# Shear Failure of Adhered Polystyrene (to Aluminum)

Hi All,

So here's the problem. A project I am working on has a composite metal panel assembly, which a previous engineer designed. The metal panels are simply glued to the polystyrene (styrofoam sm). The problem is that the previous engineer did not consider the difference in thermal expansion between the foam and the aluminum, and the foam has begun to fail in shear, and detach from the metal panels.

I'm putting together a report basically laying out the problem, and what I want to find is a temperature gradient which is "allowable" before the styrofoam will shear.

Basically what I have done is set the thermal stress due to restricting thermal expansion (σ=EαdT) equal to the shear strength of the styrofoam (452kPa) and solved for the dT...which ended up coming out to 2.39degC.....which seems extremely low to me.

Any suggestions on where I have gone wrong? The only thing I can think of is that I cant directly use the thermal stress due to restriction of thermal expansion directly as a shear force....not sure.

Thanks,

## Answers and Replies

Thermal stress (σ) created by thermal expansion resistance will be calculated using the following formula:
σ=E∙α∙dT
Where: σ= Thermal Stress (kPa)
E= Youngs Modulus (GPa)
α= Thermal Expansion Coefficient (m/(m℃))
dT= Temperature Differential (℃)
The thermal stress (σ) value will then be compared to the shear strength of the Styrofoam SM. If σ>F_v, then shear failure will occur.

The thermal stress (σ) will then be set to the shear strength (F_v) of Styrofoam SM in order to find the minimum temperature differential which shearing in the Styrofoam SM will occur.
CALCULATIONS:

σ=E∙α∙dT
σ=(3x10^6 kn/m^2 )(63x10^(-6) m/(m℃))(100℃)
σ=18,900 kPa
σ>F_v
∴, shearing WILL occur

452kPa=(3x10^6 kn/m^2 )(63x10^(-6) m/(m℃))∙dT
dT=2.39℃
∴, shearing will occur at any temperature differential greater than 2.39℃

AlephZero
Science Advisor
Homework Helper
You seem to have calculated the stress in the steel assuming it cannot expand, and then applied all that stress across the interface to the styrofoam.

That is the wrong thing to do (and your temperature difference is obviously much too small).

It would make more sense to find the difference in thermal strain between the metal and the foam (caused by the different expansion coefficients) and compare that with the elastic strain at which the foam will fail.

But the measured data here http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070008201_2007006834.pdf seems to imply the thermal expansion of the foam is very nonlinear (and large, and irreversible) above about 100 C.

AlephZero
Science Advisor
Homework Helper
You can probably simplify the analysis in that PDF, since I would guess Young's modulus for the foam is negligible compared with aluminum.