Dietmar Klingbeil

Local and non-local Gurson-based ductile damage and failure modelling at large deformation

The purpose of this work is the formulation, numerical implementation and initial application of a non-local extension of existing Gurson-based modelling for isotropic ductile damage and attendant crack growth. It is being carried out under the premise that void coalescence results not only in accelerated damage development (e.g., Needleman and Tvergaard, 1984), but also in damage delocalisation (i.e., via interaction between neighbouring Gurson RVEs). To this end, we proceed by analogy with the approach of Needleman and Tvergaard (1984) who replaced the Gurson void volume fraction f with a (local) effective damage parameter f∗ in the Gurson yield condition to account for the effect of void coalescence on the material behaviour. In the current case, the role of f∗ is taken over and generalised by an effective continuum damage field ν. A field relation for ν is formulated here in the framework of continuum thermodynamics. In the simplest case, the resulting relation is formally analogous to the inhomogeneous temperature equation in which void nucleation and growth represent (local) sources for ν and in which void coalescence takes place in a process zone whose dimension is determined by a characteristic material lengthscale. Analogous to temperature, then, ν represents an additional continuum degree-of-freedom here, resulting in a coupled deformation-damage field model. In the last part of the work, the complete model for coupled damage-deformation is implemented numerically using the finite-element method on the basis of backward-Euler integration and consistent linearisation. Using this implementation, the behaviour of the current extended Gurson-based damage model is investigated for the case of simple tension of an inhomogeneous steel block. In particular, the corresponding simulation results document quantitatively the dependence of the delocalisation of the model damage process and minimisation of mesh-dependence on the characteristic dimension of the damage process zone.

Application of the Gurson Model to Ductile Tearing Resistance

Compared with conventional fracture mechanics concepts, constitutive equations which account for local damage of the material have the advantage that the corresponding material parameters for ductile fracture can be transferred between different specimen geometries. They will hence be able to describe the physical effect of constraint on the tearing resistance in a natural way. The paper shows the capabilities of the GURSON model in predicting J R -curves for different specimen geometries under static and dynamic loading with one set of material parameters. It is shown how these parameters can be determined from the numerical simulation of simple tensile tests. Problems and open questions are discussed and perspectives for future applications are given.

Hyperelastic models for elastoplasticity with non-linear isotropic and kinematic hardening at large deformation

Abstract This work is concerned with the formulation of hyperelastic-thermodynamic-based models for associated elastoplasticity with non-linear isotropic and kinematic hardening valid for both large elastic and large plastic deformation. On this basis, one can then introduce explicitly the assumptions of (1), small incremental plastic deformation, and (2), small elastic strain, into the general model and obtain special cases whose behaviour corresponds to that of various classical hypoelastic formulations. In particular, these are obtained on the basis of two different thermodynamic formulations for kinematic hardening with respect to the intermediate configuration. The simplest of these, in which the plastic part of the free energy does not depend explicitly on the plastic deformation, leads for example to Jaumann-or Green-Naghdi-hypoelastic-type behaviour for linear kinematic hardening in simple shear. In particular, the former case is obtained in this context when the plastic spin is assumed constant and equal to zero, and the latter case when the plastic rotation is assumed constant and equal to the identity. Allowing the plastic part of the free energy to depend explicitly on the plastic deformation yields the second thermodynamic model for kinematic hardening considered in this work. Here, again in the special case of linear hardening, Oldroyd-like behaviour for the shear stress and back stress, but not for the normal stress, is obtained in simple shear.

Assessment of ductile cast iron fracture mechanics analysis within licensing of German transport packages

In the design approval of transport packages for radioactive materials, the mechanical and thermal safety assessment is carried out in Germany by competent authority BAM. In recent years BAM was involved in several licensing procedures of new spent fuel and HLW package designs, where the cask body is of Ductile Cast Iron (DCI). According to IAEA regulations package designs have to fulfill requirements for specific conditions of transport. Type B(U) packages must withstand the defined accident conditions of transport. The temperature range from -40°C up to the operational temperature has to be considered. For the cask material DCI, it is necessary to determine safety against brittle fracture. The German guideline BAM-GGR 007 defines requirements for fracture mechanics of packagings made of DCI. Due to complex cask body structure and the dynamic loading a fracture mechanical assessment by analytical approaches is not always possible. Experience of recent design approval procedures show that the application of numerical calculations are applicable to determine the stresses and stress intensity factors in the cask body. At the first step a numerical analysis has to be done to identify the loading state at the whole cask body. Secondly an analysis of a detail of the cask body is made considering the displacement boundary conditions of the global model. An artificial flaw is considered in this detailed model to calculate the fracture mechanical loading state. The finite element mesh was strongly refined in the area of the flaw. The size of the artificial flaw is based on the ultrasonic inspection acceptance criteria applied for cask body manufacture.. The applicant (GNS) developed additional analysis tools for calculation of stress intensity factor and/or J-Integral. The assessment approach by BAM led to the decision to develop own tools to the possibility for independent proof of the results. The paper describes the authority assessment approach for DCI fracture mechanics analysis. The validation procedure incl. the development of own tools is explained. BAM developed a postprocessor to determine the fracture mechanical loads. A horizontal 1 m puncture bar drop test is used to give a detailed description of the assessment procedure.

Numerical Simulation of Stable Crack Growth in Fracture Mechanics Specimens

Stable crack growth in fracture mechanics specimens, i.e. side-grooved compact tension C(T), side-grooved middle tension M(T) and side-grooved part-through surface tension PS(T) specimens, is experimentally performed and numerically analysed by finite element calculations using the node shift node release technique. The crack propagation is either controlled by J-resistance curves for the C(T) and M(T) specimens, which are modelled two-dimensionally assuming plane strain conditions, or by local CMOD-resistance curves for the PS(T) specimen, which is modelled three-dimensionally. The triaxiality, i. e. the ratio of the hydrostatic part of the stress tensor to its deviatoric part, is introduced as the quantity characterizing the stress state at the crack tip. For all specimens, the relation between the triaxiality and the slope of the J-resistance curves is shown and analysed, indicating that a decreasing triaxiality results in an increasing slope for the global J-resistance curves concerning the C(T) and M(T) specimens as well as for the local J-resistance curves regarding the PS(T) specimen.

DETERMINATION OF DUCTILE CRACK GROWTH USING GURSON'S MODEL WITH DIFFERENT VOID EVOLUTION LAWS

A new approach to fracture phenomena basing on micro-mechanical damage models becomes of increasing interest. The failure mechanism of ductile tearing is dominated by the initiation, growth and coalescence of voids. This material behaviour can be described conveniently by the Gurson model as its constitutive equations include a parameter describing the volume fraction of voids. The model has been implemented into the FE program ABAQUS. Two different evolution laws for the nucleation of voids are tested with respect to their ability to predict the crack growth inside of a smooth tensile bar made of a ductile steel.