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Journal of Materials Science

, Volume 29, Issue 15, pp 3857–3896 | Cite as

The physics and mechanics of fibre-reinforced brittle matrix composites

  • A. G. Evans
  • F. W. Zok
Review

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.

Keywords

Polymer Fatigue Tensile Strength Brittle Material Processing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

ai

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

ao

Length of unbridged matrix crack

am

Fracture mirror radius

aN

Notch size

at

Transition flaw size

b

Plate dimension

bi

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

ci

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

d

Matrix crack spacing

ds

Saturation crack spacing

f

Fibre volume fraction

fl

Fibre volume fraction in the loading direction

g

Function related to cracking of 90 ° plies

h

Fibre pull-out length

l

Sliding length

li

Debond length

ls

Shear band length

m

Shape parameter for fibre strength distribution

mm

Shape parameter for matrix flaw-size distribution

n

Creep exponent

nm

Creep exponent for matrix

nf

Creep exponent for fibre

q

Residual stress in matrix in axial orientation

sij

Deviatoric stress

t

Time

tp

Ply thickness

tb

Beam thickness

u

Crack opening displacement (COD)

ua

COD due to applied stress

ub

COD due to bridging

v

Sliding displacement

w

Beam width

B

Creep rheology parameter ɛo o n

Cv

Specific heat at constant strain

E

Young's modulus for composite

Eo

Plane strain Young's modulus for composites

Ē

Unloading modulus

E*

Young's modulus of material with matrix cracks

Ef

Young's modulus of fibre

Em

Young's modulus of matrix

EL

Ply modulus in longitudinal orientation

ET

Ply modulus in transverse orientation

Et

Tangent modulus

Es

Secant modulus

G

Shear modulus

G

Energy release rate (ERR)

Gtip

Tip ERR

Gtipo

Tip ERR at lower bound

K

Stress intensity factor (SIF)

Kb

SIF caused by bridging

Km

Critical SIF for matrix

KR

Crack growth resistance

Ktip

SIF at crack tip

Io

Moment of inertia

L

Crack spacing in 90 ° plies

Lf

Fragment length

Lg

Gauge length

Lo

Reference length for fibres

N

Number of fatigue cycles

Ns

Number of cycles at which sliding stress reaches steady-state

R

Fibre radius

R

R-ratio for fatigue (σmaxmin)

Rc

Radius of curvature

S

Tensile strength of fibre

Sb

Dry bundle strength of fibres

Sc

Characteristic fibre strength

Sg

UTS subject to global load sharing

So

Scale factor for fibre strength

Sp

Pull-out strength

Sth

Threshold stress for fatigue

Su

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)

Δtb

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)sijsij]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

σs*

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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Copyright information

© Chapman & Hall 1994

Authors and Affiliations

  • A. G. Evans
    • 1
  • F. W. Zok
    • 1
  1. 1.Materials Department, College of EngineeringUniversity of CaliforniaSanta BarbaraUSA

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