de Twj Tom Geus

Microstructural topology effects on the onset of ductile failure in multi-phase materials – A systematic computational approach

Multi-phase materials are key for modern engineering applications. They are generally characterized by a high strength and ductility. Many of these materials fail by ductile fracture of the, generally softer, matrix phase. In this work we systematically study the influence of the arrangement of the phases by correlating the microstructure of a two-phase material to the onset of ductile failure. A single topological feature is identified in which critical levels of damage are consistently indicated. It consists of a small region of the matrix phase with particles of the hard phase on both sides in a direction that depends on the applied deformation. Due to this configuration, a large tensile hydrostatic stress and plastic strain is observed inside the matrix, indicating high damage. This topological feature has, to some extent, been recognized before for certain multi-phase materials. This study however provides insight in the mechanics involved, including the influence of the loading conditions and the arrangement of the phases in the material surrounding the feature. Furthermore, a parameter study is performed to explore the influence of volume fraction and hardness of the inclusion phase. For the same macroscopic hardening response, the ductility is predicted to increase if the volume fraction of the hard phase increases while at the same time its hardness decreases.

A finite element perspective on non‐linear FFT‐based micromechanical simulations

Fourier solvers have become efficient tools to establish structure–property relations in heterogeneous materials. Introduced as an alternative to the finite element (FE) method, they are based on fixed-point solutions of the Lippmann–Schwinger type integral equation. Their computational efficiency results from handling the kernel of this equation by the fast Fourier transform (FFT). However, the kernel is derived from an auxiliary homogeneous linear problem, which renders the extension of FFT-based schemes to nonlinear problems conceptually difficult. This paper aims to establish a link between FE-based and FFT-based methods in order to develop a solver applicable to general history-dependent and time-dependent material models. For this purpose, we follow the standard steps of the FE method, starting from the weak form, proceeding to the Galerkin discretization and the numerical quadrature, up to the solution of nonlinear equilibrium equations by an iterative Newton–Krylov solver. No auxiliary linear problem is thus needed. By analyzing a two-phase laminate with nonlinear elastic, elastoplastic, and viscoplastic phases and by elastoplastic simulations of a dual-phase steel microstructure, we demonstrate that the solver exhibits robust convergence. These results are achieved by re-using the nonlinear FE technology, with the potential of further extensions beyond small-strain inelasticity considered in this paper.

Competing damage mechanisms in a two-phase microstructure: How microstructure and loading conditions determine the onset of fracture

Abstract This paper studies the competition of fracture initiation in the ductile soft phase and in the comparatively brittle hard phase in the microstructure of a two-phase material. A simple microstructural model is used to predict macroscopic fracture initiation. The simplicity of the model ensures highly efficient computations, enabling a comprehensive study: a large range of hard phase volume fractions and yield stress ratios, for wide range of applied stress states. Each combination of these parameters is analyzed using a large set of (random) microstructures. It is observed that only one of the phases dominates macroscopic fracture initiation: at low stress triaxiality the soft phase is dominant, but above a critical triaxiality the hard phase takes over resulting in a strong decrease in ductility. This transition is strongly dependent on microstructural parameters. If the hard phase volume fraction is small, the fracture initiation is dominated by the soft phase even at high phase contrast. At higher hard phase volume fraction, the hard phase dominates already at low phase contrast. This simple model thereby reconciles experimental observations from the literature for a specific combination of parameters, which may have triggered contradictory statements in the past. A microscopic analysis reveals that the average phase distribution around fracture initiation sites is nearly the same for the two failure mechanisms. Along the tensile direction, regions of the hard phase are found directly next to the fracture initiation site. This ‘band’ of hard phase is intersected through the fracture initiation site by ‘bands’ of the soft phase aligned with shear. Clearly, the local mechanical incompatibility is dominant for the initiation of fracture, regardless whether fracture initiates in the soft or in the hard phase.

Microscopic plasticity and damage in two-phase steels: on the competing role of crystallography and phase contrast

Abstract This paper unravels micromechanical aspects of metallic materials whose microstructure comprises grains of two or more phases. The local plastic response is determined by (i) the relative misorientation of the slip systems of individual grains, and (ii) the different mechanical properties of the phases. The relative importance of these two mechanisms at the meso-scale is unclear: is the plastic response dominated by the grain’s anisotropy, or is this effect overwhelmed by the mechanical contrast between the two phases? The answer impacts the modeling of such a material at the meso-scale, but also gives insights in the resulting fracture mechanisms at that length-scale. Until now, this question has been addressed only for particular crystallographies and mechanical properties. In contrast, this paper studies the issue systematically using a large set of phase distributions, crystallographies, and material parameters. It is found that the macroscopic and the mesoscopic (grain-averaged) plastic response of the two extreme modeling choices (crystal plasticity or isotropic plasticity) converge with increasing phase contrast. The effect of the crystallography is completely overwhelmed by the phase contrast when the yield stress of the hard phase is a factor of four higher compared to the soft phase. When this ratio is lower than two, its influence may not be neglected. However, even in this regime, fracture initiation is controlled by the local arrangement of the phases. The latter is quantified in this paper through the average arrangement of the phases around fracture initiation sites.

Microstructural modeling of ductile fracture initiation in multi-phase materials

The precise mechanisms underlying the failure of multi-phase materials may be strongly dependent on the material’s microstructural morphology. Micromechanical modeling has provided much insight into this dependence, but uncertainties remain about crucial modeling assumptions. This paper assesses the influence of different grain shapes, damage indicators, and stress states using a structured numerical model. A distinct spatial arrangement of phases around fracture incidents is found, consisting of hard regions in the tensile direction interrupted by soft regions in the directions of shear. These key features are only mildly sensitive to the studied variations.

Fracture initiation in multi-phase materials: A systematic three-dimensional approach using a FFT-based solver

Abstract This paper studies a two-phase material with a microstructure composed of a hard brittle reinforcement phase embedded in a soft ductile matrix. It addresses the full three-dimensional nature of the microstructure and macroscopic deformation. A large ensemble of periodic microstructures is used, whereby the individual grains of the two phases are modeled using equi-sized cubes. A particular solution strategy relying on the Fast Fourier Transform is adopted, which has a high computational efficiency both in terms of speed and memory footprint, thus enabling a statistically meaningful analysis. This solution method naturally accompanies the regular microstructural model, as the Fast Fourier Transform relies on a regular grid. Using the many considered microstructures as an ensemble, the average arrangement of phases around fracture initiation sites is objectively identified by the correlation between microstructure and fracture initiation – in three dimensions. The results show that fracture initiates where regions of the hard phase are interrupted by bands of the soft phase that are aligned with the direction of maximum shear. In such regions, the hard phase is arranged such that the area of the phase boundary perpendicular to the principal strain direction is maximum, leading to high hydrostatic tensile stresses, while not interrupting the shear bands that form in the soft phase. The local incompatibility that is present around the shear bands is responsible for a high plastic strain. By comparing the response to a two-dimensional microstructure it is observed that the response is qualitatively similar (both macroscopically and microscopically). One important difference is that the local strain partitioning between the two phases is over-predicted by the two-dimensional microstructure, leading to an overestimation of damage.

Fracture initiation in multi-phase materials: A statistical characterization of microstructural damage sites

Understanding the microstructural influence on the failure mechanisms in multi-phase materials calls for the identification of the worst-case scenario. This necessitates a statistical approach. By performing simulations directly based on micrographs, such an approach becomes feasible. This is applied here to extract the average microstructure around damage sites.

Fracture in multi-phase materials: Why some microstructures are more critical than others

Abstract Our goal is to unravel the mechanisms that lead to failure of a ductile two-phase material – that consists of a ductile soft phase and a relatively brittle hard phase. An idealized microstructural model is used to study damage propagation systematically and transparently. The analysis uncovers distinct microstructural features around early voids, whereby regions of the hard phase are aligned with the tensile axis and regions of the soft phase are aligned with the shear directions. These features are consistently found in regions exhibiting damage propagation, whereby the damage remains initiation driven, i.e. voids nucleate independently of each other. Upon localization, damage is controlled on a longer length-scale relying on a critical relative position of ‘initiation hot-spots’. The damage rapidly increases in bands of the soft phase wherein several voids are aligned with the shear directions. The relative arrangement of the voids determines whether the microstructure fails early, or at a substantially higher strain. Although much research is needed to refine these findings for real or more realistic microstructures, in particular in three-dimensions, this paper opens a route to a deeper understanding of the ultimate failure of multi-phase materials.

Systematic and objective identification of the microstructure around damage directly from images

An original experimental approach is presented to automatically determine the average phase distribution around damage sites in multi-phase materials. An objective measure is found to be the average intensity around damage sites, calculated using many images. This method has the following benefits: no phase identification or manual interventions are required, and statistical fluctuations and measurement noise are effectively averaged. The method is demonstrated for dual-phase steel, revealing subtle unexpected differences in the morphology surrounding damage in strongly and weakly banded microstructures.

Topology and Morphology Influences on the Onset of Ductile Failure in a Two-phase Microstructure☆

Abstract Multi-phase material are frequently applied in a wide variety of products, as they posses a unique set of properties by combining two or more distinct phases at the level of the microstructure. Although the macroscopic stiffness and hardening are reasonably well understood, questions remain about the dominant failure mechanism(s). We identify the role of the microstructural topology (the distribution of phases) on damage “hot-spots” in the microstructure, by performing a numerical study on a large set of randomly generated topologies. The result identifies a distinct probability distribution of phases around a typical damage “hot-spot”. This work is focused on assessing the sensitivity of the result to the assumptions made on the microstructural geometry.