Crack-inclusion interaction problems with dugdale plastic zone correction
Hoh, Hsin Jen
Date of Issue2012
School of Mechanical and Aerospace Engineering
The plastic zone correction technique is commonly used to more accurately analyse the fracture behaviour of cracks in ductile materials (such as metal-matrix-composite (MMC) materials). Previous research work on crack tip plastic zone correction restricts to such cases that the crack should be in homogeneous materials. In the current PhD study, the Dugdale plastic zone correction was applied to solve various crack-inclusion interaction problems. In the Dugdale model, the plastic zone is modelled as a thin yielded strip (at yield stress σ_Y) ahead of each crack tip. This is achieved by ensuring that the Dugdale’s condition of vanishing stress intensity factors at the each crack tip is fulfilled. The first problem investigated in our study was a Griffith crack interacting with a circular inclusion with plastic zone correction added at both crack tips. The distributed dislocation technique is used to model the crack, using the solution for a single dislocation interacting with an inclusion as the Green’s function. The problem is then formulated into a set of singular integral equations, which are subsequently solved numerically using Erdogan and Gupta’s method for the stress intensity factors. Using the applied tensile load gives the stress intensity factors K_I , while using the closure stresses (of yield stress σ_Y) gives closure stress intensity factors K_ρ. Initial values of the plastic zone sizes ρ_L and ρ_R (at the left and right crack tips, respectively) are assumed, following which K_I and K_ρ are calculated. ρ_L and ρ_R are adjusted by iteration until K_I and K_ρ are balanced at both crack tips. The obtained ρ_L and ρ_R values are subsequently used to calculate the crack tip opening displacement (CTOD) values. The influence of various parameters on the CTOD is studied. Our numerical examples show that as fracture criterion, using K_I underestimates fracture-initiation conditions compared to using CTOD. The second problem looked at a Griffith crack interacting with a coated circular inclusion under various loading conditions, with plastic zones added at both crack tips. In this problem, three different materials are involved: the matrix, the inclusion and the coating layer. The influence of the coating phase on fracture behaviour was the main consideration. The coating phase, if “harder” than the matrix material, will shield (retard) the crack propagation by reducing the CTOD, and if it is “softer” than the matrix material, will cause anti-shielding effect on the crack by increasing the CTOD. A thicker coating phase increases the shielding (if “harder”) or anti-shielding (if “softer”) effect. A Griffith crack in a three-phase composite material was investigated under various loading conditions. In this problem, the composite material reinforced by circular inclusions is simulated by the three-phase model: the crack is near a single inclusion but embedded purely in the matrix material, while the rest (the outer phase) is an equivalent composite phase. With this three-phase composite model, the influence of other inclusions on the crack is also considered. Our study indicates that increasing the inclusion concentration promotes the effect of the inclusions on the CTOD and plastic zone size (PZS). Hence if the inclusion is “harder” than the matrix, the shielding effect increases with inclusion concentration, while if the inclusion is “softer” than the matrix, the anti-shielding effect increases with inclusion concentration. The Zener-Stroh crack is complementary to the Griffith crack, with a blunt tip and a sharp tip, with the crack always propagating from the sharp crack tip. Two Zener-Stroh crack problems were solved in our study. The first is a Zener-Stroh crack interacting with a circular inclusion. The effect of various parameters on the sharp crack tip was looked into. This is followed by the Zener-Stroh crack in a three-phase composite, with both the blunt-sharp and sharp-blunt cracks studied. The influence of the shear modulus, load-to-yield-stress ratio, Poisson’s ratio, crack size, inclusion size and distance on the fracture behaviour of the crack was studied in detail. We used two different ways to verify our obtained results. One method was to reduce our current models to simpler case where the crack locates in a homogeneous material without inclusion. The three-phase problems can be reduced to the two-phase ones, and can also be further reduced to the homogeneous case. The second method for verification is to use finite element analysis.
DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics