Failure of composites John Summerscales Outline of lecture

Failure of composites John Summerscales

Outline of lecture • strength • failure mechanisms • fractography • fracture mechanics • failure criteria

Strength • strength = stress at failure • failure may be • • yielding in metals non-recoverable loss of elastic response first-ply failure ultimate failure • one material can have several different strengths

Strength • Kelly-Tyson equation for UD composites: • • σc = σf. Vf + σm*(1 -Vf) at high Vf, or σc < σm#(1 -Vf) at low Vf • • where σm* is the tensile stress in the matrix at the failure strain of the fibre, and σm# is the maximum tensile strength of the matrix • For small mis-alignments: • σc = σf. Vf / cos 2θ = σf. Vfsec 2θ

Failure mechanisms • • • matrix cracking fibre fracture debonding = interface failure delamination = interlayer failure fibre pullout • micro-buckling • kink bands • cone of fracture

Failure strain of composites • The key criterion for composite failure is the local strain to failure: ε’ a. k. a. elongation at break and not stress • Note that ε’ for the fibre/matrix interface i. e. transverse fibres = ~0. 25 %

Matrix cracking max min • • polyester resin vinyl ester epoxy resin phenolic resin ε’ = 0. 9 -4. 0 % ε’ = 1. 0 -3. 5 % ε’ = 0. 5 -1. 0 % • data from NL Hancox, Fibre Composite Hybrid Materials, Elsevier, 1981.

Fibre fracture • • • S/R-glass E-glass Kevlar 49 HS-carbon UHM-carbon ε’ = 4. 6 -5. 2 % …. ε’ = 3. 37 % ………. … ε’ = 2. 5 % ………………. ε’ = 1. 12 % ………………… ε’ = 0. 38 % …………………. . • data from NL Hancox, Fibre Composite Hybrid Materials, Elsevier, 1981.

Fibre-matrix debonding a b • Crack can run • • • through (not shown), or around the fibre ~12000 carbon or 1600 glass UD fibres / 1 mm 2

Fibre-matrix debonding:

Delamination of layers • one layer is a lamina (plural = laminae) • several layers in a composite is a laminate • separation of the layers is delamination • to avoid delamination • • • 3 -D reinforcement (often woven or stitched) vertically aligned carbon nano tubes (VACNT) Z-pinning

Stress whitening of GFRP • debonding (fibre/matrix separation) and delamination (layer separation) both create internal defects which scatter light • the consequence is that the laminate changes from transparent to opaque, referred to as “stress whitening” • similar effects may be seen in other composites (e. g. at stitches in NCF CFRP)

Fibre pullout • as parts of fractured composite separate, fibres which have debonded fail remote from Fibre fracture principal fracture plane. • relaxed fibre expands radially • energy absorbed by frictional forces as fibre pulls from the opposite face • debonding and pullout absorb high energies and result in a tough material

Micro-buckling In bending tests, failure occurs due to: • stress concentration at the loading roller • and poor fibre/matrix adhesion • local microbuckling

Kink bands (HM fibre composites) • Compressive load causes buckling followed by co-operative failure of a group of fibres to produce short lengths of parallel mis-oriented fibre • Image from • http: //coeweb. eng. ua. edu/ aem/people/samit/ nanoclay. htm

Fractography • use of optical or electron microscopes to image the fracture surface:

Fracture mechanics • stress intensity factor (Pa. m 1/2 ) • fracture toughness (critical stress intensity factor, Pa. m 1/2 ) • separate parameters in each plane crack • • mode I (x) II (y) III (z) JG Williams, Fracture mechanics of composite failure, Proc IMech. E Part C: Journal of Mechanical Engineering Science, 1990, 204(4), 209 -218.

Design to avoid failure • beware first ply failure dependent on laminate stacking sequence • failure index (FI) of >1 = failure dependent on the failure criteria selected • reserve factor (RF) <1 = failure for Tsai-Hill failure criteria, RF =1/√(FI)

Failure criteria • failure occurs at critical value of local uni- or bi-axial stress reaches : σi ≥ σi' or ij ≥ ij' (' indicates failure condition) • • criteria include von Mises yield criterion: • • Tresca yield criterion: • • maximum shear stress Tsai-Hill criterion: • • critical distortional strain energy an envelope in stress space … and many others, getting more complex/sophisticated

Failure criteria • those above plus many other criteria • no agreement ! (see MJ Hinton, AS Kaddour and PD Soden, Failure criteria in fibre reinforced polymer composites: the world-wide failure exercise, Elsevier, Amsterdam, 2004. ISBN 0 -08 -044475 -x). • Hashin’s early assumption: • "It may be argued that in the event that a failure plane can be identified, [then] the failure is produced by the normal and shear stresses on that plane"!

Summary of lecture • strength • failure mechanisms • fractography • fracture mechanics • failure criteria