Test 2.1: Single edge cracked plate in tension

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. A coarse and a fine mesh are tested.

Material:

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

Boundary conditions:

$u_{y} = 0$ along edge ED, $u_{x} = 0$ at point D.

Loading:

Uniform stress, $σ_{y y}$ = 100 N/mm².

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 2.1 from NAFEMS publication “2D Test Cases in Linear Elastic Fracture Mechanics,” R0020.

Target solution: K $I$ /K $_{0}$ = 3.0, K $_{0}$ = $σ \sqrt{π a}$

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	Coarse Mesh	Fine Mesh
CPE8	2.911 (−2.95%)	3.007 (+0.25%)
CPE8R	2.938 (−2.08%)	3.008 (+0.26%)

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

nlf21f8c.inp: CPE8 elements, coarse mesh.
nlf21f8f.inp: CPE8 elements, fine mesh.
nlf21r8c.inp: CPE8R elements, coarse mesh.
nlf21r8f.inp: CPE8R elements, fine mesh.