Mode I crack tip fields: strain gradient plasticity theory versus J2 flow theory

The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and an inner elastic K field. The inner elastic core significantly influences the crack opening profile. Crack tip plasticity is suppressed when the material length scale $\ell$ of the gradient theory is on the order of the plastic zone size estimation, as dictated by the remote stress intensity factor. A generalized J-integral for strain gradient plasticity is stated and used to characterise the asymptotic response ahead of a short crack. Finite element analysis of a cracked three point bend specimen reveals that the crack tip elastic zone persists in the presence of bulk plasticity and an outer J-field

2013 Koiter Medal Paper: Crack-Tip Fields and Toughness of Two-Dimensional Elasto-Plastic Lattices

The dependence of the fracture toughness of two dimensional elasto-plastic lattices upon relative density and ductility of cell wall material is obtained for four topologies: the triangular lattice, kagome lattice, diamond lattice, and the hexagonal lattice. Crack tip fields are explored, including the plastic zone size and crack opening displacement. The cell walls are treated as beams, with a material response given by the Ramberg-Osgood law. There is choice in the criterion for crack advance, and two extremes are considered: (i) the maximum local tensile strain anywhere in the lattice attains the failure strain, or (ii) the average tensile strain across the cell wall attains the failure strain (which can be identified with the necking strain). The dependence of macroscopic fracture toughness upon failure strain, strain hardening exponent and relative density are obtained for each lattice, and scaling laws are derived. The role of imperfections in degrading the fracture toughness is assessed by random movement of the nodes. The paper provides a strategy for obtaining lattices of high toughness at low density, thereby filling gaps in material property space

Mode I crack tip fields: strain gradient plasticity theory versus J2 flow theory

The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and an inner elastic K field. The inner elastic core significantly influences the crack opening profile. Crack tip plasticity is suppressed when the material length scale ℓ of the gradient theory is on the order of the plastic zone size estimation, as dictated by the remote stress intensity factor. A generalized J-integral for strain gradient plasticity is stated and used to characterise the asymptotic response ahead of a short crack. Finite element analysis of a cracked three point bend specimen reveals that the crack tip elastic zone persists in the presence of bulk plasticity and an outer J-field

Toughening due to shear kinking in composites

In the current study, we explore the regimes of two competing crack growth mechanisms in composites: self-similar crack extension as a result of fiber tensile damage and 90o kinking as a result of matrix shear damage. Through finite element calculations it is shown that the two damage zones extend and simultaneously shield each other under loading. Such cooperative shielding of the damage zones has a synergistic effect on the composite strength and toughness. Although the constitutive properties of the damage zones determine their relative extent, it is assumed that the preferred direction of crack extension is governed by the maximum energy release rate. The numerical values of strength and toughness against tensile/shear damage are obtained for a range of relative strength and ductility of the two damage zones. It is shown that a relatively weak and ductile shear zone is capable of increasing the macroscopic toughness by orders of magnitude. Conditions for the existence of such shear bands are stated for a range of orthotropy and a comparison is made on the toughness, strength, and preferred crack growth directions. The numerical model is then applied for an elliptical hole to examine the other extreme form of stress concentration. The extent of the shear damage is enhanced by the severity of orthotropy and initial stress concentration. As a result of this, for sufficiently long shear damage zones a panel with a sharp crack is much tougher and stronger than the one with a circular hole

Interfacial delamination of a sandwich layer by aqueous corrosion

The mechanism of aqueous delamination of a methyl methacrylate -based adhesive layer, sandwiched between two steel plates, is investigated by a systematic series of critical tests. These tests include starving the specimen of oxygen, varying the aqueous environment from de-ionised water to water with a high concentration of salt, and varying the mechanical constraint imposed by the sandwich. Sandwich construction starves the delamination crack tip of oxygen, and delamination occurs by water attack of the interface. In contrast, an adhesive coating on a steel substrate undergoes cathodic delamination when oxygen is present at the crack tip and the delamination crack is filled with salt water.<br/

Mode II Fracture of an Elastic-Plastic Sandwich Layer

The shear strength of a pre-cracked sandwich layer is predicted, assuming that the layer is linear elastic or elastic-plastic, with yielding characterized by either J2 plasticity theory or by a strip-yield model. The substrates are elastic and of dissimilar modulus to that of the layer. Two geometries are analysed: (i) a semi-infinite crack in a sandwich layer, subjected to a remote mode II K-field and (ii) a centre-cracked sandwich plate of finite width under remote shear stress. For the semi-infinite crack, the near tip stress field is determined as a function of elastic mismatch, and crack tip plasticity is either prevented (the elastic case) or is duly accounted for (the elastic-plastic case). Analytical and numerical solutions are then obtained for the centre-cracked sandwich plate of finite width. First, a mode II K-calibration is obtained for a finite crack in the elastic sandwich layer. Second, the analysis is extended to account for crack tip plasticity via a mode II strip-yield model of finite strength and of finite toughness. The analytical predictions are verified by finite element simulations and a failure map is constructed in terms of specimen geometry and crack length.ERC Advanced Grant MULTILAT 669764 Interreg 2 Seas Mers Zeeën EU programme - QUALIFY project Royal Commission for the 1851 Exhibition - Research Fellowship RF496/201

Crack kinking at the tip of a mode I crack in an orthotropic solid.

The competition between crack penetration and crack kinking is addressed for a mode I macroscopic crack in an orthotropic elastic solid. Cohesive zones of finite peak strength and finite toughness are placed directly ahead of and orthogonal to the plane of the parent crack. The cohesive zone ahead of the crack tip is tensile in nature and leads to crack penetration, whereas the inclined zones slide without opening under a combined shear and normal traction, and give crack kinking. Thereby, the competition between continued crack growth by penetration ahead of the crack tip versus kinking is determined as a function of the relative strength and relative toughness of the cohesive zones. This competition is plotted in the form of a failure mechanism map, with the role of material orthotropy emphasized. Synergistic toughening is observed, whereby the parent crack tip is shielded by the activation of both the tensile and shear (kinking) cohesive zones, and the macroscopic toughness is elevated. The study is used to assess the degree to which various classes of composite have the tendency to undergo kinking

Fracture of bio-cemented sands

Bio-chemical reactions enable the production of biomimetic materials such as sandstones. In the present study, microbiologically-induced calcium carbonate precipitation (MICP) is used to manufacture laboratory-scale specimens for fracture toughness measurement. The mode I and mixed-mode fracture toughnesses are measured as a function of cementation, and are correlated with strength, permeability and porosity. A micromechanical model is developed to predict the dependence of mode I fracture toughness upon the degree of cementation. In addition, the role of the crack tip T-stress in dictating kink angle and toughness is determined for mixed mode loading. At a sufficiently low degree of cementation, the zone of microcracking in the vicinity of the crack tip is sufficiently large for a crack tip K-field to cease to exist and for crack kinking theory to not apply. The interplay between cementation and fracture properties of sedimentary rocks is explained; this understanding underpins a wide range of rock fracture phenomena including hydraulic fracture