Computational inverse analysis of static recrystallization kinetics

© 2015 Published by Elsevier Ltd. All rights reserved. Accurate static recrystallization (SRX) models are necessary to improve the properties of austenitic steels by thermo-mechanical operations. This relies heavily on a careful and accurate analysis of "the interrupted test data" and conversion of the heterogeneous deformation data to the flow stress. A "computational-experimental inverse method" was presented and implemented here to analyze the SRX test data, which takes into account the heterogeneous softening of the post-interruption test sample. Conventional and "inverse" methods were used to identify the SRX kinetics for a model austenitic steel deformed at 1273 K (with a strain rate of 1 s-1) using the hot torsion test assess the merits of each method. Typical "static recrystallization distribution maps" in the test sample indicated that, at the onset of the second pass deformation with less than a critical holding time and a given pre-strain, a "partially-recrystallized zone" existed in the cylindrical core of the specimen near its center line. For the investigated scenario, the core was confined in the first half of the gauge radius when the holding time and the maximum pre strain were below 29 s and 0.5, respectively. For maximum pre strains smaller than 0.2, the specimen did not fully recrystallize, even at the gauge surface after holding for 50 s. Under such conditions, the conventional methods produced significant error.

Numerical simulation of the static recrystalization at micro shear bands

The main aim of this work is application of the developed cellular automata (CA) model to investigate influence of the micro shear bands that are present in the heavily deformed material on the static recrystallization. This initial work is the results of recent experimental analyses indicating that the micro shear bands are preferred sites for nucleation of the recrystallization. The procedure of creation of the initial microstructure with features such as grains and micro shear bands as well as basis of the developed CA code for the static recrystallization are also presented in the paper. Finally, the simulation results obtained from different recrystallization temperatures for the microstructures with and without micro shear bands are compared with each other and differences are discussed.

Analysis of work hardening and recrystallization during the hot working of steel using a statistically based internal variable model

A mathematical model has been developed which describes the hot deformation and recrystallization behavior of austenite using a single internal variable: dislocation density. The dislocation density is incorporated into equations describing the rate of recovery and recrystallization. In each case no distinction is made between static and dynamic events, and the model is able to simulate multideformation processes. The model is statistically based and tracks individual populations of the dislocation density during the work-hardening and softening phases. After tuning using available data the model gave an accurate prediction of the stress–strain behavior and the static recrystallization kinetics for C–Mn steels. The model correctly predicted the sensitivity of the post deformation recrystallization behavior to process variables such as strain, strain rate and temperature, even though data for this were not explicitly incorporated in the tuning data set. In particular, the post dynamic recrystallization (generally termed metadynamic recrystallization) was shown to be largely independent of strain and temperature, but a strong function of strain rate, as observed in published experimental work.

The stretching of single poly-ubiquitin molecules: Static versus dynamic disorder in the non-exponential kinetics of chain unfolding

Static disorder has recently been implicated in the non-exponential kinetics of the unfolding of single molecules of poly-ubiquitin under a constant force Kuo, Garcia-Manyes, Li, Barel, Lu, Berne, Urbakh, Klafter, and Fernandez, Proc. Natl. Acad. Sci. U. S. A. 107, 11336 (2010)]. In the present paper, it is suggested that dynamic disorder may provide a plausible, alternative description of the experimental observations. This suggestion is made on the basis of a model in which the barrier to chain unfolding is assumed to be modulated by a control parameter r that evolves in a parabolic potential under the action of fractional Gaussian noise according to a generalized Langevin equation. The treatment of dynamic disorder within this model is pursued using Zwanzig's indirect approach to noise averaging Acc. Chem. Res. 23, 148 (1990)]. In conjunction with a self-consistent closure scheme developed by Wilemski and Fixman J. Chem. Phys. 58, 4009 (1973); ibid. 60, 866 (1974)], this approach eventually leads to an expression for the chain unfolding probability that can be made to fit the corresponding experimental data very closely. (C) 2011 American Institute of Physics.

Non-exponentiality in electron transfer kinetics: Static versus dynamic disorder models

Non-exponential electron transfer kinetics in complex systems are often analyzed in terms of a quenched, static disorder model. In this work we present an alternative analysis in terms of a simple dynamic disorder model where the solvent is characterized by highly non-exponential dynamics. We consider both low and high barrier reactions. For the former, the main result is a simple analytical expression for the survival probability of the reactant. In this case, electron transfer, in the long time, is controlled by the solvent polarization relaxation-in agreement with the analyses of Rips and Jortner and of Nadler and Marcus. The short time dynamics is also non-exponential, but for different reasons. The high barrier reactions, on the other hand, show an interesting dynamic dependence on the electronic coupling element, V-el.

Inferring dynamic recrystallization in ferrite using the kinetics of static recrystallization

A general relationship between the kinetics of dynamic and static recrystallization is developed. It is predicted that conventional dynamic recrystallization will occur whenever the deformation time exceeds the adjusted start time for static recrystallization. This approach is verified using data for austenite and lead. It is then applied to current and previous work on ferrite. The model provides support for the contention that conventional dynamic recrystallization occurs in low carbon ferrite if deformation is carried out at high temperatures and low strain rates. In the present work, which was carried out at 700 °C, evidence for dynamic recrystallization was observed for strain rates less than around 0.01 s−1. At higher strain rates, the model predicts a critical strain for the onset of dynamic recrystallization that exceeds the critical strain for the beginning of the recovery steady-state region. While the model allows dynamic recrystallization to begin in this region, the critical strain for its onset is expected to increase rapidly with increasing strain rate and decreasing temperature once steady state has been reached.

A comprehensive method to identify the kinetics of static recrystallization using the hot torsion test results with an inverse solution

Many difficulties exist in directly following the static recrystallization of metals, particularly during hotworking. Indirect measurement of static recrystallization has been extensively performed in the literature where, for example, the recrystallization behavior of austenite in steels has commonly been measured indirectly using the fractional softening method. This method relies on the yield stress changes during recrystallization which are physically simulated by hot torsion or compression tests. However, the inherent heterogeneity of deformation during a mechanical test leads to a non-uniform static recrystallization distribution in the test sample. This, in turn, poses a serious question concerning the reliability of the measurement since the stress calculation techniques during recrystallization are not adequately developed in the existing literature. This paper develops a computer-based method to account for heterogeneous deformation during fractional softening measurements based on the hot torsion test data. The importance of the fractional softening gradient in determining the kinetics is emphasized and deficiencies in our understanding of the basic mechanisms are highlighted. A computer-based method is introduced to generate the experimental and computational components in a cost function. The cost function is then utilized by an inverse solution to calibrate the design parameters in a static recrystallization model.

Microstructure and texture evolution during sub-transus thermo-mechanical processing of Ti-6Al-4V-0.1B alloy: part II. static annealing in (alpha plus beta) regime

The first part of this study describes the evolution of microstructure and texture in Ti-6Al-4V-0.1B alloy during sub-transus rolling vis-A -vis the control alloy Ti-6Al-4V. In the second part, the static annealing response of the two alloys at self-same conditions is compared and the principal micromechanisms are analyzed. Faster globularization kinetics has been observed in the Ti-6Al-4V-0.1B alloy for equivalent annealing conditions. This is primarily attributed to the alpha colonies, which leads to easy boundary splitting via multiple slip activation in this alloy. The other mechanisms facilitating lamellar to equiaxed morphological transformations, e.g., termination migration and cylinderization, also start early in the boron-modified alloy due to small alpha colony size, small aspect ratio of the alpha lamellae, and the presence of TiB particles in the microstructure. Both the alloys exhibit weakening of basal fiber (ND||aOE (c) 0001 >) and strengthening of prism fiber (RD||aOE (c) aOE(a)) upon annealing. A close proximity between the orientations of fully globularized primary alpha and secondary alpha phases during alpha -> beta -> alpha transformation has accounted for such a texture modification.

Oxidation kinetics of nickel nano crystallites obtained by controlled thermolysis of diaquabis(ethylenediamine) nickel(II) nitrate

The metal complex, [Ni(en)2(H2O)2](NO3)2 (en = ethylenediamine), was decomposed in a static furnace at 200 C by autogenous decomposition to obtain phase pure metallic nickel nanocrystallites. The nickel metal thus obtained was studied by XRD, IR spectra, SEM and CHN analysis. The nickel crystallites are in the nanometer range as indicated by XRD studies. The IR spectral studies and CHN analyses show that the surface is covered with a nitrogen containing species. Thermogravimetric mass gain shows that the product purity is high (93%). The formed nickel is stable and resistant to oxidation up to 350 C probably due to the coverage of nitrogen containing species. Activation energy for the oxidation of the prepared nickel nanocrystallites was determined by non-isothermal methods and was found to depend on the conversion ratio. The oxidation kinetics of the nickel crystallites obeyed a Johnson–Mehl–Avrami mechanism probably due to the special morphology and crystallite strain present on the metal.

Static and dynamic bimolecular fluorescence quenching of porphyrin dendrimers in solution

The fluorescence quenching kinetics of two porphyrin dendrimer series (GnTPPH(2) and GnPZn) by different type of quenchers is reported. The microenvironment surrounding the core in GnPZn was probing by core-quencher interactions using benzimidazole. The dependence of quencher binding constant (K(a) ) on generation indicates the presence of a weak interaction between branches and the core of the porphyrin dendrimer. The similar free volume in dendrimers of third and fourth generation suggests that structural collapse in high generations occurs by packing of the dendrimer peripheral layer. Dynamic fluorescence quenching of the porphyrin core by 1,3-dicyanomethylene-2-methyl-2-pentyl-indan (PDCMI) in GnTPPH(2) is a distance dependent electron transfer process with an exponential attenuation factor beta=0.33 angstrom(-1). The quenching by 1,2-dibromobenzene occurs by diffusion process of the quencher toward to the porphyrin core, and its rate constant is practically independent of dendrimer generation.

The static and metadynamic recrystallization behaviour of an X60 Nb Microalloyed Steel

A rapid method has been developed to determine recrystallization kinetics of Nb microalloyed steels by interrupted hot torsion test. The softening behaviour was achieved as a function of different processing parameters. The method clearly identified three regions, where the strain dependency of the recrystallization rate varied. Firstly, at large strains the rate of recrystallization was not a function of strain; this is generally ascribed to metadynamic recrystallization. At lower strains the time to 50% recrystallization showed a power low relationship with strain, characteristic of static recrystallization. A further break point exists on the time for 50% softening curve when strain induced precipitation occurs in the material. The onset of strain induced precipitation was at strains below the strain to the peak stress at temperatures below 900°C. The experimental results were used to estimate the time for 50% softening and to anticipate the onset of the strain induced precipitation for the alloy of this study. Grain refinement of the recrystallized austenite continued to strains significantly beyond the peak stress and beyond the static to metadynamic recrystallization rate transition.

Static and metadynamic recrystallization of interstitial free steels during hot deformation

A rapid method was used to identify kinetics of the recrystallization for two IF (Interstitial Free) steels which have different phosphorous and boron contents. The static and metadynamic softening behaviour of the materials for a range of strain rates and temperatures were quantified. The critical strain for initiation of strain independent softening was estimated for the IF steels in respect to the time for 50 percent softening after deformation. The results showed that the strain for the initiation of strain independent softening (often referred to as metadynamic recrystallization) varies with the Zener Hollomon parameter. Classic static recrystallization was observed at strains below the strain independent softening for all processing conditions and the strain rate had a strong effect on the time for strain independent softening. Results also revealed that static and metadynamic recrystallization was delayed owing to the phosphorous and boron alloying elements. Hence, the large strain at above no-recrystallization temperature may be required for the early stage of Finishing Stands Unit (FSU) in hot strip rolling mills to initiate austenite grain refinement of phosphorous and boron added IF steels.

The need to revise the current methods to measure and assess static recrystallization behavior

Heterogeneous deformation developed during "static recrystallization (SRX) tests" poses serious questions about the validity of the conventional methods to measure softening fraction. The challenges to measure SRX and verify a proposed kinetic model of SRX are discussed and a least square technique is utilized to quantify the error in a proposed SRX kinetic model. This technique relies on an existing computational-experimental multi-layer formulation to account for the heterogeneity during the post interruption hot torsion deformation. The kinetics of static recrystallization for a type 304 austenitic stainless steel deformed at 900 °C and strain rate of 0.01s^-1 is characterized implementing the formulation. Minimizing the error between the measured and calculated torque-twist data, the parameters of the kinetic model and the flow behavior during the second hit are evaluated and compared with those obtained based on a conventional technique. Typical static recrystallization distributions in the test sample will be presented. It has been found that the major differences between the conventional and the presented technique results are due to the heterogeneous recrystallization in the cylindrical core of the specimen where the material is still partially recrystallized at the onset of the second hit deformation. For the investigated experimental conditions, the core is confined in the first two-thirds of the gauge radius, when the holding time is shorter than 50 s and the maximum pre-strain is about 0.5.