Mechanical behavior of ceramics at high temperatures: Constitutive modeling and numerical implementation

High-temperature creep behavior of ceramics is characterized by nonlinear time-dependent responses, asymmetric behavior in tension and compression, temperature dependent, and nucleation and coalescence of voids leading to creep rupture. Moreover, creep rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. Failure is caused by the nucleation and growth of voids at the grain boundaries.; To capture the nonlinear, asymmetric, time-dependent behavior, the standard linear viscoelastic solid model is modified. Nonlinearity and asymmetry are introduced in the volumetric components by using a nonlinear function similar to a hyperbolic sine function but modified to model asymmetry. Temperature is accounted for in the model through temperature-dependent parameters. The nonlinear viscoelastic model is implemented in an ABAQUS user material subroutine.; Damage is modeled using two scalar internal variables, one for the deviatoric component and the other for the volumetric component. Each damage internal variable is assumed to be governed by a nonlinear, first order ODE that is a function of stress and two parameters. Each element is assigned damage parameters sampled from a lognormal distribution. An element is deleted when damage is equal to one. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure.; Nonlinear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of creep rupture lives. Numerical simulation results compare well with results of experiments of four-point bending specimens. A Voronoi simulation of a tensile creep test is used to study the effects of temperature, stress and damage and to evaluate model predictions. A preliminary simulation of a two-phase material is presented.