Approximate Solutions of Characteristic Parameters of Stress Field at Crack Tip in Power Hardening Materials
1. College of Civil Engineering, Sanjiang University, Nanjing 210012, China
2. College of Harbour, Coastal and Offshore Engineering, Nanjing 210024, China
| Abstract: | The J-A two-parameter method proposed for the asymptotic analytical solution of type-I crack-tip field can effectively characterize the crack-tip stress field distribution and its constraint for power-hardening materials. This paper systematically summarizes commonly used methods for characterizing stress fields at crack tips. Taking the single-edged notched tension specimen as an example, the superiority of the J-A two-parameter method in characterizing the crack tip constraint of type I cracks is demonstrated. The J-A two-parameter method consists of three important parameters, including characteristic index, dimensionless integration constant and stress distribution angle function. Based on the existing high-order analytical solutions for the crack tip asymptotic field of power-hardening materials, a calculation program is compiled to compute these important parameters. High-precision empirical formulas for various parameters, ranging from low to high hardening levels, are obtained using the nonlinear fitting method with the determination coefficient R2 reaching above 0.999. Finally, two methods for calculating the constraint parameter A are presented. It is found that using the fitting method to determine the constraint parameter A in the fracture control zone is more reasonable. A formula for directly calculating parameter A is also provided. Combined with the fitting formulas for the three parameters, the crack tip constraint of the single-edged notched tension specimen is calculated. Results show that the proposed calculation formulas can obtain crack tip constraint parameter A with high precision, facilitating the wide application of the J-A two-parameter method. |
| Keywords: | Crack-tip Stress Field; J-A Three-term Solution; Characteristic Parameters; Nonlinear Fitting |
| DOI: | 10.57237/j.se.2023.05.002 |
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Received: 10 August 2023
Accepted: 25 September 2023
Published Online: 9 October 2023
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