Understanding the creep behavior of the ceramic shell is important because shell distortion at high temperatures must be minimized during the metal casting process.

The investment casting process is widely used for the production of small- and medium-sized parts of precision metal castings having complicated geometries. The process starts by dipping a foam or wax pattern in a slurry of ceramic powders (e.g., fused silica, zircon, alumina, etc.). Refractory powders (stucco) are next applied to the slurry coated pattern. The pattern is then removed from the ceramic shell by melting the wax or thermally decomposing the foam. Finally, the ceramic shell is cleaned of the pattern residue and fired to provide enough strength to hold the pressure of the liquid metal during the casting process.

Understanding the creep behavior of the ceramic shell is important because shell distortion at high temperatures must be minimized during the metal casting process. The high-temperature stability of the ceramic shell must be maintained in order to provide metal castings with precise dimensions.

### Creep Background

Creep is defined as the time-dependent deformation of a material that takes place at temperatures greater than one-half of its melting point. A typical creep curve is shown in Figure 1, where elongation is plotted vs. time. The three stages of creep behavior are:

- Primary—the rate of creep (dɛ/dt) decreases
- Secondary—the rate of creep (dɛ/dt) is constant; this is the region of steady-state creep
- Tertiary—the rate of creep (dɛ/dt) increases; this is the region of accelerating creep, which leads to failure

As shown in Figure 2, increasing either the temperature or stress results in both a greater strain to failure and a shorter time to failure. Classical creep analysis usually involves the determination of the steady-state creep rate as a function of stress and temperature. The equation describing the creep behavior in the steady state creep region is:

where A=a constant, gs=grain size, a=grain size exponent, σ=applied stress, n=stress power law exponent, Q=activation energy for creep, R=gas constant, and T=temperature. A linear regression of the log-log form of Equation 1 is used to determine the constant n. Holding the grain size and temperature constant, Equation 1 becomes:

where K=a constant. The log-log form of Equation 2 then becomes:

A plot of log(dɛ/dt)steadystate vs. log σ is shown in Figure 3. The slope of the resulting plot yields the stress power law exponent, n. The significance of the stress power law exponent is that it can be used to determine creep mechanisms. The value of n can be related to a physical process that contributes to the creep behavior. For example, a value of 1 is associated with diffusion or viscous flow processes, a value between 2 and 3 is associated with grain boundary sliding processes, and a value of 3 is associated with dislocation processes.

A linear regression of the ln-ln form of Equation 1 is also used to determine the constant Q. Holding the grain size and stress constant, Equation 1 becomes:

where K’=a constant. The ln-ln form of Equation 4 then

becomes:

A plot of ln(dɛ/dt)steadystate vs. 1/T is shown in Figure 4. The slope of the resulting plot yields the activation energy for creep divided by the gas constant, -Q/R. The significance of the activation energy for creep is that it can be used to determine creep mechanisms. The value of Q can be related to a physical process that contributes to the creep behavior. For example, values of Q can be associated with the activation energies for diffusion, viscous flow, grain boundary sliding and dislocation processes.

### Experimental Procedure

A schematic of the test apparatus is shown in Figure 5 (p. 25). The creep test frame and furnace was manufactured by Applied Test Systems (model number 2390). The furnace was equipped with molybdenum disilicide heating elements capable of reaching 1,700°C. The laser was manufactured by LaserMike (model number PS2140).

Alumina fixtures were used for the water-cooled load rams, support block, and top load rod and bottom support rods. The top load rod and support rods were positioned to provide three-point flexural loading.

The bottom support rod span was 3 in. in length. The samples were 3.5 in. (l) x 1 in. (w) x 0.5 in. (d). The laser beam was positioned to monitor the vertical distance between the top load rod and bottom support rods. Thus, the mid-point deflection of the sample was measured relative to the bottom support rods. Data acquisition hardware/software was used to continuously measure the mid-point deflection. The test procedures were as follows:

1. Samples were placed on the bottom support rods with the 0.5 in. dimension in the vertical (axial) direction.

2. The laser beam was aligned to measure the mid-point deflection.

3. Samples were heated at a rate of 5°C per minute until the test temperature was reached.

a. To determine the stress power law exponent, n, samples were heated to constant temperature of 1,550°C. After a 30-min hold at 1,550°C, the load was applied. The applied stresses were 15 psi, 50 psi, and 130 psi. The stresses were maintained for 2 additional hours before the samples were allowed to cool down.

b. To determine the activation energy for creep, Q, samples were tested at a constant stress of

100 psi. The samples were held at temperatures of 1,530°C, 1,565°C, and 1,600°C for 30 min prior to the application of the load. The temperatures were maintained for 1.5 additional hours before the samples were allowed to cool down.

4. The resulting strains were calculated from elastic beam theory using the following equation:

where D=the mid-point deflection, d=the sample depth, and L=the lower support span.

### Results and Discussion

The test results at a constant temperature of 1,550°C and variable stresses for the determination of the stress power law exponent, n, are shown in Figure 6 (p. 26) for a typical investment casting shell composition. Linear regression was performed over the 1 to 2-hr timeframe, where steady-state creep was assumed. A plot of log(dɛ/dt)steadystate vs. log σ is shown in Figure 7 (p. 27). The slope of the resulting plot yielded a stress power law exponent of 0.93. This result can be associated with either diffusion or viscous flow processes.

The test results at a constant stress and variable temperatures for the determination of the activation energy for creep, Q, are shown in Figure 8 for a typical investment casting shell composition. Linear regression was performed over the 0.5 hour to 1.5 hour time frame, where steady-state creep was assumed. A plot of ln(dɛ/

dt)steadystate vs. 1/T is shown in Figure 9. The slope of the resulting plot yielded an activation energy for creep of

500.6 kJoules/mole. This result can

be associated with either diffusion controlled sintering or viscous

flow processes.

### Summary

The flexural creep of ceramic investment casting shells was measured using a non-contact laser extensometer-based technique. Experiments as a function of stress at constant temperature and as a function of temperature at constant stress were used to determine fundamental creep mechanisms. Understanding the operative creep mechanisms can provide insight for modification of the chemistry and microstructure of ceramic shell molds in order to enhance their creep resistance.