Density dependent constitutive model for Bi-2212 powder compression deformation

Abstract Bi-2212 HTS materials are fabricated into multi-filamentary wires via powder-in-tube (PIT) method followed by proper heat treatment to obtain superconductivity, but how to predict the large compression deformation behaviors of the Bi-2212 powder is critical to design the processing of the Bi-2212 HTS wire. Drucker Prager/Cap (DPC) model was the most commonly used model for powders including Bi-2212 with soil-like mechanical behavior to consider its shear failure as well as hydrostatic compression. However, the parameters for DPC Cap evolve with densities change and the original model is inadequate to precisely describe the densification process of Bi-2212 powder with large strain. In this study, the modified DPC model with density dependent parameters was introduced for Bi-2212 powder compressions by measuring the failure strength and hydrostatic compressive behavior under different density states. The DPC yield surface was plotted with an evolution trend of non-linear outward expansion with density increased. FEM model of uniaxial compression based on the as-introduced model was built with subroutine VUSDFLD applied. The distribution of Mises stress and relative density were analyzed. The axial stress-density curve for FEM and experimental results were normalized and quantitively evaluated by Mean Square Error (MSE). The introduced model shows good convergence and could match the experimental results well with normalized MSE of 0.000207 and Root Mean Square Error (RMSE) of 0.0144, indicating the mean error percentage of 1.44 %. The model introduced in this article provides supports toward large strain deformation simulation of Bi-2212 powder.