Finite Element Analysis for Ceramics

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The underlying concept of any simulation is the simplification of the real world to enable it to be solved, and verifying if the results are useful. Even in the most straightforward problems, millions of variables could interact with one another. The natural course of events can only be estimated by approximating to simple rules.

Early Versions of Finite Element Analysis

A very basic example of this can be noted in certain oldest applications of finite elements. More than 2000 years earlier, geometers were keen on finding out the circumference and area of a circle. They achieved this by splitting the circle into rectangles, thereby approximately determining the area of the circle. Thus, the value of π was eventually determined.

Finite Element Analysis in the 1940s and 1950s

In the 1940s and 1950s, engineers had to develop a new aircraft design that reduced the weight to improve safety. The equations used then to design aircraft were not so accurate. In an effort to improve the design, digital computers were employed and the aircraft was divided into smaller sections, which were more easily calculable. From the 1960s onwards, this technique became very famous, and ultimately, these sections transformed into finite elements.

Modern-Day Finite Element Analysis

Currently, this technique can be applied to highly non-linear problems involving complex geometries, inelastic material behavior, and fluctuating process conditions. It has the potential to find solutions to problems involving temperature, deflection, stress, vibration, electrics, acoustics, and magnetostatics for a very wide range of materials, such as metals, plastics, ceramics, foams, and rubbers.

Applications

In the field of ceramics, a wider range of processes has been modeled. Simulations have been found to be useful while analyzing the effects of material, process, and design, beginning from stress calculation in a blast furnace refractory lining to thermal transfer in heat sinks, provided on printed circuit boards.

Refractory Linings

Widespread research has been carried out in the area of thermomechanical modeling of refractory linings. Assessing the effect of heating the lining on the brickwork’s stability is vital because thermal expansion makes the lining to apply pressure on itself and adjoining materials, for example, the backing linings or steel containment shell.

How joints behave in such an application is of particular interest as these could open up on the hot or cold face. Open joints on the hot face could result in condensation of gases or debris, which may eventually permeate into the lining and lead to variations in material integrity and hence its properties.

The FEA technique is beneficial as it indicates the problem areas that would be challenging to observe in the furnace due to dust or heat, or the fact that the problem exists within the lining. Once the potential problem area is ascertained, it would be feasible to employ the simulation to estimate the effect of modifying the geometry of the bricks, the material used, or even the containment vessel. Moreover, it could be possible to identify the effect of these anchors and to determine whether metal or ceramic anchors should be used.

Powder Flow

This technology can even be used for analyzing the behavior of powders at the time of fabrication. Granular materials are highly complex since their material properties tend to change as they become compact. It is feasible to model both die and isostatic pressing.

In die pressing, variations in density through the piece are vital to determine the product’s final shape. Since the dies employed to produce the items can be very costly, the potential to predict the way the process will work can be important in designing the tooling.

Another benefit is that the final shape of the piece can be predicted, thus minimizing the machining required to bringing the pressed component within engineering tolerances. This is an example where a material model with the ability to work in accordance with the general FEA framework has been developed.

CAD and FEA

One advantage of using an FEA package available readily in the market is that it is maintained up to date with the most recent developments in CAD technology. Files can be transferred from CAD for calculations within FEA. One such example is an H cassette used in a tunnel kiln to fire tiles. It is essential for the design of the component to allow excellent airflow surrounding the tile and support it while firing.

But the kiln furniture’s weight must be decreased to a minimum to improve fuel efficiency through the kiln. A CAD drawing acquired from the customer can be altered to a form suitable for FEA. Then, calculations can be performed to re-engineer the CAD drawing. Thus, the design engineer can gain maximum control of the geometry using the recommendations of the FEA engineer.

Setting Up a Finite Element Model

Setting up an FEA model necessitates the knowledge or analysis of various parameters. A further benefit of this approach is that the user can watch out for all process parameters (most importantly the shape of the component) and understand the behavior of the material and the process conditions.

Material Data

Listed below are the material data required for a basic FEA model:

• Thermal expansion
• Density
• Poisson’s ratio
• Thermal conductivity
• Stress/strain behavior in compression or flexure
• Creep
• Specific heat

These values can vary with the difference in temperature. Therefore, these changes must be incorporated into the model.

Process Data

Process conditions could be very difficult to model. As it can be challenging to understand the processes, the way a furnace is supported or the changes in temperature through a kiln must be assumed. Sometimes, it would be hard to simulate support conditions without creating a very large model, resulting in difficulty in interpretation and excessive run times. For example, if a furnace is supported on the ground and only what happens inside the furnace must be determined, it might not be essential to calculate the stresses in the foundations.

Moreover, process conditions can pose difficulties as a number of operations are performed under harsh conditions where it is hard to accurately measure temperatures due to erosion or corrosion. However, this is exactly where FEA engineers can use their knowledge and experience.

Conclusions

The use of computer modeling offers various advantages:

• More understanding about a process
• Confidence in radical design methods
• Predictive rather than reactive approach to design
• Eliminates the need for expensive and labor-intensive prototype development
• Reduces manufacturing defects
• Minimizes the time required for products to enter the market