Problem

Constitutive models describe the stress and internal variables (representing in an average sense the microstructural rearrangements of the material) as function of the strain, strain rate and temperature. In large-scale simulations of structures, the framework of continuum thermo-mechanics is typically adopted to formulate the constitutive models, while thermo-mechanical testing is used to identify the model parameters. Advanced constitutive models, including plastic anisotropy, non-linear isotropic and kinematic hardening, strain-rate and temperature dependence, damage evolution and failure, tend to have a large number of model parameters.

This programme is designed to apply multi-scale methods for constitutive modelling in a top-down/bottom-up methodology for large-scale numerical simulations of metal structures. This will reduce the need for calibration to thermo-mechanical tests and improve the prediction accuracy with respect to properties that are not always easily measured by testing. Qualitative and quantitative descriptions at different length scales will be closely accompanied by well-designed experiments at the length scales of relevance for the phenomena of interest (from the nano-scale to the complete structure), as a basis for achieving improved understanding, model developments and model validation. 

Objective and scope

The main objective of this programme is to develop a physical and experimentally validated multi-scale framework providing constitutive models for microstructure evolution, strength and work hardening, crystal and continuum plasticity, and damage and fracture for metallic materials. The main effort will be restricted to structures made of aluminium alloys and steels. In many critical structural applications, material properties that are beyond standard testing conditions are required; hence high and low temperatures, high pressures (from blast waves or water depths) and elevated rates of strain (including shock loading) will be given special attention.

Research tasks

The three main parts in a constitutive model for metallic materials are 1) the yield criterion and the plastic flow rule, 2) the work-hardening rule, and 3) the damage evolution rule and the fracture criterion. The research tasks defined below reflect the main parts of a constitutive model for the analysis of metal structures. 

1. Yielding and plastic flow: Metallic materials often exhibit plastic anisotropy that is important for the stress and strain distributions in a structure. Analytical yield criteria exist that capture the plastic anisotropy of metals with high accuracy, however the number of parameters is often so large that experimental identification of parameters is impossible either due to the high costs or because the tests cannot be realized. An alternative approach is to use crystal plasticity models and the finite element method to model a representative volume element (RVE) of the material and then to apply computational homogenization to identify the parameters of the yield criterion. With this approach, information about the microstructure (e.g. crystallographic texture, grain morphology and particle distribution) is used to replace some or all of the mechanical tests. The potential for cost- and time-savings in industry is substantial. Computational homogenization has already been used to determine the yield criteria for several materials, but with today’s crystal plasticity models, the numerically identified yield criterion is not always sufficiently accurate and a hybrid method (i.e., a combined use of mechanical tests and computational homogenization) may be preferred. The crystal plasticity models accurately account for the crystallographic texture, but this does not include the other effects (e.g. grain morphology, orientation gradients, sub-structure anisotropy and particle distribution). To enhance these models, material characterization at relevant scales—from the atomic to the crystal scale—should be integrated with dedicated simulations on the same scales to understand and include the influence of hardening precipitates and grain morphology and interactions. Another issue here is updating of the yield surface with large deformations owing to the evolution of the crystallographic texture.
2. Work hardening: The strength and work hardening of single-phase materials depend on several microstructural features, such as the type and amount of solute, particles, grain size, and dislocation density. Physically based work-hardening models describing the stress-strain behaviour of certain classes of materials based on chemical composition and thermal history exist, and have recently been used successfully in simulations of structural response under impact-loading conditions. The main building blocks of such models are interacting modules for the modelling of precipitation, strength and work hardening, where dislocation mechanics is used to relate the strength and work hardening to the solute content and the particle size distribution predicted by the precipitation model. However, the existing models need to be extended to new classes of materials and to a broader range of loading conditions (e.g. high strain rates, low and high temperatures, and strain path changes). Moreover, the constitutive relations should be improved with respect to prediction accuracy. This calls for extensive experimental characterization on various length scales by transmission and scanning electron microscopy, mechanical testing at wide ranges of strain rates and temperatures, and the use of lower scale simulations (e.g. ab initio simulations, molecular dynamics, and dislocation dynamics) to widen our knowledge on the underlying physics. In the case of dual-phase (or multi-phase) materials, continuum RVE simulations play an important role in understanding how the interaction between the phases affects the strength and work hardening of the material.
3. Damage and fracture: The ductile failure of metallic materials consists of three stages: nucleation, growth and coalescence of voids. For these stages, growth and coalescence are modelled accurately by using continuum unit cell simulations. Analytical porous plasticity models are available that account for void growth—and more recently models have been developed for void coalescence. However, the damage evolution at low stress triaxiality is still an important topic for research. A critical step for better and more physical-based damage and fracture models is improved understanding and quantitative description of the initial stages of void formation around constituent particles. Here, X-ray tomography may be a useful experimental tool. Atomistic simulation is also an interesting tool to obtain quantitative information of the traction-separation law for the particle-matrix interface. Other issues are the effects of the plastic anisotropy of the matrix material, void shape and interaction, and strain path changes, which may be studied by continuum unit cell and RVE simulations using the appropriate crystal plasticity or continuum plasticity models. The damage and failure of some materials depend critically on heterogeneities in the microstructure, e.g. the precipitate free zones in precipitation strengthened aluminium alloys. A better understanding of the role of the microstructure on the damage evolution and failure of metallic materials needs to be established. This can only be achieved by modelling and simulation on the nano-, micro- and meso-scales assisted by advanced experimental characterization using different microscopy techniques, tomography and field measurements of strain and temperature.