Finite-sliding contact between coupled temperature-displacement elements

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

Elements tested
Features tested
Problem description
Loading history for interface conductance tests (Abaqus/Standard)
Loading history for interface radiation tests (Abaqus/Standard)
Loading history for frictional heat generation tests (Abaqus/Standard)
Simulation with Abaqus/Explicit
Results and discussion
Input files

ProductsAbaqus/StandardAbaqus/Explicit

Elements tested

C3D4T
C3D6T
C3D8RHT
C3D8RT
C3D8T
C3D10MT

CAX3T
CAX4RHT
CAX4RT
CAX4T
CAX6MHT
CAX6MT
CAX8T
CGAX4RHT
CGAX4RT
CGAX4T
CGAX6MHT
CGAX6MT
CGAX8T

CPE3T
CPE4RHT
CPE4RT
CPE4T
CPE4PT
CPE4RPT
CPE4PHT
CPE4RPHT
CPE6MHT
CPE6MT
CPE8HT
CPE8T
CPEG4RHT
CPEG4RT
CPEG4T
CPEG6MHT
CPEG6MT
CPEG8T

CPS3T
CPS4RT
CPS6MT

SC8RT
SC6RT
S8RT
SAX2T

Features tested

Contact pair

Gap conductance

Gap heat generation

Gap radiation

Problem description

The planar tests and three-dimensional tests consist of a small block pressed against a larger block that is fixed on the bottom. The smaller block slides horizontally on the larger block according to the prescribed loading and displacement history. The axisymmetric tests are essentially the same except that the sliding structures are rings; the outer ring is shorter axially than the inner ring. Relative motion in the axisymmetric tests is in the axial direction for the tests of axisymmetric elements or has axial and circumferential components for the tests of axisymmetric elements with twist. A smoothing factor of 0.05 is used on the contact pairs. For the three-dimensional tests a three-dimensional model with width 1.0 is used. The width of the bottom block is chosen slightly larger to ensure that the upper block contacts the lower block.

The mesh in Figure 1, used for planar tests, is representative of all meshes used in these tests.

Material:

Solid

Linear elastic, Young's modulus = 30.0 × 10⁶, Poisson's ratio = 0.3, conductivity = 10.0, density = 1000.0, specific heat = 0.001.

Interface

Friction coefficient (nonzero only for the frictional heat generation tests), $μ$ =0.1.

Gap conductance varies with pressure for the interface conductance tests, k(p=200) = 5.0, k(p=100) = 20.0.

Gap conductance (for the frictional heat generation tests), 20.0.

Gap radiation constants (for the interface radiation tests only), $F_{A}$ = $F_{B}$ =1.0 × 10⁻⁶, with absolute zero at $θ^{Z}$ =−273.16.

Loading history for interface conductance tests (Abaqus/Standard)

Step 1, transient:

A downward pressure of 100 is applied on top of the smaller block, and a flux of 100 is applied into the smaller block through its surface. The center element of the large block has a film condition with a film coefficient of 10.0 and sink temperature of 0.0 at the bottom face. This step is used to check the gap conductivity. Results should be symmetric about an axis that is parallel to the line joining the centers of the two blocks, and thermal equilibrium must be satisfied.

The heat conducted away from the larger block via the film condition should nearly equal the heat conducted through the interface—they need not be exactly equal because transient effects are included in this step. Input file eia2tssc.inp illustrates the procedure to specify a time-dependent variation of the film coefficient.

Step 2, transient:

The top block is made to slide horizontally, back and forth, over the bottom block to assure that the formulation does not fail under large relative sliding. The results are consistent with thermal equilibrium. In the tests of axisymmetric elements with twist, the top block slides with circumferential motion as well.

Step 3, steady state:

The top block is in the same configuration as at the end of Step 1 but is brought to steady state to eliminate transient effects. This allows for a more exact check on thermal equilibrium of the assembly because the heat conducted across the interface must equilibrate the heat passed into the assembly by the applied flux.

Step 4, steady state:

The pressure is increased on the top surface. This is designed to test pressure-dependent interface conductivity. The temperature change across the interface should be four times that at the end of Step 3 because the interface conductivity is reduced by one-fourth.

Step 5, transient:

The applied flux is ramped down quickly, and the small block is made to slide off the larger block. This is to test that the interface heat transfer is eliminated when a secondary node slides off the end of the corresponding main surface. The smaller block becomes insulated, and the temperature is constant throughout the block.

Loading history for interface radiation tests (Abaqus/Standard)

The loading is the same for these tests as for the interface conductance tests. These problems are designed to test radiation heat transfer in the interface. Since the radiative properties are not pressure dependent, the results for Step 4 are identical to Step 3 in these runs.

Loading history for frictional heat generation tests (Abaqus/Standard)

In this analysis the top (outer) surface of the smaller block is constrained to remain straight and nonrotating via constraint equations. In this analysis the Lagrange friction formulation is used. With this formulation all relative motion is converted into heat. The default friction algorithm uses an automatic penalty method, allowing small relative motions without dissipation. In these tests this would cause the generated heat to be underestimated by about 0.7%.

Step 1:: A downward force of 200 is applied to the top surface to establish contact (an inward force of 275 is applied for the axisymmetric tests). Virtually no heat generation occurs.
Step 2:: The top block is made to slide back and forth with friction. Assuming Coulomb friction, a total of 120 units of heat is generated. Of this generated heat 60 units are absorbed by the contacting bodies because the fraction of frictional dissipation converted to heat is specified to be 0.5. Results are consistent with thermal equilibrium. In the tests of axisymmetric elements with twist, the top block slides with both axial and circumferential components of motion. The magnitude of the relative motion and the resulting heat generation is the same as in the remaining tests.
STEP 3:: The assembly sits without thermal loading to reach steady state. Because the assembly is adiabatic, it should attain a constant temperature. Based on the amount of heat generated and the heat capacity of the material, the final temperature of the assembly should be 7.5 for the planar case and 0.68 for the axisymmetric case.

Simulation with Abaqus/Explicit

A transient simulation is performed for each step. The simulation time for those steps where Abaqus/Standard performs a steady-state analysis is chosen so that enough time is allowed for the Abaqus/Explicit solution to reach steady-state conditions. Mass scaling is used to obtain an efficient solution. The rate at which the top block is forced to slide over the bottom block is reduced to ensure a quasi-static response; the amount of relative sliding between the two blocks (and, therefore, the amount of frictional heat generation, for example) is unaffected by this change. Both kinematic and penalty mechanical contact are considered.