Burton R. Patterson

Effect of the Degree of Prior Cold Work on the Grain Volume Distribution and the Rate of Grain Growth of Recrystallized Aluminum

The grain volume distribution of recrystallized aluminum, determined by separating and weighing the individual grains, has been found to be log normal, its spread in size being expressed by the standard deviation of the distribution (In σv), which remains constant during steady state grain growth. The value of In σv is established by the degree of cold working that precedes annealing, being smaller the greater the degree of cold work. Grain growth proceeds the more rapidly the larger the value of In σv that is, the smaller the degree of prior cold work. The distributions of the numbers of faces per grain and of edges per face are also log normal and are proportional to the grain volume distribution. Thus, the relative number of three-edged faces increases with In σv and accounts for the observed increase in the rate of grain growth.

Microstructure-based simulation of thermomechanical behavior of composite materials by object-oriented finite element analysis

Abstract While it is well recognized that microstructure controls the physical and mechanical properties of a material, the complexity of the microstructure often makes it difficult to simulate by analytical or numerical techniques. In this paper we present a relatively new approach to incorporate microstructures into finite element modeling using an object-oriented finite element technique. This technique combines microstructural data in the form of experimental or simulated microstructures, with fundamental material data (such as elastic modulus or coefficient of thermal expansion of the constituent phases) as a basis for understanding material behavior. The object-oriented technique is a radical departure from conventional finite element analysis, where a “unit-cell” model is used as the basis for predicting material behavior. Instead, the starting point of object-oriented finite element analysis is the actual microstructure of the material being investigated. In this paper, an introduction to the object-oriented finite element approach to microstructure-based modeling is provided with two examples: SiC particle-reinforced Al matrix composites and double-cemented WC particle-reinforced Co matrix composites. It will be shown that object-oriented finite element analysis is a unique tool that can be used to predict elastic and thermal constants of the composites, as well as salient effects of the microstructure on local stress state.

Mechanical properties of a hybrid cemented carbide composite

Microstructural effects on the mechanical properties of a hybrid metal matrix composite, double cemented (DC) carbide, have been investigated. DC carbide contains granules of WC/Co cemented carbide in a matrix of cobalt. Overall composite hardness increases with decreased granule cobalt content as well as with decreased intergranular matrix fraction of cobalt. High-stress abrasive wear resistance also increases with decreased granule cobalt content and matrix fraction. Fracture toughness of the composite increases with increased cobalt matrix fraction and to a lesser extent with increased granule cobalt content. Increased granule size increases both fracture toughness and wear resistance. DC carbide exhibits a superior combination of fracture toughness and high-stress wear resistance than conventional cemented carbide. The combination of toughness and wear resistance in the composite improves with increased granule hardness.

Computer simulation of grain growth with second phase particle pinning

Abstract The pinning effect of second phase particles on grain growth was simulated by 2-D Monte Carlo simulations. A new variable, the degree of contact between grain boundaries and second phase particles, was introduced to predict the grain size limit in the presence of second phase particles. The modified Zener pinning model containing this new variable can be expressed as: D r = K Rf , where D is the pinned grain size, r is the mean size of second phase particles, K is a constant, f is the area fraction (or the volume fraction in 3-D) of second phase, and R is the degree of contact between grain boundaries and second phase particles. In 2-D Monte Carlo simulations of grain growth the ratio of pinned grain size to second phase particle size was found to be proportional to f−0.5, but also to (Rf)−1. The degree of contact increased during grain growth and reached a stable value when the grain structure was pinned. The initial location of second phase particles did not have a significant contribution to the pinning of grain boundaries.

Relationship between grain

The relationship between the average mean grain boundary curvature,H, and the mean linear grain intercept, λ, has been experimentally determined for aluminum. The ratioH/λ- 1 = 0.31 was found to remain constant throughout grain growth. This value yields a driving pressure for grain growth approximately three times smaller than that derived by conventional modeling and yields realistic results in models of particle- or pore-inhibited grain growth.

Modeling particle size distributions by the Weibull distribution function

Abstract A method is proposed for modeling two- and three-dimensional particle size distributions using the Weibull distribution function. Experimental results show that, for tungsten particles in liquid phase sintered W-14Ni-6Fe, the experimental cumulative section size distributions were well fit by the Weibull probability function, which can also be used to compute the corresponding relative frequency distributions. Modeling the two-dimensional section size distributions facilitates the use of the Saltykov or other methods for unfoldng three-dimensional (3-D) size distributions with minimal irregularities. Fitting the unfolded comulative 3-D particle size distribution with the Weibull function enables computation of the statistical distribution parameters from the parameters of the fit Weibull function.

Grain growth inhibition by porosity

Abstract A model of pore or other second phase inhibited grain growth has been developed based on shape independent stereologically measurable parameters such as pore surface area and the degree of pore/grain boundary contact. The model prediction of a linear relationship between pore surface area and the inverse of the grain size was observed experimentally with sintered copper, tungsten, Al 2 O 3 and UO 2 . The model also quantifies the conditions for pore controlled grain growth and pore separation in terms of the pore and grain boundary mobilities and grain boundary curvature and provides a means for quantifying pore mobility from grain growth studies on porous and dense materials.

Influence of particle size distribution on coarsening

Abstract This study has examined the evolution of the particle size distribution and the effect of the initial and transient distributions on coarsening kinetics and the path of evolution. A numerical procedure has been employed to simulate the coarsening process statistically. It was found that the distribution passes through a continuous range of forms from the initial distribution towards the asymptotic state, with initially narrow distributions widening and wide distributions narrowing. Experimental studies using liquid phase sintered Cu-20 Co alloy with different initial distribution widths agreed with the above simulation results qualitatively. The simulated coarsening rate was found to be related to the width and shape of particle size distribution. A rate constant has been derived relating the instantaneous coarsening rate and the transient moments of the distribution. The effect of the initial distribution on coarsening rate was found to be particularly significant in the early stage of coarsening when rapid distribution changes occur. After these early rapid transients but still far from the asymptotic state, the instantaneous coarsening rate was closely related to the instantaneous geometric standard deviation of the distribution.

Stereological analysis of Zener pinning

Numerous models of Zener pinning in inhibited grain growth have been analysed from a stereological perspective. These analyses show that many differences among the models, such as the volume fraction exponent, are due to differences in assumed spatial location of the pinning particles. Including a stereological parameter describing the amount of contact between grain boundaries and particles yields a common volume fraction exponent of unity in essentially all models. A new general pinning criterion containing the degree of boundary contact parameter is derived.

Experimental investigation of particle size distribution influence on diffusion controlled coarsening

Abstract The influence of initial particle size distribution on coarsening during liquid phase sintering has been experimentally investigated using W-14Ni-6Fe alloy as a model system. It was found that initially wider size distribution particles coarsened more rapidly than those of an initially narrow distribution. The well known linear relationship between the cube of the average particle radius, r 3 , and time was observed for most of the coarsening process, although the early stage coarsening rate constant changed with time, as expected with concomitant early changes in the tungsten particle size distribution. The instantaneous transient rate constant was shown to be related to the geometric standard deviation, lnσ, of the instantaneous size distributions, with higher rate constants corresponding to larger lnσ values. The form of the particle size distributions changed rapidly during early coarsening and reached a quasi-stable state, different from the theoretical asymptotic distribution, after some time. A linear relationship was found between the experimentally observed instantaneous rate constant and that computed from an earlier model incorporating the effect of particle size distribution. The above results compare favorably with those from prior theoretical modeling and computer simulation studies of the effect of particle size distribution on coarsening, based on the DeHoff communicating neighbor model.