Computer simulation of recrystallization--III. Influence of a dispersion of fine particles

Two-dimensional Monte Carlo simulations of recrystallization have been carried out in the presence of incoherent and immobile particles for a range of different particle fractions, a range of stored energies and a range of densities of potential nuclei (embryos). For stored energies greater than a critical value (H/J > 1) the recrystallization front can readily pass the particles leading to a random density of particles on the front and a negligible influence of particles on the recrystallization kinetics. At lower stored energies the particles pin the recrystallization front leading to incomplete recrystallization. However at very low particle fractions, when the new grain has grown much larger than the matrix grains, before meeting any particles, the new grains can complete the consumption of the deformed grains giving complete "recrystallization" by a process that appears to be similar to abnormal grain growth. Particles are, as reported previously, very effective at pinning grain boundaries, both of the deformed and recrystallized grains, when boundaries migrate under essentially the driving force of boundary energy alone. Such boundaries show a density of particles that rises rapidly from the random value found at the start of the simulation. As a consequence, particles very strongly inhibit normal grain growth after recrystallization. Such growth can only occur if the as-recrystallized grain size is less than the limiting grain size seen in the absence of recrystallization. Under these circumstances a small increment of grain growth occurs until the grain boundaries once again acquire a higher than random density of particles.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29718/1/0000052.pd

Microstructural simulation of dynamic recrystallization

A Monte Carlo model for dynamic recrystallization has been developed from earlier models used to simulate static recrystallization and grain growth. The model simulates dynamic recrystallization by adding recrystallization nuclei and stored energy continuously with time. The simulations reproduce many of the essential features of dynamic recrystallization. The stored energy of the system, which may be interpreted as a measure of the flow stress, goes through a maximum and then decays, monotonically under some conditions and in an oscillatory manner under others. The principle parameters that were studied were the rate of adding stored energy, [Delta]H, and the rate of adding nuclei, [Delta]N. As [Delta]H increases, for fixed [Delta]N, the oscillations decay more rapidly and the asymptotic energy rises. As [Delta]N increases again the oscillations decay more rapidly but the asymptotic stored energy decreases. The mean grain size of' the system also oscillates in a similar manner to the stored energy but out of phase by 90[deg]. The flow stress oscillations occurred for conditions which lead to both coarsening and refinement of the initial grain size. Necklacing of the prior grain structure by new grains were observed for low [Delta]H and high [Delta]N; it is, however, not an invariable feature of grain refinement. The initial grain size has a profound influence on the microstructure that evolves during the first cycle of recrystallization but at long times, a mean grain size is established which depends on the values of [Delta]H and [Delta]N alone. Comparison of the relationships between the energy storage rate, maximum and asymptotic stored energy and the grain size suggest that in physical systems the energy storage rate and the nucleation rate are coupled. Comparison of the simulation results with experimental trends suggests that the dependence of nucleation rate on storage should be positive but weak. All of these results were obtained without the addition of special parameters to the model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30270/1/0000671.pd

Computer simulation of recrystallization in non-uniformly deformed metals

The classical Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation [F = 1 - exp(- kt)n] for nucleation and growth transformations works very well for most solid state transformations but fails regularly when applied to recrystallization of plastically deformed metals. Under conditions of near constant growth rate, a high exponent (n [ges] 3) is predicted but low exponents (n [les] 2) are typically measured. Another common observation is that the slope of a JMAK plot, from which the exponent is inferred, decreases as recrystallization proceeds. Analysis of the published data suggested the hypothesis that the failure of the JMAK theory as applied to recrystallization is because of the lack of uniformity of the stored energy of plastic deformation on the grain size scale. This hypothesis was tested by use of Monte Carlo simulations of the type previously used successfully to model grain growth and recrystallization. The earlier simulations of recrystallization used uniform stored energies whereas the simulations presented here varied the stored energy from grain to grain. The kinetics were plotted on JMAK plots which exhibited low and varying exponents closely resembling experimental data. Specific simulations were performed to test the basic JMAK assumption that makes a correction for the effect of impingement under conditions of random nucleation, namely dF/dFe = (1 - F), where F is the actual volume fraction and Fe is the extended volume fraction--that which would obtain in the absence of impingement and overlap between new grains. It was found the assumption is accurate under conditions of uniform stored energy. With non-uniform stored energy, however, the correction underestimated the effect of impingement by a factor that rapidly increased (to over two orders of magnitude) during recrystallization.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28082/1/0000528.pd

Simulation and theory of abnormal grain growth--anisotropic grain boundary energies and mobilities

Abnormal grain growth has been studied by means of a computer-based Monte Carlo model. This model has previously been shown to reproduce many of the essential features of normal grain growth. The simulations presented in this work are based on a modified model in which two distinct types of grains are present. These two grain types might correspond to two components of different crystallographic orientation, for example. This results in three classes of grain boundaries: 1. (a) between unlike types,2. (b)between grains of the first type and3. (c) between grains of the second type, to which different grain boundary energies or different mobilities can be assigned. Most simulations started with a single grain of the first type embedded in a matrix of grains of the second type. Anisotropie grain boundary energies were modeled by assigning a higher energy to boundaries between like type than to boundaries between grains of unlike type. For this case, abnormal grain growth only occurred for an energy ratio greater than 2 and then wetting of the matrix by the abnormal grain occurred. Anisotropie grain boundary mobilities were modeled by assigning a lower mobility to boundaries between grains of like type than to boundaries between unlike type. For this case the extent of abnormal grain growth varied with the ratio of mobilities and it is tentatively concluded that there is a limiting ratio of size of the abnormal grain relative to the matrix. A simple treatment of anisotropic grain boundary mobility was developed by modifying Hillert's grain growth model [Acta metall. 13, 227 (1965)]. This theoretical treatment also produced a limiting ratio of relative size that is a simple function of the mobility ratio.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28006/1/0000442.pd

Computer simulation of pencil glide in bcc metals

An existing computer code for simulation of texture development in polycrystals has been modified to model ''pencil glide'' as observed in some bcc metals. Pencil glide can be thought of as a limiting case where the slip direction is restricted to (111) directions but the slip plane is arbitrary. The existing code simulates ''restricted glide'', i.e., (111)(110) slip systems, by using the Bishop-Hill method to find the ative vertex of the single crystal yield surface for each grain. It then corrects this trial solution by using a nonlinear viscous law based on the total (111)-resolved stress component. Only a small increase in computation time required is required compared to restricted glide. The results of the pencil glide modification of the code are that the texture development in tension is essentially the same as for restricted glide but that significant differences appear in plane strain compression (rolling). The Taylor Factor in tension for a random polycrystal is found to be 2.74. 20 refs., 5 figs., 1 tab

Back calculation of parent austenite orientation using a clustering approach

A new approach is presented for calculating the parent orientation from sets of variants of orientations produced by phase transformation. The parent austenite orientation is determined using the orientations of bainite variants that transformed from a single parent austenite grain. In this approach, the five known orientation relationships are used to back transform each observed bainite variant to all their potential face-centered-cubic (f.c.c.) parent orientations. A set of potential f.c.c. orientations has one representative from each bainite variant, and each set is assembled on the basis of minimum mutual misorientation. The set of back-transformed orientations with the minimum summation of mutual misorientation angle (SMMA) is selected as the most probable parent (austenite) orientation. The availability of multiple sets permits a confidence index to be calculated from the best and next best fits to a parent orientation. The results show good agreement between the measured parent austenite orientation and the calculated parent orientation having minimum SMMA

The influence of texture on strain hardening

It is well known that the strain hardening behavior of metals is not the same in tension, compression, torsion and rolling, for example. We report on a new set of experiments, comprising wire-drawing interrupted by tensile tests, free compression, channel-die compression, and short-tube torsion in aluminum, an Al-Mg alloy, copper, silver, and 70:30 brass. The texture was measured before straining and at vonMises strain levels of roughly 1.0 and 2.0. Computer simulations of the deformation starting from a set of random grains weighted by observed initial texture, predicted deformation textures in qualitative agreement with the observed ones in most cases. Quantitatively the simulations yielded the Taylor factors as a function of strain for all paths and, with an assumed hardening law for the representative grain, the macroscopic stress/strain curves. The grain hardening rate as a function of resolved shear stress was described in tabular form such as to match one of the macroscopic curves, and then used to predict the others. The eventual fit was quite good; we will describe what judgments needed to be made to achieve this result. The conclusion is that the strain-path dependence of work hardening can be explained simply as a consequence of texture development. 13 refs., 5 figs., 1 tab

The high-strain-rate and spallation response of tantalum, Ta-10W, and T-111

The compressive true stress-true response of tantalum, Ta-10W, and T-111 were found to depend on the applied strain rate, in the range 0.001 to 7000 s{sup {minus}1}. The strain-rate sensitivities of the flow stress of tantalum, Ta-10W, and T-111 a 1% strain are 0.062, 0.031, and 0.024, respectively. The rates of strain hardening in Tantalum, Ta-10W, and T-111 are seen to exhibit differing behavior with increasing strain rate. The calculated average strain-hardening rate in tantalum, {Theta}, for the quasi-static (0.001 s{sup {minus}1}) data at 25{degrees}C is 2080 MPa/unit strain. The hardening rate at 3000s{sup {minus}1} at 25{degrees}C decreases to 846 MPa/unit strain. Normalizing the work hardening rate in tantalum with the Taylor Factor for a random polycrystal, ({Theta} / (3.07){sup 2}), yields work hardening rates of {mu}/276 at quasi-static strain rates and {mu}/680 at high-rates, assuming a shear modulus of 61 GPa for tantalum at room temperature. While the work hardening of all the tantalum-based materials are similar at quasi-static rates, alloying results in a small reduction in hardening rate. With increasing strain rate, the work hardening rate in tantalum decreases by approximately a factor of two compared to the alloys. Alloying tantalum with substitutional or interstitial elements is thought to result in increased edge dislocation storage and screw dislocation cross-slip due to interactions with the alloying elements at high strain rates. 28 refs

Measurement and modeling of interface heat transfer coefficients

The results of preliminary work on the modeling and measurement of the heat transfer coefficients of metal/mold interfaces is reported. The system investigated is the casting of uranium in graphite molds. The motivation for the work is primarily to improve the accuracy of process modeling of prototype mold designs at the Los Alamos Foundry. The evolution in design of a suitable mold for unidirectional solidification is described, illustrating the value of simulating mold designs prior to use. Experiment indicated a heat transfer coefficient of 2 kW/mS/K both with and without superheat. It was possible to distinguish between solidification due to the mold and that due to radiative heat loss. This permitted an experimental estimate of the emissivity, epsilon = 0.2, of the solidified metal