1. Laminate and stresses around the hole

Classical laminate theory gives E_x, E_y, G_xy, ν_xy from the NCAMP ply data at room temperature^{[12, 15]}, the same on every test page: IM7/8552 E₁ 158.5, E₂ 8.96, G₁₂ 4.69 GPa, ν₁₂ 0.316; AS4/8552 E₁ 127.3, E₂ 9.24, G₁₂ 4.83 GPa, ν₁₂ 0.302. The coupon is loaded along 0° and scaled with the hole: width 5D for the thin plies, 6D for the standard plies, as in the tests. The tested layups: IM7/8552 thin plies (0.125 mm), Bristol open-hole and unnotched tests^{[7, 8, 9]}; IM7/8552 and AS4/8552 standard plies (0.183 and 0.188 mm), NCAMP qualification tests^{[12, 15]}.

The strength uses the stress across the ligament from Konish and Whitney^[3], an approximation of the orthotropic solution, scaled by the finite-width correction of Tan^[2]. The exact solution for an orthotropic plate with a hole^[1] is used only for the strain map and the ply panels.

K_T^∞ = 1 + √[2(√(E_x/E_y) − ν_xy) + E_x/G_xy]

2. Fiber fracture: finite fracture mechanics

The laminate fails when a crack of length Δa from the hole edge meets a stress condition and an energy condition at the same time^[4]. K(a) uses the two-crack-from-a-hole factor^[5], scaled to the stress concentration.

(1/Δa)∫σ_y dx = σ₀ and (1/Δa)∫G(a) da = G_c

G_c = mean over plies of [G₀cos⁴θ + G₉₀(1 − cos⁴θ)] · n_block^0.5, K_IC = √(E_xG_c)

σ₀ is the unnotched laminate strength at fiber failure from the shared tension calculation, the same as on the Tension page: laminate theory with cure residual stresses and progressive ply cracking (in-situ strengths), until a 0° ply reaches X_T. When that plain coupon delaminates first, the Tension page shows the lower delamination strength; the hole calculation still uses the fiber value, and the result strip says so. θ is each ply angle from the load: a crack across a ply cuts fibers in proportion to their stiffness along the load (cos⁴θ): a 0° ply gives G₀, a 90° ply G₉₀, a ±45° ply G₀/4 + 3G₉₀/4. n_block is the number of plies in the thickest same-angle block: blocked plies split and pull out more, while single plies of any thickness get 1.

3. Delamination

Delamination grows at the −45/0 interface, driven by shear (mode II)^{[6, 7]}. The strength is where the energy released from a ply crack reaches G_IIc, reduced near the hole by φ, which depends on the hole size relative to the ply-block thickness^{[7, 9]}. The unnotched value uses the fitted form shared by every test page, σ_d = √(E_xG_IIc/(A t_block)) with A = 0.47, fitted once to the unnotched IM7/8552 block tests of Wisnom, Khan and Hallett^[6] (2-, 4- and 8-ply blocks of 0.125 mm plies: 660, 458 and 321 MPa; the form gives 633, 447 and 316 MPa). t_block is the thickest same-angle off-axis block on one half of a symmetric laminate.

σ_d = √(E_xG_IIc / (0.47 t_block)) · φ(D_e), φ = 0.58 + 0.36/(1 + (12/D_e)^2.5), D_e = D · 0.5 mm / t_block

The lower of fiber fracture and delamination governs, capped at the net-section strength σ₀(1 − D/W). With ply blocks of 0.4 mm or more, delamination comes first and isolates the hole.

4. Failure mode label

From the layup^{[8, 7]}: 60% or more ±45° plies, shear damage; same-angle blocks of 0.4 mm or more (on one half of a symmetric laminate), delamination; 0.2 to 0.4 mm, pull-out; otherwise brittle fiber fracture. Delamination is shown whenever it is the lower strength.

5. Damage in each ply (display only)

Each ply takes the laminate strains around the hole plus the cure residual stresses (cool-down from the stress-free temperature, ΔT = −156 °C, α₂ = 28×10⁻⁶/°C), with in-situ strengths for each same-angle block; both come from the shared engine, as on the Tension page. Orange marks where matrix cracking starts^[10]; in 0° plies these are splits. The percentage is the load at onset over the failure load. This does not change the failure load.

(σ₂⁺/Y_T^is)² + (τ₁₂/S_L^is)² ≥ 1, Y_T^is = max(Y_T, √(8G_Ic/(π t Λ₂₂))) for an embedded block of thickness t (1.79√(G_Ic/(π t Λ₂₂)) at a surface), S_L^is = √2·S_L

6. Inputs and fitted constants

IM7/8552 inputs: NCAMP ply data^[12] X_T 2238 (inside a laminate, backed out of the cross-ply test; a 0° coupon gives 2501), Y_T 64.1, S_L 91.1 MPa; interlaminar G_Ic 0.277 and G_IIc 0.788 kJ/m²^[11]; typical in-plane values G₀ = 100 kJ/m² (Camanho et al. measured 81.5) and G₉₀ = 5 kJ/m².

AS4/8552 inputs: NCAMP ply data^[15] X_T 1872 (inside a laminate; coupon 1996), Y_T 63.9, S_L 91.6 MPa; G₀ = 50 kJ/m², the crack-initiation value of compact-tension R-curves^[16] (they rise to about 215 kJ/m² over an 8 mm process zone, much longer than the 1 to 3 mm crack at failure here); the 8552 interlaminar values and G₉₀ as for IM7/8552, since no verified AS4/8552 values were found. With G₀ = 100 the AS4/8552 tests are 22% high on average, with 215 they are 47% high.

None of the open-hole tests is used to set the inputs. Three model constants come from Bristol tests and stay fixed for every material, layup and hole size:

• 0.47: delamination geometry factor, from the unnotched block tests (660, 458, 321 MPa for 0.25, 0.5, 1 mm blocks)^[6].
• φ: from the hole-size series with 0.5 mm blocks^[7].
• Exponent 0.5 on the number of plies in a block: from the blocked-ply series^[8].

7. Limits

• IM7/8552, 38 tests (Bristol^{[7, 8, 9]} and NCAMP^[12]): mean error 7.1% (worst 26%, hard laminate hot-wet). AS4/8552, 9 NCAMP tests^[15]: mean 9.7% (worst 22%, hot-wet); at room temperature it is 6 to 14% low. A cohesive finite element model gives 7% on the Bristol tests^[9].
• No thickness effect for dispersed plies: the 1 mm laminate is stronger in tests (570 against 476 MPa at 8 mm).
• Two-ply blocks on small holes are about 11 to 14% low: the inner sublaminate delays delamination.
• Room-temperature ply data: the NCAMP cold-dry and hot-wet tests are predicted with the same values, so hot-wet splitting at the hole is missed (IM7/8552 hard −21%, soft +23%).
• Ply damage is onset only, without load redistribution; 0° splits start earlier in tests.
• The load–displacement curve uses the gross section and a 150 mm free length; the drop at failure is illustrative.
• Point and average stress criteria^[13] are not used: they need a characteristic distance fitted for each layup.

References

1. S.G. Lekhnitskii, Anisotropic Plates, Gordon and Breach, 1968 (book).
2. S.C. Tan, Finite-width correction factors for anisotropic plate containing a central opening, J. Compos. Mater. 22 (1988) 1080–1097. doi:10.1177/002199838802201105
3. H.J. Konish and J.M. Whitney, Approximate stresses in an orthotropic plate containing a circular hole, J. Compos. Mater. 9 (1975) 157–166. doi:10.1177/002199837500900206
4. P.P. Camanho, G.H. Erçin, G. Catalanotti, S. Mahdi and P. Linde, A finite fracture mechanics model for the prediction of the open-hole strength of composite laminates, Compos. Part A 43 (2012) 1219–1225. doi:10.1016/j.compositesa.2012.03.004
5. H. Tada, P.C. Paris and G.R. Irwin, The Stress Analysis of Cracks Handbook, 3rd ed., ASME Press, 2000 (book).
6. M.R. Wisnom, B. Khan and S.R. Hallett, Size effects in unnotched tensile strength of unidirectional and quasi-isotropic carbon/epoxy composites, Compos. Struct. 84 (2008) 21–28. doi:10.1016/j.compstruct.2007.06.002
7. M.R. Wisnom and S.R. Hallett, The role of delamination in strength, failure mechanism and hole size effect in open hole tensile tests on quasi-isotropic laminates, Compos. Part A 40 (2009) 335–342. doi:10.1016/j.compositesa.2008.12.013
8. B.G. Green, M.R. Wisnom and S.R. Hallett, An experimental investigation into the tensile strength scaling of notched composites, Compos. Part A 38 (2007) 867–878. doi:10.1016/j.compositesa.2006.07.008
9. M.R. Wisnom, S.R. Hallett and C. Soutis, Scaling effects in notched composites, J. Compos. Mater. 44 (2010) 195–210. doi:10.1177/0021998309339865
10. P.P. Camanho, C.G. Dávila, S.T. Pinho, L. Iannucci and P. Robinson, Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear, Compos. Part A 37 (2006) 165–176. doi:10.1016/j.compositesa.2005.04.023
11. P.P. Camanho, P. Maimí and C.G. Dávila, Prediction of size effects in notched laminates using continuum damage mechanics, Compos. Sci. Technol. 67 (2007) 2715–2727. doi:10.1016/j.compscitech.2007.02.005
12. NCAMP, Hexcel 8552 IM7 unidirectional prepreg: statistical analysis report NCP-RP-2009-028 Rev B, and test report CAM-RP-2009-015 Rev B, Wichita State University, 2019. www.wichita.edu
13. J.M. Whitney and R.J. Nuismer, Stress fracture criteria for laminated composites containing stress concentrations, J. Compos. Mater. 8 (1974) 253–265. doi:10.1177/002199837400800303
14. ASTM D5766/D5766M, Standard Test Method for Open-Hole Tensile Strength of Polymer Matrix Composite Laminates, ASTM International (standard).
15. NCAMP, Hexcel 8552 AS4 unidirectional prepreg: statistical analysis report NCP-RP-2010-008 Rev D, and test report CAM-RP-2010-002 Rev A, Wichita State University (report).
16. S. Haldar, M. Herráez, F. Naya, C. González and C.S. Lopes, Relations between intralaminar micromechanisms and translaminar fracture behavior of unidirectional FRP supported by experimental micromechanics, Compos. Part B 174 (2019) 107000. doi:10.1016/j.compositesb.2019.107000

Test method: ASTM D5766^[14].