In thermally tempered glass of thickness t = 10 mm, let y be the distance from the mid-plane; the stress follows the parabolic distribution σ(y) = σc(1 − 12y²/t²) (tension positive, σc is the tensile stress at the mid-plane). If the surface compressive stress is 120 MPa, which correctly pairs the mid-plane tensile stress σc with the depth from the surface to the end of the compressive layer?

Answer: B. About 60 MPa, about 2.1 mm

At the surface, y = t/2, σ = σc(1 − 3) = −2σc, so 2σc = 120 MPa gives σc = 60 MPa. The stress is zero where 12y²/t² = 1, that is, at y = t/√12 ≈ 2.89 mm, so the depth from the surface is 5.0 − 2.89 ≈ 2.1 mm (about 21% of the thickness). This distribution satisfies force balance: summed through the thickness, the stress is zero. About 2.9 mm takes the distance measured from the mid-plane as the depth from the surface. A pairing with the mid-plane tension equal to the 120 MPa surface compression does not satisfy force balance. A surface compression about twice the mid-plane tension and a compressive layer about one fifth of the thickness are the usual guidelines for thermal tempering.