A texture-component Avrami model for predicting recrystallization textures, kinetics and grain size

Abstract

The study presents an analytical model for predicting crystallographic textures and the final grain size during primary static recrystallization of metals using texture components. The kinetics is formulated as a matrix variant of the Johnson–Mehl–Avrami–Kolmogorov equation. The matrix form is required since the kinetic and crystallographic evolution of the microstructure is described in terms of a limited set of growing (recrystallizing) and swept (deformed) texture components. The number of components required (5–10) defines the order of the matrix since the kinetic coupling occurs between all recrystallizing and all deformed components. Each such couple is characterized by corresponding values for the nucleation energy and grain boundary mobility. The values of these parameters can be obtained by analytical or numerical coarse graining according to a renormalization scheme which replaces many individual grains which grow via recrystallization in a deformed texture component by a single equivalent recrystallization texture component or by fitting to experimental data. Each deformed component is further characterized by an average stored deformation energy. Each element of the kinetic matrix, reflecting one of the possible couplings between a deformed and a recrystallizing texture component, is then derived in each time step by a set of two differential equations. The first equation describes the thermally activated nucleation and growth processes for the expanded (free) volume for a particular couple of a deformed and a recrystallizing texture component and the second equation is used for calculating the constrained (real) volume for that couple which corrects the free volume for those portions of the deformation component which were already swept. The new method is particularly developed for the fast and physically based process simulation of recrystallization textures with respect to processing. The present paper introduces the method and applies it to the primary recrystallization of low carbon steels.

On the thermal stability of the nanostructured tungsten coatings

“…temperature, impurities, initial size, texture, etc [38,39,41]. Our values and those reported in literature suggest a correlation between the initial grain size and the activation energy thus, the smaller the grain size, the lower the activation energy.…”

“…In general, the grain growth occurs due to the movement of grain boundaries, where the boundary movement can be discontinuous, and change the direction of the motion unexpectedly. This activation enthalpy is related to the activation energy for boundary mobility which theoretically should be near to the self-diffusion energy although frequently that is not the case [36,38,39]. For example, for pure coarse-grained tungsten, the activation enthalpy for self-diffusion is within the range of 586-628 kJ/mol for single crystal, and 502-586 kJ/mol for polycrystalline tungsten [33], whereas the activation enthalpy for grain growth for a polycrystalline tungsten is 210.7±13.2 kJ/mol [36].…”

A large strain thermoplasticity model including recovery, recrystallisation and grain size effects

“…In the literature, several recrystallisation models can be found that are typically limited to specific thermomechanical conditions, focusing on simulating either static recrystallisation, see for example [8,9], or dynamic recrystallisation, see for example [10][11][12][13]. These models commonly adopt a purely phenomenological Avrami type formulation [14,15] or are based on a physically motivated recrystallised volume fraction evolution that is coupled to hardening related energy contributions.…”

Mesoscale simulation of microstructure evolution during multi-stage hot forging processes

“…To obtain desirable mechanical properties of forged products, dynamic recrystallization (DRX), which affects the grain size distribution of final forging for metals with moderate-to-low stacking fault energy, is one of the most valuable microstructure evolution processes [1]. To simulate the microstructure evolution caused by DRX, many physical and empirical models have been developed [2][3][4][5][6][7][8]. In these studies, the traditional approach is based on empirical equations, such as the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory [9].…”