Avrami Kolmogorov Research Articles

Microstructure evolution and recrystallization behavior of cold-rolled Zr-1Sn-0.3Nb-0.3Fe-0.1Cr alloy during annealing

Abstract The effects of cold-rolling reduction, annealing temperature, and time on recrystallization behavior and kinetics of cold-rolled Zr-1Sn-0.3Nb-0.3Fe-0.1Cr alloy were investigated using the Vickers hardness test, scanning electronic microscopy (SEM), transmission electron microscopy (TEM) and electron backscatter diffractometry (EBSD). The results show that the rate of the recrystallization increased with increasing annealing temperature and rolling reduction. Recrystallized grains nucleated preferentially at sites with high density dislocation and deformation stored energy and then grew into integral grains. Recrystallization texture changed from 〈 10 1 ¯ 0 〉 //RD to 〈 11 2 ¯ 0 〉 //RD. The grain orientation changed from random orientation to the orientation with the maximum misorientation around 30°. Recrystallization kinetics and maps were constructed based on the Johnson–Mehl– Avrami–Kolmogorov (JMAK) equation to derive parameters sensitive to the microstructure. The activation energies for recrystallization of 30%, 50% and 70% cold-rolling reductions were determined to be 240, 249 and 180 kJ/mol, respectively.

Crystallization kinetics of orthorhombic paracetamol from supercooled melts studied by non-isothermal DSC

A simple and highly reproducible procedure was established for the study of orthorhombic paracetamol crystallization kinetics, comprising melting, quench-cooling of the melt and scanning the formed glass by DSC at different heating rates. Results were analyzed on the basis of the mean as well as local values of the Avrami exponent, n, the energy of activation, as well as the Šesták–Berggren two-parameter autocatalytic kinetic model. The mean value of the Avrami kinetic exponent, n, ranged between 3 and 5, indicating deviation from the nucleation and growth mechanism underlying the Johnson–Mehl, Avrami–Kolmogorov (JMAK) model. To verify the extent of the deviation, local values of the Avrami exponent as a function of the volume fraction transformed were calculated. Inspection of the local exponent values indicates that the crystallization mechanism changes over time, possibly reflecting the uncertainty of crystallization onset, instability of nucleation due to an autocatalytic effect of the crystalline phase, and growth anisotropy due to impingement of spherulites in the last stages of crystallization. The apparent energy of activation, Ea, has a rather low mean value, close to 81 kJ/mol, which is in agreement with the observed instability of glassy-state paracetamol. Isoconversional methods revealed that Ea tends to decrease with the volume fraction transformed, possibly because of the different energy demands of nucleation and growth. The exponents of the Šesták–Berggren two-parameter model showed that the crystallized fraction influences the process, confirming the complexity of the crystallization mechanism.

Optimizing materials properties using modeling tools to simulate solidification and heat treatment

To read more about her, turn to page 8. To join TMS, visit www.tms.org/Society/Membership.aspx. Computer aided materials design has become increasingly important in mode rn materials design and development. Many modeling tools have been developed or are currently under development within the scope of Integrated Computational Materials Engineering (ICME). These modeling tools are used to understand the effects of alloy chemistry and processing conditions on the evolution of microstructure and ultimately mechanical properties, so that the materials performance can be “designed” and “optimized” even before the materials are produced. The following three papers demonstrate such efforts for the simulation of three different processes: solidifi cation, homogenization, and precipitation. The paper titled “Modeling of Alloy Casting Solidifi cation” by J. Guo and M. Samonds presents casting simulation of the solidifi cation process. As stated in the paper: “Alloy casting solidifi cation processes involve many physical phenomena such as chemistry variation, phase transformation, heat transfer, fl uid fl ow, microstructure evolution, and mechanical stress.” Two commonly used approaches for microscopic modeling of solidifi cation are reviewed; the deterministic method and the stochastic method. The deterministic method is used for the simulation of phase fraction, dendrite grain size, and the secondary dendrite arm spaces. The as-cast room temperature yield strength can be calculated based on the microstructure predicted. The cellular automaton (CA) model based on the stochastic method can be used to simulate the dendritic structure at different solidifi cation stages. Defects formed during the casting process, such as porosity, hot tearing, and macrosegregation were then discussed in the paper. The formation of these defects is found to be related to thermodynamics, fl uid fl ow, thermal, and/or stress, and all these factors are intertwined. Next, “An Integrated Computational Tool for Precipitation Simulation” by Weisheng Cao et al. presents an integrated computational thermodynamics and kinetics approach to simulate the microstructural evolution and the corresponding mechanical properties during the precipitation process. Three built-in precipitation models for microstructure simulation at multi-levels were discussed in the paper, which are the JMAK model (Johnson–Mehl– Avrami–Kolmogorov) for the estimation of the overall transformation rate, the fast-acting model based on the Langer and Schwartz theory for the simulation of the evolution of particle number density and mean size, and the more advanced KWN (Kampmann & Wagner Numerical) model for the predication of the full evolution of particle size distribution (PSD) in addition to average quantities. The modeling tools were applied to study a model Cubased alloy and a number of Ni-based superalloys to demonstrate its capability in microstructural simulation. This paper also discusses the integration of the microstructure information with strengthening models for the prediction of the age hardening behavior. Aluminum alloys (AA6XXX series) are used to demonstrate the application in this regard. The paper titled “Microstructural Modeling of the Homogenization Heat Treatment for AA3XXX Alloys” by Qiang Du et al. mainly discusses the microstructure evolution during homogenization of AA3XXX alloys. The model developed by the authors is fully coupled with thermodynamic calculation, and is able to simulate the reduction of the microsegregation formed during solidifi cation, the nucleation, growth and coarsening of intra-granular dispersoids, and the growth/dissolution of inter-granular constituent particles during the homogenization process of AA3XXX alloys. Simulation was performed for an AA3003 alloy to predict the microstructure change under different homogenization heat treatment conditions. With the positive experimental validations of the simulation results the authors concluded that the model has a potential to be used as a valuable tool for optimizing the heat treatment parameters of the AA3XXX alloys.