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Representative Input Material Parameters

In addition to the height and width, the aspect ratio of the EMF mesh could also be varied. The metallic mesh aspect ratio is given by SWD/LWD where SWD is the short way of the diamond and LWD is the long way of the diamond, as described by Dexmet, a commercial producer of EMF.

Figure 3. Von-Mises stress patterns due to thermal air-to-ground heating cycle. EMF mesh bleed-through is evident in the central portion of the figure, and relatively large displacement variations are observed above the metal and voids. Note that the displacements have been magnified for illustrative purposes.
The material properties needed for each of the layers were the CTE, heat capacity, density, thermal conductivity, Young's Modulus, and Poisson's ratio. Many of these parameters have a dependency on temperature, but for the simple model references here, researchers used the values across the temperature range of interest. The one exception was the CTE of the paint layer where a step function was employed at the glass transition temperature.

The paint had a larger CTE, heat capacity, and Poisson's Ratio than the underlying layers. Among other effects, this meant that the paint would undergo compressive stress when the layers were heated, and tensile strain when cooled. Hot materials under stress relax through creep, but this effect was not included in this particular model. For the other material parameters used, the density, thermal conductivity, and Young's Modulus were larger than the paint layer. In particular, for the EMF, Al has a larger CTE than Cu, and a smaller Young's Modulus.

Simulation Results

For the purposes of this research, Boeing confined its simulations to heating over a representative air-to-ground temperature range that the surface protection scheme was expected to perform. The resulting false color Von-Mises stress and displacement patterns are shown in Figure 3. In this figure, the view is from the top paint layer with cross-sectional views from the four sides. Obviously, the displacements have been magnified to highlight the movement that is induced by the temperature cycle. In the central portion of the figure, the pattern of the underlying EMF can be seen.

Variations in the displacement above the metal mesh and voids are quite evident in the cross-sectional profiles. Also, high stress (red—high, blue—low) can be seen in the mesh itself and the region in the mesh voids where surfacer material was modeled. The profiles show that the stress decreases from the bottom to the top of the surface layers. High stresses are clearly indicated in the EMF, where a semi-transparent stress image was generated.

A more quantitative examination of the EMF stresses and displacements could be determined by creating profiles along a selected path through the metallic layer. For this profile, the EMF was composed of Al with a SWD/LWD ratio of 0.50. It was expected that the profile would show five transitions as each metal-void region is crossed.

The arrows in Figure 4 indicate central locations where stress and displacements were determined for parametric variations of EMF SWD/LWD ratio, width, and height. These determinations were made for both Al and Cu EMFs. The nominal SWD/LWD ratio was 0.50. Fiberglass was modeled above and below both Al and Cu, but in practice is used only below the Al EMF.

For the variation of SWD/LWD from 0.25 to 0.75 for both Al and Cu, the displacement decreased slightly with an increasing SWD/LWD ratio. A higher SWD/LWD ratio corresponded to a more open mesh structure (as shown in Figure 2), resulting in lower metal density and hence lower weight. Also, inclusion of fiberglass below the Cu increased the displacement.

By varying the EMF width by a factor of 2.6 for both Al and Cu, the displacement remained essentially constant, but was significantly greater for Al than Cu. Varying the EMF height by a factor of 2.7 for both Al and Cu resulted in a displacement that increased with metal height and was also significantly greater for Al than Cu.

Boeing used a representative temperature dependence of the CTE for the paint layer to simulate the effect of a shift of the glass transition temperature, tg, from within the nominal temperature range to above it at 350 K. This variation permitted the examination of what occurs if the paint CTE remains constant throughout the nominal operating range.

There was a reduction in the surface displacement of the paint when the tg was above the maximum expected operating temperature. However, when the tg was above the operating temperature range, the paint remained in a more brittle, glassy state, which is expected to be prone to crack formation. Moving the tg below the operating range reduced the modulus that may compensate for the increased CTE that would occur. Such trade studies will be the subject of future simulations using this model.