Ceramic Matrix Composites – Solidifying it all

Ceramic Matrix Composites – Solidifying it all


In the preceding Blogs on Ceramic Matrix Composites we have provided an outline of an intimately coupled multiphysics problem and how the controlling factors can be formulated to develop a predictive physics-based computational model. But what we really need to do if we are to help this technology develop and mature into real world applications is to take it out of the hands of the computational engineers and make it available for use by the manufacturing engineers responsible for developing the production technology that will give rise to real world components. To do this we need to remember that their skills lie in the production technology and not understanding nuances of complex multiphysics modeling.


In an attempt to provide analysis tools that the manufacturing world can use we have further developed the computational analysis discussed in the previous Blogs to allow domain specific users who are not experts in computational analysis to reliably use the computational analysis procedures through a user specific GUI to predict the CMC Manufacturing Process.


The computational tool operates in conjunction with COMSOL Multiphysics which provides the underlying finite element solver, geometry import and post processing capability. Two options of the software have been created:


  1. Option 1: Includes fluid flow, temperature, reaction kinetics, phase distribution.
  2. Option 2: In addition to the phenomena above the residual stress and component distortion are predicted.


A user specific GUI provides input windows with restricted input screens for specific parameters, in addition predefined inputs that are of interest to users are available as default selections. This provides the user with great flexibility and also allows them to input proprietary data relevant for their specific manufacturing technology and materials.


The input data appear in two forms:


  1. Application specific: These data represent critical information that may be specific to the user’s CMC materials and processing; these data generally require some level of knowledge.
  2. User specific: These data sets are for proprietary information that individuals may have for their CMC system but is difficult to measure directly and for which limited information is available in the open literature.


The components of interest to the end user are of sufficient complexity that continued rebuilding for individual analysis is prohibitive. In addition to providing the capability for the user to define simple shapes that are variants on 3D rectangles, functionality has been included to import typical parts of interest from existing CAD files. The user is automatically provided with standardized data output for the following parameters:


  1. Effective saturation
  2. Surface temperature
  3. Infiltrated mass as a function of time
  4. Component displacement
  5. Residual stress distribution


Examples of typical output data are provided in Figures 8-12. Additional output of interest to the user can also be obtained through post-processing of the analysis file.


Figure 8: Example output showing effective saturation

Figure 8: Example output showing effective saturation


Figure 9: Example output showing surface temperature

Figure 9: Example output showing surface temperature


Figure 10: Example output showing infiltrated mass as a function of time

Figure 10: Example output showing infiltrated mass as a function of time


Figure 11: Example output showing component displacement

Figure 11: Example output showing component displacement


Figure 12: Example output showing residual stress distribution

Figure 12: Example output showing residual stress distribution



The functionality demonstrated here has been implemented using the existing Physics Interface Builder tool in COMSOL Multiphysics. Further development of the analysis tool will integrate this functionality with COMSOL’s Application Builder to further improve ease of use and extend application. Further information on these developments will follow in future blogs when available. Stay Tuned!


Residual Stress and Distortion – Ceramic Matrix Composites

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:

Eq10       (10)

with the following constitutive relation:

Eq11  (11)

where:   Eq11-1        is the elastic tensor and Eq11-2is the elastic strain.


Elastic strain is defined by the following set of relations:

total strain:                      Eq12                         (12)

thermal strain:              Eq13                            (13)

dilatational strain:         Eq14                                    (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.

Residual Stress and Distortion

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

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:


Thermal Equation                         (7)


Volume averaging is used to account for the liquid and solid phases,

giving an equivalent thermal conductivity Eq7-1 and

heat capacity  Eq7-2   of porous media as:

Eq8                                                              (8)

Eq9                                               (9)

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.

Reaction-Ceramic Matrix Composites

Reaction-Ceramic Matrix Composites


In the last Blog we looked at analyzing fluid flow into a porous medium, in the manufacture of CMCs using the RMI process simultaneously with the fluid infiltration a reaction takes place between the infiltrating molten liquid and the porous preform. Thus the second step in developing a computational analysis of the RMI process for producing CMCs is to integrate the reaction behavior between the infiltrating liquid silicon and the porous carbon preform.

The reaction kinetics of the SiC formation are calculated using a general reaction kinetics equation with constants for the Si+C reaction:


Reaction Kinetics Equation                                (4)



Reaction Kinetics Equation Explained












The volume fraction of Si is obtained as:

volume fraction of Si                                                            (5)


The mass balance assumes that reaction proceeds to full completion and all Si transforms into SiC. To account for the effect of reaction termination, the mass balance can be modified as:


Reaction Termination Mass Balance Miodification              (6)





Integration of this approach in the model allows the distribution of SiC and Si species to be predicted as a function of both spatial location and time into the infiltration (Figure 6). Convection of the moving fluid and the reaction rate define the distribution of both species. The sum of the volume fractions of Si and SiC equals the total volume fraction of fluid.



Figure 6. Distribution of (a) SiC and (b) Si volume fractions along x=0

The next blog in this series will consider the issue of heat transfer associated with infiltration of molten silicon, reaction between the liquid silicon and the carbon preform, and heat evolved on solidification.

Fluid Flow in Ceramic Matrix Composites

Fluid Flow in Ceramic Matrix Composites

In a previous Blog we discussed some of the background to the production of Ceramic Matrix Composites (CMCs) using the Reactive Melt Infiltration (RMI) process. In this Blog we will address some of the issues associated with the first step in the process: infiltration of molten material into a porous preform.


Unsaturated flow through a porous media can be simulated using modified Richard’s and Darcy’s equation:






In this formulation, Darcy’s law provides the fluid velocity in the unsaturated media as:


Eq2 (2)





For which:




The effective saturation, relative permeability, and moisture capacity are functions of pressure:

Eq3 (3)




Results of the infiltration analysis show agreement with experimental results published by Einset for non-reactive flow (Figure 1) and reactive flow (Figure 2) in systems with different pore sizes.


Ceramics Matrix Composites-Fluid Flow1

Figure 1. Calculated and experimental acetone infiltration profiles for different pore diameter parameters.


Ceramics Matrix Composites-Fluid Flow2

Figure 2. Calculated and experimental infiltration profiles for silicon.


Once validated the analyses can predict other critical factors such as the flow front and its velocity during processing, examples are provided in 3 through 5.

Ceramics Matrix Composites-Fluid Flow3

Figure 3. Calculated saturation level as a function of infiltration time and distance from inlet.

Ceramics Matrix Composites-Fluid Flow4

Figure 4. Results of saturation during flow of Silicon into perform for infiltration times of 1s, 10s and 20s.

Ceramics Matrix Composites-Fluid Flow5

Figure 5. Distribution of the velocity in the fill direction for both layers at t= 1s.

The next blog in this series will consider the issues associated with the chemical reaction between infiltrating liquid and the porous preform, with specific focus on the infiltration of molten silicon into a porous carbon preform to produce a silicon carbide composite.