Residual Stress and Distortion – Ceramic Matrix Composites
Now that we have the analysis formulated to address the issues associated with fluid flow, reaction and thermal history the approach can be extended to predict the development of residual stresses and resulting component distortion in the final component. The residual stress generated during processing was calculated using the integrated solid mechanics solution capabilities to solve the equilibrium equation:
with the following constitutive relation:
where: is the elastic tensor and is the elastic strain.
Elastic strain is defined by the following set of relations:
total strain: (12)
thermal strain: (13)
dilatational strain: (14)
This approach treats the residual stresses at the continuum level based on any constraint that is applied to the fixtures during manufacturing and not at the constituent level of the individual ply layers. The mechanical properties a must be treated to reflect the changes that occur with temperature to the point that volumes of liquid cannot bear any load. When correctly integrated into the analytical routines prediction of the distribution residual stresses and the resulting component distortion can be made, see Figure 7.
Figure 7: Predicted distortion of CMC component after liquid infiltration and cooling.
The final two blogs in this series will consider how to integrate the functionality into a unified tool that can be used by engineers who are not experts in multiphysics computational analysis.
Thermal-Ceramic Matrix Composites
In addition to fluid flow and chemical reaction, the thermal response during infiltration of liquid is important to include in any analysis of the RMI process. For CMCs of interest for aerospace use the liquid is molten Silicon with a melting temperature of approximately 1687K, and during infiltration this thermal energy must be dissipated. In addition, heat is also generated from two other sources: first, latent heat of fusion on transition from liquid to solid and secondly, heat of reaction as the molten silicon reacts with the carbon preform to form silicon carbide. All the thermal effects occur simultaneously with the liquid infiltration and chemical reaction.
Thermal effects due to the temperature of the liquid and the phase change form liquid to solid can be easily incorporated into the heat transfer calculations. Heat transfer from the reaction can be calculated using energy balance equations for a porous media:
Volume averaging is used to account for the liquid and solid phases,
giving an equivalent thermal conductivity and
heat capacity of porous media as:
where the subscript “L” refers to the liquid phase and the subscript “S” refers to the solid perform.
Figures 7 and 8 compare the predictions from the analytical routines with experimental data for a range of assumed values of the heat of reaction and thermal conductivity.
Figure 7. Comparison of predicted temperature distribution showing effect of heat generation due to reaction.
Figure 8. Comparison of predicted temperature distribution showing effect of thermal conductivity
The next blog in this series will consider the development of residual stress and distortion in the CMC arising from phase changes and thermal mismatch. We welcome sharing of this information with your colleagues and coworkers.