Tensile instability in creep damaging solids

Abstract

Tensile instability in creep damaging bars subject to geometrical and/or material non-uniformities is investigated for the constant load and constant stress tests provided the longwavelength approximation is maintained. The constitutive model employed in the study is valid for the moderate stress-elevated temperature regime which is dominated by completely creep constrained cavity growth. Two definitions of instability are used to study initial rates of imperfection growth and imperfection growth through failure. The first is concerned with the immediate response to a disturbance (stability in the small) while the second is related to a loss of correspondence between increments of perturbed and unperturbed field variables. A linearized stability analysis based on the first definition reveals that, like the pure viscous creep case, the deformation is unstable however, in contrast to viscous creep, the characteristic time for neck growth is much shorter. A nonlinear analysis based on the second definition associates the onset of instability with fracture occurring at a finite area but infinite local section strain. Histories of strain and area differences reveal the tendency for a highly localized neck to form, however this is countered by stability loss (fracture) at a finite area.