Modified Model of Crack Tip Stress Field Considering Dislocation Slip Accumulation and Crack Tip Blunting

Abstract

This study uses the digital image correlation technique to measure the crack tip displacement field at various crack lengths in U71MnG rail steel, and the interpolated continuous displacement field was obtained by fitting with a back propagation (BP) neural network. The slip and stacking of dislocations affect crack initiation and growth, leading to changes in the crack tip field and the fatigue characteristics of crack growth. The Christopher-James-Patterson (CJP) model describes the elastic stress field around a growing fatigue crack that experiences plasticity-induced shielding. In the present work, this model is modified by including the effect of the dislocation field on the plastic zone of the crack tip and hence on the elastic field by introducing a plastic flow factor ρ, which represents the amount of blunting of the crack tip. The Levenberg-Marquardt (L-M) nonlinear least squares method was used to solve for the stress intensity factors. To verify the accuracy of this modified CJP model, the theoretical and experimental plastic zone errors before and after modification were compared, and the variation trends of the stress intensity factors and the plastic flow factor ρ were analysed. The results show that the CJP model, with the introduction of ρ, exhibits a good blunting trend. In the low plasticity state, the modified model can accurately describe the experimental plastic zone, and the modified stress intensity factors are more accurate, which proves the effectiveness of dislocation correction. This plastic flow correction provides a more accurate crack tip field model and improves the CJP crack growth relationship.

Determining Stress Intensity Factors at Varied Inclination Angles through Innovative Discontinuous Digital Image Correlation

“…Using MATLAB software to iteratively solve the system of Eq (7), when the calculation results converge, the stress intensity factors І K and П K at the crack tip can be obtained.…”

“…To validate the stress intensity factor calculation method proposed in this paper, the theoretical displacement for a mixed-mode I/Ⅱ crack (taking the first term of the Williams series) is applied to actual speckle pattern images to generate digital images of a mixed-mode I/Ⅱ crack with a 30° inclination angle. In the local coordinate system at the crack tip as shown in Figure 3(a), the formula for the theoretical displacement field is given by [18]: (10) In this paper, the values of І K and П K are specified as follows: І K = 50 To calculate the stress intensity factor based on the AD-DIC measurement of the displacement field (Figure 6) for this crack, it is necessary to solve the system of nonlinear equations composed of Eq (7), and this requires providing initial values for the variables. Based on the measurement results obtained through AD-DIC, the crack tip inclination angle was calculated to be 28.5°, and the crack tip coordinates were designated as 255 255…”

“…A total of 1240 displacement values from the region around the crack tip, as indicated by the blue markings in Figure 6, were selected. These values were then used as inputs in Eq (7), and MATLAB was employed to calculate the system of 2480 nonlinear equations.…”

“…Therefore, by employing DIC to calculate displacement values in the crack tip region and substituting them as known quantities into the equations represented by the Williams series, the stress intensity factor at the crack tip can be determined. Many researchers [7][8][9][10] have successfully computed stress intensity factors, using this straightforward and efficient method.…”

“…Figure 6. AD-DIC measurement results of a Mix-mode I/Ⅱ crack with a 0° inclination angle.To calculate the stress intensity factor based on the AD-DIC measurement of the displacement field (Figure6) for this crack, it is necessary to solve the system of nonlinear equations composed of Eq(7), and this requires providing initial values for the variables. Based on the measurement results obtained through AD-DIC, the crack tip inclination angle was calculated to be 28.5°, and the crack tip…”