An improved dislocation density based work hardening model for Al-Alloys

The objective of the present work is to develop a unified work hardening model to predict the flow behaviour of aluminium and its alloys. A particular advantage of the model presented in the present work is that the output from the model can directly be used as input for subsequent recovery and recrystallisation models. This model in conjunction with FEM codes can be used to model the complex metal forming operations like rolling. The present model is ideal to be included in a through process model. The present model is a statistical dislocation density based work hardening model based on our contemporary understanding of the microstrucature. All the statistical models like the present one make use of one or more fit parameters. A truly unified work hardening model should be able to fit flow curves over a complete deformation conditions range using the same set of fitting parameters. There are many work hardening models available today for modeling the flow behaviour of Aluminium and its alloys. However, these models almost always restrict themselves to very narrow temperature ranges. In the present work we endevour to provide a unified work hardening model, to describe the plastic flow behaviour of aluminium (99.9% purity) over a wide range of temperatures and strain rates. The concepts in the present models are inspired from the 3IVM (3 internal variables model). The 3IVM was developed mainly for the high temperature range. As will be demonstrated in chapter 3 the 3IVM makes excellent fits when confined to a high temperature range. At low temperatures or when a wide temperature range is considered the fits are not satisfactory. It has limited capability at low temperatures. The 3IVM considers edge dislocations, and hence only dislocation climb as a possible recovery mechanism. However, cross slip can be the ruling recovery process especially at low temperatures. Another shortcoming of the model is the neglection of the interaction of mobile dislocations with immobile dislocations. Keeping these deficiencies in mind, we developed an improved 3 internal variables model called the 3IVM+ (with a + sign indicating an improved version). Our model makes an inherent assumption of a cellular microstructure, hence consider 3 internal state variables similar to the 3IVM. The 3IVM+ introduces a novel kinetic equation of state to calculate the total stress needed to accommodate a particular strain rate. Various new reactions of individual dislocations and hence their effect on the various dislocation populations is considered as compared to the 3IVM. To validate the models, compression tests were performed on rather pure aluminium (99.9% purity) over a wide range of temperatures and strain rates. These experimental results were compared to the model fits in each case to judge the ability of the models. Like many statistical dislocation density based models, our model also makes use of many fitting parameters whose exact values are not known. Hence, these fitting parameters are given a physically viable range of values. An optimisation technique is used to determine the values of these parameters that minimise the sum of the differences between the experimental and simulated flow curves. For the same set of optimising parameters, we fit the complete flow field for a range of temperatures and strain rates. The original 3IVM makes good fits when we confine ourselves to a narrow temperature range. The fits from this model are especially good at high temperatures. At relatively low temperatures the model is unsatisfactory. When a wide range of temperatures is choosen, the model fails to make reasonable fits. The 3IVM+ on the other hand successfully fits the flow curves not only at high and low temperatures separately but also over a wide range of deformation conditions