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2019 | Buch

Mathematical Framework Kapitel lesen Erstes Kapitel lesen

Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials

verfasst von: Prof. Oana Cazacu, Dr. Benoit Revil-Baudard, Dr. Nitin Chandola

Verlag: Springer International Publishing

Buchreihe : Solid Mechanics and Its Applications

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

Offering a well-balanced blend of theory and hands-on applications, this book presents a unified framework for the main dissipative phenomena in metallic materials: plasticity and damage. Based on representation theory for tensor functions and scale-bridging theorems, this framework enables the development of constitutive models that account for the influence of crystallographic structures and deformation mechanisms on the macroscopic behavior. It allows readers to develop a clear understanding of the range of applicability of any given model, as well as its capabilities and limitations, and provides procedures for parameter identification along with key concepts necessary to solve boundary value problems, making it useful to both researchers and engineering practitioners. Although the book focuses on new contributions to modeling anisotropic materials, the review of the foundations of plasticity and models for isotropic materials, completed with detailed mathematical proofs mean that it is self-consistent and accessible to graduate students in engineering mechanics and material sciences.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Mathematical Framework
Abstract
The theory of scalar- and tensor-valued functions constitutes the mathematical framework based on which modeling of the elasticity, plasticity, and damage in polycrystalline metallic materials is built. In this chapter, we provide the basic concepts and key mathematical results to be used in the rest of the book.
Oana Cazacu, Benoit Revil-Baudard, Nitin Chandola
Chapter 2. Constitutive Equations for Elastic–Plastic Materials
Abstract
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.
Oana Cazacu, Benoit Revil-Baudard, Nitin Chandola
Chapter 3. Plastic Deformation of Single Crystals
Abstract
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.
Oana Cazacu, Benoit Revil-Baudard, Nitin Chandola
Chapter 4. Yield Criteria for Isotropic Polycrystals
Abstract
Chapter 4 is devoted to modeling the plastic behavior of isotropic polycrystalline metallic materials. A review of the classic yield criteria and corresponding stress-based plastic potentials with discussion concerning the predicted mechanical response for various three-dimensional loadings is presented along with the most recent contributions devoted to the description of the behavior of incompressible materials displaying tension–compression asymmetry. On the basis of these new models, a new interpretation and explanation of the Swift phenomenon, occurring in monotonic and cyclic free-end torsion are provided.
Oana Cazacu, Benoit Revil-Baudard, Nitin Chandola
Chapter 5. Yield Criteria for Anisotropic Polycrystals
Abstract
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.
Oana Cazacu, Benoit Revil-Baudard, Nitin Chandola
Chapter 6. Strain-Rate-Based Plastic Potentials for Polycrystalline Materials
Abstract
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.
Oana Cazacu, Benoit Revil-Baudard, Nitin Chandola
Chapter 7. Plastic Potentials for Isotropic Porous Materials: Influence of the Particularities of Plastic Deformation on Damage Evolution
Abstract
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.
Oana Cazacu, Benoit Revil-Baudard, Nitin Chandola
Chapter 8. Anisotropic Plastic Potentials for Porous Metallic Materials
Abstract
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.
Oana Cazacu, Benoit Revil-Baudard, Nitin Chandola
Metadaten
Titel
Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials
verfasst von
Prof. Oana Cazacu
Dr. Benoit Revil-Baudard
Dr. Nitin Chandola
Copyright-Jahr
2019
Electronic ISBN
978-3-319-92922-4
Print ISBN
978-3-319-92921-7
DOI
https://doi.org/10.1007/978-3-319-92922-4

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