Modelling the evolution of recrystallization texture for a non-grain oriented electrical steel

Highlights

• A new model is introduced to predict the evolution of recrystallization texture.

• The methodology is an unprecedented combination of some developed models.

• The recrystallized γ-fiber was successfully predicted for the electrical steel.

Abstract

A new methodology based on the strain energy release maximization (SERM) theory and Avrami-type kinetics is introduced to predict the evolution of recrystallization texture in a non-grain oriented (NGO) electrical steel. The deformation orientation and the activated slip system of each orientation, which can be developed by cold rolling for a hot-rolled NGO electrical steel, were calculated using the finite element method and visco-plastic self-consistent model. Afterwards, the recrystallization orientations that can evolve from each deformation orientation were determined by the SERM theory, and their fraction over the annealing time was calculated based on the Avrami-type kinetic equation. As a result, this approach for the NGO electrical steel could successfully predict the formation of γ-fiber with strong {1 1 1}〈1 1 2〉 component during recrystallization, which was in good agreement with the experimental results.

Introduction

As a soft magnetic material with a body-centered cubic (BCC) structure, Si steel exhibits easiest magnetization along the 〈1 0 0〉 crystal direction. For non-grain oriented (NGO) electrical steels, 〈1 0 0〉 directions parallel to sheet surface plane are preferred for superior magnetic properties [1], [2], [3]. Unfortunately, conventional rolling process is known to strengthen α-fiber (〈1 1 0〉//RD) and γ-fiber (〈1 1 1〉//ND), which are unfavorable for the magnetization. In order to transform the crystal orientation developed by cold rolling into texture favorable for the magnetization, recrystallization is essential, but the changes in microstructure and texture during recrystallization are vastly complex and not fully understood. Therefore, in an effort to nurture the easy magnetization direction, the evolution of recrystallization texture for NGO electrical steels is still an ongoing subject of interest.

Because recrystallization texture of a polycrystalline material strongly depends on its processing history [1], [2], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], diverse processing methods including cold rolling of columnar grains [7], [8], α → γ → α phase transformations [9], [10], and conventional [12], [13], [14] and unconventional rolling schemes [15], [16], [17], [18] have been studied to understand the evolution of recrystallization texture for the NGO electrical steel. While these works laid valuable grounds for how specific orientations may nucleate or grow, very few efforts have been made in actually predicting the evolution of recrystallization texture for the NGO electrical steel, which can significantly aid the development of processing methods.

For a model to properly predict the evolution of recrystallization texture, the model should firstly be able to predict what orientations will be formed during recrystallization, and secondly be able to describe the kinetics of recrystallization. While the latter can be handled by employing Avrami-type equation, the former one is often problematic. Currently, most of the theories used to describe the evolution of recrystallization texture are based on oriented nucleation (ON) and oriented growth (OG) theories, but both theories are not quite clear as to which nuclei are preferred given a certain deformation history. This difficulty often becomes an obstacle in predicting the final recrystallization texture because recrystallization texture heavily depends on deformation history.

A suitable theory to correlate deformation mode with stable recrystallization texture is the strain energy release maximization (SERM) theory [19], [20]. The theory postulates that a stable recrystallized grain is developed if the grain is oriented in a way such that the strain energy by dislocations in the deformed grain is minimized, or the strain energy release upon recrystallization is maximized. This theory has been successfully utilized in a diverse class of materials such as Al containing high Mn austenitic steels [21], Al and Cu [22], Co thin film [23], low carbon steels [24], and grain-oriented electrical steels [25]. Also, in calculating the orientation of the recrystallized grain, the activities of slip systems are used, which means that orientation of the recrystallized grain depends on deformation modes. The fact that the SERM theory accounts for deformation mode is a huge advantage for predicting deformation history dependent recrystallization textures.

In this work, we employed a combined finite element method (FEM) and visco-plastic self-consistent (VPSC) modeling approach to characterize the evolution of deformation texture developed by cold rolling for a hot-rolled NGO electrical steel. Afterwards, the recrystallization orientations that can evolve from each deformed grain were predicted based on the SERM theory, using the slip activities calculated in the combined FEM-VPSC. Finally, the evolution of the recrystallization texture at the specific annealing time and temperature was evaluated using the Avrami-type kinetic equation.