A laminate fails three ways at once

With a metal you mostly chase yield and ultimate, plus fatigue and stability, and they are largely separable problems. A composite laminate fails as a system of plies, and the ply that fails first is rarely the one that fails the part. Worse, the failure that actually loses the structure is often interlaminar — out of the plane your in-plane criterion can even see. You have to analyse the committee, not the chairman.

The modes worth naming

• First-ply failure (FPF). The first lamina to reach its limit, usually matrix cracking transverse to the fibres in an off-axis ply. It is a real event, but it is conservative as a design limit — sometimes far too conservative, because the laminate keeps carrying load happily afterward.
• Last-ply / ultimate (LPF). Plies fail progressively and load sheds to the survivors until the laminate finally lets go. This is closer to test, but justifying it means modelling progressive damage and stiffness degradation, which is harder to defend on certification than a clean FPF cutoff.
• Stability. Thin laminates buckle long before they break in-plane. Skin panels are usually stability-critical, not strength-critical — the panel buckles, post-buckles, and either survives in a stiffened design or fails by a secondary mechanism. Buckling load is stiffness-driven (D-matrix, boundary conditions, aspect ratio), so it cares about layup order, not just ply percentages.
• Bearing and bolt pull-through at joints. Discussed elsewhere — bearing-bypass governs fastened composite joints, and pull-through governs the out-of-plane case.
• Interlaminar failures — the ones that bite. Free-edge delamination (driven by the interlaminar stresses that arise wherever the laminate is cut), ply-drop delamination (taper regions), and impact-induced delamination (BVID). These are dominated by interlaminar tension and shear and by fracture toughness G_Ic / G_IIc, not by the in-plane allowables — so a laminate that is comfortable on Tsai-Wu can still delaminate at a free edge.

Why the in-plane criteria fight each other

Tsai-Wu, max-stress, max-strain, Hashin, LaRC — they disagree, and they are supposed to, because each encodes a different physical assumption:

• Max-stress / max-strain treat the modes as independent — no interaction between, say, transverse tension and shear. Simple, transparent, and what many certification bases default to (strain-based limits are popular because they travel well across layups).
• Tsai-Wu is a single smooth interactive quadratic. Convenient for one number, but it blends fibre and matrix failure into one surface and does not tell you which mode you hit — a real drawback when the consequence differs (a popped matrix crack is not a severed fibre).
• Hashin and LaRC separate fibre and matrix modes and try to capture the physics of matrix failure under combined stress, including the in-situ effect. More faithful, more inputs, more to justify.

The job is not to find the “right” criterion. It is to know which one your certification basis accepts, to understand what physics it ignores, and to stay conservative exactly where the test evidence is thin. A failure criterion you cannot defend in a design review is worse than a conservative one you can.

The practical order

On a typical composite part I size in this sequence:

1. Skin and webs for stability — buckling and post-buckling first, because that is usually what sets the laminate. Tune the layup for the D-matrix the stability case wants.
2. Joints for bearing and bypass, with the interaction diagram, and pull-through where the load is out-of-plane.
3. Free edges, ply drops, and cutouts for delamination — the interlaminar check the in-plane criterion can’t do. Taper ply drops gently, stagger them, and respect the free-edge stress field.
4. Impact / CAI where the certification basis requires demonstrated load capability with BVID present — frequently the real driver on a compression-loaded skin.
5. In-plane strength last. On a well-laid-up laminate, raw strength is rarely what gets you.

The honest summary

A composite laminate fails where the design detail is sloppy, not where the in-plane stress is highest. The high-stress region usually has fibres pointed the right way and plenty of margin; the failure shows up at the free edge nobody capped, the ply drop nobody staggered, the joint that carries bearing it wasn’t sized for, or the panel that buckled into a mode the analysis didn’t chase. Respect the interlaminar modes and the impact requirement, pick a criterion you can defend, and check strength last — because by then the laminate has usually already told you where it wants to fail.