Microstructural Based Continuum Plasticity Models for BCC, FCC and HCP Metals, and Metal Alloys with Strain Rate and Temperature Dependency

In this pioneering work Voyiadjis consistently incorporates the microstructure in physical based constitutive models in order to characterize the deformation behavior of body centered cubic (bcc) and face centered cubic (fcc) metals, and metal alloys under different strain rates and temperatures. The concept of thermal activation energy as well as the dislocations interaction mechanisms is used in the derivation procedure taking into consideration the effect of the mobile dislocation density evolution on the flow stress of the deformed material. The derivation of the Zerilli-Armstrong (Z-A) physical based model for both (bcc) and (fcc) metals is investigated and a number of modifications are incorporated such as the evolution of mobile dislocation density. The authors conclude that in spite of the physical basis used in the derivation of the Z-A model, its parameters cannot be interpreted physically since the approximation ln(1+x) ~= x is used in the final step of the derivation (for small values of x). This expansion, however, is valid only for values x = 1.0 which is not the case at high strain rates and temperatures. The contributions in this area include:

  • new bcc and fcc, and metal alloys relations for the flow stress are therefore suggested and derived using the exact results of the expansion of ln(1+x).
  • several experimental data obtained by different authors for Tantalum (Ta), Niobium (Nb), Molybdenum, (Mo), Vanadium (V) (bcc metals) and Oxygen Free High Conductivity (OFHC) Copper (Cu) (an fcc metal) are used in evaluating the proposed models,
  • good agreement between the experimental results and the proposed models are obtained.
  • the predicted results show that the assumption of ignoring the generation of dislocation density during the plastic deformation is not appropriate particularly in the case of high strain rates and temperatures, which causes the values of the thermal stresses to be overestimated, numerical identification for the physical quantities used in the definition of the model parameters is also presented,
  • thermomechanical response is characterized for bcc, fcc and hcp structures of metals at low and high strain rates and temperatures,
  • material parameters of the proposed modeling are physically defined and related to the nano and micro-structure quantities,
  • the predicted results show that the effect of mobile and forest dislocation densities evolution with plastic strain on the thermal stress of bcc metals is almost negligible and pertained totally to the athermal stress part whereas, the plastic strain evolution of these dislocation densities play crucial roles in determining the plastic thermal flow stress of most fcc metals,
  • thermal and athermal flow stresses for hcp metals, show a behavior that is a combination of that for both bcc and fcc plastic deformation models,
  • a finite strain hypoelasto-viscoplastic framework is developed for body centered cubic (bcc) metals using the corotational formulation approach,
  • material length scales are implicitly introduced into the governing equations through material rate-dependency (viscosity),
  • an implicit objective stress update, which is an efficient algorithm for the type of nonlinear problems considered here, is employed,
  • effectiveness of the approach is tested by studying strain localizations in a simple tensile plane strain problem and in a cylindrical hat-shaped sample over a wide range of initial temperatures and strain rates, finite element simulations of material instability problems converge to meaningful results upon further refinement of the finite element mesh,
  • comparisons of the simulation results of adiabatic shear localizations are also made with experimental results conducted by different authors which indicate an excellent performance of the present framework in describing the strain localization problem for niobium, vanadium and tantalum.