic waves and, in particular, shear surface acoustic waves in solids are presented. The results of calculations for various types of shear surface acoustic waves are described, and corresponding physical explanations are given.     

Temporal homogenization of viscoelastic and viscoplastic solids subjected to locally periodic loading

 As a direct extension of the asymptotic spatial homogenization method we develop a temporal homogenization scheme for a class of homogeneous solids with an intrinsic time scale significantly longer than a period of prescribed loading. Two rate-dependent material models, the Maxwell viscoelastic model and the power-law viscoplastic model, are studied as an illustrative examples. Double scale asymptotic analysis in time domain is utilized to obtain a sequence of initial-boundary value problems with various orders of temporal scaling parameter. It is shown that various order initial-boundary value problems can be further decomposed into: (i) the global initial-boundary value problem with smooth loading for the entire loading history, and (ii) the local initial-boundary value problem with the remaining (oscillatory) portion of loading for a single load period. Large time increments can be used for integrating the global problem due to smooth loading, whereas the integration of the local initial-boundary value problem requires a significantly smaller time step, but only locally in a single load period. The present temporal homogenization approach has been found to be in good agreement with a closed-form analytical solution for one-dimensional case and with a numerical solution in multidimensional case obtained by using a sufficiently small time step required to resolve the load oscillations. Received: 22 November 2001 / Accepted: 21 May 2002     

Cracks in two-phase solids under longitudinal shear loading

International Journal of Fracture - A continuously distributed dislocation model has been used to study the stress fields near to the tips of cracks in composite solids deformed in antiplane...     

FE-investigation of shear localization in granular bodies under high shear rate

Shear localization in granular materials under high shear rate is analysed with the finite element method and a micro-polar hypoplastic constitutive model enhanced by viscous terms. We consider plane strain shearing of an infinitely long and narrow granular strip of initially dense sand between two very rough walls under conditions of free dilatancy. The constitutive model can reproduce the essential features of granular materials during shear localization. The calculations are performed under quasi-static and dynamic conditions with different shear rates. In dynamic regime, the viscosity terms are formulated based on a modified Newtonian fluid and according to the formula by Stadler and Buggisch (Proceedings of the conference on Reliable flow of particulate solids, EFCE Pub. Series, vol 49. Chr. Michelsen Institute, Bergen, 1985). Emphasis is given to the influence of inertial and viscous forces on the shear zone thickness and mobilized wall friction angle.     

Thermal conductivity of moist porous solids

A structural model and the method of computing the effective thermal conductivity of porous moist solid materials are proposed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 2, pp. 278–283, August, 1976.     

Weak shock waves and shear bands in thermoelastic solids

The linear weak shock wave (acoustic wave) propagation and the existence of shear bands are examined in finitely deformed thermoelastic solids within the framework of the theory of singular surfaces. The jumps of certain field variables across the shock wave front are obtained by using Taylor series expansions of them. The propagation condition of shock waves in a thermoelastic solid is obtained by using the strain–energy function corresponding to Duhamel–Neumann expression. The propagation speeds of weak shock waves are determined for a particular state of deformation, that is, general dilation. The formation of shear bands and the magnitudes of critical stretches are obtained for the deformation states of uniaxial, biaxial extension and for uniform dilation.     

The influence of microstructure-induced gradients on the localization of deformation in viscoplastic materials

Summary We suggest here a generalization of the conventional constitutive models of viscoplasticity. This is accomplished by the inclusion of spatial gradients of the equivalent stress and strain in the evolution equation for the equivalent plastic strain rate. We restrict attention to plane deformation and elastic effects are neglected for simplicity. The implications of the new terms in the constitutive model are discussed for the case of a general eigenvalue problem of an initially homogeneous and stationary viscous flow. It turns out that the nonclassical material parameters can be chosen in such a way that the governing differential equations are always strongly elliptic irrespective of whether the mateiral is strain softening. As it is well known, the latter typically leads to loss of ellipticity in the conventional theories. Explicit results are presented for the case of a shear band instability. Within the framework of the present theory, and in contrast to conventional models, the shear band kinematics have a well defined geometrical structure.