Which Court?

Generation and packing algorithms are developed to create models of mesoscale heterogeneous concrete with randomly distributed elliptical/polygonal aggregates and circular/elliptical voids in two dimensions (2D) or ellipsoidal/polyhedral aggregates and spherical/ellipsoidal voids in three dimensions (3D). The generation process is based on the Monte Carlo simulation method wherein the aggregates and voids are generated from prescribed distributions of their size, shape, and volume fraction. A combined numerical-statistical method is proposed to investigate damage and failure of mesoscale heterogeneous concrete: the geometrical models are first generated and meshed automatically, simulated by using cohesive zone model, and then results are statistically analysed. Zero-thickness cohesive elements with different traction-separation laws within the mortar, within the aggregates, and at the interfaces between these phases are preinserted inside solid element meshes to represent potential cracks. The proposed methodology provides an effective and efficient tool for damage and failure analysis of mesoscale heterogeneous concrete, and a comprehensive study was conducted for both 2D and 3D concrete in this paper

A moving boundary model for fatigue corrosion cracking

Fatigue 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

Perturbation model for composite materials applied to analysis of cracks

The behaviour of the stress intensity factor is investigated for long plane cracks with one tip interacting with a region of graded material properties. The material outside the region is considered to be homogeneous elastic. The analysis is based on assumed small differences in stiffness in the entire body. The linear extent of the body is assumed to be large compared with that of the graded region. The crack tip, including the graded region, is assumed embedded in a square-root singular stress field. The stress intensity factor for an arbitrarily shaped region is given by a singular integral. Solutions are presented for rectangular regions with elastic gradient parallel to the crack plane. The limiting case of infinite strip is solved analytically, leading to a very simple expression. Further, a fundamental case of material properties variation is considered, allowing the solution for an arbitrary variation to be represented by Fourier’s series expansion. An interesting feature of the solution is that the stress intensity factor remains finite and does neither vanish nor become unbounded as for the cases where modulus of elasticity posses jumps. A numerical study of the fundamental strip case, with finite variations of material properties, performed using the finite element method is communicated in brief. The analytical solution is compared with the numerical results and is shown to have a surprisingly large range of validity. If an error of 5% is tolerated, modulus of elasticity in the strip may drop by around 40% or increase with around 60%

Strain-assisted corrosion cracking and growth rate inhibitors

A 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

Surface irregularities as sources for corrosion fatigue

Corrosion 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