windows were confused by the simultaneous deflection of the windows and the O-ring before the window came in contact with the flange. The recesses at the center of the flange were deep enough to assure that the flexing disks would not come into contact with the bottom of the flange during pressure testing. The deflection of the disk being tested was always measured to verify that no contact occurred. A small axial hole at the center of the flange assured that the window was holding pressure and provided access to measure disk deflection as well as a means for connecting strain gauges attached to the bottom of the windows.

Central deflection was measured using an inductive displacement sensor (Microstrain, Inc.). This device has a maximum non-linearity of approximately 0.4% its 8 mm full scale. It has a resolution of a few microns. Strain was measured at the center of the disks during pressure tests using standard resistance strain gauges with an accuracy of a few percent. Time response was not important for either measurement device.

Windows Tested. During the Phase I and Phase II programs approximately 75 windows of diameters between 12.5 mm and 102 mm were tested in a variety of ways. Window thickness varied from 0.33 mm to 3 mm.

More than 30 windows were tested to failure (see Table 1). Most of the windows were high quality sapphire; no bulk defects were observed in any of the windows. The major variable in window preparation was window polish. Surfaces varied in preparation from a matt finish to an almost epitaxial surface. Most of the windows tested were R-plane for reasons of cost, although some C-plane windows were tested.

Testing Techniques. Four basic types of testing were done. The primary test was failure testing; increasing the pressure on edge-sealed windows until they failed, measuring the failure pressure. Central deflection and central strain measurements were performed specifically to validate modeling. Measurements were recorded by a computer data acquisition system. The final type of testing was polish inspection, either using optical techniques or SEM imaging.

Data Analysis. Analysis of window failure pressure, central deflection, and central strain measurements was performed to achieve the following goals:

Table 1. Windows Failure Tested.

Diameter(mm)................. # Tested

......12.5..........................10

......25.............................. 9

......50.............................. 2

...... 75..............................3

.....100............................... 7

1) To show that large deflection modeling accurately predicts the experimental behavior of sapphire disks under pressure loading.

2) To determine the increase in the failure strength of sapphire that results from polish strengthening relative to the standard quoted strength of sapphire.

3) To predict the thickness reduction that could be achieved for a sapphire disk as a result of membrane effects compared with the standard window design that assumes a simply supported thin flexing disk.

4) To predict the maximum thickness reduction that can be achieved for a sapphire disk using polish strengthening, cantilevering, and membrane effects compared with the standard window design that assumes a simply supported thin flexing disk.

The major important physical effects that control the behavior of very thin edge mounted sapphire disks under pressure loading are:

1. Membrane effects (in addition to bending).

2. Failure strength of the sapphire.

3. Real edge boundary conditions.

Since all of these effects interact with each other, it is difficult to isolate each effect and assess how it affects the behavior of the disk under load. This work leads to the belief that large deflection theory provides a guide for analyzing these effects. A matrix of experimental tests that varies the polish, edge boundary conditions, and disk thickness relative to diameter has been used to achieve the stated analysis goals.

Strength Testing Without Membrane Effects. The discussion of data will begin with the analysis of the data where membrane effects do not dominate the stress performance of the disk. There are two available data sets to discuss for this case. The first data set was taken during work on a previous NASA contract. Tests were performed on 25.4 mm diameter, 1 mm thick, C-plane disks in a hydraulic fixture where the disks were O-ring sealed in the same manner used in this program. The sealing radius was 11.7 mm and the aperture radius was 9.5 mm. Disks with two types of polish were tested; a standard 80/50 polish, and an "epi" polish provided by INSACO (Quakertown, PA). The data is shown in Fig. 10. The average failure pressure is approximately 8 MPa for the standard disks, and 26 MPa for the selected epi polished disks.

Disk behavior during pressure testing is dominated by both polish strengthening and the edge boundary condition at the aperture diameter. The experimental and theoretical difficulty is to establish the magnitude of both of these effects separately. The separation is made more difficult because of the statistical nature of the strength of sapphire.

An exact analytic solution to the cantilevered disk problem has not been found during this program, except for the case of a specific radius ratio where the edge of the disk is in the plane of the aperture. The equation for the stress at the center of a simply supported disk is given in Eqs. 1 and 2, whereas the analogous equations for the clamped case are given in Eq. 3 for the central stress, and in Eq. 4 for the edge stress. The peak stress in the simply supported disk is at the center, whereas the peak stress for the clamped disk is at the edge and is approximately 60% less than that for the simply supported case. In some sense these conditions represent extreme specifications of bending at the edge of the disk - no edge bending for the simply supported case, and maximum bending forces for the clamped case. Where membrane effects are negligible, increased cantilevering decreases the stress at the center of the disk, which is also the maximum stress in the disk. At the aperture radius the stress for the cantilevered case is less than that of the clamped case until the amount of cantilevering is such that the slope at the aperture becomes horizontal. For cantilevering in normal configurations, the load that can be added beyond the aperture is limited by the condition that the outer edge comes in contact with the flange surface. This condition occurs at a radius ratio of approximately 0.7 and results in a reduction of the peak stress by approximately a factor of 2. Smaller radius ratios will give a smaller stress reduction, whereas larger ratios will give about the same reduction because the added load is absorbed in the contact between the outer edge and the flange.

Calculating the failure pressure of the 25.4 mm diameter, 1 mm thick disks using linear simply supported disk theory based on the standard 420 MPa strength of sapphire and the aperture radius gives a failure pressure of 3.8 MPa. The seal to aperture radius ratio is approximately 0.7. Assuming a stress reduction of a factor of 2, the predicted failure load is about 7.5 MPa. This is reasonable agreement with the data, although the number of samples is not large. The polish strengthened disks indicate an average strength increase of more than a factor of 3. It

Figure 10. Failure pressure of a set of 2.5 mm diameter, 1.0 mm thick sapphire windows with a standard 80/50 polish and a nominal epitaxial finish.

Figure 11. Failure pressure of a set of 25.4 mm diameter, 0.51 mm thick sapphire windows with a standard 80/50 polish (Tests # 1-4) and a nominal epitaxial finish (Tests # 6-10).

should also be noted that the set of four high strength windows was selected on the basis of a lack of flaws and then tested. Although there are only 4 samples the probability of choosing 4 high strength windows from a standard set is almost zero. These windows were not selected based on failure strength results.

A series of pressure failure tests (Fig. 11) were done on a similar set of 2.54 mm diameter, 0.51 thick disks during the development of polishing in Phase 2. The aperture and seal radii were approximately as in the NASA tests. These disks are still thick and small enough so that membrane effects are negligible. Figure 12 shows the failure pressure of 9 disks, four with a standard polish, and 5 with what was hoped to be an epi polish. Since the aperture is approximately the same as the NASA tests, and the thickness 0.5 times as much, the failure pressure would be expected to be approximately a factor of 4 less, or about 2 MPa, with strengthened disks 3-4 times as strong - or 6-8 MPa failure pressure.

One item of note is the large variation between weakest and strongest sample, a factor of 18.6 variation in strength. Given that the strengthened disks are often apparently not strengthened, the specially polished disks were inspected under the SEM. This inspection showed that while the center of the disks were polished without defects, most of the area of the disks were poorly polished, with the polish deteriorating toward the edge. In fact, near the edge the polish was not far different than the standard disks. The lack of strengthening was therefore explained by the lack of good polish, where the one high-strength case was probably just polished enough to achieve the strengthening effect. The cause of the problem apparently is associated with the extreme thinness of the disks - the polishing plates are so close together that the polishing debris is swept onto the edges of the disks again and proper polishing is not possible. It is important to note that the standard samples are normal commercial samples that would be obtained by an industrial sapphire user with no knowledge beyond the size specifications of an optical window.

There is no question that the highest failure pressure disk broke at a much higher stress level, because the breaking stress determines the size of the broken pieces. The broken pieces of this disk was much smaller in average size. The immovable edge cases do approach each other for large loading, differing by a small amount at 19 MPa. The predicted stress is 3 GPa, which is 5 times the nominal strength of sapphire. This seems high, but not impossible. Apparently the much higher pressure results from the change in slope of the stress vs. load curve - a much higher percentage change in load is required to cause the same percentage change in stress compared with changes at lower values of load. Presumably the strengthened disks entered into this less sensitive regime and allowed much higher loads to be tolerated. It thus seems that the 2.5 cm disks happened to be in a transition region of disk behavior, which accounts for the large variation in failure pressure.

Another relevant set of data was taken by testing 12.5 mm diameter, 0.5 mm thick disks. A set of random orientation, standard 80/50 polish windows were failure tested, together with a set of Union Carbide disks of the same dimensions cut out of a 100 mm diameter disk. The aperture radius was 3.85 mm, whereas the seal radius was approximately 5.2 mm, giving a radius ratio of about 0.75, and thus leading again to a stress reduction of about 30%. Calculating the failure pressure of the disks using simply supported disk theory based on a 420 MPa strength of sapphire and the aperture radius gives a failure pressure of 6.0 MPa. Accounting for the 30% stress reduction implies a failure pressure of about 8.5 MPa. Strengthening by approximately a factor of 3 would give a failure pressure of 27 MPa for epi polished disks.