Test 10C: 2D plane stress – biaxial (negative) stepped load, primary 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:

ProductsAbaqus/Standard

Elements tested

CPS8R

Problem description



Material:

Young's modulus = 200 × 103 N/mm2, Poisson's ratio = 0.3, Creep law: ε = Aσn⁢tm, A = 3.125 × 10−14 per hour (σ in N/mm2), n = 5, m = 0.5.

Boundary conditions:

ux=0 on line AD and uy=0 on line AB.

Loading:

σ1 = 200 N/mm2 for t≤​ 100 hours and σ1 = 250 N/mm2 for t>​ 100 hours;

σ2 = −200 N/mm2 for t≤​ 100 hours and σ2 = −250 N/mm2 for t>​ 100 hours.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 10(c) from NAFEMS Publication Ref: R0027, “NAFEMS Fundamental Tests of Creep Behaviour,” June 1993.

  εx⁢xc=-εy⁢yc=0.135⁢t for t≤​ 100 hours
Time hardening: εx⁢xc=-εy⁢yc=0.4120⁢t-2.7699 for t>100 hours
Strain hardening: εx⁢xc=-εy⁢yc=0.4120⁢t-89.2605 for t>100 hours

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.

Abaqus Results
Time HardeningStrain Hardening
tεx⁢xctεx⁢xc
0.00 0.0000 (0.00%) 0.00 0.0000 (0.00%)
0.52 0.0976 (−0.19%) 0.52 0.0978 (−0.05%)
8.39 0.3909 (−0.03%) 8.39 0.3910 (0.00%)
76.78 1.1828 (−0.01%) 76.78 1.1829 (0.00%)
136.78 2.0483 (−0.01%) 136.78 2.8399 (−0.22%)
176.78 2.7077 (−0.01%) 176.78 3.8541 (−0.01%)
200.00 3.0564 (0.00%) 200.00 4.3354 (0.00%)



Remarks

The total creep time for this test is 200 hours. The times listed in the above table are the times calculated by the Abaqus automatic time stepping algorithm with CETOL = 5. × 10−3.