Thermal Stresses in a Layered Plate

Thermal Stresses in a Layered Plate

Thermal Stresses in a Layered Plate

The thermal stress in a layered plate is studied in this example. A plate consisting of two layers, a coating and a substrate layer, is stress and strain free at 800 degrees C. The temperature of the plate is reduced to 150 degrees C and thermal stresses are induced due to the difference in coefficients of thermal expansion. A third layer, the carrier layer, is then introduced in a stress-free state. Finally, the temperature is reduced to 20 degrees C, and as a result, there are thermal stresses in all layers.

Introduction

In this example, thermal stresses in a layered plate are analyzed. The plate consists of three layers: a coating, a substrate, and a carrier. The coating is deposited onto the substrate at a temperature of 800  ͦC. At this temperature both the coating and the substrate are stress-free. During the first stage of the analysis, the temperature of the plate is lowered to 150  ͦC, which induces thermal stresses in the coating/substrate assembly. At this temperature the coating/substrate assembly is epoxied to a stress-free carrier layer. During the second stage of the analysis, the temperature in the entire assembly is lowered to 20 ͦC, and the thermal stresses are examined.

Model Definition

The plate is considered to be thick and therefore in a state of plane strain. It is modeled using the 2D Solid Mechanics interface. The geometry of the plate is shown in Figure 1. The bottom layer of the geometry is the carrier, the middle layer is the substrate, and the top layer is the coating.

Figure 1. The plate geometry.
Figure 1. The plate geometry.

Material Properties

The three layers are modeled as isotropic and linear elastic. Their coefficients of thermal expansion are constant. The material properties of the layers are shown in Table 1, Table 2, and Table 3.

MATERIAL PROPERTYVALUE
E215 GPa
ν0.3
r1000 kg/m3
a6.6·10-6 K-1
MATERIAL PROPERTIES OF THE CARRIER.
MATERIAL PROPERTYVALUE
E130 GPa
ν0.28
r1000 kg/m3
a3·10-6 K-1
MATERIAL PROPERTIES OF THE SUBSTRATE.
MATERIAL PROPERTYVALUE
E70 GPa
ν0.17
r1000 kg/m3
a5·10-6 K-1
MATERIAL PROPERTIES OF THE COATING.

– Activation of the Carrier

The carrier is only present at the second stage of the analysis. The activation of this layer is readily performed using the Activation sub-node under Linear Elastic Material. Note that the carrier will be activated in a stress-free state, even though its strain reference temperature (800 °C) is different from the temperature at activation.

– Loading and Boundary Conditions

Loading on the plate consists of an applied homogeneous temperature field. First, the temperature of the coating and substrate is reduced from the initial temperature 800 ͦC to 150 ͦC. During this temperature change, the carrier is not yet present. At 150 ͦC, the carrier is activated using the Activation sub-feature, and the temperature of the whole assembly is reduced to 20 ͦC.

The plate is constrained using the Rigid Motion Suppression feature.

Results and Discussion

Figure 2 shows the normal stress in the x direction after the first stage of the analysis. The substrate material has a higher coefficient of thermal expansion than the coating material. This means that the substrate shrinks more than the coating, causing tensile stresses in the substrate area next to the coating and compressive stresses in the coating.

Figure 2. Normal stress in the x direction for the first stage of the analysis.
Figure 2. Normal stress in the x direction for the first stage of the analysis.

Note that during the first stage of the analysis, the carrier is inactive.

Figure 3 shows the normal stress in the x direction after the second stage of the analysis, where the temperature is lowered to 20 ͦC. The stress levels in the substrate have increased slightly near to the coating, as have the compressive stresses in the coating compared to after the first stage.

Figure 3. Residual thermal stress at room temperature.
Figure 3. Residual thermal stress at room temperature.

The coefficient of thermal expansion is higher in the carrier than in the substrate. As the temperature is decreased, the carrier experiences tensile stresses, while the substrate near the carrier experiences compressive stresses.



Source: COMSOL Blogs, Models, Cyclopedia

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