Test 1.1: Center 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. One-quarter 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:

$u_{x} = 0$ along edge AB, $u_{y} = 0$ along edge DE.

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 1.1 from NAFEMS publication “2D Test Cases in Linear Elastic Fracture Mechanics,” R0020.

Target solution: K $I$ /K $_{0}$ = 1.325, 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	K $I$ /K $_{0}$ (Coarse)	K $I$ /K $_{0}$ (Fine)
CPE8	1.325 (0.0%)	1.333 (+0.63%)
CPE8R	1.329 (+0.3%)	1.334 (+0.63%)

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

nlf11f8c.inp: CPE8 elements, coarse mesh.
nlf11f8f.inp: CPE8 elements, fine mesh.
nlf11r8c.inp: CPE8R elements, coarse mesh.
nlf11r8f.inp: CPE8R elements, fine mesh.