# A Damage-Based Interface Model: Application to the Degradation and Failure of a Polycrystalline Microstructure

[Doktorsavhandling]

A constitutive model for material interfaces is presented. The model is based on damage coupled to plastic (or viscoplastic) slip and dilatation, and it is able to describe the successive degradation and failure of an interface. The constitutive relations are derived from a free energy for the interface surface with internal variables representing inelastic slip and dilatation, mixed hardening and scalar damage. The adopted (quasistatic) yield criterion and potential function are both of the Drucker-Prager type, representing internal friction and dilatancy effects. The development of damage, which is kinetically coupled to the inelastic relative motion, is derived from a damage potential. The parameters in the damage law can be determined so that a predefined amount of mechanical energy (fracture energy) is dissipated in different modes of loading (simple tension or simple shear). For the modelling of rate-dependent (including creep) effects, the Duvaut-Lions' formulation of viscoplasticity is adopted. It can be ensured that the model is thermodynamically consistent, i.e. the CDI is satisfied (with certain exceptions discussed in the thesis).

The developed interface theory is implemented as a user-defined (interface) element in the commercial FE-code ABAQUS. In order to provide for quadratic convergence in equilibrium iterations, the Algorithmic Tangent Stiffness tensor, associated with the fully implicit integration scheme, is derived.

The main application of the interface model is in the context of a mesomechanics analysis of a polycrystalline microstructure which may consist of two phases. A preprocessor code, which is based on Voronoi polygonization, is developed for the generation of the microstructure. The grains are either in direct contact (one-phase structure) and bonded to each other via interfaces, or embedded in a contiguous matrix (two-phase structure) and bonded to the matrix via interfaces.

FE-calculations are carried out for a unit cell of the microstructure, whereby the unit cell is defined by the number of grains contained in the cell, the area fraction of grain versus matrix, and the interface width parameter .delta. The grain size defines the length scale of the microstructure. A sensitivity analysis is carried out for possible variation of the interfacial parameters. For example, it is shown how the interfacial strength will affect the macroscopic ductility. Localization and shear bands are detected in the analytically predicted range.

**Nyckelord: **interfaces, damage, plasticity, viscoplasticity, slip and dilatation, FE-calculations, polycrystalline microstructure, degradation, failure

Denna post skapades 2006-09-20. Senast ändrad 2013-09-25.

CPL Pubid: 1030