Effect of crack tip shape on near-tip deformation and fields in plastically compressible solids

Abstract

In the present study, the crack tip shape effect on near-tip deformation and fields is numerically investigated for a mode I crack under plane strain and small-scale yielding conditions. We explore here the quasi-static deformations of solids characterized by finite strain elastic-viscoplastic material model with bilinear hardening and hardening-softening-hardening hardness functions. For comparative analyses, both plastically incompressible and plastically compressible solids have been considered. It has been observed that the crack tip shape can have great consequence on the near-tip deformation and plastic fields. As the crack tip radius is increased, the plastic strain and stresses advance more to the tip of a crack as compared to the crack surface. It has also been revealed that the combination of crack tip curvature radius, material softening and plastic compressibility provides some useful and fundamental information for the near-tip deformation and plastic fields.

Distribution of crack-tip stresses during fatigue loading with an overload event: role of initial crack-tip shape, plastic compressibility and material softening

“…Furthermore, Rozumek et al (2006) studied the influence of crack-tip curvature on fatigue crack growth experimentally for steel and aluminum, and they observed higher fatigue crack growth for a blunter notch. In the study of Alam et al (2019), similar observations were also revealed. To find out the root cause of this bizarre observation, complete evolution of the near-tip stress-strain field is necessary, however, in the works of Rozumek et al (2006) and Alam et al (2019), the same was not discussed in detail.…”

“…In the study of Alam et al (2019), similar observations were also revealed. To find out the root cause of this bizarre observation, complete evolution of the near-tip stress-strain field is necessary, however, in the works of Rozumek et al (2006) and Alam et al (2019), the same was not discussed in detail. The crack-tip deformation and stress field studies are not only fundamental for understanding of the crack propagation but also for satisfactory development of predictive tools.…”

“…The constitutive model used here is the same as that given in (Mohan et al, 2013;Khan et al, 2017;Singh and Khan, 2018;Alam et al, 2019). Here, the rate of deformation tensor d is written as the sum of the isotropic elastic part d e = L −1 : τ characterized by Young's modulus E and Poisson's ratio ν and the viscoplastic plastic part d p .…”

“…The outer radius R 0 of the geometry is 2.0 in any arbitrary units. For describing various crack-tip profiles, we consider a similar kind of an elliptical arc as taken in our earlier work (Alam et al, 2019). This sort of the crack profile is more realistic as compared to a crack with a circular arc tip usually adopted for numerical simulation or a mathematically sharp crack assumed for academic interest.…”

Role of Initial Crack Tip Shape, Plastic Compressibility and Strain Softening on Near-Tip Stress-Strain State in Fatigue Cracks during Simulation of a Finite Deformation based Elastic-Viscoplastic Constitutive Model

“…al. [6] investigated the impact of crack tip shape on the deformation and fracture of plastically compressible materials under monotonic loading.…”