Relationship Between the Fracture Toughness and the Crack Tip Radius

Abstract

The conditions that surround the tip of a sharp crack in a ductile metallic material dictate the onset of plastic flow and crack extension. The problem of predicting the onset of unstable fracture is related directly to the difficulty of measuring or calculating the actual stresses and strains within the plastic enclave that encompasses the crack tip. Beeuwkes has obtained an approximate solution for the elastic-plastic state in the vicinity of the crack tip and concludes that the crack tip radius after deformation together with the fracture strength at nil ductility of the material form the basis for a fracture criterion. In this study measurements have been made of the crack opening of fatigue cracked double cantilever beam specimens of 6061-T6 and annealed 4340VM steel. The crack opening measurements have been used to compute the crack tip radius at different loads by fitting the experimental data with an nth order polynomial (n = 2, 4, 6, and 8). The polynomial for which the average deviation in the computed values is a minimum with respect to the measured values was chosen to represent the crack geometry. The values of the crack tip radius as given by this polynomial were plotted against the stress intensity factor. It has been found for both the selected materials that the stress intensity factor and the crack tip radius follow a linear relation when plotted on a log-log basis. The stress intensity factor and the ratio of the crack tip radius to a critical crack tip radius also plot as a straight line on a log-log basis. It is concluded that the concept of a critical crack tip radius is consistent with a crack extension model that depends on void coalescence and growth. The data also support the fracture criterion based on the elastic-plastic analysis proposed by Beeuwkes.

Short bar (and short rod) fracture toughness of an aluminium 6061 metal matrix composite

“…By comparison, I~ for monolithic A1 6061-T6 is around 33 MPa m [7]. In the present case, fracture toughness values for COMRAL-85-T6 in the L-R and C-R orientations are similar, but that in the R-L orientation is less than the others.…”

A CTOD equation based on the rigid rotational factor with the consideration of crack tip blunting due to strain hardening for SEN(B)

“…This is based in the assumption where r p sh converges at a fixed constant value for materials behaving in an elastic–perfect plastic behaviour. Data from σ ys / σ uts = 0.98 would be exhibiting elastic dominant properties where a blunted crack tip could give a significant larger CTOD and therefore was not used in the fitting …”

“…Data from σ ys /σ uts = 0.98 would be exhibiting elastic dominant properties where a blunted crack tip could give a significant larger CTOD and therefore was not used in the fitting. 31,32 Based on the fitting of the data, the r p sh equation can be described using the following equation:…”

Comparison of methods to determine CTOD for SENB specimens in different strain hardening steels

“…Crack tip opening displacement was defined from the original crack tip for both the FE model and silicone replicas. 19,20 To check the accuracy of the FE CTOD, percentage error of CTOD estimated by the FE model was calculated using The latter was due to the initial blunted crack tip assumed in the FE model, FIGURE 10 Comparison between the 45°crack tip opening displacement and the original tip crack tip opening displacement for different tensile ratio which predicted an artificially higher initial stress intensity factor compared to the experimental sharp fatigue pre-crack.…”

“…Fully 3-dimensional quarter SENB models were simulated using commercially available software (ABAQUS v6.14). 19,20 The roller ahead of the crack tip was fixed, whereas the displacement was set in the negative y-direction for the roller on the top of the model to simulate 3-point bending. Twenty-noded quadratic brick elements (C3D20R) were used in the models.…”