MVD Design Review

SECTION 5: HYDROSCOPIC EXPANSION OF FOAM

5.1. PROBLEM STATEMENT

The "Rohacell" foam used in the framework expands when exposed to moisture. Jan Boisssevain quotes that the foam increases in length 0.22 mm over a length of 24.6 mm when the humidity is changed from 28% RH to 78% RH. The silicon panels do not undergo such an effect. There was, therefore, a concern that stresses might arise from the different rates of growth between the two materials.

5.2. HAND CALCULATION

Appendix 5A gives the details of a hand calculation that was done. The calculation assumes that the foam expands linearly while the silicon is stretched linearly. Therefore, bending of the silicon is not considered in this calculation. A compressive stress in the foam of 96.86 g / mm² occurs (Maximum compressive stress is listed as 154.7 g / mm²) A tensile stress of 219.3 g / mm² occurs in the silicon. (Silicon strength not available, but glass would be about 3500 g / mm² or higher) [To get units of PSI (lb / in²), multiply g / mm² by 1.422]

From the results of this hand calculation, it would appear that the strength of the foam is marginal, and the silicon is acceptable. Even this hand calculation raises some doubt about the suitability of the foam. The FEA analysis in the following sections shows that with bending allowed to occur, a potentially serious condition exists.

5.3. SINGLE C-MODULE FEA

A model was made using FEA of a single C-module. The module was constrained in the lateral directions (X, Y) about one of the holes through which the locating plastic tubes pass. The other hole was allowed to float. The model was restrained about its axial centerline. (Z direction) Modeling a single cell is considered reasonable, as the forces compressing the group of cells together are low, and therefore a single cell can grow axially without significant axial restraint.

The 0.22 mm growth in 24.6mm corresponds to a 0.008943 mm/mm strain over a 50% relative humidity change, or a 0.0001789 (mm/mm)/%RH coefficient of hydroscopic expansion. This was entered into the model as a coefficient of thermal expansion, with node temperatures being set at 50 deg temperature, corresponding to a 50% humidity change.

The model showed quite high stresses in the area where the silicon plates are attached to the foam. A Von Mises stress of 8,011 g / mm² (11,392 psi) occurs on the inner surface of the middle inside plate at the inside corners where the silicon joins with the foam. (See diagram) Stresses in excess of 4,500 g / mm² (6,399 psi) are typical in the model at foam-silicon interfaces. Note that tensile strength of 71WF foam is listed as only 323 psi. (227 g / mm²) Deflections higher than 2.0 mm (0.079 in) also occur in the structure. A serious problem would seem to exist.

It appears that the differential expansion between the foam and the silicon is causing a shear stress to occur where the foam is joined to the silicon. The differential expansion also causes the foam/silicon section to bend, with the silicon panel in the inside of the bend. This bending creating large fiber stresses in the thin (hence, low section modulus, [ / c] ) silicon panels. The most likely point of initial failure might be at the glue joint between the silicon panels and the foam. As the glue would probably be stronger than the foam, actual failure would probably be in the foam closely adjacent to the glue joint. It is possible enough foam might remain attached to the silicon so that the assembly might appear intact, and the panels in place, under a cursory inspection. It might take several humidity cycles for the effect to fully manifest itself. However, it is likely that under shock load or other external forces the plates would easily become detached after having been subjected to humidity changes.

5.4. FINE MESH FEA MODEL

The mesh used for the model of the C-module was fairly coarse, due in large part to element count limitation necessary to model the entire module. Perhaps most notable, but not the only instance, was that many of the 0.3 mm thick silicon plates were extremely off-cubic in aspect ratio. (It is desirable to have all the elements in an FEA mesh as close as practical to "Cubic" - with height, depth and width being the same.) It was decided to model a single silicon plate in a "window frame" of foam. A quarter section of this frame was modeled, as it was quadra-symmetric. By concentrating on a smaller portion of the C-module, a finer mesh would be possible without a prohibitively large problem. The finer mesh would enable a more accurate and detailed idea of what was happening at the silicon-foam interface.

The frame approximated a section of the silicon panel that is mounted on the outside of the C-module. In the model, the entire (not quarter section) silicon plate measures 74 mm long by 53 mm wide and is 0.3 mm thick. The side of the foam frame is 3 mm wide and 6 mm deep, and its 3 mm face is completely attached to the silicon. The foam end frame is 7 mm wide by 6 mm deep, with the silicon attached to a 1.5 mm strip on the inside edge of the 7 mm side. The mesh is based on a 1.0 mm cube size, although some elements are off-cubic to realize a practical model size.

The results are shown in the diagrams following the diagrams of the C-module model. The highest Von Mises stress is in between the silicon and foam, as would be expected from the previous results. It is at the corner, inside of the corner area instead of the edges of the frame. A value of 10,111 g / mm² (14,378 psi) is indicated. This is slightly more (26%) than the previous value, possibly due to the more refined mesh, but not to a degree which would indicate a major discrepancy with the C-module model. It appears the C-module model is obtaining somewhat accurate results, and that a problem actually exists. The stress in the foam falls off rapidly as distance from the interface increases, and the highest stresses are concentrated very near the interface. An upward (+Z) deflection of approximately 1.8 mm (0.10 in) (a quite notable amount) occurs at the corner of the frame. Without the constraints of the framework, notable and significant deflection is possible.

5.5. CONCLUSION

The expansion of the Rohacell foam due to humidity causes distortion in the framework and high stresses in the area of the foam-silicon interface. It is deemed that a potentially serious problem exists, with potential for non-functioning of the assembly.

5.6. RECOMMENDATIONS

A single silicon plate in a single frame (not a C-module) of Rohacell should be tested by exposing it to several cycles of humidity. This would test the silicon-foam interaction while isolating any secondary effects occurring in the C-module structure. Afterward, the foam-silicon interface should be closely inspected for cracking or separation.

Testing of the foam on a stress-strain tester should be done to get a more accurate idea of the foam's stress-strain curve and what the elastic limit of the material is. Effects in both compression and tension should be measured, as well as inelastic behavior. This would enable more realistic modeling of the structure.

Further, more careful, testing of the foam's expansion under humidity should be done. It appears that the curves of humidity versus expansion that were previously done did not allow the expansion of the foam to fully stabilize and level off at a constant value. The foam should be measured at some baseline relative humidity representative of ambient conditions in New Mexico, probably about 20%. It should then be exposed to some higher humidity until it has fully stabilized, while periodically measuring the expansion. This stabilization may take several weeks. 100% relative humidity may be easy to obtain by saturating a small sealed container with water. It is probably better that just one value of the higher humidity be used, rather than ramping-up through several steps of progressively increasing humidity. Several steps of humidity could confuse results and make postulation of a moisture-diffusion model more difficult. Paralyene coatings, as well as other coating, may be tried to see if they reduce total expansion reached at equilibrium, or only decrease the rate of expansion by decreasing the rate of water absorption.

Note that even quite slight changes of humidity theoretically result in stresses that exceed the yield point of the foam. Unless the humidity the foam is exposed to, during all phases of the foam's use, is controlled extremely carefully, to a degree that is probably not practical, some distortion or yielding of the foam in the C-module could occur. Coating the foam with paralyene may not be an adequate solution, as the coating may not sufficiently reduce even the short-term expansion. It is possible that the equilibrium expansion eventually reached by the coated foam may be similar to that of uncoated foam, only taking longer to occur.

Therefore, if it is desired to continue to use the Rohacell foam material in the final design, it may be desirable to use some sort of hold-downs that attach the silicon panels to the foam C-module while allowing the silicon to move relative to the foam. An other alternative could be a significantly thick layer of adhesive, such as RTV, that would be used to accommodate expansion differences between the foam and silicon. Other possibilities would be blocks of flexible material, possibly pre-cast RTV, between the silicon and foam; or designing the foam structure so that it attaches to the silicon panels by flexible legs or stand-offs that allow flexing to occur, constructed of foam or other materials.

It may be desirable to consider other materials besides the foam, if it is possible to do so, so late in the design. A major consideration is that the density of material must be kept low so that exiting particles are not impeded. "Density" in this case actually refers to (length)X(Relevant Particle Cross Section), however cross section generally is somewhat proportional to macroscopic material mass density, with some exceptions.

Carbon-epoxy laminates present a possible alternative. They offer a low density with a high strength.

Thin, bent structures of more conventional materials like sheet aluminum may be possible. Note that if the foam, density 0.075 g/cm³, which is 6 mm thick in the C-module, is ratioed with aluminum, density 2.70 g/cm³, a thickness of 0.167 mm (0.0065 in.) is obtained for the aluminum, based on (mass density) X (thickness), without cross-section considerations. Aluminum sheet 0.0065 inches thick, particularly if bent to stiffen it, might be used to construct a credible support for the silicon panels. The aluminum-silicon junction would have to be electrically insulated to avoid conduction between the panels.