Test 7: Axisymmetric – pressurized cylinder, secondary creep

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

CAX8R

CCL24R

Problem description

Material:

Young's modulus = 200 × 10³ N/mm², Poisson's ratio = 0.3, Creep law: $ε$ = A $σ^{n} t$ , A = 3.125 × 10⁻¹⁴ per hour ( $σ$ in N/mm²), n = 5.

Boundary conditions:

$u_{z} = 0$ on line AB and $u_{z} = 0$ on line CD.

Loading:

Prescribed pressure P = 200 N/mm² on line AD.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 7 from NAFEMS Publication Ref: R0027, “NAFEMS Fundamental Tests of Creep Behaviour,” June 1993.

\begin{matrix} σ_{r r} & ​ = 625.96 [1 - {(\frac{200}{r})}^{\frac{2}{5}}] \\ σ_{θ θ} & ​ = 625.96 [1 - 0.6 {(\frac{200}{r})}^{\frac{2}{5}}] \\ σ_{z z} & ​ = 625.96 [1 - 0.8 {(\frac{200}{r})}^{\frac{2}{5}}] \end{matrix}

Results and discussion

The results are shown in the following tables. The values enclosed in parentheses are percentage differences with respect to the reference solution. A graphic following each table gives a representation of the different stresses through the thickness of the cylinder.


Abaqus results for CAX8R elements
Radius	$σ_{r r}$	$σ_{θ θ}$
	(steady state)	(steady state)
100.0	−197.95 (−1.02%)	131.68 (1.00%)
125.0	−128.03 (−1.11%)	173.55 (0.49%)
150.0	−75.416 (−1.21%)	205.12 (0.27%)
175.0	−33.708 (−1.84%)	230.15 (0.16%)
200.0	0.499	250.67 (0.11%)


Abaqus results for CCL24R elements
Radius	$σ_{r r}$	$σ_{θ θ}$
	(steady state)	(steady state)
100.0	−197.95 (−1.02%)	130.38 (1.00%)
125.0	−128.03 (−1.11%)	172.70 (0.49%)
150.0	−75.417 (−1.21%)	204.12 (0.26%)
175.0	−33.707 (−1.85%)	230.15 (0.16%)
200.0	0.505	250.67 (0.11%)

Remarks

The total creep time for this test is 1000 hours. In the case where CAX8R elements have been used, four elements were used to model the cylinder. In the case where CCL24R elements were used, four elements were used in the radial direction and eight elements were used to model the full cylinder in the circumferential direction; that is, a total of 32 elements.

Input files

ncr7xr8x.inp: CAX8R elements.
ncr7xrccl24.inp: CCL24R elements.