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continuum mechanics
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Book Chapter
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005431
EISBN: 978-1-62708-196-2
... methods. This article introduces the methods of so-called meshed solutions, with an emphasis on the FEM. It presents some basic differential equations that are used to model the responses of structures, components, processes, or systems with emphasis on continuum mechanics. The article provides an outline...
Abstract
Several methods are developed for the numerical solution of partial differential equations, namely, meshed-solution methods such as the finite-element method (FEM), finite-difference method, and boundary-element method; and numerical algorithms consisting of so-called meshed-solution methods. This article introduces the methods of so-called meshed solutions, with an emphasis on the FEM. It presents some basic differential equations that are used to model the responses of structures, components, processes, or systems with emphasis on continuum mechanics. The article provides an outline on the mathematical principles of solving differential equations. It also reviews linear structural problems to illustrate the concept of the FEMs.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
... analysis (BEA). While FEA discretizes the entire volume into small elements (normally tetrahedra or hexahedra), BEA only discretizes the boundary. Both methods, however, employ continuum material models and produce only approximations. In general, accuracy improves as the number of elements increases...
Abstract
This article describes concepts and tools that can be used by the failure analyst to understand and address deformation, cracking, or fracture after a stress-related failure has occurred. Issues related to the determination and use of stress are detailed. Stress is defined, and a procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear elastic fracture mechanics analysis, with some mention of elastic-plastic fracture mechanics analysis. The article describes the probabilistic aspects of fatigue and fracture. Information on crack-growth simulation of the material is also provided.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005424
EISBN: 978-1-62708-196-2
... symmetries are anisotropies of the mechanical properties, both elastic and plastic, of the individual crystals. Anisotropy is evident even at the continuum scale in aggregates of crystals having preferred orientations of the crystal lattices, known as crystallographic texture. The behaviors observed during...
Abstract
This article provides an explanation on how crystal plasticity is implemented within finite element formulations by the use of physical length scales: crystal scale and continuum scale. It provides theoretical formulations for kinematic framework for deforming crystals and polycrystals, elastic and plastic behaviors of single crystals, refinements to the single-crystal constitutive, and crystal-scale finite-element. The article also presents examples that illustrate the capabilities of the formulations at the length scales.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005418
EISBN: 978-1-62708-196-2
... Abstract Self-consistent models are a particular class of models in continuum micromechanics, that is, the field concerned with making predictions of the properties and evolution of aggregates whose single-crystal deformation behavior is known. This article provides information on the...
Abstract
Self-consistent models are a particular class of models in continuum micromechanics, that is, the field concerned with making predictions of the properties and evolution of aggregates whose single-crystal deformation behavior is known. This article provides information on the measurement and representation of textures as well as prediction of texture evolution in single-phase materials and two-phase aggregates.
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005237
EISBN: 978-1-62708-187-0
... Abstract In order to model macrosegregation, one must consider convection and the partitioning of the segregating elements at the dendritic length scale. This article describes microsegregation with diffusion in the solid. It presents a continuum model of macrosegregation and illustrates the...
Abstract
In order to model macrosegregation, one must consider convection and the partitioning of the segregating elements at the dendritic length scale. This article describes microsegregation with diffusion in the solid. It presents a continuum model of macrosegregation and illustrates the simulation of macrosegregation and microsegregation.
Book Chapter
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 November 1995
DOI: 10.31399/asm.hb.emde.a0003025
EISBN: 978-1-62708-200-6
... Abstract Mechanical properties are often the most important properties in the design and selection of engineering plastics. Temperature, molecular structure, crystallinity, viscoelasticity, and effects of environment, fillers and reinforcements are considered as the basic factors affecting the...
Abstract
Mechanical properties are often the most important properties in the design and selection of engineering plastics. Temperature, molecular structure, crystallinity, viscoelasticity, and effects of environment, fillers and reinforcements are considered as the basic factors affecting the mechanical properties of engineering plastics. The testing methods for determining mechanical properties, including stress-strain test, modulus-directed tensile test, strength test, strength-directed tensile test, impact test, and dynamic mechanical test are discussed.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005404
EISBN: 978-1-62708-196-2
... to a physical representation of the microstructure, such as changes in dislocation density, grain size, precipitate size, morphology, and volume fraction. To effectively model the creep behavior of engineering alloys using these kinematic creep equations, one can use the continuum damage mechanics...
Abstract
This article, to develop an understanding of the underlying mechanisms governing deformation at elevated temperatures, discusses the phenomenological effects resulting from temperature-induced thermodynamic and kinetic changes. It describes the deformation behavior of engineering materials using expressions known as constitutive equations that relate the dependence of stress, temperature, and microstructure on deformation. The article reviews the characteristics of creep deformation and mechanisms of creep, such as power-law creep, low temperature creep, power-law breakdown, diffusional creep, twinning during creep deformation, and deformation mechanism maps. It discusses the creep-strengthening mechanisms for most structural engineering components. The article provides a description of the microstructural modeling of creep in engineering alloys.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006774
EISBN: 978-1-62708-295-2
... Abstract Engineering component and structure failures manifest through many mechanisms but are most often associated with fracture in one or more forms. This article introduces the subject of fractography and aspects of how it is used in failure analysis. The basic types of fracture processes...
Abstract
Engineering component and structure failures manifest through many mechanisms but are most often associated with fracture in one or more forms. This article introduces the subject of fractography and aspects of how it is used in failure analysis. The basic types of fracture processes (ductile, brittle, fatigue, and creep) are described briefly, principally in terms of fracture appearances. A description of the surface, structure, and behavior of each fracture process is also included. The article provides a framework from which a prospective analyst can begin to study the fracture of a component of interest in a failure investigation. Details on the mechanisms of deformation, brittle transgranular fracture, intergranular fracture, fatigue fracture, and environmentally affected fracture are also provided.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006775
EISBN: 978-1-62708-295-2
... behavior, they become tools to use for quantitative evaluation of fracture in failure analysis. Multiple approaches have been used; some are based on continuum mechanics to predict behavior of the bulk assembly (without assumptions of the microscopic-scale details and operative mechanisms of crack...
Abstract
This article focuses on characterizing the fracture-surface appearance at the microscale and contains some discussion on both crack nucleation and propagation mechanisms that cause the fracture appearance. It begins with a discussion on microscale models and mechanisms for deformation and fracture. Next, the mechanisms of void nucleation and void coalescence are briefly described. Macroscale and microscale appearances of ductile and brittle fracture are then discussed for various specimen geometries (smooth cylindrical and prismatic) and loading conditions (e.g., tension compression, bending, torsion). Finally, the factors influencing the appearance of a fracture surface and various imperfections or stress raisers are described, followed by a root-cause failure analysis case history to illustrate some of these fractography concepts.
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006271
EISBN: 978-1-62708-169-6
... focuses on simulation of the quenching step, because this step is mainly responsible for component residual stresses and distortion. Heat treatment simulation is presented on a macroscopic, continuum mechanical scale, using the finite-element method. Figure 1 shows the schematic course...
Abstract
Heat treatment simulation helps to predict heat treatment results such as component microstructures, properties, residual stresses, and distortion, and thereby assists in reducing experimental effort in defining heat treatment parameters. This article discusses the modeling and simulation of age hardening as being the most important heat treatment to strengthen aluminum alloys. It provides information on the heat treatment simulation model, the yield strength model based on the responsible strengthening mechanisms, and the flow curve model based on mechanical tests. The article also discusses simulation of the quenching process, and provides examples for aluminum quenching simulation.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005433
EISBN: 978-1-62708-196-2
... scientists have worked on phenomenological and physics-based equations. On the other hand, engineering mechanics researchers have come up with continuum-based constitutive equations. For more details on constitutive equations, see the article “Constitutive Equations” in Metalworking: Bulk Forming , Volume...
Abstract
This article presents a mechanical description of superplasticity and discusses constitutive equations that are essential for simulating superplastic forming processes, applicable to structural superplasticity. It presents the phenomenological constitutive equations of superplasticity and classical physical constitutive equations. The article also reviews the accommodation mechanisms that are divided into two major groups, namely, diffusional accommodation and accommodation by dislocations.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006778
EISBN: 978-1-62708-295-2
... along the shear plane in the basic principles of continuum mechanics). Thus, even though the overall applied stress is still a tensile load, deformation makes a transition to the shear plane in the outer regions of the specimen. In the mode II region, voids grow in sheets at an oblique angle (~45° to...
Abstract
This article aims to identify and illustrate the types of overload failures, which are categorized as failures due to insufficient material strength and underdesign, failures due to stress concentration and material defects, and failures due to material alteration. It describes the general aspects of fracture modes and mechanisms. The article briefly reviews some mechanistic aspects of ductile and brittle crack propagation, including discussion on mixed-mode cracking. Factors associated with overload failures are discussed, and, where appropriate, preventive steps for reducing the likelihood of overload fractures are included. The article focuses primarily on the contribution of embrittlement to overload failure. The embrittling phenomena are described and differentiated by their causes, effects, and remedial methods, so that failure characteristics can be directly compared during practical failure investigation. The article describes the effects of mechanical loading on a part in service and provides information on laboratory fracture examination.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005455
EISBN: 978-1-62708-196-2
... Abstract A computational tool would require the contribution of the strengthening mechanisms of metallic material to be predicted and then summed in an appropriate way to derive an estimate of the tensile properties. This article focuses on the modeling of deformation mechanisms pertinent to...
Abstract
A computational tool would require the contribution of the strengthening mechanisms of metallic material to be predicted and then summed in an appropriate way to derive an estimate of the tensile properties. This article focuses on the modeling of deformation mechanisms pertinent to structural materials, namely, solid-solution strengthening, age/precipitation hardening, dispersion strengthening, grain size reduction, strengthening from cold work, and strengthening from interfaces. It explains the application of predictive models in the atomistic modeling of dislocation structures and cast aluminum property prediction. The article concludes with information on the use of rules-based approaches and data-mining techniques for quantitative predictions of tensile properties.
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006645
EISBN: 978-1-62708-213-6
... characteristic peaks of x-rays associated with fluorescence (from electrons that move from outer atomic orbits to inner orbits of the sample). There is some background x-ray radiation with a continuum of energies from many different interactions, but the characteristic energies of electrons moving within atoms...
Abstract
This article provides a detailed account of X-ray spectroscopy used for elemental identification and determination. It begins with an overview of the operating principles of X-ray fluorescence (XRF) spectrometer, as well as a comparison of the operating principles of wavelength-dispersive spectrometer (WDS) and energy-dispersive spectrometer (EDS). This is followed by a discussion on the mechanism and effects of X-ray radiation, X-ray emission, and X-ray absorption. The article then discusses components used, operation, and applications of WDS and EDS. Some of the factors and processes involved in sample preparation for XRF analysis are also included. The article further provides information on the practical procedure for and the applications of WDS and EDS qualitative and quantitative analyses.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005421
EISBN: 978-1-62708-196-2
..., the function F( σ M / σ ¯ ) has been determined using continuum mechanics approaches ( Ref 30 , Ref 31 , Ref 32 ) as well as semiempirical methods ( Ref 34 ). In many cases, cavities do not grow as simple spheres whose radii increase with strain; rather, they grow as...
Abstract
This article focuses on the modeling and simulation of cavitation phenomena. It summarizes the experimental observations of cavitation and reviews the modeling of cavity nucleation and growth. The article discusses the modeling of the cavity growth based on mesoscale and microscale under uniaxial versus multiaxial tensile-stress conditions. Mesoscale models incorporate the influence of local microstructure and texture on cavitation. The article outlines the descriptions of cavity coalescence and shrinkage. It also describes the simulation of the tension test to predict tensile ductility and to construct failure-mechanism maps.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005405
EISBN: 978-1-62708-196-2
... distributions of slip and various fatigue indicator parameters (FIPs). These FIPs enable assessment of the relative potency of fatigue crack formation based on continuum-level quantities associated with each relevant mechanism. For example, the Fatemi-Socie ( Ref 43 , 44 ) shear-dominated parameter can be...
Abstract
The purposes and methods of fatigue modeling and simulation in high-cycle fatigue (HCF) regime are to design either failsafe components or components with a finite life and to quantify remaining life of components with pre-existing cracks using fracture mechanics, with the intent of monitoring via an inspection scheme. This article begins with a discussion on the stages of the fatigue damage process. It describes hierarchical multistage fatigue modeling and several key points regarding the physics of crack nucleation and microstructurally small crack propagation in the HCF regime. The article provides a description of the microstructure-sensitive modeling to model fatigue of several classes of advanced engineering alloys. It describes the various modeling and design processes designed against fatigue crack initiation. The article concludes with a discussion on the challenges in microstructure-sensitive fatigue modeling.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005419
EISBN: 978-1-62708-196-2
... stress fields and driving forces by g a linear elastic fracture mechanics or energy-based continuum approach. Because of this, they can offer some insight into the forces that drive the crack, but they are still dependent upon the experimental crack-growth data that incorporates the stress-ratio effects...
Abstract
Understanding fatigue crack growth is critical for the safe operation of many structural components. This article reviews the standard fracture mechanics and methods to determine the crack growth rate for a material and loading condition experimentally. It also addresses the two most important aspects of crack-growth modeling: loading environment and crack geometry.
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009003
EISBN: 978-1-62708-185-6
... encountered in multiaxial stress states. The construction of a processing map based on deformation mechanisms is also discussed. ductile fracture multiaxial stress stress-strain curve workability WORKABILITY refers to the relative ease with which a metal can be shaped through plastic deformation...
Abstract
This article provides the definitions of stress and strain, and describes the relationship between stress and strain by stress-strain curves and true-stress/true-strain curves. The emphasis is on understanding the factors that determine the extent of deformation a metal can withstand before cracking or fracture occurs. The article reviews the process variables that influence the degree of workability and summarizes the mathematical relationships that describe the occurrence of room-temperature ductile fracture under workability conditions. It discusses the most common situations encountered in multiaxial stress states. The construction of a processing map based on deformation mechanisms is also discussed.
Book Chapter
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005450
EISBN: 978-1-62708-196-2
... travelled between each molecular collision of 6.35 × 10 −6 cm. Therefore, the overall motion of the fluid is of interest, not the motion of individual molecules, and the fluid can be treated as a continuous medium, also called a continuum. Pressure is defined at a point in a continuum as: (Eq 1) p...
Abstract
This article is a comprehensive collection of fluid dynamic equations for properties of fluids, fluid statics, fluid motion, dimensional analysis, and boundary layer flow. It presents equations for analyzing problems in fluid mechanics, continuity equation, momentum equation, and energy equation for solving various problems related to fluid dynamics.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005403
EISBN: 978-1-62708-196-2
... properties of which will be obtained by averaging that of all the grains in the aggregate. Such an approach is close to the self-consistent models commonly used in the continuum mechanics of heterogeneous materials. It precludes topological effects, such as necklacing, which are expected, however, to be...
Abstract
Recrystallization is to a large extent responsible for their final mechanical properties. This article commences with a discussion on static recrystallization (SRX) and dynamic recrystallization (DRX). The DRX includes continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX). The article discusses the assumptions and simplifications for the Avrami analysis. It describes the effects of nucleation and growth rates on recrystallization kinetics and recrystallized grain size based on the Johnson-Mehl-Avrami-Kolmogorov model for static recrystallization. The article reviews the kinetics of DRX with the aid of the Avrami relations. It considers the basic framework of the mesoscale approach for DDRX, including the three basic equations for grain size changes, strain hardening and dynamic recovery, and nucleation. The article explains the mesoscale approach for CDRX to predict microstructural evolutions occurring during hot deformation, along with an illustration of the main features of the CDRX mesoscale model.