# Modelling of Inelastic Effects in Metal Sheets and Identification of Material Parameters

[Doktorsavhandling]

The continuum modelling of the macroscopic behaviour of metallic sheets and the identification of corresponding material parameters for models selected are dealt with in the thesis. Thermodynamics with internal variables provides a framework for the derivation of the models. Inelastic effects, such as mixed plastic hardening, and either isotropic or anisotropic ductile damage are included in the models. For isotropic damage, represented by a scalar variable, the effective stress concept is combined with the principle of strain equivalence. The extension to anisotropy is affected by replacing the strain equivalence principle with the elastic energy equivalence. A second-order damage tensor is shown to give rise to a degradation of elastic stiffness. The elasticity law assumes material isotropy, since there is no damage in the initial undamaged state. The concept of small elastic and large plastic deformations is applied to Belytcshko shell elements. The plastic yield criterion is evaluated in the space of the real stresses, which simplifies the numerical algorithm. A limitation of the model is that damage propagates only during plastic hardening. Since cyclic loading causes opening and closing of microcracks, the microcrack reopening and closing mechanism is intended to model the corresponding damage growth. Accordingly, damage propagates mainly in the tensile state. The incorporation of the dynamic yield surface ensures an upper asymptotic limit to the viscoplastic stress state. The time integration of the constitutive models is done by using the Backward Euler method in combination with the Newton-Raphson iteration technique. These algorithms are later implemented as user material subroutines in the explicit Finite Element program LS-DYNA. Three experimental methods are used to identify material parameters: uniaxial tension tests at different strain rates, a three-point cyclic bending test, and continuous uniaxial tension loading and unloading of metal sheets. Since steel alloys exhibit strain-rate dependence, stress-strain curves from uniaxial tension tests at different strain rates are used for calibration of the viscoplastic material parameters. The three-point cyclic bending test methodology is assessed for identification of material hardening parameters. Continuous uniaxial loading and unloading of metal sheets was performed with the objective of identifying the isotropic growth of damage. This identification technique is based on the coupling between damage propagation and degradation of the elastic properties of a material.

**Nyckelord: **constitutive modelling, plasticity, viscoplasticity, mixed hardening, damage, MCR mechanism, dynamic yield surface, material parameter identification

Denna post skapades 2006-08-28. Senast ändrad 2013-09-25.

CPL Pubid: 5045