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

2. Strength and Stiffness
Stress is applied to a material by loading it
Strain – a change of shape – is its response
Stiffness is the resistance to change of shape that is elastic – the material will return to its original shape when unloaded
Strength is the resistance to permanent distortion or total failure
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

3. Material Properties
Stress and strain are not material properties – they
describe a stimulus and a response
Stiffness and strength are material properties which are
measured by the elastic modulus (E), elastic
limit (σy), and tensile strength (σts)
Stiffness, strength, and density are three material
properties central to mechanical design
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

4. Double-weighing method for calculating density
Mass per unit volume – kg/m3 or lb/in3
Figure 4.1
Double-weighing method for calculating density
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

5. Modes of Loading
Figure 4.2
(a) – axial tension (b) – compression (c) – axial tension on one side and compression on the opposite side (d) – torsion (e) – bi-axial tension or compression
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

6. Stress 1 N/m2 = 1 Pascal (Pa) 103 Pa = 1 MPa 1 lb/in2 = 1 psi
103 psi = 1 ksi
Figure 4.3
(a)
Force applied normal to surface
Positive F indicates tension
Negative F indicates compression
(b)
Force applied parallel to surface
Shaded plane carries the shear stress
(c)
Equally applied tensile and compressive forces on all six sides of a cubic element
Hydrostatic pressure
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

7. Strain is the ratio of two lengths
Figure 4.3
Strain is the ratio of two lengths
and is therefore
dimensionless
(a)
Tensile stress lengthens the element causing a tensile strain (+)
Compressive stress shortens the element causing a compressive strain (-)
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

8. Stress-Strain Curves Initial portion of curve is approximately
Figure 4.4
Initial portion of curve is approximately
linear and is elastic – the material
returns to its original shape once the
stress is removed
Within the linear elastic region, strain is
proportional to stress
E: Young’s modulus
G: shear modulus
K: bulk modulus
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

9. Stress-Strain Curve – Brittle Response
Entire response is elastic –
no plastic deformation
Yield strength not reached
before failure
Young’s modulus determined
by calculating the slope of
this region
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

10. Ductile Response Tensile strength is maximum stress on the curve
Yield strength determined by
standard offset methods
Permanent deformation occurs at stresses beyond the yield strength – material will not return to its original shape past this point
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

11. Poisson’s Ratio Relates the Young’s modulus, shear modulus, and
Negative of the ratio of transverse strain
to axial strain in tensile loading
Relates the Young’s modulus, shear modulus, and
bulk modulus to one another
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

12. Poisson’s Ratio - Elastomers
Rubber is easy to stretch in tension, but becomes very stiff
when constrained from changing shape or loaded
hydrostatically
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

13. Stress-Free Strain
In certain situations, strain is not caused by stress;
however, stresses can develop if the body suffering
the strain is constrained
Figure 4.5
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

14. Material-Property Charts: Modulus - Density
Figure 4.6
Identifies materials that
are both stiff and light
Critical for material selection
of stiffness-limited designs
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

15. Modulus – Relative Cost
Figure 4.7
Identifies materials that are both stiff and cheap
Useful when the objective is minimizing cost
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

16. Anisotropy
The properties of most materials – glasses, ceramics, polymers and metals – do not depend on the direction in which they are measured across the material
Certain materials are considered anisotropic – meaning their properties are dependant upon which direction in the material they are being measured
Woods are stiffer along the grain than with it;
fiber composites are stronger and stiffer parallel
to the direction of the fibers than perpendicular
to them
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

17. What Determines Density
Density is mostly dependant on atomic weight
Metals are dense because their atoms are heavy –
iron has an atomic weight of 56
Polymers have low densities because they are made of light
atoms – carbon has an atomic weight of 12 while hydrogen
has an atomic weight of 1
The size of atoms and the way in which they are packed also
influence density, but to a much lesser degree
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

18. Atomic Packing Most materials are crystalline – have a regularly
repeating pattern of structural units
Atoms often behave as if they are
hard and spherical
Layer A represents the close-packed
layer – there is no way to pack the atoms
more closely than this
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

19. Atomic structures are close-packed in three dimension
Close-packed hexagonal: ABABAB stacking sequence
Face-centered cubic: ABCABC stacking sequence
Packing fraction for CPH and FCC structures is 0.74 – meaning
spheres occupy 74% of all available space
Figure 4.8
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

20. Non Close-Packed Structures
Figure 4.9
Body-centered cubic:
ABABAB packing sequence
Packing fraction = 0.68
Figure 4.10
Amorphous structure:
Packing fraction ≤ 0.64
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

21. Unit Cell Red lines define the cell while spheres represent
individual atoms
Shaded regions represent close or closest packed plane
Figure 4.11
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

22. Crystal Lattice (a): hexagonal cell
Figure 4.12
(a): hexagonal cell
(b): cubic cell
(c): cell with different length edges
Lattice points are the points at which cell edges meet
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

23. Atomic Packing in Ceramics
Figure 4.13
(a): Hexagonal unit cell with a W-C atom pair associated
with each lattice point
(b): Cubic unit cell with a Si-C atom pair associated with each
lattice point
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

24. Atomic Packing in Glasses
Amorphous silica is the bases of most glasses
Rapid cooling allows material to maintain amorphous
structure achieved after melting
Figure 4.14
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

25. Atomic Packing in Polymers
Figure 4.15
Atomic Packing in Polymers
Figure 4.16
Polymers have a
carbon-carbon
backbone with
varying side-groups
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

26. Polymer chains bond to each other through weak hydrogen bonds
Figure 4.17
Polymer chains bond to each other through weak hydrogen
bonds
Red lines indicate strong cross-linked carbon-carbon bonds
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

27. Polymer Structure (a): No regular repeating pattern of
Figure 4.18
(a): No regular repeating pattern of
polymer chains – results in a
glassy or amorphous structure
(b): Regions in which polymer chains
line up and register – forms
crystalline patches
(c): Occasional cross-linking allowing
they polymer to stretch – typical
of elastomers
(d): Heavily cross-linked polymers
exhibit chain sliding – typical of
epoxy
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

28. Cohesive Energy Atoms are held together by bonds
Figure 4.19
Atoms are held together by bonds
that behave like springs
Cohesive energy is a measure of
the strength of the bonds
Bond Stiffness
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

29. Bond stiffness largely determines the value of the modulus - E
Table 4.1
Bond stiffness largely determines the value
of the modulus - E
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

30. Elastic Moduli of Elastomers
Undeformed polymer chains has high randomness (entropy)
Stretched polymer chains resemble more of a crystalline structure and has a lower entropy
Moduli of elastomers is generally low and unlike metals, increases with temperature
Figure 4.20
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

31. Rule of Mixtures Density of solid solution or hybrid materials
Modifying the modulus and density is most effective when done at a macro scale such as creating a hybrid rather than a micro scale such as alloying a metal
Density of solid solution or hybrid materials
f volume fraction of material or element A
ρA density of material or element A
ρB density of material or element B
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

32. Composites – Density and Modulus
Figure 4.21
Polymer matrix composite (PMC)
Ceramic matrix composite (CMC)
Metal matrix composite (MMC)
Modulus can be altered by
combining stiff fibers with a
less-stiff matrix
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

33. ρr – density of reinforcement ρm – density of matrix
Modulus of composite bracketed by two bounds:
Upper bound: assumes that, on loading, both components strain
by the same amount, like springs in parallel
Lower Bound: assumes that, on loading, each component carries
the same stress, like springs in series
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

34. Range of modulus and density properties for composites
with a ceramic reinforcement and polymeric matrix
Figure 4.22
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

35. Foams – Density and Modulus
Figure 4.23
ρs and Es are the density and modulus f the solid from which the foam is made
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

36. Modulus and density range for foams made from
elastomers and polymers – foaming lowers
both of these properties
Figure 4.24
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon