The material model (CMP97) simulates compaction and sintering of (foremost hard-) metal powder. CMP97 was developed at LiTH/Solid Mechanics (compaction) and at KTH/Physical Metallurgy/BRIEE (sintering), in cooperation with AB Sandvik Coromant, AB Sandvik Hard Materials, SECO TOOLS AB, Uniroc AB and with financial support by Nutek. It follows a description of the features of the model.

Compaction

• Basically it is a CAP-model + deformation induced anisotropy (kinematic hardening); non-associated flow rule; fracturing criterion by Hillerborg, Nilsson, Ottosen & Dahlblom
  
  
• Hardening parameters: a scalar measure of "the degree of anisotropy" e; together with a tensorial quantity C, that settles the principal directions of the accumulated plastic deformation, from which the relative density follows as d = det(C); the kinematical shift/back stress K is coaxial with C
  
  
• Parameters related to stress: The 1st and 2nd invariants J₁ and (of the deviator); the stress character (pressure/shear) by the polar angle, of a stress state, J_j  in the  J₁, -plane
  
  
• Flow direction: j_A is settled as the ratio of distortional- (shear) over volumetric strain, measured as a polar angle in the invariant plane of I₁, (duals of J₁, )
  
  
• Material parameters: mapped from experimental data, with a newly developed interpolation technique(FE+LSQ)
  
  
  • K(d,e), G(d,e) elastic modules
  • X(d) compressibility
  • Cohesion C₀(d) » tensile failure stress s_t
  • Failure stress in compression Y(d)
  • h(d,e,J_j) the amplitude of the back stress
  • j_A(d,e,J_j) current plastic flow direction

Sintering

• Viscoelastic, with modules K* and G*
• Sintering Stress s^s representing the capillary forces i.e. ”shrinkage drive"”
• A mix of physical parameters (coefficients of surface- and volume diffusion, grain size, etc.) and phenomenological parameters (e.g. a ”measure of mobility” x that handles the marked -dependence of K* and G*)

FE-implementation
DYNA2D, DYNA3D, a simplified model (1D-functions, no FE+LSQ) CMP01 in LS-DYNA

Bench mark
Compaction + sintering of ”hard metal spacer” RNXX, see figure below: blue contour = start configuration with d = 0.42, green contour = compacted to d  » 0.56 , red mesh =  sintered with hold temperature 1250 °C and duration 3 t, to d » 0.93 , * = measured shape .