Modelling of microstructure evolution during hot rolling of AA5083 using an internal state variable approach integrated into an FE model

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Abstract

Hot rolling, a critical process in the manufacturing of aluminum sheet products, can significantly impact the final properties of the cold rolled sheet. In this research, a mathematical model was developed to predict the through-thickness thermal and deformation history of a sheet undergoing single stand hot rolling using the commercial finite element (FE) package, ABAQUS. A physically based internal state variable microstructure model has been incorporated into the FE simulation for an AA5083 aluminum alloy to predict the evolution of the material stored energy and the subsequent recrystallization after deformation is complete. The microstructure predictions were validated against experimental measurements conducted using the Corus pilot scale rolling facility in IJmuiden, the Netherlands for an AA5083 aluminum alloy. The model was able to predict the fraction recrystallized as well as the recrystallized grain size reasonably well under a range of industrially relevant hot deformation conditions. A sensitivity analysis was carried out to determine the influence of changing the material constants in the microstructure model and deformation conditions on the predicted recrystallization behaviour. The analysis showed that the entry temperature was the most sensitive process parameter causing significant changes in the predicted driving force for recrystallization, nucleation density, fraction recrystallized, and recrystallized grain size.

Introduction

Metal forming operations are used extensively in industry to alter the shape of the metal through plastic deformation [1], [2]. During these forming operations, control of the evolved microstructure is critical, as it will have a direct impact on the final properties of the product. One example of this is in aluminum alloy sheet production, where controlling recrystallization and grain size represents the very heart of quality control and improvement [3]. One method of achieving this control is to develop physically-based mathematical models that predict the microstructure evolution at each stage of the process and thereby achieve a greater understanding of the effect of the process variables on the properties of the final product [4]. Mathematical models of this nature attempt to describe the complex interactions between deformation, heat flow, and microstructural evolution that occur during industrial manufacturing processes. Microstructural modelling which focuses on quantitatively linking the microstructure development in a material to its processing parameters using fundamentally based mathematical models, is the key to meeting this challenge.

During hot rolling of aluminum for sheet products, a preheated ingot is deformed in the temperature range of 300–500 °C from an initial thickness of ∼600 mm to a final sheet thickness of ∼2 mm. The microstructure changes that occur during hot rolling of aluminum alloys are very sensitive to the conditions that apply during this thermomechanical deformation. These conditions are normally quantified in terms of the strain, strain rate and temperature experienced during the deformation operation as well as the temperature and time conditions experienced in the interstand regions and after rolling is complete. These changes include both dynamic (during rolling), metadynamic (initiated during rolling and continuing between the rolling passes) as well as static (between rolling passes and after rolling) structural changes involving such phenomena as recovery and recrystallization [5].

Although modelling can be a useful tool for understanding microstructure evolution, to date, only a few mathematical models have been developed to predict the microstructure evolution in aluminum alloys during hot rolling [3], [6], [7], [8], [9], [10], [11]. The main difficulty in developing a fundamentally based model to quantify the effect of hot rolling parameters on the microstructure evolution stems from the fact that the effect of the rolling process parameters on the deformed microstructure and subsequent recrystallization process is not well understood. As a result, the development and application of fundamentally based predictive models linking the microstructural changes that occur in aluminum during industrial hot deformation processes are sparse in the literature. To date, most of the relationships that describe microstructure evolution are based on semi-empirical equations developed from laboratory measurements.

Traditionally, the equation that has been used to describe recrystallization in aluminum alloys and steels is the classical theory developed independently by Johnson Mehl, Avrami, and Kolmogorov, frequently referred to as the JMAK equation, for isothermal phase transformation kinetics [12], [13], [14]. Based on the JMAK equation, the volume fraction of material recrystallized Xv in time t is given by:Xv=1exp(Btn)where B and n are empirical constants related to the nucleation and growth rate.

A different form of the JMAK equation has been developed based on the time to obtain 50% recrystallization, t0.5 [5]:Xv=1exp0.693tt0.5n

The deformation conditions experienced by the material have been empirically related to the time to 50% recrystallization [15], [16] as shown in Eq. (3):t0.5=βεaZbdocexpQrecRTrecwhere Z is the average Zener–Hollomon parameter for the deformation (Z=ε˙exp(Qdef/RTdef))[5], ɛ is the applied strain during the deformation, do is the initial grain size prior to deformation, R is the universal gas constant, Qdef is an activation energy for deformation, and Qrec is the activation energy for recrystallization. Tdef is the deformation temperature, Trec is the recrystallization temperature, ε˙ is the average strain rate during the deformation and a, b, c andβ are material based constants [17], [18].

Although models of this form have provided useful insight into the influence of deformation conditions on microstructure and property evolution in the material, the large number of material constants and relatively simplistic method of representing the deformation history experienced by the material limit their use. An improvement on the existing empirically based approach to describe recrystallization after hot deformation was developed by Vatne et al. in the 1990's [19]. This approach characterized the deformed microstructure and identified various mechanisms for potential nucleation sites for recrystallization as a function of the deformation conditions. This approach also predicts the evolution of recrystallized texture, which is an important microstructural feature in some aluminum alloy systems. Although an improvement over earlier empirically based models, Vatne's model contains many “fitting” constants which are alloy specific.

More recently some semi-empirical physically-based internal state variable approaches have been used to determine recrystallization behavior [20], [21], [22]. Although these models show improvement in the understanding of the evolution of the stored energy in the deformed microstructure and subsequent recrystallization process, there are still important areas where the models need further development. For example, the models have been shown to work well for laboratory-based deformation conditions where the temperature and strain rate are relatively uniform, but little work has been done to address the ability of these models to predict recrystallization correctly following deformation conditions which more accurately reflect the extreme transient conditions that occur throughout an industrial metal forming operation. These models also need to be further extended as well to account for the material stored energy which provides the driving force for recrystallization under multi-pass deformation conditions where full, partial or no recrystallization may occur in the region between deformations which is quite typical for many commercially significant aluminum alloys.

The key variables that describe the microstructure within the deformed grains can be characterized in terms of “internal state variables” including: (1) the average subgrain size, (2) the average misorientation between neighboring subgrains and (3) the internal dislocation density of the subgrains [20], [23]. These variables influence the material stored energy during deformation, which acts as the driving force for subsequent recrystallization and microstructure evolution. This physically based model has established the level of microstructural complexity needed to describe the evolution of state variables, and hence the recrystallization kinetics. However, the model still contains some material-based constants that need to be fit to experimental results.

Integrating the internal state variable model into an FE programs to predict recrystallization kinetics has been reported by Q. Zhu et al. for an Al–1% Mg. [24] and Duan et al. for an AA5083 alloy [22]. Key to the successful prediction of microstructure evolution is accurate boundary conditions that characterize both the friction as well as the heat transfer conditions during hot rolling as shown in this paper. Although sensitivity studies has been carried out previously [22], this work highlights the sensitivity of the model predictions to some important microstructure parameters such as the driving force for recrystallization, the nucleation density and the recrystallized grain size. Sensitivity of the model predictions to these parameters has not been cited previously.

Most of the investigations done to validate recrystallization model predictions have been performed using plane strain compression or torsion testing machines where the temperature and strain rate are controlled independently to remain relatively constant during the deformation [17], [25]. During industrial hot rolling, large transients in the temperature and strain rate are experienced at each location in the strip during the rolling process. There is also interdependency between these parameters, hence it becomes difficult to determine the temperature and strain rate that best represent the deformation process.

The main purpose of this work is to develop a mathematical model using finite elements and employing thermal and mechanical boundary conditions to describe the changes that occur during hot rolling process which can be integrated into the internal state variable approach to predict recrystallization kinetics for an aluminum alloy AA5083. The validation of the model in this work is carried out based on extensive experimental measurements conducted using an industrial rolling mill under different rolling conditions to ensure the applicability of the model under different rolling scenarios. Once validated, a sensitivity analysis is carried out to investigate the sensitivity of some of the model fundamental variables, namely the driving force for recrystallization, and the nucleation density as well as the model predicted fraction recrystallized and recrystallized grain size to changes in the rolling parameters at the centre of the strip.

In the following section of this paper, the general finite element (FE) and the microstructure and model framework is presented.

Section snippets

Finite element model

A 2D rolling model has been developed to simulate a single pass of the hot rolling process for aluminum alloys using the commercial finite element software package, ABAQUS. Employing symmetry along the centreline, only the top half of the strip is considered in the model. The initial geometry is 24 cm long, and 14 mm thick with 75 elements in the longitudinal direction, and four elements in the through-thickness direction with an aspect ratio of approximately three. A sensitivity analysis was

Plant trials

An experimental program was undertaken using the Corus Multi-mill facility located in IJmuiden, The Netherlands. This pilot-scale single-stand reversible rolling facility is capable of hot rolling aluminum under a variety of strains, strain rates and temperatures comparable to those typically found in an industrial hot rolling operation. The Corus Multi-mill consists of: a large furnace capable of heating samples to a desired rolling temperature, a fully instrumented single stand rolling

Results and discussion

The model developed within ABAQUS was validated by comparing the model predictions of temperatures and strains to the experimental measurements. Validation of the physically-based microstructure model integrated into the FE hot rolling model consisted of comparing the model predictions of the fraction recrystallized and the recrystallized grain size through the thickness of the sheet to the experimental measurements made on the sample.

Summary and conclusions

The development, application and linking between a mathematical model developed to simulate industrial hot rolling of an AA5083 aluminum alloy using the commercial FE package ABAQUS and an internal state variable model used to predict recrystallization kinetics for single stand hot rolling has been presented. The predicted microstructure evolution parameters, namely the through-thickness fraction recrystallized and the recrystallized grain size, based on the thermomechanical history during

Acknowledgements

The authors are grateful to Corus for funding this research project as well as providing access to their experimental rolling mill. The financial support of the Canadian Natural Science and Engineering Research Council (NSERC) in the form of an equipment grant and a graduate scholarship is gratefully acknowledged.

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