# Impact and Fracture Mechanics Assessment of a Fused Silica Window

## Analysis

## Objective

Determine the survival probability of a fused silica window subjected to a large particle impact event within a hypersonic wind tunnel using numerical methods (LS-DYNA) and fracture mechanics theories for brittle solids. If damage is predicted, provide an assessment of the windows’ service life under repetitive pressure cycling of 14 psi.

A finite element (FE) solid model of a 18” diameter, 1.5” thick disk was constructed based on information provided by the engineering team at Arnolds AFB (see Appendix). The FE model idealized a fused silica window that was potted into a steel frame using Ultracal 60 cement. The window is subjected to a differential pressure of 14 psi during hypersonic wind tunnel operation. This pressure tends to bow the window outward into the wind tunnel (internal side).

It is hypothesized that there exists a potential, during a specific wind tunnel test, for large particle debris (Pyroceram) to impact the window at

high velocities (12.27 ft/s tangential and 10.18 ft/s normal to the window). A nominal particle size was determined (see Appendix) and idealized

as a sphere with a diameter of 42.90 mm.

Mechanical property data for fused silica and Pyroceram 9606 is presented in the Appendix. It should also be noted that the mechanical

properties for fused silica are similar at 25 and 176C. Data for Pyroceram 9606 at 176 C was not available but is believed to follow a similar trend

as that for fused silica.

The analysis approach consists of model validation, impact simulation and interpretation of the results using fracture mechanics for brittle solids.

Auxiliary static stress models are also used to provide additional substantiation of the fracture mechanics predictions.

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The debris particle (Sphere with 42.90 mm (1.689”) diameter) was impacted against the fused silica window at a velocity of 3739.9 mm/s tangential and 3102.9 mm/s normal. The model was used to provide an idea of the peak stress during impact but more importantly, a peak contact force. It is this peak contact force that was leveraged for subsequent fracture mechanics analysis.

This figure presents data for cone cracking as a function of load (kN) and indenter radius in soda-lime glass. It can be assumed that the same trend would hold for fused silica. Data at a sphere radius of 20 mm is approximately close to the nominal particle size of 21.45 mm (42.90 mm diameter) to be of engineering use. At the figure’s maximum sphere radius, the maximum normal load is 2,100 N (472 lbf) for cone-crack formation. LS-DYNA results calculate a maximum normal load of 9,400 N (2,110 lbf). This value exceeds the limit shown in the above figure and a high probability of cone-crack initiation is predicted for the wind tunnel impact event.

At this stage of the analysis, it is probable that a crack has formed on the surface of the window from the impact of a Pyroceram particle. Having a small crack in the window does not necessary mean that the window will catastrophically fail. What determines the survivability of the window is how deep this crack penetrates. Analytical formulas for crack length prediction from an impact event are not available leading to a more general inference of crack penetration. From the prior page, a tensile stress field of greater than 7 MPa exists up to 6 mm deep into the window due the large particle impact (42.90 mm diameter). This tensile stress field would initiate and propagate a crack size to a length of 5.74 mm (0.226”). This logic would conclude that the large particle impact would initiate and propagate a crack 5.74 mm deep into the window. This then provides a starting point to determine if the fused silica window will be stable or catastrophically fail under the applied differential pressure of 14 psi.

From the prior arguments, it is reasoned that a crack of 5.74 mm (0.226”) exists in the fused silica window from the impact of a large particle. Further crack propagation is driven by the tensile tresses state due to the applied differential pressure (14 psi). The stress intensity for a edge crack under bending (which approximates the window bending due to the pressure load) is given by Barsom and Rolfe. Performing some basic algebra, the allowable crack size to prevent catastrophic failure is 8.4 mm or 0.331”. This analysis indicates that the window would be stable with an embedded 5.74 mm deep crack.