Orthotropic damage in high-strength steel sheets. An elasto-viscoplastic material model with mixed hardening

Within the scope of thermodynamics with internal variables, constitutive and evolution equations (representing ductile deformation of sheets made of high strength steel alloys) with mixed hardening and damage have been derived. As a result of the derivation, the rate-dependent elastoplastic constitutive model is identified. The material is assumed to be oriented in the principal damage directions, indicating orthotropic damage. Owing to postulates within continuum damage mechanics, a general expression for degradation of elastic properties in materials has been obtained. A numerical algorithm for the integration of the constitutive equations has been developed as well, based on an elastic predictor – plastic/damage corrector procedure. The plastic/damage corrector is based on a fully implicit backward Euler scheme. In order to consider viscoplastic material properties, the overstress (in the definition of the plastic multiplier) is a function of the plastic yield function

Oriented damage in ductile sheets: Constitutive modeling and numerical integration

Thermodynamics with internal variables provides a framework for constitutive modeling of elasto-plastic deformations. Within the scope of the theory, constitutive and evolution equations for ductile, elasto-plastic materials with mixed (isotropic and kinematic) hardening and anisotropic damage have been developed. Postulates within continuum damage mechanics were used in order to incorporate damage as an internal variable. Owing to this, and to a simplified definition of the inverted damage effect tensor, a general expression for degradation of the elastic properties in materials has been obtained. The corresponding numerical algorithm for integration of the constitutive equations is based on an elastic predictor - plastic/ damage corrector procedure. The plastic/damage corrector is uncoupled, which further simplifies and expedites the corrector procedure

Influence of ring growth rate on damage development in hot ring rolling

As an incremental forming process of bulk metal, ring rolling provides a cost effective process route to manufacture seamless rings. In the production of hot rolled rings, defects such as porosity can sometimes be found in high alloyed steel, manufactured from ingots having macro-segregation. For the reduction of the waste of material and improvement of product quality, a better understanding of the relations between parameters in the hot ring rolling process and the occurrence of porosity is needed. In this study round bars were used to manufacture rings on an industrial ring rolling mill. Different ring growth rates were applied to investigate the influence on the occurrence of porosity in the final rings. The hot rolled rings were inspected by ultrasonic testing, of which the results were also validated by metallographic investigation. In addition to the experimental investigations, coupled thermo-mechanical multi-stage finite element (FE) analysis was performed with integrated adaptive motion control of the rolls. A damage indicator was implemented in a user-defined elasto-viscoplastic material model. The deformations, stresses as well as temperature history from preform forging were included as initial conditions for the rolling stage. Damage indication from the numerical model matches the experimental result in the considered process conditions. In spite of the suggestion of a more careful process when a low ring growth rate is used in hot ring rolling, experimental and numerical studies demonstrate that with a low ring growth rate there is an increased susceptibility to damage as compared to application of a high ring growth rate