In-situ X-ray computed tomography characterisation of 3D fracture evolution and image-based numerical homogenisation of concrete

In-situ micro X-ray Computed Tomography (XCT) tests of concrete cubes under progressive compressive loading were carried out to study 3D fracture evolution. Both direct segmentation of the tomography and digital volume correlation (DVC) mapping of the displacement field were used to characterise the fracture evolution. Realistic XCT-image based finite element (FE) models under periodic boundaries were built for asymptotic homogenisation of elastic properties of the concrete cube with Young’s moduli of cement and aggregates measured by micro-indentation tests. It is found that the elastic moduli obtained from the DVC analysis and the FE homogenisation are comparable and both within the Reuss-Voigt theoretical bounds, and these advanced techniques (in-situ XCT, DVC, micro-indentation and image-based simulations) offer highly-accurate, complementary functionalities for both qualitative understanding of complex 3D damage and fracture evolution and quantitative evaluation of key material properties of concrete

Multifractal-based assessment of Gilsocarbon graphite microstructures

Three-dimensional X-ray tomographs of the microstructures of virgin and radiolytically oxidised polygranular Gilsocarbon nuclear graphite have been analysed with a multifractal approach, to consider the evolution of the porous structures of the filler particles and matrix regions. Correlations between the Rényi dimensions and structural parameters such as the total porosity, elastic modulus, and pore sizes have been revealed. The multifractal analysis has been used to develop an algorithm to detect the spatial distribution of filler particles, which has been applied to analyse the effects of filler particles on a crack path

A multi-scale three-dimensional Cellular Automata fracture model of radiolytically oxidised nuclear graphite

A multi-scale approach for fracture simulation, based on the Cellular Automata technique, has been developed and then applied to a nuclear graphite that is used in structural components of the UK Advanced Gas-cooled Reactors (AGR). High resolution X-ray computed tomographs of Gilsocarbon grade graphite, with up to 68% weight loss by radiolytic oxidation, provide quantitative descriptions of the porosity within its constitutive filler particles and their surrounding matrix. The statistical distributions for tensile strength and elastic modulus obtained from small models of the filler and matrix are introduced to a large scale model of the heterogeneous microstructure. These microstructure-derived simulations achieve a good agreement with experimental data. The computationally efficient analysis is then used to investigate the stochastic effects on mechanical properties of possible variations in the microstructure between individual small test specimens. As these may represent material of nominally the same microstructure, there is an apparent increase in the variability of strength and modulus at high weight loss

A multi-scale three-dimensional Cellular Automata fracture model of radiolytically oxidised nuclear graphite

A multi-scale approach for fracture simulation, based on the Cellular Automata technique, has been developed and then applied to a nuclear graphite that is used in structural components of the UK Advanced Gas-cooled Reactors (AGR). High resolution X-ray computed tomographs of Gilsocarbon grade graphite, with up to 68% weight loss by radiolytic oxidation, provide quantitative descriptions of the porosity within its constitutive filler particles and their surrounding matrix. The statistical distributions for tensile strength and elastic modulus obtained from small models of the filler and matrix are introduced to a large scale model of the heterogeneous microstructure. These microstructure-derived simulations achieve a good agreement with experimental data. The computationally efficient analysis is then used to investigate the stochastic effects on mechanical properties of possible variations in the microstructure between individual small test specimens. As these may represent material of nominally the same microstructure, there is an apparent increase in the variability of strength and modulus at high weight loss

3D cellular automata fracture model for porous graphite microstructures

Nuclear graphite has a complex porous microstructure, which depends on raw materials and manufacturing process; porosity can change with radiolytic oxidation and also in the absence of oxidation with very high neutron fluences. Porosity directly affects the fracture process and the graphite tensile strength. To understand the effects of porosity on component strength and its relation to small specimen data, microstructure sensitive models are needed that can simulate the statistics of strength of porous microstructures, also addressing size and strain gradients effects such as notches. This requires multi-scale models that capture the key microstructural features with sufficient fidelity, and also with sufficient computational economy to simulate component behaviour. To achieve this, an innovative technique to calculate the elastic stress distribution in a 3D porous solid under uniaxial or biaxial tension has been developed that uses cellular automata. Synthetic microstructures with arbitrary distributions of pore sizes and shapes are created that simulate realistic microstructures; a fracture algorithm simulates failure initiation and crack growth. The model calculates the tensile strength of a microstructure volume for any arbitrary failure criteria; the critical strain energy release rate is used as an example to demonstrate how porosity affects the fracture process. The presented Cellular Automata (CA) model is at least an order of magnitude more efficient than finite element methods of equivalent discretisation; CA are also scale independent and well suited for parallel computing. This would allow large volumes of representative microstructures to be simulated, with a Monte-Carlo based approach to investigate strength variability

3D cellular automata fracture model for porous graphite microstructures

Nuclear graphite has a complex porous microstructure, which depends on raw materials and manufacturing process; porosity can change with radiolytic oxidation and also in the absence of oxidation with very high neutron fluences. Porosity directly affects the fracture process and the graphite tensile strength. To understand the effects of porosity on component strength and its relation to small specimen data, microstructure sensitive models are needed that can simulate the statistics of strength of porous microstructures, also addressing size and strain gradients effects such as notches. This requires multi-scale models that capture the key microstructural features with sufficient fidelity, and also with sufficient computational economy to simulate component behaviour. To achieve this, an innovative technique to calculate the elastic stress distribution in a 3D porous solid under uniaxial or biaxial tension has been developed that uses cellular automata. Synthetic microstructures with arbitrary distributions of pore sizes and shapes are created that simulate realistic microstructures; a fracture algorithm simulates failure initiation and crack growth. The model calculates the tensile strength of a microstructure volume for any arbitrary failure criteria; the critical strain energy release rate is used as an example to demonstrate how porosity affects the fracture process. The presented Cellular Automata (CA) model is at least an order of magnitude more efficient than finite element methods of equivalent discretisation; CA are also scale independent and well suited for parallel computing. This would allow large volumes of representative microstructures to be simulated, with a Monte-Carlo based approach to investigate strength variability

Multifractal-based assessment of Gilsocarbon graphite microstructures

Three-dimensional X-ray tomographs of the microstructures of virgin and radiolytically oxidised polygranular Gilsocarbon nuclear graphite have been analysed with a multifractal approach, to consider the evolution of the porous structures of the filler particles and matrix regions. Correlations between the Rényi dimensions and structural parameters such as the total porosity, elastic modulus, and pore sizes have been revealed. The multifractal analysis has been used to develop an algorithm to detect the spatial distribution of filler particles, which has been applied to analyse the effects of filler particles on a crack path

Multi-scale modelling of nuclear graphite tensile strength using the Site-Bond lattice model

Failure behaviour of graphite is non-linear with global failure occurring when local micro-failures, initiated at stress-raising pores, coalesce into a critically sized crack. This behaviour can be reproduced by discrete lattices that simulate larger scale constitutive responses, derived from knowledge of microstructure features and failure mechanisms. A multi-scale modelling methodology is presented using a 3D Site-Bond lattice model. Microstructure-informed lattices of both filler and matrix constituents or ‘phases’ in Gilsocarbon nuclear graphite are used to derive their individual responses. These are based on common elastic modulus of “pore-free” graphite, with individual responses emerging from pore distributions in the two phases. The obtained strains compare well with experimentally obtained data and the stress-strain behaviour give insight into the deformation and damage behaviour of each phase. The responses of the filler and matrix are used as inputs to a larger scale composite lattice model of the macroscopic graphite. The calculated stress-strain composite behaviour, including modulus of elasticity and tensile strength, is in acceptable agreement with experimental data reported in the literature, considering the limited microstructure data used for model's construction. The outcome supports the applicability of the proposed deductive approach to the derivation of macroscopic properties

In situ quantitative three-dimensional characterisation of sub-indentation cracking in polycrystalline alumina

The three-dimensional deformation beneath a Vickers indentation in polycrystalline alumina has been measured, in situ, by digital volume correlation of high resolution synchrotron X-ray computed tomographs. The displacement fields at the peak indentation load and after unloading are used to study the shape and orientation of sub-surface cracks induced by the indentation; lateral cracking due to residual stresses, bounded by a system of radial cracks, is revealed. For the first time, it is shown that radial cracks have mixed mode opening displacements, which are affected by the relaxation of residual stresses via lateral cracking. This novel technique may find applications in the study of surface damage by abrasive wear in brittle materials. © 2014 Elsevier Ltd

In situ quantitative three-dimensional characterisation of sub-indentation cracking in polycrystalline alumina

The three-dimensional deformation beneath a Vickers indentation in polycrystalline alumina has been measured, in situ, by digital volume correlation of high resolution synchrotron X-ray computed tomographs. The displacement fields at the peak indentation load and after unloading are used to study the shape and orientation of sub-surface cracks induced by the indentation; lateral cracking due to residual stresses, bounded by a system of radial cracks, is revealed. For the first time, it is shown that radial cracks have mixed mode opening displacements, which are affected by the relaxation of residual stresses via lateral cracking. This novel technique may find applications in the study of surface damage by abrasive wear in brittle materials. © 2014 Elsevier Ltd