Nonuniform crack-face loading and J-integrals

This example verifies nonuniform crack-face loading in two-dimensional and three-dimensional analyses.

This page discusses:

ProductsAbaqus/Standard

Problem description

For the two-dimensional case an edge crack of length 1 m is modeled in a linear elastic specimen. The results are effectively for an infinitely long plate. The geometry is symmetric about the crack line, so only the top half is modeled. The geometry is meshed using CPE8R elements. The crack faces are loaded in five steps. In the first step a load of constant magnitude 1 MPa is applied. In all subsequent steps the load is zero at the surface of the specimen and has magnitude 1 MPa at the crack tip. The load varies linearly in Step 2, quadratically in Step 3, cubically in Step 4, and quartically in Step 5.

For the three-dimensional case the model../SIMAINPRefResources/3DDoubleEdgedNotchC3D20_model.py is modified to apply a uniform crack-face loading via user subroutine DLOAD.

Results and discussion

Results for the two-dimensional and three-dimensional analyses are discussed in the following sections.

Two-dimensional results

Abaqus results are compared with the results taken from page 8.8 of The Stress Analysis of Cracks Handbook by H. Tada, P. C. Paris, and G. R. Irwin. The crack-face loading is given by p=xγ MPa. Results for the J-integral in Pa are presented in Table 1.

Input files

pjinnu2d.inp

Checks the nonuniform loads applied to plane strain elements via user subroutine DLOAD.

pjinnu2d.f

User subroutine DLOAD used in pjinnu2d.inp.

pjinnu3d.inp

Uses subroutine DLOAD and, therefore, “nonuniform” load types, to apply a uniform load to the crack faces.

pjinnu3d.f

User subroutine DLOAD used in pjinnu3d.inp.

Tables

Table 1. J-integral results in Pa.
γ0 1234
Tada et al. 17.98 6.67 3.94 2.78 2.27
Abaqus 18.57 6.81 4.01 2.81 2.16

Figures

Figure 1. Crack model.