Two kinds of material. Tested materials (IM7/8552, AS4/8552): stiffness and strengths are the NCAMP lamina means at room temperature, dry. IM7/8552 is offered in two ply thicknesses with the same ply properties: standard 0.183 mm (the NCAMP normalizing thickness) and thin 0.125 mm (the ply of the Bristol tests of Wisnom and co-workers); AS4/8552 in 0.188 mm. The ply thickness sets the laminate thickness, the in-situ strengths and the thickness of the plies that delaminate. Your material: ply properties estimated from the fiber, resin and fiber volume fraction (rule of mixtures and Halpin–Tsai for stiffness, nominal ply strengths as in the app). Against NCAMP these estimates give E₁ +4 to +6%, E₂ 0 to −10%, G₁₂ −11 to −23%, X_T +31 to +36%, Y_T +33 to +36% and S_L +17 to +20%, so estimated strengths are rough. Fracture energies and expansion coefficients are not estimated: estimates have no residual stresses, and no delamination check or thin-ply strengths unless you type G_Ic and G_IIc.

Classical laminate theory, membrane only (the layups are symmetric). The coupon is loaded along x (0°, vertical in the drawing) with σ_y = τ_xy = 0, in small strain steps. In each step the transverse strains are solved so that the ply stresses add up to zero across the load, then every ply is checked for cracking and fiber failure. Tested materials include the cure residual stresses from a cool-down from 177 °C to 21 °C (α₁ = 0, α₂ = 28×10⁻⁶/°C).

Ply response: σ₁, σ₂ linear elastic (E₁, E₂, ν₁₂); shear non-linear, τ₁₂ = S_∞ tanh(G₁₂γ₁₂/S_∞), with S_∞ set so that τ₁₂ = S_L at 5% shear strain (the NCAMP definition of the shear strength). This lets the ±45° plies keep carrying load as they yield.

Matrix cracking (progressive ply discount): a ply cracks when (σ₂/Y)² + (τ₁₂/S_L^is)² ≥ 1, with Y = Y_T^is for σ₂ ≥ 0 and Y_C for σ₂ < 0, and then carries no σ₂. In-situ strengths (Camanho et al. 2006): Y_T^is = max(Y_T, √(8G_Ic/(π t Λ₂₂))) for an embedded block of thickness t, max(Y_T, 1.79√(G_Ic/(π t Λ₂₂))) for a surface block: thin blocks gain strength, thick blocks crack at the unconstrained Y_T, where the cure stresses matter most; Λ₂₂ = 2(1/E₂ − ν₂₁²/E₁); S_L^is = √2 S_L. Without G_Ic the plies keep Y_T and S_L. A unidirectional coupon uses Y_T itself; with no fibers near the load (90° coupon) the first crack is the failure.

Fiber failure (maximum stress): the laminate fails when σ₁ in any ply reaches X_T (or −X_C in compression). Layups with no plies near 0° but with ±45° plies fail in shear instead, when τ₁₂ in the ±45° plies reaches S_L (5% shear strain); layups with neither fail at the first matrix crack. X_T is the 0° strength inside a laminate: for the tested tapes the NCAMP value backed out of the cross-ply test (2238 MPa for IM7/8552, 1872 MPa for AS4/8552), lower than a 0° coupon gives (2501 and 1996 MPa), because the cracks in neighbouring plies load the 0° fibers unevenly. For estimates, 0.92 times the estimated coupon strength, the same ratio as for the tested tapes (0.90 and 0.94).

Delamination (fitted form, the same on every test page): σ_d = √(E_x G_IIc / (0.47 t_block)), with E_x the laminate modulus and t_block the thickest block of same-angle off-axis plies, counted on one half of a symmetric laminate. A matrix crack in a block of thickness t_block releases energy into a shear (mode II) delamination; the delamination grows when that energy reaches G_IIc, so σ_d falls as 1/√t_block. The constant 0.47 is fitted once to the unnotched IM7/8552 ply-block tests of Wisnom, Khan and Hallett (2008): blocks of 2, 4 and 8 plies of 0.125 mm, 660, 458 and 321 MPa. It applies to laminates with a run of off-axis plies of two or more angles between 0° plies (such as 45/90/−45), not to off-axis plies isolated between 0° plies (cross-ply, hard laminate), and it needs a matrix crack in the run first: σ = max(σ_d, first crack in the run). Estimates have no G_IIc, so no delamination check unless you type one.

Alternative without a fitted constant (in the engine, not used here): the cracked run carries no load behind the delamination front, so at constant load G = σ² h t_b E_b / (2n E_c E_r (h − t_b)) and σ_d = √(2n G_IIc E_c E_r (h − t_b) / (h t_b E_b)), with t_b the run thickness, E_b its axial stiffness with the plies cracked, E_r the modulus of the rest, E_c = (t_bE_b + (h − t_b)E_r)/h and n = 1 or 2 interfaces, once all plies of the run have cracked.

Strength = lower of fiber failure and delamination. Failure mode drawn: delamination when it governs; shear failure of the ±45° plies; otherwise lateral fiber fracture when the 0° plies outnumber the ±45° plies, angled fracture when they do not, explosive splitting for a 0° coupon, and a single matrix crack for a 90° coupon.

Checked against tests (room temperature, dry, unnotched). NCAMP cross-ply, quasi-isotropic, soft and hard laminates, both tapes, none used to set an input: mean error 4.9%, largest 8.7% (AS4/8552 quasi-isotropic). IM7/8552 laminates of Wisnom, Khan and Hallett (2008) and Wisnom, Hallett and Soutis (2010) with 0.125 mm plies: dispersed, 1 to 4 mm thick, fiber failure 1 to 10% low, as in the tests; ply blocks of 0.25, 0.5 and 1 mm, delamination, −4%, −2% and −2% (these three set the constant 0.47). All 14 tests: mean 4.7%, largest 9.5%. The form without a fitted constant gives a mean of 7.9% and a largest error of 21% on the same tests.

The calculation is the shared failure engine of the test pages (ply-failure.js), with the material data of test-materials.js. Known gaps: free-edge delamination is not checked; the cracking model is a ply discount (cracked plies lose all transverse stiffness at once); there is no size effect. The load–displacement curve uses the gauge length; the drop after failure is illustrative.

Sources: NCAMP reports NCP-RP-2009-028 Rev B and CAM-RP-2009-015 Rev B (8552 IM7 unidirectional tape, 2019) and NCP-RP-2010-008 Rev D and CAM-RP-2010-002 Rev A (8552 AS4 unidirectional tape, 2011); M.R. Wisnom, B. Khan and S.R. Hallett, Compos. Struct. 84 (2008) 21; M.R. Wisnom, S.R. Hallett and C. Soutis, J. Compos. Mater. 44 (2010) 195; T.K. O'Brien, Characterization of delamination onset and growth in a composite laminate, ASTM STP 775 (1982) 140 (strain energy release rate of a delamination at constant load); P.P. Camanho, C.G. Dávila, S.T. Pinho, L. Iannucci and P. Robinson, Compos. Part A 37 (2006) 165 (in-situ strengths); P.P. Camanho, P. Maimí and C.G. Dávila, Compos. Sci. Technol. 67 (2007) 2715 (8552 interlaminar fracture energies, also used for AS4/8552); ASTM D3039/D3039M, Tensile Properties of Polymer Matrix Composite Materials.