1. Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

2. Strength vs.Toughness Strength Resistance of a material
to plastic flow
Toughness
Resistance of a material
to the propagation
of a crack
Figure 8.1
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

3. Testing for Toughness
Figure 8.2
This type of test provides a comparison of the toughness of
materials – however, it does not provide a way to express
toughness as a material property
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

4. Remote stress applied to a cracked material:
Figure 8.3
The local stress σlocal is
proportional to the number
of lines of force which rises
steeply as the crack tip is
approached
c – crack length
r – distance from crack tip
σ – remote stress
Y – geometric constant
* valid when r << c
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

5. Stress Intensity Factor
For any value of r, the local
stress scales with σ√πc
Mode 1 stress intensity factor
Mode 1 indicates tensile loading normal to the crack
Typically, loading modes are designated by Roman
numerals – K1 would be designated as KI – K1 is used
throughout the book which goes against the universally
accepted use of Roman numerals
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

6. Fracture Toughness Cracks propagate when the stress intensity factor
exceeds a critical value – the critical value is known
as the fracture toughness K1c
Figure 8.4
σ* - tensile stress at
which the crack
propagates
* For this geometry, the value of Y
is 1 if c << w
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

7. Energy Release Rate G and Toughness Gc
For a crack to grow, sufficient external work must be
done which is in the form of released elastic energy
Figure 8.5
γ – surface energy
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

8. Process Zone A plastic zone forms at the crack tip where the stress
Figure 8.6
A plastic zone forms at the
crack tip where the stress
would otherwise exceed
the yield strength
Size of process zone:
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

9. A material transitions from yield to fracture
Crack length necessary
for fracture at a materials
yield strength
A material transitions
from yield to fracture
at a critical crack length
Figure 8.7
Stress required for
fracture for a given
crack length
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

10. Critical crack lengths are a measure of the
damage tolerance of a material
Table 8.1
Tough metals are able to contain
large cracks but still yield in a
predictable, ductile, manner
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

11. Fracture Toughness – Modulus Chart
Figure 8.8
Values range from
0.01 – 100 MPa√m
Contours show
the toughness, Gc
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

12. Fracture Toughness – Strength Chart
Figure 8.9
Transition crack
length plotted on
chart – values can
range from near-
atomic dimensions
for ceramics
to almost a meter
for ductile metals
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

13. Surface Energy When a new surface is created, atomic bonds
are broken, requiring some fraction of the
cohesive energy, Hc
Figure 8.10
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

14. Brittle ‘Cleavage’ Fracture
Figure 8.11
Characteristic of ceramics
and glasses
Local stress rises as 1/√r toward
the crack tip – if it exceeds that
required to break inter-atomic
bonds they separate, giving
a cleavage fracture
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

15. Tough ‘Ductile’ Fracture
Materials contain inclusion which act as stress
concentrations when loaded – the inclusions
separate from the matrix causing voids to n
nucleate and grow, causing fracture
Figure 8.12
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

16. Ductile Fracture of Cracked Sample
Figure 8.13
If a material is ductile, a plastic
zone forms at the crack tip
Within the plastic zone, voids
nucleate, join, and link to cause
fracture
The plasticity blunts the crack tip,
reducing the severity of the stress
concentration
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

17. Ductile-to-Brittle Transition
At low temperatures some metals and all
polymers become brittle
As temperatures decrease, yield strengths
of most materials increase leading to a
reduction in the plastic zone size
Only metals with an FCC structure remain
ductile at the lowest temperatures
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

18. Embrittlement from Chemical Segregation
Impurities in an alloy
are normally found in
grain boundaries – this
leads to a network of
low-toughness paths
that can lead to brittle
fracture
Figure 8.14
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

19. The Strength-Toughness Trade-Off
Figure 8.15
Increasing the yield
strength of a metal
decreasing the size
of the plastic zone
surrounding a crack –
this leads to decreased
toughness
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

20. Manipulating Polymers
Fillers, impact modifiers, and fiber reinforcement
can significantly alter the fracture toughness
of polymers
Figure 8.16
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

21. Toughening by Fibers When a crack grows in a matrix, the fibers
remain intact and bridge the crack
Figure 8.17
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon