Generalization of the slip line field theory for temperature sensitivevisco-plastic materials

Abstract:

Material instabilities in solids are classically approached as material
bifurcations of a rate-independent, isothermal, elasto-plastic solid. However,
previous research has shown that temperature and deformation
rate are important factors and are fully coupled with the mechanical
deformation. Early experiments in steel revealed a distinct
pattern of localized heat dissipation and plastic deformation
known as heat lines. Further, earth materials, soils, rocks and
ceramics are known to be greatly influenced by
temperature with strain localization being strongly affected by
thermal loading. In this work, we provide a theoretical framework
for the evolution of plastic deformation for such coupled systems,
with a two-pronged approach to the prediction of localized
failure. First, slip line field theory is employed to
predict the geometry of the failure patterns and second,
failure criteria are derived from an energy bifurcation analysis.

The bifurcation analysis is concerned with the local energy balance of a material and
compares the effects of heat diffusion terms and heat production terms where
the heat production is due to mechanical processes. Commonly, the heat is
produced locally along the slip lines and if the heat production outweighs
diffusion the material is locally weakened which eventually leads to failure.
The effect of diffusion and heat production is captured by a dimensionless
quantity, the Gruntfest number, and only if the Gruntfest number is larger than
a critical value localized failure occurs. This critical Gruntfest number
depends on boundary conditions such as temperature or pressure and hence this
critical value gives rise to localization criteria. We find that the results of
this approach agree with earlier contributions to the theory of plasticity but
gives the advantage of a unified framework which might prove useful in
numerical schemes for visco-plasticity.