Interpolation methodology for elastic–plastic J-integral solutions for surface cracked plates in tension

• A solution database for elastic–plastic surface cracks in tension is generated.
• The solutions provide the full three-dimensional elastic–plastic J-integral values.
• The solutions cover a wide range of crack geometries and materials.
• Methods are developed to interpolate between the solutions.
• A computer program is provided for easy access to the solutions.

No closed form solutions exist for the elastic–plastic J-integral for surface cracks due to the nonlinear, three-dimensional (3-D) nature of the problem. Traditionally, each surface crack case must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3-D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 ⩽ a/c ⩽ 1.0, depth: 0.2 ⩽ a/B ⩽ 0.8) and material flow properties (elastic modulus to yield ratio: 100 ⩽ E/σys ⩽ 1000, and hardening: 3 ⩽ n ⩽ 20). The authors have developed a methodology for interpolating between the geometric and material property variables that allows the user to reliably evaluate the full elastic–plastic J-integral and force versus CMOD solution; thus, a solution can be obtained very rapidly by users without elastic–plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format as well as a computer program for calculating the interpolated solutions.