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The physics and mechanics of fibre-reinforced brittle matrix composites

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Abstract

This review compiles knowledge about the mechanical and structural performance of brittle matrix composites. The overall philosophy recognizes the need for models that allow efficient interpolation between experimental results, as the constituents and the fibre architecture are varied. This approach is necessary because empirical methods are prohibitively expensive. Moreover, the field is not yet mature, though evolving rapidly. Consequently, an attempt is made to provide a framework into which models could be inserted, and then validated by means of an efficient experimental matrix. The most comprehensive available models and the status of experimental assessments are reviewed. The phenomena given emphasis include: the stress/strain behaviour in tension and shear, the ultimate tensile strength and notch sensitivity, fatigue, stress corrosion and creep.

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Abbreviations

a i :

Parameters found in the paper by Hutchinson and Jensen [33], Table IV

a o :

Length of unbridged matrix crack

a m :

Fracture mirror radius

a N :

Notch size

a t :

Transition flaw size

b :

Plate dimension

b i :

Parameters found in the paper by Hutchinson and Jensen [33], Table IV

c i :

Parameters found in the paper by Hutchinson and Jensen [33], Table IV

d :

Matrix crack spacing

d s :

Saturation crack spacing

f :

Fibre volume fraction

f l :

Fibre volume fraction in the loading direction

g :

Function related to cracking of 90 ° plies

h :

Fibre pull-out length

l :

Sliding length

l i :

Debond length

l s :

Shear band length

m :

Shape parameter for fibre strength distribution

m m :

Shape parameter for matrix flaw-size distribution

n :

Creep exponent

n m :

Creep exponent for matrix

n f :

Creep exponent for fibre

q :

Residual stress in matrix in axial orientation

s ij :

Deviatoric stress

t :

Time

t p :

Ply thickness

t b :

Beam thickness

u :

Crack opening displacement (COD)

u a :

COD due to applied stress

u b :

COD due to bridging

v :

Sliding displacement

w :

Beam width

B :

Creep rheology parameter ɛo/σ no

C v :

Specific heat at constant strain

E :

Young's modulus for composite

E o :

Plane strain Young's modulus for composites

Ē :

Unloading modulus

E * :

Young's modulus of material with matrix cracks

E f :

Young's modulus of fibre

E m :

Young's modulus of matrix

E L :

Ply modulus in longitudinal orientation

E T :

Ply modulus in transverse orientation

E t :

Tangent modulus

E s :

Secant modulus

G :

Shear modulus

G :

Energy release rate (ERR)

G tip :

Tip ERR

G otip :

Tip ERR at lower bound

K :

Stress intensity factor (SIF)

K b :

SIF caused by bridging

K m :

Critical SIF for matrix

K R :

Crack growth resistance

K tip :

SIF at crack tip

I o :

Moment of inertia

L :

Crack spacing in 90 ° plies

L f :

Fragment length

L g :

Gauge length

L o :

Reference length for fibres

N :

Number of fatigue cycles

N s :

Number of cycles at which sliding stress reaches steady-state

R :

Fibre radius

R :

R-ratio for fatigue (σmax/σmin)

R c :

Radius of curvature

S :

Tensile strength of fibre

S b :

Dry bundle strength of fibres

S c :

Characteristic fibre strength

S g :

UTS subject to global load sharing

S o :

Scale factor for fibre strength

S p :

Pull-out strength

S th :

Threshold stress for fatigue

S u :

Ultimate tensile strength (UTS)

S * :

UTS in the presence of a flaw

T :

Temperature

ΔT :

Change in temperature

Δt :

Traction function for thermomechanical fatigue (TMF)

Δt b :

Bridging function for TMF

α:

Linear thermal coefficient of expansion (TCE)

αf :

TCE of fibre

αm :

TCE of matrix

γ:

Shear strain

γc :

Shear ductility

δc :

Characteristic length

δɛ:

Hysteresis loop width

ɛ:

Strain

ɛ* :

Strain caused by relief of residual stress upon matrix cracking

ɛe :

Elastic strain

ɛo :

Permanent strain

ɛo :

Reference strain rate for creep

ɛτ :

Transient creep strain

ɛs :

Sliding strain

λ:

Pull-out parameter

μ:

Friction coefficient

ξ:

Fatigue exponent (of order 0.1)

κ:

Beam curvature

ν:

Poisson's ratio

φ:

Orientation of interlaminar cracks

ρ:

Density

σ:

Stress

σb :

Bridging stress

¯σb :

Peak, reference stress

σe :

Effective stress = [(3/2)s ijsij]1/2

σf :

Stress in fibre

σi :

Debond stress

σm :

Stress in matrix

σmc :

Matrix cracking stress

σo :

Stress on 0 ° plies

σo :

Creep reference stress

σrr :

Radial stress

σR :

Residual stress

σs :

Saturation stress

σ *s :

Peak stress for traction law

στ :

Lower bound stress for tunnel cracking

σT :

Misfit stress

τ:

Interface sliding stress

τf :

Value of sliding stress after fatigue

τo :

Constant component of interface sliding stress

τs :

In-plane shear strength

¯τc :

Critical stress for interlaminar crack growth

τss :

Steady-state value of τ after fatigue

δR :

Displacement caused by matrix removal

Δɛp :

Unloading strain differential

δɛo :

Reloading strain differential

Γ:

Fracture energy

Γi :

Interface debond energy

Γf :

Fibre fracture energy

Γm :

Matrix fracture energy

ΓR :

Fracture resistance

Γs :

Steady-state fracture resistance

ΓT :

Transverse fracture energy

Ω:

Misfit strain

Ωo :

Misfit strain at ambient temperature

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  1. Materials Department, College of Engineering, University of California, 9310-5050, Santa Barbara, CA, USA

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Evans, A.G., Zok, F.W. The physics and mechanics of fibre-reinforced brittle matrix composites. JOURNAL OF MATERIALS SCIENCE 29, 3857–3896 (1994). https://doi.org/10.1007/BF00355946

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