Fundamentals of Materials Modelling for Metals Processing Technologies

The following sections are included:

• Preface
• Introduction
• Contents

The aim of this chapter is to introduce the concept of metal forming processes, their characteristics and applications. Typical features of metal forming processes are compared with those of other types of manufacturing processes. The basic modelling concept is then introduced, leading to the discussion of why mechanics and modelling are fundamentals for metal forming research and development.

The aim of this chapter is to give a brief introduction to the physics, metallurgy and structure of metals, and the basic mechanics theories used to characterise metals for developing mathematical models. This is necessary for the fundamental understanding of deformation mechanisms of metals under different loading conditions, and thus for the formulation of mechanism-based constitutive equations. Firstly, structures of crystallised materials are introduced, and then dominant mechanisms for plastic deformation of metals are presented. Finally in this chapter, the basic concept of mechanics, including elastic and plastic theories, is introduced, which is related to various metal forming applications.

In high temperature creep rupture analysis, scientists (such as Kachanov, 1958; Hayhurst 1972; Dyson and McLean, 1977; Leckie and Hayhurst, 1977) introduced internal state variables to represent damage evolution, which enables the damage and creep strain development of materials in service conditions to interact, so that lifetime and tertiary creep can be predicted. Lemaitre and Chaboche (1990) introduced isotropic hardening and kinematic hardening state variables, which were incorporated into elastic-plastic and elastic-viscoplastic flow laws to predict the hardening behaviour of materials under cyclic loading conditions. These represent the early stage development of unified constitutive equations and mainly concentrated on the modelling of stress–strain response, hardening and failure of materials under different loading conditions. The developments on formulating unified constitutive equations established the basis for the creation of unified theories for metal forming simulations…

In this chapter, the phenomenological and mathematical modelling of elastic-plastic solids will be discussed in detail. This is based on the early scientific work of the maximum shear stress yield criterion (by Tresca in 1864) and von-Mises yield criterion (by von-Mises in 1913). The theories for anisotropic plastic deformation were developed further by Hill in 1948 (Rodney Hill, British, 1921–2011). Ford (Hugh Ford, British, 1913–2010) developed the slip line field theory and plane strain compression test method in the 1950s. He built metal forming research at Imperial College London in 1948 and, along with his co-workers, successfully developed advanced mechanics theories for metal forming applications, such as cold rolling and extrusion (Ford and Alexander, 1977)…

Viscoplasticity is a theory in continuum mechanics that describes the rate-dependent inelastic behaviour of solids. The inelastic behaviour that is the subject of viscoplasticity is plastic deformation. Rate-dependent plasticity is important for transient plasticity calculations. The main difference between rate-independent plasticity and viscoplasticity is that the latter exhibits not only permanent deformation as a load is applied but also continues to undergo a creep flow with time under the applied load. Viscoplasticity theories are often used for metal forming at elevated temperatures. Due to the effects of temperature and deformation, microstructure evolution, such as recrystallisation, grain growth, annealing etc., may take place. This will change the deformation mechanisms and thus affect the viscoplastic flow of the material…

Continuum damage mechanics (CDM) is concerned with the modelling of degradation/deterioration of materials under thermal-mechanical deformation and/or ageing. The material deteriorates due to loading and/or ageing to a stage that it could not sustain any load, and then ultimate failure takes place. Damage mechanics is suitable for making engineering predictions about micro-crack initiation, growth, and failure of materials without resorting to a microscopic description that would be too complex for practical engineering analysis. Damage mechanics illustrates the typical engineering approach to model complex phenomena. As said by Krajcinovic (1989) (Dusan Krajcinovic, Croatian/American, 1935–2007), “It is often argued that the ultimate task of engineering research is to provide not so much a better insight into the examined phenomenon but to supply a rational predictive tool applicable in design”. Most of the work on damage mechanics uses state variables to represent the effects of damage on the structural stiffness, remaining life and failure of the material…

In the previous chapters, the basic techniques for formulating phenomenological unified elastic-plastic and elastic-viscoplastic unified constitutive equations have been introduced. Based on these concepts, different types of constitutive equations can be formulated for individual materials and applications. These equations cannot normally be solved analytically and numerical integration methods are required. Additionally, the determination of a set of constitutive equations from experimental data requires optimisation techniques. In this chapter, the relevant numerical methods for solving the constitutive equations, and determining their material constants from experimental data, are introduced…

Based on the discussion of basic theories for formulation of unified viscoplastic constitutive equations, which include state variables representing the evolution of physical properties and material damage during thermal mechanical processing, in this chapter a few examples on the use of materials and process modelling theories are introduced for practical metal forming applications. For most cases, unified constitutive equations are given without detailed explanation.

Plastic flow in a single crystal is anisotropic and the constitutive equations introduced in the previous chapters cannot be used to accurately model the plastic deformation of the material. Thus, constitutive equations are required to model the slip activity in the crystal directly and the rotation of individual grains (crystals) for polycrystalline structures…

The following sections are included:

• Appendix A: Sets of Unified Constitutive Equations
• References
• Index