> If brass numbers are epoxied to marble stone, will > their different coefficients of thermal expansion > break the bond?
Sorry to be coming in so late on this. Work pressures - got to go there five days a week and work eight hours (or more) too. Ridiculous! This is a transient thermal problem but let's say the brass temperature follows the stone's temperature well because the glue is thermally conductive enough to sink it. Ordinary brasses' coefficients of thermal expansion (CTEs) hover around 20E-6 per degree C. The CTE of granite is 7E-6 per degree C. +/- 10%. I think it's true that granite weathers better than marble, though its aesthetics may leave something to be desired in your application. Marble can be a bit anisotropic, but below is a typical maximum value. Marble also displays some hysteresis, so you can heat it once and expect a lower CTE thereafter. The CTE of marble is 10E-6 per degree C in the maximum expansion direction and near zero in the other direction. As suggested previously, a compliant form of epoxy will help handle the shear from the differing CTEs. You can make epoxy more compliant by adding ascorbic acid or you can buy it that way. Another thing that helps compliance is to make sure the bond line is thick enough. Epoxy is available with glass beads in it to set bond line thickness precisely, but you could simulate that with strategically-placed shims. Just don't put shims near the edge of a bond. A thicker bondline is better even though it will weaken the bond, because bond strength isn't your problem here. The edge of the bond is where rips start. A good rip-stop is a chamfer on the edge of the letter. About a 10 degree angle is good. Since a radian is about 60 degrees, 10 degrees would be an angle of about 1 in 6. Try to at least double the bondline thickness at the edges. Also, leave the curve of epoxy at the edge in place if you possibly can. This is also great rip-stop protection. If it is naturally too big and unsightly, wipe the excess off while the epoxy is still "wet". Your marble could easily get to 80 C if it's sitting in the sun. That should also help the compliance. So let's say you bonded at 25 C because epoxy sets up better and faster when it's warm. In use the temp settles out at 80 C. Difference is 55 C. The difference in CTEs is either 20E-6/C or 20 - 10 = 10E-6/C and we pick the larger figure. Your numeral is maybe 25 mm at its largest extent, so asuming the center of the numeral stays put, the distance to the farthest edge is 12.5 mm. Then that farthest edge moves (55C)*(20E-6/c)*(12.5 mm) = .014 mm = .0005 inches. OK, so the shear strain (gamma) is .014 mm divided by your bond line thickness, which is maybe 0.14 mm: .014/.14 = 0.1 By Hooke's law, stress and strain are proportional. For tension and compression, the proportionality constant is E, and for shear, the proportionality constant is G. For Dexter Hysol 9309.3NA, a compliant epoxy Modulus of rigidity, G, is 855 Mpa or 124 ksi The maximum allowable shear stress, tau, is 29 MPa or 4200 psi These figures are for 25C and I'm having the devil of a time finding G for elevated temp, though max stress falls to 6.9 MPa or 1000 psi at 82C. I'd assume G would also fall, maybe faster than allowable stress, so we can probably get away with using the 25C figures. For Dexter Hysol 9394, a rigid epoxy G is 1204 MPa or 148.5 ksi at 25C Tau max is 29.0 MPA or 4200 psi @ 25C (same as for 9309.3NA) Tau max is 20.7 MPA or 3000 psi @ 82C (better than 9309.3NA) The elegant way would be to look at the allowable strain for each epoxy. Maximum allowable stress (tau) divided by G will give us maximum allowable strain (gamma). Whatever allows the most strain is best in the respect we've been discussing. For Dexter Hysol 9309.3NA, a compliant epoxy @ 25C gamma max = tau/G = 29 MPa / 855 Mpa = .034 For Dexter Hysol 9394, a rigid epoxy @ 25 C gamma max = tau/G = 29 MPa / 1204 Mpa = .024 Neither of these make the grade with the .14 bondline thickness so we have to triple or quadruple the bondline thickness to get strain down to what we can live with. Conclusion. You need half a millimeter (.020") or more bondline thickness to pull this off, based on this cursory examination. That's a thick bondline. Summary. The amount of movement is related to the difference in the CTEs and the temperature change. The amount of movement divided by the bondline thickness is the strain. The maximum allowable strain is related to the maximum allowable shear stress and the modulus of rigidity. What else can you do? Well, titanium's CTE matches granite's pretty darned well. How about gold-plated Ti on granite? 8-) Other than that, I'd take Bill Gottesman's advice, but check the suggested adhesives at 80C, just in case. John B
