Overview

Test Case

A sandwich seal made of an alumina plate with G-11 glass cladding on both sides is cooled at 3° per minute from 618°C to 460°C and held isothermally for four hours. The seal is further cooled at 3° per minute to 18°C. FInd the maximum in-plane stress (σ_max) developed in the seal along with the corresponding temperature.

Figure 310: Viscoelastic Sandwich Seal Problem Sketch

Material Properties	Geometric Properties	Loading
Material: G-11 Glass Material Variables H/R (°K) = 6.45e4 X = 0.53 No. of Maxwell Elements = 6 For Volume Decay Function Cfi = 0.108, 0.443, 0.166, 0.161, 0.046, 0.076 τfi = 3.00, 0.671, 0.247, 0.091, 0.033, 0.008 Cli = 3.43e-5 Cgi = 64.7e-7, 0.02e-7 Tfi(°) = 618, 618, 618, 618, 618, 618, GXY(0) = 2.79e4 GXY( ) = 0.0 K(0), MPa = 6.05e4 K( ), MPa = 6.05e4 No. of Maxwell Elements for Shear Modulus Relaxation = 3 Csmi = 0.422, 0.423, 0.155 λsmi = 0.0689, 0.0065, 0.0001 No. of Maxwell Elements for Bulk Modulus Relaxation = 0 Material: Alumina Material Variables Cgi = 52.6e-7, 0.119e-7, -1.0e-11 GXY(0), MPa = 1.435e5 GXY( ), MPa = 1.435e5 K(0), MPa = 3.11e5 K( ), MPa = 3.11e5 See Viscoelastic Material Constants in the Material Reference for more explanation regarding the material parameters.	a = 0.05 cm b = 0.325 cm	Reference Temp. = 618°C Temp. Offset = 273 Load Step 1; Uniform Temp. (TUNIF) = 618°C Load Step 2: TUNIF = 460°C TIME = 3160 sec. Load Step 3: TUNIF = 460°C TIME = 17560 sec. Load Step 4: TUNIF = 18°C TIME = 26400 sec.

Analysis Assumptions and Modeling Notes

The problem is solved first using 2D structural solid elements (PLANE183) and then using 3D structural solid elements (SOLID186).

In the 2D case, due to the fact that the stresses will be the same in X and Z directions because of symmetry, an axisymmetric analysis is performed with the nodal degrees of freedom coupled in appropriate directions. The radial thickness of 0.2 cm is arbitrarily selected. Nodes 21 through 25 are coupled in the X-direction (radial coupling). Nodes with the same Y-location are coupled in Y-direction (axial coupling).

In the 3D case, an arbitrary thickness of 0.2 cm is assumed in both Y and Z directions. Nodal degrees of freedom are coupled in appropriate directions to simulate the correct physical behavior in the finite element model.

The alumina is not a viscoelastic material, however, its material properties are input using viscoelastic format so that only one element type (PLANE183 in 2D and SOLID186 in 3D) can be used for both materials. Also, note that the viscoelastic material does not require the MP command for inputting the material properties. POST26 is used to extract the results from the solution phase.

Results Comparison

Figure 311: In-plane Stress Versus Temperature