Investigation of shear damage considering the evolution of anisotropy

The damage that occurs in shear deformations in view of anisotropy evolution is investigated. It is widely believed in the mechanics research community that damage (or porosity) does not evolve (increase) in shear deformations since the hydrostatic stress in shear is zero. This paper proves that the above statement can be false in large deformations of simple shear. The simulation using the proposed anisotropic ductile fracture model (macro-scale) in this study indicates that hydrostatic stress becomes nonzero and (thus) porosity evolves (increases or decreases) in the simple shear deformation of anisotropic (orthotropic) materials. The simple shear simulation using a crystal plasticity based damage model (meso-scale) shows the same physics as manifested in the above macro-scale model that porosity evolves due to the grain-to-grain interaction, i.e., due to the evolution of anisotropy. Through a series of simple shear simulations, this study investigates the effect of the evolution of anisotropy, i.e., the rotation of the orthotropic axes onto the damage (porosity) evolution. The effect of the evolutions of void orientation and void shape onto the damage (porosity) evolution is investigated as well. It is found out that the interaction among porosity, the matrix anisotropy and void orientation/shape plays a crucial role in the ductile damage of porous materials.     

Model of plastic anisotropy evolution with texture-dependent yield surface

Model of evolution of plastic anisotropy due to crystallographic texture development, in metals subjected to large deformation processes, is presented. The model of single grain with the regularized Schmid law proposed by Gambin is used. Evolution of crystallographic texture during drawing, rolling and pure shear is calculated. Phenomenological texture-dependent yield surface for polycrystalline sheets is proposed. Evolution of this yield surface is compared with evolution of phenomenological higher order yield surfaces proposed by Hill and Barlat with Lian for drawing, rolling and pure shear processes. The change of the Hill yield surface and the Barlat–Lian yield surface is obtained by replacing material parameters present in these conditions by texture-dependent functions.     

Modeling of deformation induced anisotropy in free-end torsion

The main purpose of this work is to develop a phenomenological model, which accounts for the evolution of the elastic and plastic properties of fcc polycrystals due to a crystallographic texture development and predicts the axial effects in torsion experiments. The anisotropic portion of the effective elasticity tensor is modeled by a growth law. The flow rule depends on the anisotropic part of the elasticity tensor. The normalized anisotropic part of the effective elasticity tensor is equal to the 4th-order coefficient of a tensorial Fourier expansion of the crystal orientation distribution function. Hence, the evolution of elastic and viscoplastic properties is modeled by an evolution equation for the 4th-order moment tensor of the orientation distribution function of an aggregate of cubic crystals. It is shown that the model is able to predict the plastic anisotropy that leads to the monotonic and cyclic Swift effect. The predictions are compared to those of the Taylor–Lin polycrystal model and to experimental data. In contrast to other phenomenological models proposed in the literature, the present model predicts the axial effects even if the initial state of the material is isotropic.     

An endochronic theory accounted for deformation induced anisotropy

An anisotropic quadratic form of plastic strain increment is used to define the intrinsic time in the endochronic theory of plasticity. Based on this new definition, a yield function can be derived. This new version of endochronic theory can describe the expansion, translation, rotation, and distortion of the yield surface. While the initial yielding is in the form of the Mises yield criterion, the distortion of subsequent yield surfaces is expressed by the compression or stretching of the Mises yield surface. The effect of sharp front and blunt rear of the yield surface is considered to be of secondary importance and neglected in the interest of keeping the equations simple. This idealization will not much affect the prediction power of the model, because the plastic strain increment is in the radial direction emanating from the center of the current yield surface and is not normal to the current yield surface. In this theory, the plastic deformation is thus not sensitive to the exact shape of the yield surface. It has been shown that the proposed theory is capable of describing the experimental results of three different metals considered. The test series investigated include several different paths of prestress.     

On pre-straining and the evolution of material anisotropy in sheet metals

Uniaxial tension tests have been carried out along different angles from the rolling direction for both as-received and pre-strained sheet. By comparing the differences in the flow stress vs. orientation curves between the as-received and pre-strained sheets, the effect of pre-straining on material anisotropy is studied. It is demonstrated that the conventional methodology for determining material anisotropy would overestimate the pre-straining effect and would result in a completely erroneous yield surface.     

Multiscale modelling of the induced plastic anisotropy in bcc metals

This paper presents a new framework to predict the qualitative and quantitative variation in local plastic anisotropy due to crystallographic texture in body-centered cubic polycrystals. A multiscale model was developed to examine the contribution of mesoscopic and local microscopic behaviour to the macroscopic constitutive response of bcc metals during deformation. The model integrated a dislocation-based hardening scheme and a Taylor-based crystal plasticity formulation into the subroutine of an explicit dynamic FEM code (LS-DYNA). Numerical analyses using this model were able to predict not only correct grain rotation during deformation, but variations in plastic anisotropy due to initial crystallographic orientation. Optimal results were obtained when {1 1 0}〈1 1 1〉, {1 1 2}〈1 1 1〉, and {1 2 3}〈1 1 1〉 slip systems were considered to be potentially active. The predicted material heterogeneity can be utilised for research involving any texture-dependent work hardening behaviour, such as surface roughening.     

The effect of stress induced anisotropy on shear band formation

Summary This paper describes the effect of non-coaxiality arising from material anisotropy on bifurcation phenomena such as shear band formation. The elasto-plastic model originally proposed by Sekiguchi and Ohta [7] is one of the typical models which include anisotropy and it is used to examine the effect of anisotropy on shear band formation. First, we shall extend this elasto-plastic model for infinitesimal strain to a model for finite strain and discuss the mathematical structure of this model. The stress induced anisotropy is found to bring about a vertex-like effect, such as the non-coaxiality between the Cauchy stress tensor and a plastic stretching tensor, into the constitutive relation. Then, we shall examine the effect of this non-coaxiality on bifurcation conditions in relation to the material rigidity which changes with the angle of simple shear. Finally, it will be concluded that this non-coaxiality arising from the anisotropy does not contribute much to triggering instability by localization of the deformations which result in shear band formation, while on the other hand, the non-coaxiality due to the yield vertex effect is rather inclined towards instability by localization of the deformations.

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Der Einfluß spannungsinduzierter Anisotropie auf die Scherzonenbildung

Übersicht Beschrieben wird der Einfluß anisotropie-bedingt verschiedener Achsen von Spannung und Deformationsgeschwindigkeit auf Verzweigungsphänomene wie die Scherzonenbildung. Das elastisch-plastische Modell von Sekiguchi und Ohta wird als typisch anisotropes Modell zur Untersuchung des Einflusses der Anisotropie auf die Scherzonenbildung benutzt. Zunächst wird es zu einem Modell für endliche Deformationen erweitert und seine mathematische Struktur erörtert. Es zeigt sich, daß die spannungsinduzierte Anisotropie einen Effekt ähnlich einer Fließortspitze erzeugt wie z. B. verschiedene Achsen von Cauchy-Spannungstensor und plastischem Strecktensor. Danach wird in Zusammenhang mit der Materialsteifigkeit, die vom Winkel der einfachen Scherung abhängt, der Einfluß verschiedener Achsen auf Verzweigungsbedingungen untersucht. Es wird gefolgert, daß anisotropie-bedingt verschiedene Achsen wenig zur Auslösung der Instabilität durch lokalisierte Deformation beitragen, andererseits verschiedene Achsen infolge einer Fließortspitze die Neigung zur lokalisierten Deformation unterstützen.

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Presented at the workshop on Numerical Methods for Localization and Bifurcation of Granular Bodies, held at the Technical University of Gadansk (Poland), September 25–30, 1989     

Effect of elastic anisotropy on surface pattern evolution of epitaxial thin films

Stress-induced surface instability and evolution of epitaxial thin films leads to formation of a variety of self-assembled surface patterns with feature sizes at micro- and nanoscales. The anisotropy in both the surface and bulk properties of the film and substrate has profound effects on the nonlinear dynamics of surface evolution and pattern formation. Experimentally it has been demonstrated that the effect of anisotropy strongly depends on the crystal orientation of the substrate surface on which the film grows epitaxially. In this paper we develop a nonlinear model for surface evolution of epitaxial thin films on generally anisotropic crystal substrates. Specifically, the effect of bulk elastic anisotropy of the substrate on epitaxial surface pattern evolution is investigated for cubic germanium (Ge) and SiGe films on silicon (Si) substrates with four different surface orientations: Si(0 0 1), Si(1 1 1), Si(1 1 0), and Si(1 1 3). Both linear analysis and nonlinear numerical simulations suggest that, with surface anisotropy neglected, ordered surface patterns form under the influence of the elastic anisotropy, and these surface patterns clearly reflect the symmetry of the underlying crystal structures of the substrate. It is concluded that consideration of anisotropic elasticity reveals a much richer dynamics of surface pattern evolution as compared to isotropic models.     

An endochronic model of yield surface accounting for deformation induced anisotropy

In this article, an endochronic model of yield surface is proposed. Based on this model, the yield surface is simulated such that the forward and rear parts of the yield surface are described by different ellipses which are characterized by corresponding aspect ratio functions, respectively. Verification of the endochronic theory used the experimental results of yield surfaces obtained by Wu and Yeh for 304 stainless steel (Wu, H.C., Yeh, W.C., 1991. On the experimental determination of yield surfaces and some results of annealed 304 stainless steel. Int. J. Plasticity 7, 803–826). The experiments were performed cyclically under uniaxial, torsional, and combined axial–torsional loading conditions. The result has shown that the agreement between the prediction and experiments is quite satisfactory. In addition to the distortion of the yield surface plastically behaving a sharp front accompanied by a blunt rear, the anisotropic kinematic hardening effect has been addressed in this investigation. Although the experimental results of yield surfaces subjected to non-proportional loading conditions can be found in the literature, lack of information about the plastic strain history makes it impossible to verify the theory under such complicated loading conditions. The domain of applicability and validity of the theory, which is defined in terms of plastic strain increments, need be further investigated with the aim to set up related experiments.     

Deformation induced anisotropy and memorized back stress in constitutive model

Plastic-deformation induced anisotropy and memorization of back stress due to pre-loading affect the current loading. These phenomena are examined with tension and/or torsion tests, using SUS 304. Considering both anisotropy, and movement and memorization of back stress, equi-plastic surfaces are predicted. This explains the dependence of current loading on pre-loading well. Simulated strain paths during radial loading after shear straining show good agreement with experiments.     

Finite element modeling of plastic anisotropy induced by texture and strain-path change

Consideration of plastic anisotropy is essential in accurate simulations of metal forming processes. In this study, finite element (FE) simulations have been performed to predict the plastic anisotropy of sheet metals using a texture- and microstructure-based constitutive model. The effect of crystallographic texture is incorporated through the use of an anisotropic plastic potential in strain-rate space, which gives the shape of the yield locus. The effect of dislocation is captured by use of a hardening model with four internal variables, which characterize the position and the size of the yield locus. Two applications are presented to evaluate the accuracy and the efficiency of the model: a cup drawing test and a two-stage pseudo-orthogonal sequential test (biaxial stretching in hydraulic bulging followed by uniaxial tension), using an interstitial-free steel sheet. The experimental results of earing behavior in the cup drawing test, maximum pressure and strain distribution in bulging, and transient hardening in the sequential test are compared against the FE predictions. It is shown that the current model is capable of predicting the plastic anisotropy induced by both the texture and the strain-path change. The relative significance of texture and strain-path change in the predictions is discussed.     

Experimental study of the evolution of plastic anisotropy in 5754 Al-Mg cold rolled sheets

Experimental Techniques - Modeling the evolution of material anisotropy accurately is essential to sheet metal forming simulation and springback prediction. The objective of this preliminary study...     

Overall softening and anisotropy related with the formation and evolution of dislocation cell structures

In this work, a model, based on a representation of the dislocation cell microstructures by a non-local two-phase material with evolving microstructures, is proposed for the elastic–plastic behavior of metals under monotonic and sequential loading. The first phase represents the cell interior and the second one, the cell walls. The evolution of the microstructure is taken into account considering the cell-wall interfaces as free boundaries. Finally, the accumulation within walls of dislocations crossing the cells defines a non-local hardening process. Assuming a piecewise uniform plastic strain field and assuming ellipsoidal cells, the free energy of the system is calculated. The driving and critical forces associated with the plastic flow of the two-phases and the morphology of the cells are established. In a third part, numerical results are presented for monotonic and sequential loading. The results show an overall softening related to the destabilization of the dislocation microstructures which occurs in sequential as well as monotonic paths.     

Liquid and gas flows in porous media with allowance for induced anisotropy

The changes in the permeability of a porous medium resulting from the reorientation of the solid matrix particles under the influence of the percolating flow are considered. The mathematical model also contains the angular momentum equation, including the moment of the viscous flow forces. The state of the elastic matrix is characterized not only by the repacking strains but also by the particle orientation vector. The latter determines the anisotropy of the permeability tensor. The effective stress, strain, pore pressure and orientation vector fields in the neighborhood of an operating well are constructed. The effect of the induced permeability anisotropy on well productivity is noted.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 96–103, May–June, 1992.The authors are grateful to G. A. Zotov and V. A. Chernykh for their interest and support.     

An endochronic theory accounting for deformation induced anisotropy of metals under biaxial load

Using the experimental results of yield surfaces obtained by Wu and Yeh [1991] (Int. J. Plasticity, 7, 803) for 304 stainless steel, this work provides a verification of the endochronic theory of plasticity accounting for deformation induced anisotropy. The experiments were performed under proportional loading conditions. The main difference between this paper and other papers that attempt to describe the distortion of a yield surface is that, in addition to distortion, motion of yield surface (kinematic hardening) has also been addressed by this paper. The result has shown that the theory predicts the experimental data with substantial accuracy. However, since in this theory the plastic strain increment, although normal to the initial yield surface, is in the radial direction emanating from the center of the subsequent yield surface, validity of the present model must be further studied for the case involving nonproportional loading conditions.     

Open-cell cellular solids: A constitutive equation for hyperelasticity with deformation induced anisotropy

A constitutive theory is developed for an open-cell flexible cellular solid consisting of a network of struts each connecting two vertex points. A hypothesis is proposed that vertex points move affinely in the large-deformation regime, when the struts buckle, and that the force carried by a strut is a function of the longitudinal and rotational change of its vertex-to-vertex vector. The forces consist of one longitudinal force, parallel with the vertex-to-vertex vector of the strut and one transverse force. The overall stress response is initially dominated by the longitudinal force whilst the addition of the transverse force becomes significant at large deformations. The model contains three parameters: longitudinal stiffness, bending stiffness and critical stretch of a strut. These three parameters are calibrated against a simple compression test. The model is then validated against independent experiments in a simple tension, simple shear and a combined shear-compression test on an isotropic flexible polyether urethane foam. Excellent agreement is obtained between the experiments and the model.     

On the modeling and simulation of induced anisotropy in polycrystalline metals with application to springback

The presence of initial, and the development of induced, anisotropic elastic and inelastic material behavior in polycrystalline metals, can be traced back to the influence of texture and dislocation substructural development on this behavior. As it turns out, via homogenization or other means, one can formulate effective models for such structure and its effect on the macroscopic material behavior with the help of the concept of evolving structure tensors. From the constitutive point of view, these quantities determine the material symmetry properties. Most importantly, all dependent constitutive fields (e.g., stress) are by definition isotropic functions of the independent constitutive variables, which include these evolving structure tensors. The evolution of these tensors during loading results in an evolution of the anisotropy of the material. From an algorithmic point of view, the current approach leads to constitutive models which are quite amenable to numerical implementation. To demonstrate the applicability of the resulting constitutive formulation, we apply it to the case of metal plasticity with combined hardening involving both deformation- and permanently induced anisotropy. Comparison of simulation results based on this model for the bending tension of aluminum-alloy sheet-metal strips with corresponding experimental ones show good agreement.