Skip to main content
. 2017 Dec 1;9(12):664. doi: 10.3390/polym9120664
Subscript #i Subscript #1 and #2 are adherends and #3 is adhesive.
Di, Ei, Gi, hi Flexural rigidity, elastic modulus, shear modulus, thickness of member #i.
D¯ Flexural compliance of the bonded structure.
M±il, N±il, Q±il Moment, sectional stretching force, sectional shear force applied on adherend #i at x = ±l.
l Half-length of the bonded structure.
α, β Characteristic parameters of a bonded structure in peeling, shearing.
αi Coefficient of thermal expansion of adherend #i.
εT, ε±Nl, ε±Ml Differential strain between adherends #2 and #1 at x = ±l due to temperature and edge stretching; effective bending strain due to edge bending at x = ±l.
κ ±il Edge curvature of adherend #i at x = ±l.
κsi, κs Shear compliance of member #i, of the bonded structure between the centroid planes of adherends #1 and #2.
λxi, λx x-compliance of adherend #i, of the bonded structure.
λ Additional x-compliance of the bonded structure attributed to its flexural deformation.
λzi, λz z-compliance of member #i, of the bonded structure between the centroid planes of adherends #1 and #2.
θi Rotation of the centroid axis of adherend #i (due to bending).
σm(x), σa(x) Mean, amplitude of variation, of transverse stress along the thickness of the adhesive (or between the bonded interfaces).
σp(x) Peeling stress along the bonded interfaces.
τ(x) Shear stress within the adhesive (and along the interfaces).
ΔT Temperature change.
Basic formulas
4α4=D¯4λz; β2=λxκs.
Di=Eihi312(plane stress); D¯=1D1+1D2.
κs=κs1+κs2+ κs3
κsihi8Gi,i=1,2;κs3=h3G3
λx=λx1+λx2+λxθ
λxi=1Eihi, i=1,2; λxθ=14[h1(h1+h3)D1+h2(h2+h3)D2]
λz=λz1+λz2+λz3
λzi 1332hiEi, i=1,2;λz3=h3E3
μσ=12(h2D2h1D1),μτ=12(h2+h3D2h1+h3D1)