4.7.5 Test 4: Cracks at a hole in a plate

Product: ABAQUS/Standard

Elements tested

CPE8 CPE8R CPS8 CPS8R

Problem description

Mesh:

Collapsed elements with 1/4 point midside nodes are used at the crack tip. One-quarter of the test geometry is modeled.

Material:

Young's modulus = 207 GPa, Poisson's ratio = 0.3

Boundary conditions:

along edge AB, along edge ED.

Loading:

Uniform stress, = 100 N/mm².

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 4.1 and 4.2 from NAFEMS publication “2D Test Cases in Linear Elastic Fracture Mechanics,” R0020.

Target solution: K/K = 1.050, K =

Results and discussion

The results are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.

Element Type	K/K
CPE8	1.060 (+0.9%)
CPE8R	1.059 (+0.8%)
CPS8	1.060 (+1.0%)
CPS8R	1.059 (+0.8%)

Remarks

K = . for plane stress, for plane strain. An average of the J values calculated by ABAQUS, excluding the first contour, is used in reporting the results. Experience has shown that the crack-tip elements do not give sufficiently accurate results to give good estimates of the J-integral for the first contour.

Input files

CPE8 elements.

CPE8R elements.

CPS8 elements.

CPS8R elements.