The Net Shape approach of building post-machining free parts from metallic powders by Hot Isostatic Pressing requires the development of efficient numerical simulations of the deformations to predict the final shape. The implementation of such simulations by finite elements in a useable tool for retro-design of the containers must take into account:
- constitutive laws for a powder seen as a material composed of particles and voids, both mechanical and thermal,
- different behaviours of the powder, from a rearrangement stage of the particles at the beginning of compaction, to a viscoplastic deformation of a porous material at the end,
- the number of experimental setups necessary to adjust the different homogenization models used for the constitutive laws.
The majority of the densification process is achieved by creep at the highest temperatures. We use the LPS model for the behaviour of a porous material. It first requires to determine the creep law of the constitutive material of the powder. The procedure using our Spark Plasma Sintering (SPS) device to perform vacuum uniaxial compressive tests at high temperature will be presented. Then the model itself must be adjusted on a densification course. The procedure based on the use of one single spherical container undergoing successive HIP interrupted tests and a simple diameter measurement will be presented.
This procedure leads to a suitable model which gives good prediction results on small parts where the temperature is uniform. In large parts, as in nuclear industry, the onset of temperature gradients due to a low thermal diffusivity of the powder will induce distortions due to a heterogeneous densification rate and the model must be improved. A complete model coupling thermal and mechanical behaviour of the powder must be developed. The increasing thermal conductivity with the powder density can be approached using the Argento-Bouvard model.
But, as the viscoplastic model strongly underestimates the first compaction stages, it overestimates the temperature gradients in bulk parts and the consecutive densification heterogeneity to finally overestimate the distortions. To simulate the thermal diffusion properly, it is then necessary to complete the viscoplastic model used at high temperature with a plastic model that accounts for particles’ rearrangement at low temperature and pressure. We use the modified Cam-Clay model adapted to granular materials (soils). The experimental procedure to characterise the compressive behaviour of the rearranging powder using the SPS device will be presented. The model is finally combined to the viscoplastic one to be adjusted on the previous HIP interrupted tests on a sphere.
The methodology will be presented for the case of a 316L steel powder.