Characteristic ‐ plots for metals
35
Characteristic ‐ plots for metals
Typ I
Continuous transition from elastic to plastic deformation.
Typically observed in fcc metals and their alloys like
aluminum, nickel, copper, austenitic stainless steel etc.
36
Characteristic ‐ plots for metals
Typ II
Characterized by the presence of lower yield point and an
almost horizontal region.
Sporadically observed in some solid solution strengthened
Cu‐ and Al‐based alloys 37
Characteristic ‐ plots for metals
Typ III
Characterized by both upper and lower yield point followed
by almost horizontal region.
Typically observed in low carbon steels
38
Characteristic ‐ plots for metals
Typ IV
Characterized by elastic, ideal plastic behavior with little or
no strain hardening.
Sporadically observed in heavily pre‐worked materials and
in certain materials deformed at high temperatures. 39
Characteristic ‐ plots for metals
Typ V
Characterized by almost brittle behavior with little plastic
strain, no necking.
Observed in alloyed and unalloyed steel in martensitic
condition 40
Characteristic ‐ plots for metals
Typ VI
Characterized by serrated stress‐strain curves.
Typically observed plain carbon steels in the temperature
range of 250–400 °C
41
Un‐ and reloading in plastic region
Unloading in plastic region
traces a straight line with
slope virtually equal to the
loading Young‘s modulus.
Elastic portion of the total
strain is recovered
Reapplication of load
traverses the same path as
during unloading
Yielding at reloading occurs
at the initial unloading
stress level
42
Toughness
Toughness is the ability of a material to absorb energy
before fracturing
It is the area under the ‐ plot upto the point of
fracture
43
Toughness
Question: Why are metals more popular than ceramics as
structural components? 44
Hardness testing
Defined as resistance of a material against localized plastic
deformation (indentation or scratch).
Basic principle
An indenter is forced into the test surface under
controlled loading conditions
Depth/size of the indentation is measured and hardness
is calculated therefrom
Most used materials analysis technique, because:
Simple, inexpensive – no special sample preparation
The procedure is quasi non‐destructive
Can often be easily correlated to other material
properties like tensile strength 45
Schematic of typical hardness test
46
Different hardness test methods
47
Brinell hardness test
Hard, spherical indenter made of
either hardened steel or
tungsten carbide is used
Standard loads range between
500 and 3000 kg in 500 kg
intervals.
After load application for a specific time, the indentation
diameter is measured using low power microscope
Hardness (denoted as BHN) is calculated using load,
indenter and indentation diameter
48
Vickers hardness test
Indenter is a square
based diamond
pyramid.
Careful sample
preparation is
necessary.
Applied loads usually vary between 1 kg. And 120 kg.
Lengths of the two diagonals of the indenter are
measured under a microscope
Vickers hardness (VHN or DPH) is calculated from the
applied load and the measured average length of the
two indentation diagonals 49
Rockwell hardness test
Most common method due to ist simplicity
Several scales based on indenter type and load are used
A unitless hardness number is determined from the
difference of depth of penetration resulting from a
minor load and subsequent major load 50
Fracture
Fracture is defined as the separation of a body into two or
more parts in response of an external load. Fracture is the
ultimate failure of a component and design should avoid it.
Modes of fracture in metals
Ductile fracture: Involves
substantial plastic deformation
with high energy absorption
before fracture
Brittle fracture: Involves little
or no plastic deformation with
very little energy absorption. 51
Ductile fracture
The most common feature of ductile fracture is the
appearance of a moderate to significant amount of
necking
Stages of ductile fracture
Stage I
After the initiation of necking, small cavities
or microvoids form at local inhomogeneities
at the neck region.
52
Ductile fracture
The most common feature of ductile fracture is the
appearance of a moderate to significant amount of
necking
Stages of ductile fracture
Stage II
With continuing deformation the
microvoids grow and coalesce to form
elliptical crack with long axis normal to
loading direction.
53
Ductile fracture
The most common feature of ductile fracture is the
appearance of a moderate to significant amount of
necking
Stages of ductile fracture
Stage III
Final fracture occurs by rapid propagation of
the crack around the outer periphery of the
neck by shear deformation at an angle of
45° with the tensile axis.
54
Brittle fracture
The direction of crack propagation is nearly perpendicular
to the direction of applied stress. Fracture surfaces are
macroscopically flat and shiny.
Broad classes of brittle fracture
Transgranular fracture: The
cracks pass through grains with
little or no change of direction
Intergranular fracture: Crack
propagation occurs mostly
along the grain boundaries
55
Fractography
Detailed study of the microscopic features of the fracture
process, normally using scanning electron microscope
(SEM). SEM is used due to its higher resolution and depth
of field.
Fractographic appearance of ductile fracture
Fracture surface consists of
numerous spherical
dimples
Each dimple correspond to
one half of a microvoid
formed before crack
nucleation 56
Fractography
Detailed study of the microscopic features of the fracture
process, normally using scanning electron microscope
(SEM). SEM is used due to its higher resolution and depth
of field.
Fractographic appearance of brittle transgranular fracture
57
Fractography
Detailed study of the microscopic features of the fracture
process, normally using scanning electron microscope
(SEM). SEM is used due to its higher resolution and depth
of field.
Fractographic appearance of brittle intergranular fracture
58
Real world examples of fracture
59
Real world examples of fracture
60
Real world examples of fracture
61
Real world examples of fracture
62
Theoretical fracture strength
Curve showing the variation of cohesive force as a
function of interatomic spacing
Maximum of the curve theoretical fracture strength
Approximately (E/10)
63
Theoretical strength & actual strength
Theoretical fracture strength of materials is approx. 35 – 70
times higher than the real strength of materials
64
Concept of fracture mechanics
The actually observed lower fracture strength of materials
can be attributed to defects like
Preexisting surface/interior cracks
Flaws introduced by microscopic or macroscopic plastic
deformation
Macroscopic discontinuities like voids, inclusions,
notches, sharp corners, scratches etc.
The defects cause stress concentration in their vicinity,
thereby significantly raising the local stress values to much
higher values fracture occurs at lower applied stress
Due to this stress raising effect, these flaws are also called
stress raisers 65
Stress concentration at crack tip
For an elliptical internal crack of length 2a, tip radius of
curvature t, oriented normal to the applied stress 0
1
a 2 m = Maximum stress at the crack
m 2 0 tip
66
Stress concentration at crack tip
1
m a 2
Kt 2
0 t
The quantity Kt is known as – stress concentration factor
Stress concentration factor increases with increasing
crack length and decresing crack tip radius
The maximum stress at the crack tip for an internal crack
with length 2a is identical to that of a surface crack of
length a
Surface cracks are more deleterious than internal
cracks
67
Fracture of a brittle material
Griffith theory of brittle fracture
Under tensile stress a crack propagates to cause brittle
fracture when the decrease in elastic strain energy is at
least equal to the energy increase necessary to create the
new crack surface.
For thin plates, the fracture stress in a brittle solid is
denoted as:
1
2 E 2
E = Young‘s modulus
F c = Half length of an internal crack
c
is defined as the surface energy per unit area and for
completely brittle solids,
Material toughness, c = 2 68
Fracture involving plastic deformation
Any plastic deformation corresponds to additional work
expended for crack propagation crack extension is
hindered and higher fracture stress than that predicted
for truly brittle solids is necessary.
Stress intensity at the crack tip causes local yielding at
the crack tip and the plastic zone extends a distance
above and below the fracture plane.
The toughness in Griffitth equation becomes:
c = 2( + p)
p is a function of material yield strength and also
temperature.
69
Fracture involving plastic deformation
70
Crack propagation modes
Mode I, tensile Mode II, shear Mode III, shear
stress normal to stress normal to stress parallel to
crack surface crack surface crack leading edge
Toughness corresponding to each crack propagation
mode is different
A combination of three modes observed in general case
Mode I is most common and this will be the focus of
further discussion 71
Fracture toughness
Defined as the resistance to brittle fracture in a material
containing cracks.
c = Critical stress for crack propagation
a = Crack length
Y = Dimensionless constant with value almost unity
Kc = Fracture toughness
Fracture toughness has a unit of MPa√m
For relatively thin specimens, fracture toughness is a
function of material thickness and generally increases
with thickness.
72
Fracture toughness
The fracture toughness value for thick specimens (under
plain strain conditions) is constant.
KIc, defined as the plane strain fracture toughness for Mode
I loading, is a material constant and is most commonly cited
as the fracture toughness of a material
Factors affecting Kic
KIC as Temperatur and strain rate
Within a class of alloys, KIc as yield strength
As grain size of a material , KIc
73
Fracture toughness & material class
Material design aims for both high yield strength and high
fracture toughness 74
Fracture toughness & material class
Fracture toughness of ceramics are rather low, they are
inherently brittle 75
Fracture toughness & material class
Metals have high fracture toughness
76
Fracture toughness & material class
Steels have both high toughness and high yield strength
reason behind their widespread use as structural material 77
Fracture mechanics design philosophy
Design presupposes that cracks are present in the
structure
The size of the cracks needs to be estimated
The largest crack that may be present is taken as that
crack size that is not detected by Non‐Destructive
Testing (NDT) e.g.
‐ ultrasonic testing (UT)
‐ Magnetic testing (MT)
‐ X‐ray imaging (RT)
‐ Computer tomography (CT)
Using fracture toughness definition, the fracture
strength is determined based on this crack length the
operating stress must be less than this stress 78
Fracture mechanics design philosophy
79
Impact testing
Prior to the advent of fracture mechanics, impact testing
was the preferred testing method.
Fracture toughness testing Impact testing
Relatively new method Much older method and
is still widely used
Results are more Mainly qualitative
quantitative
Test equipment, sample Rather inexpensive
preparation and testing method of testing
are expensive
80
