Domain

Explanation

Composites

• Anisotropic materials, fibres & laminates: distinct planes & directions of strengths & weaknesses)
• Traditional: separate analysis (uncoupled) like RC design
• Modern: lightweight, flexible, wide-range of properties

Examples of composite use

• Boron/Epoxy patch: with high wrapping strength (axially strong) for repair, bridge deck & airplanes
• Ceramic/composite armour: with brittle outer ceramic for fragmentation & flexible inner composite for wave deflection & protection; used in tanks (layered armour), pilot seats, naval ships (sandwiched composite-foam-composite shell)

Joints

• Composite joints:

1. flat: flatly laid & bonded with binding medium (clued), high interface normal stresses & sudden failure at discontinuity
2. wavy: zig-zag laid & bonded, lower stresses & opposing directions s.t. effectively close-up joint (strengthening)

Loading/unloading cycle

• Exhibit nonlinear, hysterical & viscous behaviour
• Especially off-axial loading (skew angle >0)
• Loading: increase stress, but relaxation at constant load (creep)
• Unloading: decrease stress, but stiffening at constant load due to viscous elasticity
• Note strength is proportional to load direction

Laminate

• Isotropic materials: no boundary stresses
• Anisotropic materials: presence of boundary, 3D (out-of-plane) induced stresses, in addition to the usual in-plane stresses
• 3D stresses: also called boundary stresses, free edge stresses, induced stresses
• If cut straight edges, high 3D stresses
• But if cut with jugged (uneven) edges, destroy 3D stresses
• Axial failure load test: for notched laminate (center-holed)
• Failures: 2 types – stress concentration at notch & along free edges parallel to axial load

Nonlinear behaviour

• Axial testing:
• Along fibre direction: skew angle=0 – Linear behaviour
• Off-axial direction: skew angle¹ 0 – Nonlinear behaviour
• Higher skew angle, higher plasticity, higher e ^P, lower strengths (mean & ultimate)
• Thus require convenient mathematical model

PP & Flow rule

• de =de ^e + de ^p
• de ^p = ¶ f/¶ s *dl , where f: plastic potential, transversely isotropic
• dl =3/2*( de ^p/ds )* (ds /s ): flow rule from the yield surface
• Thus this model effectively reduces all skew angle stress-strain curves into a single asymptotic curve (e ^p=A.s ⁿ)

Rate dependency

• Strain rate affects model behaviour
• Using this viscoplasticity model, found:
• At higher strain rate, A higher, stiffness higher

Microbuckling

• Laminate in compression is similar to:

1. Rosen (1965): laminate = series of perfectly straight beams leading to extension & shear (dominant) failures: s _c=G₁₂
2. Argon (1972): laminate is slightly skewed (not straight), thus shear stresses induced along edges
3. Sun & Jun (1994): Argon (1972) + s _cr = G^ep.( s _cr,f ) where G^ep: tangent shear modulus

Remarks

• Composite studies approximates soil analysis
• Confining stress s ₂₂ higher, s _cr lower (due to effect on the G^ep
• Temperature effects not included: in ballistic, crashes & explosions
• Buckling + instability: linked – always lesser than Euler’s buckling load