A simplified estimation method for tensile softening curve of quasi-brittle materials

Abstract

Based on cohesive zone model (CZM), a simplified method for estimating the tensile softening curve of quasi-brittle materials is proposed. First, assume that the virtual crack opening displacement is linearly distributed. According to Castigliano's theorem, a cohesive displacement proportional function $fk(a_0,a)$ is proposed, which can obtain Crack Tip Opening Displacement (CTOD) directly from Crack Mouth Opening Displacement (CMOD). This simplifies the governing equations of CZM and the tensile softening curve can be obtained quickly. Finally, the effectiveness of the method is verified by experiment and finite element.

Highlights

1. A simplified method for estimating the tensile softening curve of quasi-brittle materials is proposed.

2. The proposed simplified method does not require sophisticated mathematical techniques or finite element modeling.

3. The effectiveness of this method is verified by previous experimental results and finite element simulations.

4. It is reasonable to assume that the crack opening displacement in the fracture process zone conforms to the linear distribution.

5. The cohesive displacement proportional function $fk(a_0,a)$ is proposed. CTOD can be directly obtained from CMOD using the $fk(a_0,a)$ function.

Keywords:

• Tensile softening curve
• traction-separation relationship
• fracture process zone
• linear displacement assumption
• cohesive displacement proportional function
• weight function

Additional information

Funding

This work was supported by the Natural Science Research Project of Department of Education of Guizhou Province, China (Project No. Qianjiao He KY [2020]118) and the Fund of Department of Science and Technology of Guizhou Province (Project No. [2019]1291; [2019]5620; [2014]7457) and the Fund of Department of Education of Guizhou Province (Project No. XKTJ[2020]23; [2016]02; [2012]017; [2018]029; [2018]380).