Test 6: Compact tension specimen

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:

Elements tested
Problem description
Reference solution
Results and discussion
Remarks
Input files

ProductsAbaqus/Standard

Elements tested

CPE8

CPE8R

Problem description

Mesh:

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

Material:

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

Boundary conditions:

$u_{x} = 0$ at point A, $u_{y} = 0$ along edge BA.

Loading:

Concentrated force, P = 1000 N.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 6 from NAFEMS publication “2D Test Cases in Linear Elastic Fracture Mechanics,” R0020.

Target solution: K $I$ /K $_{0}$ = 9.659, K₀ = $\frac{P}{t \sqrt{w}}$

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 $I$ /K $_{0}$
CPE8	9.572 (−0.9%)
CPE8R	9.639 (−0.2%)

Remarks

K $I$ = $\sqrt{J E / (1 - ν^{2})}$ . 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

nlf6xf8x.inp: CPE8 elements.
nlf6xr8x.inp: CPE8R elements.