Test 4: Cracks at a hole in a plate

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

This page discusses:

ProductsAbaqus/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:

ux=0 along edge AB, uy=0 along edge ED.

Loading:

Uniform stress, σyy = 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: KI/K0 = 1.050, K0 = σπa

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 TypeKI/K0
CPE8 1.060 (+0.9%)
CPE8R 1.059 (+0.8%)
CPS8 1.060 (+1.0%)
CPS8R 1.059 (+0.8%)

Remarks

KI = JE. E=E for plane stress, E=E/(1-ν2) 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.