A Micromorphic Model for the Multiple Scale Failure of Heterogeneous Materials (original) (raw)
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Catastrophic failure due to cleavage fracture is caused by the rapid propagation of a micro-crack in the vicinity of a macroscopic flaw. Micro-cracks are initiated at second-phase brittle particles, present in the steel in different sizes and distributed randomly in the volume. The current understanding is that such particles rupture when overloaded by the plastically deforming matrix. To predict the experimentally observed statistical nature of cleavage fracture under different constraint conditions, it is pertinent to develop a particle size and constraint dependent criterion for the failure of a brittle particle in a ductile matrix. In this work the failure energy of an elastic-brittle spherical particle in a ductile matrix is analysed. Several loading conditions were examined, from constrained-uniaxial through to plane strain with varying levels of constraint. To develop a size dependent condition, results for multiple particle radii were investigated within a fixed matrix volume. The particle and matrix were deformed initially; subsequently nodes along the particle mid-plane were released progressively imitating crack opening. The energy associated with particle rupture was determined from the change in reaction force before and after release and corresponding opening displacements. The results for each loading case show clear linear relation between rupture energy and particle size. Further the results show the dependence of rupture energy on constraint, with a distinct increase of failure probability with increasing constraint. Finally, an expression for particle rupture dependence on size, stress triaxiality, and plastic strain level is derived. It is intended that this model will then be used to advance continuum-based local approach models to cleavage and meso-scale models for distributed interacting micro-cracks.
Mechanical failure in microstructural heterogeneous materials
2007
Various heterogeneous materials with multiple scales and multiple phases in the microstructure have been produced in the recent years. We consider a mechanical failure due to the initiation and propagation of cracks in places of high pore density in the microstructures. A multi–scale method based on the asymptotic homogenization theory together with the mesh superposition method (s-version of FEM) is presented for modeling of cracks.
Micromechanical modelling of damage behaviour of multiphase steels
Computational Materials Science, 2008
Multiphase steels offer very attractive combinations between strength and formability, due to the coexistence of different microstructural components and their interactions. The advantages of multiphase steels can be utilised by adjusting the type, the amount and the spatial distribution of the different phases, which are ferrite, martensite, bainite, and retained austenite. Understanding damage initiation and evolution are important to successfully process the material with only small scatter band of the formability properties. In the investigations two failure modes were simultaneously observed on a micro-scale, cleavage and dimple fractures. The model presented here attempts to describe the influence of the multiphase microstructure on the complex failure mechanism as well as mechanical properties by approaching the problem using representative volume elements (RVE) within the framework of continuum damage mechanics. Simulations for the dimple failure of TRIP steels, using the Gurson–Tvergaard–Needleman (GTN) model with two void nucleation mechanisms, will be presented. The cohesive zone model, based on the traction-separation law, is applied to the cleavage failure modelling.
Multi-length scale micromorphic process zone model
Computational Mechanics, 2009
The prediction of fracture toughness for hierarchical materials remains a challenging research issue because it involves different physical phenomena at multiple length scales. In this work, we propose a multiscale process zone model based on linear elastic fracture mechanics and a multiscale micromorphic theory. By computing the stress intensity factor in a K-dominant region while maintaining the mechanism of failure in the process zone, this model allows the evaluation of the fracture toughness of hierarchical materials as a function of their microstructural properties. After introducing a multi-length scale finite element formulation, an application is presented for high strength alloys, whose microstructure typically contains two populations of particles at different length scales. For this material, the design parameters comprise of the strength of the matrix-particle interface, the particle volume fraction and the strain-hardening of the matrix. Using the proposed framework, trends in the fracture toughness are computed as a function of design parameters, showing potential applications in computational materials design.
Micromechanics-based modelling of properties and failure of multiphase steels
Computational materials …, 2007
Within this study mechanical properties and damage mechanisms including crack initiation and propagation of multiphase steels have been investigated. Starting with one chemical composition, five different multiphase microstructures have been realised by different annealing treatments. A wide variety of mechanical properties and of failure mechanisms has been observed using tensile tests of round tensile bars without and with notch.A description of flow curves for these different microstructures has been realised using finite element calculations of representative volume elements (RVE) within a continuum mechanical framework using the isotropic von Mises plasticity law for individual phases. In creating the RVE, carbon partitioning as well as metallographically identified phase fractions has been taken into account.Two failure modes have been detected experimentally in parallel: dimple and cleavage fracture. The mode-affecting parameters have been identified in terms of microstructural features and triaxiality.For ductile damage it can be shown, that two void nucleation mechanism are in competition: those due transformation of austenite to martensite and due to the presence of inclusions. In order to model the ductile dimple failure mode within the ferritic phase, the Gurson–Tveergard–Needleman approach is used. A model parameter study has been realised for both nucleation mechanisms.
On a continuum theory of brittle materials with microstructure
Computational & Applied Mathematics, 2004
This paper deals with a finite strain continuum theory of elastic-brittle solids with microstructure. A single scalar microstructural field is introduced, meant to represent -even if in a summary way -the concentration of microdefects within the material. A system of microforces, dual to the microstructural field, is axiomatically introduced. The corresponding balance, augmented with suitable constitutive information, yields, inter alia, a kinetic equation for the microstructural field, criteria for damage nucleation, growth and healing as well as a failure criterion based on attainment of a critical value of the microstructural field. The theory is applied for the description of the Mullins effect.
Mechanics of materials, 2003
Numerical aspects of the grain level micromechanical model presented in part I are discussed in this study. They include, an examination of solution convergence in the context of cohesive elements used as an approach to model crack initiation and propagation; performance of parametric studies to assess the role of grain boundary strength and toughness, and their stochasticity, on damage initiation and evolution. Simulations of wave propagation experiments, performed on alumina, are used to illustrate the capabilities of the model in the framework of experimental measurements. The solution convergence studies show that when the length of the cohesive elements is smaller than the cohesive zone size and when the initial slope of the traction-separation cohesive law is properly chosen, the predictions concerning microcrack initiation and evolution are mesh independent. Other features examined in the simulations were the effect of initial stresses and defects resulting from the material manufacturing process. Also described are conditions on the selection of the representative volume element size, as a function of ceramic properties, to capture the proper distance between crack initiation sites. Crack branching is predicted in the case of strong ceramics and sufficient distance between nucleation sites. Rate effects in the extension of microcracks were studied in the context of damage kinetics and fragmentation patterns. The simulations show that crack speed can be significantly varied in the presence of rate effects and as a result crack diffusion by nucleation of multiple sites achieved. This paper illustrates the utilization of grain level models to predict material constitutive behavior in the presence, or absence, of initial defects resulting from material manufacturing. Likewise, these models can be employed in the design of novel heterogeneous materials with hierarchical microstructures, multi-phases and/ or layers.
SPECIAL ISSUE MULTISCALE MECHANICAL MODELING OF COMPLEX MATERIALS AND ENGINEERING APPLICATIONS 2
2011
The present volume is a special issue of selected papers from the second edition of a special symposium session on Multiscale Mechanical Modelling of Complex Materials and Engineering Applications, organized within the frame-The early focus of the symposium was to bridge the gap between solid mechanics and material science, providing a forum for the presentation of fundamental, theoretical, experimental, and practical aspects of mechanical modelling of materials with complex microstructures and complex behaviour. This volume follows the issues already edited in connection with the THERMEC 2006 conference of the same symposium session held in Vancouver, Canada, in July 2006. 1 Each contribution has undergone a standard review process, and only papers that received positive reviews by at least two international referees have been included.