Lin / Balint / Pietrzyk Microstructure Evolution in Metal Forming Processes

1. Auflage 2012
ISBN: 978-0-85709-634-0
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 416 Seiten

Reihe: Woodhead Publishing Series in Metals and Surface Engineering

Monitoring and control of microstructure evolution in metal processing is essential in developing the right properties in a metal. Microstructure evolution in metal forming processes summarises the wealth of recent research on the mechanisms, modelling and control of microstructure evolution during metal forming processes.Part one reviews the general principles involved in understanding and controlling microstructure evolution in metal forming. Techniques for modelling microstructure and optimising processes are explored, along with recrystallisation, grain growth, and severe plastic deformation. Microstructure evolution in the processing of steel is the focus of part two, which reviews the modelling of phase transformations in steel, unified constitutive equations and work hardening in microalloyed steels. Part three examines microstructure evolution in the processing of other metals, including ageing behaviour in the processing of aluminium and microstructure control in processing nickel, titanium and other special alloys.With its distinguished editors and international team of expert contributors, Microstructure evolution in metal forming processes is an invaluable reference tool for metal processors and those using steels and other metals, as well as an essential guide for academics and students involved in fundamental metal research. - Summarises the wealth of recent research on the mechanisms, modelling and control of microstructure evolution during metal forming processes - Comprehensively discusses microstructure evolution in the processing of steel and reviews the modelling of phase transformations in steel, unified constitutive equations and work hardening in microalloyed steels - Examines microstructure evolution in the processing of other materials, including ageing behaviour in the processing of aluminium

Autoren/Hrsg.

Lin, J.

Balint, D.

Pietrzyk, M.

Leseproben

2 Techniques for modelling microstructure in metal forming processes
Y. Chastel,     RENAULT, France R. Logé and M. Bernacki,     MINES ParisTech, France Abstract:
This chapter discusses several types of numerical models for metallurgical evolution. First, some basic notions of microstructure representations and microstructure state variables, some features of hardening and recovery and some features of recrystallization are recalled. Then, constitutive models coupled with state variables are introduced and examples of applications are given. Mean field methods are also presented and applied to necklace structures produced in discontinuous dynamic recrystallization. Finally, future trends are described, with an emphasis on digital material models and how they will provide powerful models of recrystallization on the microscopic scale. Key words microstructure state variables recrystallization mean field digital material 2.1 Introduction: importance of microstructure prediction in metal forming
In the mechanics of metal forming, emphasis is placed on the macroscopic flow of the material and on the stress state it is experiencing. Over recent decades, a vast collection of analytic and numerical methods has been developed to provide full 3D macroscopic analyses of all processes, namely predictions of stress, strain and temperature fields throughout a metal as it is processed. These methods rely on continuum mechanics and integrate process conditions as macroscopic boundary conditions. Depending on the process, various mechanical integral formulations for solids can be used, either Eulerian formulations, particularly for steady-state or quasi-steady-state flow, or updated Lagrangian formulations, for dealing with non-stationary operations. Metallurgical modelling comes into play when the target properties need to match the material microstructure or, more often, when a final microstructure is required which achieves the desired final material properties. Metallurgical analyses inform our understanding of process–property relationships and of how optimizing the process can optimize the properties. This is today’s challenge both in academic research and in industry. Metallurgical simulations also provide a means to imagine and validate processing routes for novel or even virtual grades of metals. In the near future, one will even be able to evaluate how a new alloy should be designed in order to behave in a particular way during process operations to achieve the desired properties. Coupling the metallurgical state to the mechanical behaviour can be performed in several different ways, assuming that the macroscopic calculations of the mechanical and temperature fields are accurate enough. The focus of this chapter is on modelling techniques for microstructure evolution during forming, that is to say, typically under large strains and under cold, warm or hot forming conditions. Several levels of observation and description are available today when microscopy or chemical analysis techniques are used. As a general feature, one should look at a metal as a poly crystalline ensemble. An appropriate length scale is that of a representative elementary volume (REV) for which a thermo-mechanical loading can be determined using continuum mechanics analysis on the macroscopic scale. This mesoscopic scale is typically the scale of a polycrystal, i.e. a collection of grains including all the different phases, substructures or precipitates that are present. The use of a finer length scale would rely on explicit descriptions of dislocations or atoms. Such models can provide information about interactions between the individual defects in the microstructure, but they are limited to the analysis of small volumes of material. An extremely promising set of approaches rely on explicit modelling of the heterogeneity of the metal at different microscopic and mesoscopic scales – using finite element models, for instance – and on the derivation of more tractable models for large-scale macroscopic simulations. This approach will be discussed as a future trend in the last section of this chapter. 2.2 General features of models based on state variables
2.2.1 Notion of microstructure state variables
Based on observations with devices such as electron microscopes, combined with chemical and crystallographic analyses, a large set of microstructural features can be identified and quantified to describe a metallurgical state. One can then make use of metallurgical state variables describing features such as grains, metallurgical phases and crystallographic texture, and morphological parameters of the grains/phases/inclusions, to name but a few. If a description of the material behaviour is sought, the well-known correlation between the flow stress and the dislocation density or the grain size can provide a first hint about the appropriate state variables S and their integration into a constitutive law: [2.1] where s0 is a threshold stress, and e, , T are the strain, strain rate and temperature, respectively. However, the way in which microstructures are described is inherently linked to the type of microstructure evolution model being considered. For instance, when dealing with recrystallization processes, one often finds either simplified approaches using analytical models of the Johnson–Mehl–Avrami–Kolmogorov (JMAK) type (Avrami, 1939; Dehghan-Manshadi et al., 2008; Jonas et al., 2009), or more elaborate numerical schemes based on explicit representations of microstructures, meshed in different ways, which will be discussed in the last section of this chapter (Rollett et al., 1992; Yazdipour et al., 2008; Hallberg et al., 2010; Takaki et al., 2009; Logé et al., 2008; Bernacki et al., 2008; Bernacki et al., 2009; Bernacki et al., 2010). In the former case, the microstructure is typically reduced to a scalar value, the average grain size. At the other extreme, the second type of model includes topological aspects of the microstructure, and is associated with a large number of variables. Intermediate approaches consider a series of state variables which give significant information about the microstructure, but do not require an explicit construction. The choice of the state variables is made such that the evolution equations of the state variables can have a clear physical basis (Montheillet et al., 2009; Roucoules et al., 2003; Sandstrom and Lagneborg, 1975; Estrin, 1998; Thomas et al., 2007). Since the driving forces for recrystallization are related to stored energies and local grain boundary curvatures, it is meaningful to consider dislocation densities and grain sizes as state variables (Montheillet et al., 2009). Depending on the accuracy sought within the model, a number of grains that are representative of the microstructure can be defined or generated, each one being associated with an average dislocation density and size. The microstructure description is then finalized by fixing the volume fractions associated with the different representative grains. An example of a general evolution of a scalar microstructure variable S is [2.2] where S0 is a constant, and S* is a limit value which can be defined as a function of the Zener–Hollomon parameter Z: [2.3] Here, Q is an activation energy for the active metallurgical phenomena, R is the gas constant, and ? is the particle derivative of S: [2.4] for a velocity field v. And, indeed, when one is dealing with a coupled problem, the first step consists in calculating a velocity field, before integrating microstructural kinetic laws such as, [2.5] 2.2.2 Nucleation and grain boundary migration
A number of nucleation laws have been considered in the literature, and many assume that a critical dislocation density must be reached before nucleation can happen. The probability of activating nucleation usually increases with dislocation density and temperature, and, when dealing with necklace-type nucleation, with the amount of grain boundaries. Under dynamic conditions, an increasing strain rate generally leads to an increased critical dislocation density, but also to an increased probability of activating nucleation beyond the dislocation density threshold. The driving force ?E for grain boundary migration is described as the sum of a stored-energy term related to the dislocation content (Humphreys and Hatherly, 2004) and a capillarity term (Hillert, 1965) related to the grain boundary energy and curvature: [2.6] where t ˜ µb2/2 is the average energy per unit dislocation length, ?b is the energy per unit...