451 research outputs found
Structure of micro-crack population and damage evolution in quasi-brittle media
Full text linkMechanical behaviour of quasi-brittle materials, such as concrete and rock, is controlled by the generation and growth of micro-cracks. A 3D lattice model is used in this work for generating micro-crack populations. In the model, lattice sites signify solid-phase blocks and lattice bonds transmit forces and moments between adjacent sites. Micro-cracks are generated at the interfaces between solid-phase blocks, where initial defects are allocated according to given size distribution. This is represented by removal of bonds when a criterion based on local forces and defect size is met. The growing population of micro-cracks results in a non-linear stress-strain response, which can be characterised by a standard damage parameter. This population is analysed using a graph-theoretical approach, where graph nodes represent failed faces and graph edges connect neighbouring failed faces, i.e. coalesced micro-cracks. The evolving structure of the graph components is presented and linked to the emergent non-linear behaviour and damage. The results provide new insights into the relation between the topological structure of the population of micro-cracks and the material macroscopic response. The study is focused on concrete, for which defect sizes were available, but the proposed methodology is applicable to a range of quasi-brittle materials with similar dominant damage mechanisms. © 2014 The Author
Strain-assisted corrosion cracking and growth rate inhibitors
No full textA model for evolution of cracks as a result of strain-assisted corrosion is presented. The considered cracks possess a realistic geometry, where the tip region is an integral part of the crack surface instead of being a singular point. This geometry is either implicitly defined or is a consequence of crack nucleation from surface irregularities. The evolution model poses a moving boundary value problem, where material dissolution advances the boundary exposed to the corrosive environment. A controlling mechanism for the boundary advancement is the rupture of a brittle corrosion-protective film, which is continually building-up along the corroding surface. The rate of boundary evolution is a function of the degree of the protective film damage, caused by mechanical straining. Thus, no crack growth criterion is needed for the analysis. A FEM based program with various procedures for tracking the moving boundary is used as a solution tool. A number of problems are considered – cracks with realistic geometries with tips embedded in a square-root singular stress field, and cracks nucleating from surface pits and propagating in either a homogeneous material or in a bi-material system. The presented results show the importance of the crack width, interpreted as grain boundaries inter-phase thickness, as well as the various shape parameters describing the crack tip region, for the stress corrosion crack growth rate. Further, the results clearly demonstrate that the interaction between the surface deformation and the protective film is primarily responsible for the dissolution localisation along a narrow surface region, such that a crack is formed from a pit and the crack shape is maintained during the evolution. The influence of the initial pit aspect ratio on the crack nucleation phase is investigated, as well as the competition of cracks evolving from closely situated pits. It is shown how these results could be used for estimation of the arrested cracks distribution along a corroding surface. In the cases of corrosioncracks growing across bi-material interfaces the numerical results for the crack morphology are shown to be in qualitative agreement with a real life example. In all these cases the cracks pass the interface being either accelerated or inhibited, depending on the elastic mismatch of the bi-material system. Design recommendations are proposed on the bases of the presented results. Finally, a perturbation model for a non-homogeneous material is proposed. The model is used in the analysis of an ideal crack with one tip interfering with an inclusion, introduced in a plane homogeneous elastic body, and having arbitrarily varying elastic characteristics. The solution is given in terms of an area integral and further specialised to an inclusion shaped as a layer stretching perpendicularly to the crack plane. A closed form result for this special case is derived and compared with numerical results obtained for finite variations of the elastic modulus. A wide range of validity of the perturbation solution is discovered
Stress corrosion cracking as evolving interface problem
Full text linkIt has been long recognised that stress corrosion crack initiation and propagation are triggered by the interaction between electro-chemical processes and mechanical deformation in the crack tip region. Recently, the author of the present work proposed a model for corrosion crack nucleation and growth, which allows for incorporation in a continuum mechanical theory. In the model, the corrosion is forming the geometry of the crack tip, thus creating the conditions for strain concentration. This leads to a smooth crack surface evolution represented as a problem of evolving interface, where crack growth criterion is not needed. As a start, the chemical environment of the crack tip is assumed to be constant and unaffected by the changing geometry as the crack is developing. This leads to a linear relationship between strain and corrosion rate, in the sense of removed material per unit of area. This work reviews the results obtained so far on the basis of the linear model. In addition, mathematical and finite element analyses of stationary cracks with appropriate geometry are involved to explain the behaviour predicted by, the model
Site-Bond Lattice Modelling of Damage Process in Nuclear Graphite under Bending
Full text linkGraphite is used as neutron moderator and structural material in the core of the UK's fleet of Magnox and Advanced Gas-cooled Reactors (AGRs). The graphite cores are non-replaceable in these two designs and therefore potentially life-limiting. Graphite is a multi-phase, aggregated and porous material which could have a non-linear stress-strain response because of distributed damage accumulation within the material prior to rupture: quasi-brittle characteristics. Lattice models provide a way of capturing the resulting non-linear behaviour by incorporating microstructural features and damage mechanisms within the discrete system. Here, the 3D site-bond model (Jivkov and Yates 2012) is used to simulate a near-isotropic nuclear reactor core Gilsocarbon graphite under bending in a micro-cantilever test (Liu et al 2014). Experimentally measured pore-size distributions and volume densities are used for model construction. Previous work on graphite site-bond modelling (Morrison et al 2014b) is further developed to consider pore effect on the deformation and failure behaviour of the bonds. Damage evolution and accumulation with increasing load is simulated by the consecutive removal of bonds subject to failure criterion. The simulated mechanical properties and force-deflection relationship were validated by experimental results
Fracture energy of graphite from microstructure-informed lattice model
Full text linkGraphite remains a key structural material in the nuclear industry, the integrity assessment of which in demanding reactor environments is critical for safe operation of plant. Fracture of graphite is preceded by growth and coalescence of distributed micro-cracks within a process zone, classifying it as a quasi-brittle material alongside cement-based and ceramic materials. The evolution of micro-crack population to failure is well represented by discrete lattice models, e.g. (Wang and Mora 2008). Here, a recently developed 3D lattice (Jivkov and Yates 2012), with elastic spring elements and brittle-damage behaviour is used to generate microstructure representative models of two graphite grades at a representative meso length scale. Micro-cracks are represented by spring failures and the macroscopic damage results from their collective behaviour. Presented results capture a transition from graceful, plastic-like failure at lower porosities, with energy dissipation via micro-cracking, to glass-like behaviour with negligible energy dissipation at higher porosities. The results are in good agreement with experimental data. Thus, the proposed methodology can calculate fracture energy from the stress-strain curve, or formulate cohesive and damage evolution laws for continuum models, based exclusively on microstructural features
Site-Bond Lattice Modelling of Damage Process in Nuclear Graphite under Bending
Full text linkGraphite is used as neutron moderator and structural material in the core of the UK's fleet of Magnox and Advanced Gas-cooled Reactors (AGRs). The graphite cores are non-replaceable in these two designs and therefore potentially life-limiting. Graphite is a multi-phase, aggregated and porous material which could have a non-linear stress-strain response because of distributed damage accumulation within the material prior to rupture: quasi-brittle characteristics. Lattice models provide a way of capturing the resulting non-linear behaviour by incorporating microstructural features and damage mechanisms within the discrete system. Here, the 3D site-bond model (Jivkov and Yates 2012) is used to simulate a near-isotropic nuclear reactor core Gilsocarbon graphite under bending in a micro-cantilever test (Liu et al 2014). Experimentally measured pore-size distributions and volume densities are used for model construction. Previous work on graphite site-bond modelling (Morrison et al 2014b) is further developed to consider pore effect on the deformation and failure behaviour of the bonds. Damage evolution and accumulation with increasing load is simulated by the consecutive removal of bonds subject to failure criterion. The simulated mechanical properties and force-deflection relationship were validated by experimental results
A moving boundary model for fatigue corrosion cracking
Full text linkFatigue corrosion crack initiation and propagation is modelled as a moving boundary value problem. The model is based on three physical processes operating at the solid-environment interface – material dissolution, passive film formation and surface straining. The dissolution triggers boundary advancement. The rate of boundary advancement depends on the passive film damage caused by the surface straining. Plane edge cracks, nucleating from surface irregularities, are considered. The cracks obtain realistic geometrical shapes where the near-tip region is an integral part of the crack surface. Elastic-perfectly plastic materials are considered and a low-cycle fatigue load is assumed. The problem is solved using a FEM based program and procedures for moving boundary tracking and interior re-meshing. A crucial ingredient of the boundary tracking is the evolved surface re-meshing, where a scheme based on length and curvature constraints is utilised. The work studies how the choice of these constraints influences the results for crack surface evolution. It is shown that characteristic length parameters in crack nucleation and short crack growth depend on the choice of the constraints. It is concluded that an additional physical process operating at the surface has to be accounted for in order to describe the length scales observed in reality
Surface irregularities as sources for corrosion fatigue
Full text linkCorrosion fatigue crack nucleation from surface irregularity is modelled as a mov-ing boundary value problem. The model is based on material dissolution proportional to the surface stretch. Dissolution and re-passivation processes are forming the ge-ometry of the crack tip, thus creating con-ditions for strain concentration. No crack growth criterion is used. The interaction between the electrochemical processes and the deformation of the crack tip region is incorporated in continuum mechanical theory. Elastic-perfectly plastic materials under low frequency cyclic load are con-sidered. The model simulates how cracks form and grow in a single continuous process. The resulting natural variation of lengths of the formed cracks makes them grow with different rates. One crack after another falls into a wake behind a larger crack and the crack tip load of the smaller decreases leading to its arrest
Strain-assisted corrosion cracking and growth rate inhibitors
Full text linkA model for evolution of cracks as a result of strain-assisted corrosion is presented. The considered cracks possess a realistic geometry, where the tip region is an integral part of the crack surface instead of being a singular point. This geometry is either implicitly defined or is a consequence of crack nucleation from surface irregularities. The evolution model poses a moving boundary value problem, where material dissolution advances the boundary exposed to the corrosive environment. A controlling mechanism for the boundary advancement is the rupture of a brittle corrosion-protective film, which is continually building-up along the corroding surface. The rate of boundary evolution is a function of the degree of the protective film damage, caused by mechanical straining. Thus, no crack growth criterion is needed for the analysis. A FEM based program with various procedures for tracking the moving boundary is used as a solution tool. A number of problems are considered – cracks with realistic geometries with tips embedded in a square-root singular stress field, and cracks nucleating from surface pits and propagating in either a homogeneous material or in a bi-material system. The presented results show the importance of the crack width, interpreted as grain boundaries inter-phase thickness, as well as the various shape parameters describing the crack tip region, for the stress corrosion crack growth rate. Further, the results clearly demonstrate that the interaction between the surface deformation and the protective film is primarily responsible for the dissolution localisation along a narrow surface region, such that a crack is formed from a pit and the crack shape is maintained during the evolution. The influence of the initial pit aspect ratio on the crack nucleation phase is investigated, as well as the competition of cracks evolving from closely situated pits. It is shown how these results could be used for estimation of the arrested cracks distribution along a corroding surface. In the cases of corrosion cracks growing across bi-material interfaces the numerical results for the crack morphology are shown to be in qualitative agreement with a real life example. In all these cases the cracks pass the interface being either accelerated or inhibited, depending on the elastic mismatch of the bi-material system. Design recommendations are proposed on the bases of the presented results. Finally, a perturbation model for a non-homogeneous material is proposed. The model is used in the analysis of an ideal crack with one tip interfering with an inclusion, introduced in a plane homogeneous elastic body, and having arbitrarily varying elastic characteristics. The solution is given in terms of an area integral and further specialised to an inclusion shaped as a layer stretching perpendicularly to the crack plane. A closed form result for this special case is derived and compared with numerical results obtained for finite variations of the elastic modulus. A wide range of validity of the perturbation solution is discovered
Analysis of materials systems represented by graphs
Full text linkPresented is a rigorous mathematical formulation of boundary value problems defined on discrete systems described by mathematical graphs. The formulation is applicable to mechanical and physical problems and includes an effective algebraic framework and efficient computational implementation. Me- chanical problems involving damage initiation and evolution are soled to illus- trate the proposed method. It is concluded that the graph-theoretical approach to discrete systems offers substantial benefits in terms of conceptual clarity and computational efficiency
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