Adhesion Testing
Thin-film adhesion tests: Benjamin–Weaver shear stress from a scratch critical load, Kendall peel energy, ASTM D3359 tape classes, and bend-test film stress with crack and delamination driving forces.
Interfacial shear stress τ
696 MPa
H a / √(R² − a²)
Contact radius a
23.0 µm
√(L_c / (π H))
Model
Benjamin–Weaver: a spherical stylus sinks into a fully plastic substrate until the mean contact pressure equals the hardness H, and τ is the shear stress at the leading edge of the contact, with the prefactor k = 1 (later analyses give 0.2–1, Bull & Berasetegui 2006, so τ is an upper estimate). It ranks coatings tested with one stylus; the critical load also depends on friction, film thickness, the stylus wear and the failure mode, so τ is not a work of adhesion. Use the substrate hardness from indentation at a similar depth (optical glasses ≈ 5–7 GPa).
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Benjamin–Weaver shear stress for a plastic substrate (ranks coatings; not a work of adhesion); Kendall elastic peel; ASTM D3359 B classes; bend-test G for a thin film, matched moduli (Hutchinson–Suo).
- Benjamin P., Weaver C. (1960). Measurement of adhesion of thin films. Proc. R. Soc. Lond. A 254, 163–176. doi:10.1098/rspa.1960.0012
- Bull S. J., Berasetegui E. G. (2006). An overview of the potential of quantitative coating adhesion measurement by scratch testing. Tribol. Int. 39, 99–114. Eq. 1: τ = kHa/√(R² − a²), k = 0.2–1. doi:10.1016/j.triboint.2005.04.013
- Kendall K. (1975). Thin-film peeling — the elastic term. J. Phys. D 8, 1449–1452. doi:10.1088/0022-3727/8/13/005
- Hutchinson J. W., Suo Z. (1991). Mixed mode cracking in layered materials. Adv. Appl. Mech. 29, 63–191. doi:10.1016/S0065-2156(08)70164-9
- ASTM D3359-23. Standard Test Methods for Rating Adhesion by Tape Test. ASTM International. doi:10.1520/D3359-23
- Ohring M. (2002). Materials Science of Thin Films, 2nd ed., ch. 12 (adhesion tests). Academic Press. doi:10.1016/b978-012524975-1/50015-x