Thomas Linse

A modeling approach for the complete ductile–brittle transition region: cohesive zone in combination with a non-local Gurson-model

The present study deals with the simulation of crack propagation in the ductile–brittle transition region on the macro-scale. In contrast to most studies in the literature, not only the ductile softening by void growth and coalescence is incorporated but also the particular material degradation by cleavage. A non-local Gurson-type model is employed together with a cohesive zone to simulate both failure mechanisms simultaneously. This consistent formulation of a boundary value problem allows arbitrary high mesh resolutions. The results show that the model captures qualitative effects of corresponding experiments such as the cleavage initiation in front of a stretch zone, the formation of secondary cracks and possible crack arrest. The influence of the temperature on the predicted toughness is reproduced in the whole ductile–brittle transition region without introducing temperature-dependent fit parameters. A comparison with experimental data shows that the shift of the ductile–brittle transition temperature associated with a lower crack-tip constraint can be predicted quantitatively.

Application of the Small-Punch Test to Irradiated Reactor Vessel Steels in the Brittle-Ductile Transition Region

In this paper, a method is applied for the identification of hardening parameters in the brittle-ductile transition region and the determination of Weibull parameters in the brittle region using small-punch tests. A small-punch-test device is developed to measure the load-displacement curve for non-irradiated and irradiated specimens of a reactor vessel steel at different temperatures inside a hot cell. In a global optimization algorithm for the identification of hardening properties, time-consuming finite element method (FEM) calculations are avoided by using neural networks that were trained with the help of a database previously generated by FEM. Identified material properties are compared with data from tensile tests, where available. The influence of irradiation and temperature on the material and fracture behavior is analyzed.

Micromechanical-Based Models for Describing Damage of Ferritic Steels

Usually the safety margin against failure for precracked components is calculated with fracture mechanics approaches. Due to several severe limitations of these approaches, it was searched for alternative calculation models. Starting with McClintock and Berg in the sixties, so-called damage models have been developed for describing ductile fracture on the basis of micromechanical processes. The development of such kind of models is in progress now for nearly 50 years, but until today no model is generally accepted and incorporated into the international standards. In an extended introduction, the micromechanical phases of ductile rupture of metal and alloys are presented. Against this background, a summary of the evolution and the different kinds of micromechanical-based model approaches is given. The theoretical background, the advantages/ disadvantages and the limitations of the models are discussed critically. Finally non-local formulations of damage models are presented. Combinations of ductile damage models and models for cleavage to describe fracture in the brittle-ductile transition region are discussed.

Phase-Field Modelling of Damage and Fracture—Convergence and Local Mesh Refinement

In this contribution, we outline the combination of a phase-field model of brittle fracture with adaptive spline-based approximations. The phase-field method provides a convenient way to model crack propagation without topological updates of the used discretisation as the crack is represented implicitly in terms of an order parameter field that can be interpreted as damage variable. For the accurate approximation of the order parameter field that may exhibit steep gradients, we utilise locally refined hierarchical B-splines in conjunction with Bezier extraction. The latter allows for the implementation of the approach in any standard finite element code. Moreover, standard procedures of adaptive finite element analysis for error estimation and marking of elements are directly applicable due to the strict use of an element viewpoint. Two different demonstration problems are considered. At first we examine the convergence properties of the phase-field approach and explain the influence of the domain size and the discretisation for the one-dimensional problem of a bar. Afterwards, results of the adaptive local refinement are compared with uniformly refined Lagrangian and spline-based discretisations. In the second example, the developed algorithms are applied to simulate crack propagation in a two-dimensional single-edge notched, shear loaded plate.