Unified Constitutive Equations for Creep and Plasticity


Book Description

Constitutive equations refer to 'the equations that constitute the material response' at any point within an object. They are one of the ingredients necessary to predict the deformation and fracture response of solid bodies (among other ingredients such as the equations of equilibrium and compatibility and mathematical descriptions of the configuration and loading history). These ingredients are generally combined together in complicated computer programs, such as finite element analyses, which serve to both codify the pertinent knowledge and to provide convenient tools for making predictions of peak stresses, plastic strain ranges, crack growth rates, and other quantities of interest. Such predictions fall largely into two classes: structural analysis and manufacturing analysis. In the first category, the usual purpose is life prediction, for assessment of safety, reliability, durability, and/or operational strategies. Some high-technology systems limited by mechanical behavior, and therefore requiring accurate life assess ments, include rocket engines (the space-shuttle main engine being a prominent example), piping and pressure vessels in nuclear and non-nuclear power plants (for example, heat exchanger tubes in solar central receivers and reformer tubes in high-temperature gas-cooled reactors used for process heat applications), and the ubiquitous example of the jet engine turbine blade. In structural analysis, one is sometimes concerned with predicting distortion per se, but more often, one is concerned with predicting fracture; in these cases the informa tion about deformation is an intermediate result en route to the final goal of a life prediction.




Unified Constitutive Laws of Plastic Deformation


Book Description

High-technology industries using plastic deformation demand soundly-based economical decisions in manufacturing design and product testing, and the unified constitutive laws of plastic deformation give researchers aguideline to use in making these decisions. This book provides extensive guidance in low cost manufacturing without the loss of product quality. Each highly detailed chapter of Unified Constitutive Laws of Plastic Deformation focuses on a distinct set of defining equations. Topics covered include anisotropic and viscoplastic flow, and the overall kinetics and thermodynamics of deformation. This important book deals with a prime topic in materials science and engineering, and will be of great use toboth researchers and graduate students. - Describes the theory and applications of the constitutive law of plastic deformation for materials testing - Examines the constitutive law of plastic deformation as it applies to process and product design - Includes a program on disk for the determination and development of the constitutive law of plastic deformation - Considers economical design and testing methods




Unified Plasticity for Engineering Applications


Book Description

Considerably simplified models of macroscopic material behavior, such as the idealization for metals of elastic-time independent plastic response with a yield (onset) criterion, have served the engineering profession well for many years. They are still basic to the design and analysis of most structural applications. In the need to use materials more effectively, there are circumstances where those traditional models are not adequate, and constitutive laws that are more physically realistic have to be employed. This is especially relevant to conditions where the inherent time dependence of inelastic deformations, referred to as "viscoplasticity", is pronounced such as at elevated temperatures and for high strain rates. Unified theories of elastic-viscoplastic material behavior, which are primarily applicable for metals and metallic alloys, combine all aspects of inelastic response into a set of time dependent equations with a single inelastic strain rate variable. For such theories, creep under constant stress, stress relaxation under constant strain, and stress-strain relations at constant rates are each special cases of a general formulation. Those equations mayor may not include a yield criterion, but models which do not separate a fully elastic region from the overall response could be considered "unified" in a more general sense. The theories have reached a level of development and maturity where they are being used in a number of sophisticated engineering applications. However, they have not yet become a standard method of material representation for general engineering practice.




Crystal Plasticity Finite Element Methods


Book Description

Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.




Inelastic Deformation of Metals


Book Description

Using a totally new approach, this groundbreaking book establishesthe logical connections between metallurgy, materials modeling, andnumerical applications. In recognition of the fact that classicalmethods are inadequate when time effects are present, or whencertain types of multiaxial loads are applied, the new, physicallybased state variable method has evolved to meet these needs.Inelastic Deformation of Metals is the first comprehensivepresentation of this new technology in book form. It developsphysically based, numerically efficient, and accurate methods forpredicting the inelastic response of metals under a variety ofloading and environmental conditions. More specifically, Inelastic Deformation of Metals: * Demonstrates how to use the metallurgical information to developmaterial models for structural simulations and low cyclic fatiguepredictions. It presents the key features of classical and statevariable modeling, describes the different types of models andtheir attributes, and provides methods for developing models forspecial situations. This book's innovative approach covers such newtopics as multiaxial loading, thermomechanical loading, and singlecrystal superalloys. * Provides comparisons between data and theory to help the readermake meaningful judgments about the value and accuracy of aparticular model and to instill an understanding of how metalsrespond in real service environments. * Analyzes the numerical methods associated with nonlinearconstitutive modeling, including time independent, time dependentnumerical procedures, time integration schemes, inversiontechniques, and sub-incrementing. Inelastic Deformation of Metals is designed to give theprofessional engineer and advanced student new and expandedknowledge of metals and modeling that will lead to more accuratejudgments and more efficient designs. In contrast to existing plasticity books, which discuss few if anycorrelations between data and models, this breakthrough volumeshows engineers and advanced students how materials and modelsactually do behave in real service environments. As greater demandsare placed on technology, the need for more meaningful judgmentsand more efficient designs increases dramatically. Incorporatingthe state variable approach, Inelastic Deformation of Metals: * Provides an overview of a wide variety of metal responsecharacteristics for rate dependent and rate independent loadingconditions * Shows the correlations between the mechanical response propertiesand the deformation mechanisms, and describes how to use thisinformation in constitutive modeling * Presents different modeling options and discusses the usefulnessand limitations of each modeling approach, with material parametersfor each model * Offers numerous examples of material response and correlationwith model predictions for many alloys * Shows how to implement nonlinear material models in stand-aloneconstitutive model codes and finite element codes An innovative, comprehensive, and essential book, InelasticDeformation of Metals will help practicing engineers and advancedstudents in mechanical, aerospace, civil, and metallurgicalengineering increase their professional skills in the moderntechnological environment.




Continuum Mechanics with Eulerian Formulations of Constitutive Equations


Book Description

This book focuses on the need for an Eulerian formulation of constitutive equations. After introducing tensor analysis using both index and direct notation, nonlinear kinematics of continua is presented. The balance laws of the purely mechanical theory are discussed along with restrictions on constitutive equations due to superposed rigid body motion. The balance laws of the thermomechanical theory are discussed and specific constitutive equations are presented for: hyperelastic materials; elastic–inelastic materials; thermoelastic–inelastic materials with application to shock waves; thermoelastic–inelastic porous materials; and thermoelastic–inelastic growing biological tissues.




Creep and Damage in Materials and Structures


Book Description

This textbook gives a concise survey of constitutive and structural modeling for high temperature creep, damage, low – cycle fatigue and other inelastic conditions. The book shows the creep and continuum damage mechanics as rapidly developing discipline which interlinks the material science foundations, the constitutive modeling and computer simulation application to analysis and design of simple engineering components. It is addressed to young researchers and scientists working in the field of mechanics of inelastic, time-dependent materials and structures, as well as to PhD students in computational mechanics, material sciences, mechanical and civil engineering.




The Mechanics of Constitutive Modeling


Book Description

Constitutive modelling is the mathematical description of how materials respond to various loadings. This is the most intensely researched field within solid mechanics because of its complexity and the importance of accurate constitutive models for practical engineering problems. Topics covered include: Elasticity - Plasticity theory - Creep theory - The nonlinear finite element method - Solution of nonlinear equilibrium equations - Integration of elastoplastic constitutive equations - The thermodynamic framework for constitutive modelling – Thermoplasticity - Uniqueness and discontinuous bifurcations • More comprehensive in scope than competitive titles, with detailed discussion of thermodynamics and numerical methods. • Offers appropriate strategies for numerical solution, illustrated by discussion of specific models. • Demonstrates each topic in a complete and self-contained framework, with extensive referencing.




Continuum Mechanics and Plasticity


Book Description

Tremendous advances in computer technologies and methods have precipitated a great demand for refinements in the constitutive models of plasticity. Such refinements include the development of a model that would account for material anisotropy and produces results that compare well with experimental data. Key to developing such models-and to meeting many other challenges in the field- is a firm grasp of the principles of continuum mechanics and how they apply to the formulation of plasticity theory. Also critical is understanding the experimental aspects of plasticity and material anisotropy. Integrating the traditionally separate subjects of continuum mechanics and plasticity, this book builds understanding in all of those areas. Part I provides systematic, comprehensive coverage of continuum mechanics, from a review of Carteisian tensors to the relevant conservation laws and constitutive equation. Part II offers an exhaustive presentation of the continuum theory of plasticity. This includes a unique treatment of the experimental aspects of plasticity, covers anisotropic plasticity, and incorporates recent research results related to the endochronic theory of plasticity obtained by the author and his colleagues. By bringing all of these together in one book, Continuum Mechanics and Plasticity facilitates the learning of solid mechanics. Its readers will be well prepared for pursuing either research related to the mechanical behavior of engineering materials or developmental work in engineering analysis and design.




Physics of Strength and Plasticity


Book Description

The title of this book is derived from a graduate course in which Professor Egon Orowan presented to M.I.T. students a clear and simple picture of the basic concepts in crystal plasticity and the mechanics of fracture of materials. Since the publication of his pioneering papers on dislocations and atomic mechanisms of fracture in the early 1930's,Professor Orowan has been one of the principal contributors to the field of physics of plasticity and strength. During the past 10 to 15 years, the perfection of many direct experimental methods has caused a great increase of activity in the elucidation of the effects of dislocations on mechanical and physical properties. Equally intensive activity is taking place in the field of physics and mechanics of fracture processes. Professor Ali Argon felt that the retirement of Professor Orowan from the M.I.T. faculty was an appropriate occasion to take stock of the developments in the immediate past and to produce a needed synthesis of this technologically important field. For this purpose he invited 37 of the world's leading figures in the field to contribute theoretical papers of original work. The 17 papers on the Physics of Plasticity fall into two categories: (1) Individual Dislocations and Basic Deformation Mechanisms, and (2) Hardening Mechanisms and Dislocation Dynamics. The 10 papers on the Physics of Strength concentrate on (1) Cracks and Fracture, and (2) Geology.