Predicting the stress-strain behavior of polycrystalline α-lron containing hard spherical particles

Recent interest in the work hardening of metal crystals containing a dispersion of hard particles has resulted in analytical expressions relating the work hardening to strain, particle diameter, and volume fraction as well as other material parameters. In this study, these models have been used to calculate the tensile stress-strain behavior of polycrystalline α iron containing dispersions of the intermetallic compound Fe₂Ta. The structural characteristics of the Fe-Ta alloys were thoroughly evaluated. The particle morphology was measured for randomness, mean particle diameter, standard deviation of the particle diameter, volume fraction, and planar interparticle spacing. Also, the matrix flow strength, composition, crystallographic randomness, dislocation morphology and grain size were evaluated. It was found that an Orowan type relationship as modified by Ashby satisfactorily described the yield strength as a function of the interparticle spacing and particle diameter. An experimental slope of 11.1 x 10^-5 kg-cm/mm² and a calculated slope of 9.75 x 10^-5 kg-cm/mm² were found. Both the Hart revised FHP work hardening model and Ashby’s model based on the generation of secondary dislocations were in good agreement with the experimental data. Hart’s revised FHP model required the use of empirically obtained values for the particle volume fraction which differed by a factor of 10 from the measured volume fraction and therefore is not suitable for predictive purposes. At tensile strains greater than 5 pct, the work hardening was characteristic of the matrix without particles; therefore, deviation between the experimental and calculated results based on Ashby’s model occurred at large strains. It is hoped that this study represents a step towards applying work hardening models to more complex polycrystalline alloys.