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Applications of linear fracture mechanics

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Failure in Polymers

Part of the book series: Advances in Polymer Science ((POLYMER,volume 27))

Abstract

The development of linear elastic fracture mechanics is given with a special emphasis on its application to the testing of polymers. The modelling of crazes and plastic zones is discussed and then developed to describe time-dependent crack and craze growth, including crack stability phenomena.

These results are then applied to particular problems, such as environmental stress cracking, fatigue and impact testing.

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Abbreviations

A :

Craze pore area

a :

Crack length

B :

Plate thickness

B c :

Crack width (for grooved specimens)

b :

Craze thickness; position of point load

C :

Compliance (Δ/P); constant for craze growth; creep compliance function

c :

Specific heat

D :

Depth of specimen

d 0 :

Craze parameter

E :

Young's modulus

e :

Strain

G :

Strain energy release rate

G IC :

Energy per unit area of crack in mode I

H :

Activation energy

K :

Stress intensity factor (SIF)

K I :

SIF in mode I

K II :

SIF in mode II

K IC :

SIF in mode I at fracture

K c1 :

Plane strain K IC

Kc2 :

Plane stress K IC

k :

Thermal conductivity

L :

Half span

l 0 :

Craze parameter

m :

Constant; mass of specimen

N :

Number of cycles

n :

Constant; (d ln e)/(d ln t) in creep

P :

Load

R :

Stress rate; gas constant

r :

Coordinate

r p :

Plastic zone size or craze length

r c :

π/8K 2IC /σ 2c

S :

Surface length

T :

Temperature — absolute degrees

t :

Time

U :

Energy

u :

Displacement or velocity in x direction

V :

Velocity

v :

Displacement or velocity in y direction

W :

Strain energy density

X :

a−ξ

x :

Coordinate or a/D

Y :

Finite width correction factor

y :

Coordinate

α :

Constant; viscoelastic transition

β :

Viscoelastic transition

γ :

Viscoelastic transition; surface work

Δ :

Deflection

δ :

Displacement in craze

δ * :

Displacement in craze at crack tip

δ * c :

Critical value of δ * at fracture

κ :

3 − 4 ν for plane strain 3−ν/1+ν for plane stress

λ:

Constant

μ :

Shear modulus; viscosity

ν :

Poisson's ratio

ξ :

Working variable — length

ρ :

Density

σ :

Stress

σ c :

Craze or cohesive stress

σ y :

Yield stress

τ :

Working variable — time

φ :

Stress function; axisymmetric parameter; calibration function

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Authors and Affiliations

  1. Department of Mechanical Engineering, Imperial College of Science and Technology, SW7 2BX, London, Great Britain

    J. Gordon Williams

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  1. J. Gordon Williams
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© 1978 Springer-Verlag

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Williams, J.G. (1978). Applications of linear fracture mechanics. In: Failure in Polymers. Advances in Polymer Science, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08829-6_2

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  • DOI: https://doi.org/10.1007/3-540-08829-6_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08829-5

  • Online ISBN: 978-3-540-35823-7

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