Nitin Chandola

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.

Application of the VPSC Model to the Description of the Stress–Strain Response and Texture Evolution in AZ31 Mg for Various Strain Paths

Accurate description of the mechanical response of AZ31 Mg requires consideration of its strong anisotropy both at the single crystal and polycrystal levels, and its evolution with accumulated plastic deformation. In this paper, a self-consistent mean field crystal plasticity model, viscoplastic self-consistent (VPSC), is used for modeling the room-temperature deformation of AZ31 Mg. A step-by-step procedure to calibrate the material parameters based on simple tensile and compressive mechanical test data is outlined. It is shown that the model predicts with great accuracy both the macroscopic stress–strain response and the evolving texture for these strain paths used for calibration. The stress–strain response and texture evolution for loading paths that were not used for calibration, including off-axis uniaxial loadings and simple shear, are also well described. In particular, VPSC model predicts that for uniaxial tension along the through-thickness direction, the stress–strain curve should have a sigmoidal shape.

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.

Prediction of plastic anisotropy of textured polycrystalline sheets using a new single-crystal model

Abstract In this paper, we predict the effect of texture on the plastic anisotropy and consequently the drawing performance of polycrystalline metallic sheets. The constituent grain behavior is modeled using the new single-crystal yield criterion developed by [1] . For ideal texture components, the yield stress and plastic strain ratios can be obtained analytically. For the case of strongly textured sheets containing a spread about the ideal texture components, the polycrystalline response is obtained numerically on the basis of the same single-crystal criterion. It is shown that for textures obtained with rotationally symmetric misorientations of scatter width of up to 35° from the ideal orientation, the numerical predictions have the same trend as those obtained analytically for an ideal texture, but the anisotropy is less pronounced. Furthermore, irrespective of the number of grains in the sample, Lankford coefficients have finite values for all loading orientations. Illustrative examples for sheets with textures containing a combination of few ideal texture components are also presented. The simulations of the predicted polycrystalline behavior based on the new description of the plastic behavior of the constituent grains capture the influence of individual texture components on the overall degree of anisotropy. The polycrystalline simulation results are also compared to analytical estimates obtained using the closed-form formulas for the ideal components present in the texture in conjunction with a simple law of mixtures. The analytical estimates show the same trends as the simulation results. Therefore, the trends in plastic anisotropy of the macroscopic properties can be adequately estimated analytically.

New Yield Criterion for Description of Plastic Deformation of Face-Centered Cubic Single Crystals

In this paper an analytical yield criterion for description of the plastic behavior of face-centered cubic single crystals is presented. The new criterion is written in terms of the generalized invariants of the stress deviator proposed by Cazacu and Barlat (Int J Eng Sci 41:1367–1385, 2003 [1]), specialized to cubic symmetry. The octahedral projections of the yield surfaces for different crystal orientations according to the new model are presented, and compared with the yield surfaces according to the regularized Schmid law (Bishop and Hill, in Lond Edinb Dublin Philos Mag J Sci 42:1298–1307 (1951) [2], Darrieulat and Piot, in Int J Plas 12:575–612 (1996) [3]).