Benoit Revil-Baudard

On the Combined Effect of Pressure and Third Invariant on Yielding of Porous Solids With von Mises Matrix

In this paper, a new plastic potential for porous solids with von Mises perfectly-plastic matrix containing spherical cavities is derived using a rigorous limit analysis approach. For stress-triaxialities different from 0 and ±∞, the dilatational response depends on the signs of the mean stress and the third invariant of the stress deviator. The classic Gurson potential is an upper-bound of the new criterion. A full-field dilatational viscoplastic Fast Fourier Transform (FFT)-based approach is also used to generate numerical gauge surfaces for the porous material. The numerical calculations confirm the new features of the dilatational response, namely: a very specific dependence with the signs of the mean stress and the third invariant that results in a lack of symmetry of the yield surface.

New three-dimensional strain-rate potentials for isotropic porous metals: Role of the plastic flow of the matrix

Abstract At present, modeling of the plastic response of porous solids is done using stress-based plastic potentials. To gain understanding of the combined effects of all invariants for general three-dimensional loadings, a strain-rate based approach appears more appropriate. In this paper, for the first time strain rate-based potentials for porous solids with Tresca and von Mises, matrices are obtained. The dilatational response is investigated for general 3-D conditions for both compressive and tensile states using rigorous upscaling methods. It is demonstrated that the presence of voids induces dependence on all invariants, the noteworthy result being the key role played by the plastic flow of the matrix on the dilatational response. If the matrix obeys the von Mises criterion, the shape of the cross-sections of the porous solid with the octahedral plane deviates slightly from a circle, and changes very little as the absolute value of the mean strain rate increases. However, if the matrix behavior is described by Tresca’s criterion, the shape of the cross-sections evolves from a regular hexagon to a smooth triangle with rounded corners. Furthermore, it is revealed that the couplings between invariants are very specific and depend strongly on the particularities of the plastic flow of the matrix.

Importance of the coupling between the sign of the mean stress and the third invariant on the rate of void growth and collapse in porous solids with a von Mises matrix

Recently, Cazacu et al (2013a J. Appl. Mech. 80 64501) demonstrated that the plastic potential of porous solids with a von Mises matrix containing randomly distributed spherical cavities should involve a very specific coupling between the mean stress and , the third invariant of the stress deviator. In this paper, the effects of this coupling on void evolution are investigated. It is shown that the new analytical model predicts that for axisymmetric stress states, void growth is faster for loading histories corresponding to than for those corresponding to . However, void collapse occurs faster for loadings where than for those characterized by . Finite-element (FE) results also confirm these trends. Furthermore, comparisons between FE results and corresponding predictions of yielding and void evolution show the improvements provided by the new model with respect to Gursons. Irrespective of the loading history, the predicted rate of void growth is much faster than that according to Gursons criterion.

Unusual plastic deformation and damage features in titanium: Experimental tests and constitutive modeling

Abstract In this paper, we present an experimental study on plastic deformation and damage of polycrystalline pure HCP Ti, as well as modeling of the observed behavior. Mechanical characterization data were conducted, which indicate that the material is orthotropic and displays tension-compression asymmetry. The ex-situ and in-situ X-ray tomography measurements conducted reveal that damage distribution and evolution in this HCP Ti material is markedly different than in a typical FCC material such as copper. Stewart and Cazacu (2011) anisotropic elastic/plastic damage model is used to describe the behavior. All the parameters involved in this model have a clear physical significance, being related to plastic properties, and are determined from very few simple mechanical tests. It is shown that this model predicts correctly the anisotropy in plastic deformation, and its strong influence on damage distribution and damage accumulation. Specifically, for a smooth axisymmetric specimen subject to uniaxial tension, damage initiates at the center of the specimen, and is diffuse; the level of damage close to failure being very low. On the other hand, for a notched specimen subject to the same loading the model predicts that damage initiates at the outer surface of the specimen, and further grows from the outer surface to the center of the specimen, which corroborates with the in-situ tomography data.

Constitutive Equations for Elastic–Plastic Materials

While in the literature, there is ample exposure of elastic–plastic models formulated in the stress space, the dual formulations in the strain-rate space are less known. Chapter 2 presents the fundamental assumptions concerning the form of stress-based and strain-rate-based elastic–plastic models along with the corresponding numerical integration algorithms for solving boundary-value problems.

Anisotropic Plastic Potentials for Porous Metallic Materials

In all the constitutive models for porous plastic materials presented in previous chapters, it was presumed that the matrix can be regarded as isotropic. However, most engineering materials display plastic anisotropy (see Chaps. 5 and 6 ). In this chapter are presented key contributions toward understanding the role played by the matrix plastic anisotropy on yielding and damage evolution in single crystals and strongly textured polycrystalline materials containing randomly distributed spherical voids.

Plastic Potentials for Isotropic Porous Materials: Influence of the Particularities of Plastic Deformation on Damage Evolution

In Chap. 7, key contributions toward elucidating the role of the plastic deformation on damage evolution in isotropic metallic materials are introduced. The ductile damage models presented are derived using rigorous upscaling techniques and limit-analysis methods. Previously unrecognized combined effects of the mean stress and third-invariant of the stress deviator on yielding of porous materials with matrix described by von Mises and Tresca yield criteria are presented. It is shown that the fastest rate of void growth or collapse occurs in a porous Tresca material. Most importantly, it is revealed that depending on the yield criterion for the matrix, the third-invariant effects (or Lode effects) on void evolution can be either enhanced or completely eliminated.

Yield Criteria for Anisotropic Polycrystals

Chapter 5 is devoted to modeling the elastic–plastic behavior of anisotropic polycrystalline metals. After introducing the only two rigorous methodologies for extending isotropic formulations such as to account for anisotropy, the most versatile three-dimensional orthotropic yield criteria for materials with the same response in tension and in compression are presented. While the need for analytic yield criteria that account for both anisotropy and tension–compression asymmetry in the plastic deformation of hexagonal materials such as magnesium, zirconium, and titanium alloys has been long recognized, only recently models that describe these key features have been developed. These contributions along with applications for a variety of loadings are discussed.

Plastic Deformation of Single Crystals

Chapter 3 is devoted to constitutive relations for metallic single crystals. After introducing the key concepts of crystallography, an overview of the experimental evidence of plastic deformation mechanisms is presented. The yield criteria for description of the onset of plastic deformation in cubic crystals are introduced. Applications of the most recent single crystal yield criterion to the prediction of the directionality of the macroscopic tensile properties of polycrystalline sheets are also provided.

Strain-Rate-Based Plastic Potentials for Polycrystalline Materials

Although the existence of strain-rate based potentials which are work-conjugate of given stress potentials has been theoretically demonstrated, analytical expressions of strain-rate potentials are only known for a very few cases. In this chapter, closed-form expressions for strain-rate-based plastic potentials are derived for both isotropic and anisotropic fully-dense polycrystalline materials. Besides their intrinsic importance in design and optimization of metal forming processes, these analytic strain-rate potentials enable the development of the closed form expressions of plastic potentials for porous metallic materials that are presented in Chaps. 7 and 8.