Strength Prediction. Large deflection theory solves for the deflection of a disk as a function of loading and boundary condition. Stress is a derived parameter of this solution. Pressure failure testing gives a pressure loading at which the disk fails. By definition, the disk always fails when its failure strength has been exceeded. If large deflection theory is accurate, it should be able to predict the failure strength of the disk given the loading. Conversely, given the failure strength of sapphire, the theory should allow an accurate derivation of the load at failure. An exact correlation of prediction and experiment is not practical as a result of the variation in the failure strength of sapphire from piece to piece. The effects of polish strengthening broaden the failure strength range of sapphire.

There are three classes of disks tested for this program. The Union Carbide disks will be defined as Class 1 disks. These disks have the highest quality polish and are most likely to be polished strengthened. The standard 80/50 polish disks are defined as Class 3. These disks are characterized only by the fact that they meet optical standards for polish, and they are not expected to be significantly polish strengthened. The disks that have undergone non-standard polishing at TvU form an intermediate Class 2, which presumably consist of some disks that are polish strengthened, and some that are not. Experimental testing has demonstrated that even the Class 1 disks are not reliably strengthened.

Figure 15. Large deflection modeling compared with experimental results for a thin unclamped 50 mm diameter sapphire window: a) central deflection vs. load, and b) central stress vs. load.

The expectation of large strength variations in disks of the varying classes is best shown in the test data on the 25 mm diameter disks shown in Fig. 11. In this data set that includes samples from Class 1 and Class 2 the failure pressure varies by a factor of 19 as a result of one apparently unusually strong sample.

There is another piece of data that confirms the accuracy and relative magnitude of the failure pressure results for disk testing. The strain energy that is contained in the disk at the time of failure pressure is released during fracture. The higher the strain energy the smaller the pieces that result from the fracture. Figure 16 shows this phenomenon for a 2.5 cm diameter, 0.5 mm thick disk. The 100 mm diameter disks were tested with an adhesive backed paper attached to keep the pieces in place after failure. For the strengthened disks the 100 mm diameter disks failed such that the largest remaining pieces in the aperture were only a few mm in length. The fracture size results were totally consistent with the failure pressure results: disks that failed at low pressure broke into large pieces, while disks that failed at high pressure broke into very small pieces.

First the Union Carbide Class 1 disks will be considered. The tests on this material included sets of 12.5, 50, 75, and 100 mm diameter disks. One characteristic of the dependence of stress on load in the large deflection theory is that the central stress increases much less than linearly with load. This means that a small increase in strength will lead to a much larger increase in failure loading. At the same time, a small variation in failure load will imply approximately the failure stress.

A reanalysis was done for Phase 1 tests based on the results of large deflection modeling. Table 2 presents a summary of the failure testing results from Phase 1, plus the stress,σ _fc, at the center of the disk predicted by large deflection theory when the disk fails. In Table 1 d_w is the window diameter, t_w is the window thickness, HPS denotes high pressure side, LPS denotes low pressure side, d_a is the window aperture diameter, d_s is the diameter of the pressure seal. Disks with different polishes on one side were used because one-side polished disks are 30% cheaper, and it was originally thought that the cheaper disks would be

Figure 16. Photograph of a broken 50 mm diameter. 0.33 mm thick disk after failure testing.

adequate because the maximum stress would be only on one side, the side not facing the pressure. The two 100 mm diameter disks (Tests # 4 & 5) failed at approximately 5 and 6 atm. Large deflection theory indicates that the radial stress at the aperture was approximately 400 MPa, implying that the overall performance of the disk was limited by the strength of the matt polished side rather than the epi polished side. The stress at center of the disk on the low-pressure side was approximately 800 MPa, implying that the polish strengthening was at least a factor of 2.7.

Table 2. Phase 1 Sapphire disk pressure failure testing results.

The data on the 51 mm diameter disks leads to similar conclusions. Tests #1 and #3 provide the same evidence for failure of the matt polish, since the stress at the edge was approximately 400 MPa. Test #2 indicates failure at the center, again as a result of the matt polish. Tests # 6 and #7 give information on the failure strength of an epi-polished disk; test #6 indicates a factor of 1.7 strengthening, whereas test #7 indicates a factor of 3.3.

One added complication is that it was later discovered that only one side of the Union Carbide disks is guaranteed to be an epi polish; the other side is a "best effort" epi polish. Which side was which was not recorded for the Phase 1 tests. Phase 1 tests thus provide 6 data points for a polish strengthening of approximately a factor of 2 or more.

76 mm Disks. A set of Union Carbide 76 mm diameter disks finished were also pressure tested. All of the 76 mm diameter disks were tested after being brazed or soldered. This process first involves an aggressive metalization process of the sapphire to allow the joining metal to wet and bond to the sapphire.

Two of these were the disks that were soldered onto a microwave fixture during the Phase 1 program. The testing of these disks is also discussed in Task 2. Both of these disks were 76 mm diameter disks with a 63.5 mm aperture, and they both broke under 1 atm pressure. These disks had a matt finish on the high pressure side and an epi polish on the low pressure side. One disk broke immediately; the other broke after extensive deflection testing. The process of soldering to the copper fixture resulted in a central deflection of the disk of 0.15 mm toward the high pressure side. This deflection implies an equivalent loading of about 1/5 of an atm, which should not significantly affect the stress at the center of the disk. However, if the solder joint and its supporting copper provided a clamped boundary condition for the disk at the aperture, then the stress on the matt side of the disk would be approximately the normal failure stress of sapphire and this would explain the failure of the disk. The stress at the disk center would be far below what would be expected from the strengthening effect of the epi polish.

Using the large deflection theory for the case of a 32 mm radius, simply supported, immovable edge, the measured deflection at 1 atm pressure of approximately 1 disk thickness agrees with modeling. The predicted stress at the center of the disk is about 200 MPa, but a similar stress level is predicted to exist on the top of the disk at its edge. This is very close to the failure strength of matt polished sapphire, which is presumably why the disk broke. The theory thus agrees fairly well with this data. The shape of the deflection vs. radius is also well predicted. It should be noted that the linear theory predicts a factor of 6 higher stress.

A third failure test also used a 76 mm diameter disk with a 63.5 mm aperture, but in this case the disk was polished on both sides and face brazed to a thin kovar ring that had a 89 mm OD and 63.5 mm ID. This disk broke at a pressure of 3.7 atm, for which the predicted strength at the disk center is about 600 MPa, implying a 50% strengthening. This may imply that the brazing process has a negative impact on the strengthening.