Short Notes: Fatigue Strength and The S-N Diagram | Short Notes for Mechanical Engineering PDF Download

 Page 1


Fatigue Strength and The S-N Diagram 
Fatigue is a phenomenon associated with variable loading or more precisely to 
cyclic stressing or straining of a material. Just as we human beings get fatigue 
when a specific task is repeatedly performed, in a similar manner metallic 
components subjected to variable loading get fatigue, which leads to their 
premature failure under specific conditions.
Fatigue loading is primarily the type of loading which causes cyclic variations in the 
applied stress or strain on a component. Thus any variable loading is basically a 
fatigue loading. In reality, most mechanical components experience variable 
loading due to
• Change in the magnitude of applied load Example: punching or shearing 
operations
• Change in direction of load application Example: a connecting rod -
• Change in point of load application Example: a rotating shaft.
There are different types of fatigue/variable loading. The worst case of fatigue 
loading is the case known as a fully-reversible load. One cycle of this type of 
loading occurs when a tensile stress of some value is applied to an unloaded part 
and then released, then a compressive stress of the same value is applied and 
released.
The fatigue behaviour of a specific material, heat-treated to a specific strength 
level, is determined by a series of laboratory tests on a large number of apparently 
identical samples of that specific material.
Fatigue Failure
Page 2


Fatigue Strength and The S-N Diagram 
Fatigue is a phenomenon associated with variable loading or more precisely to 
cyclic stressing or straining of a material. Just as we human beings get fatigue 
when a specific task is repeatedly performed, in a similar manner metallic 
components subjected to variable loading get fatigue, which leads to their 
premature failure under specific conditions.
Fatigue loading is primarily the type of loading which causes cyclic variations in the 
applied stress or strain on a component. Thus any variable loading is basically a 
fatigue loading. In reality, most mechanical components experience variable 
loading due to
• Change in the magnitude of applied load Example: punching or shearing 
operations
• Change in direction of load application Example: a connecting rod -
• Change in point of load application Example: a rotating shaft.
There are different types of fatigue/variable loading. The worst case of fatigue 
loading is the case known as a fully-reversible load. One cycle of this type of 
loading occurs when a tensile stress of some value is applied to an unloaded part 
and then released, then a compressive stress of the same value is applied and 
released.
The fatigue behaviour of a specific material, heat-treated to a specific strength 
level, is determined by a series of laboratory tests on a large number of apparently 
identical samples of that specific material.
Fatigue Failure
• Machine elements subjected to fluctuating stresses usually fail at stress 
levels much below their ultimate strength and in many cases below the yield 
point of the material too. These failures occur due to a very large number of 
stress cycle and are known as fatigue failure.
• A fatigue failure resembles to a brittle fracture and occurs without any 
noticeable plastic deformation or necking.
• It's sudden occurrence, without any noticeable warning, makes it dangerous. 
The fracture surfaces are flat and perpendicular to the stress axis.
• Fatigue failure begins with a microscopic crack that occurs due to some 
discontinuity (oil holes, keyways, screw threads etc.), surface irregularities 
due to machining (scratches, stamp marks, inspection marks etc.) or material 
defects. This crack propagates due to fluctuating stresses, grows continually 
and finally, sudden fracture takes place.
Types of Cyclic Stress
• For design purpose, only maximum and minimum value of stress is important 
and not the waveform
• Important types of cyclic stresses depending upon the level of minimum and 
maximum stress between which the stress fluctuates.
Completely Reversed Stress
• Extreme values of stress are of equal magnitude and opposite nature with 
mean equal to zero
Repeated Stress
• Stress varies from zero to certain maximum value (nature of stress does not 
change)
Fluctuating Stress
• The minimum value and maximum value of stress is of same nature (tensile 
or compressive)
Page 3


Fatigue Strength and The S-N Diagram 
Fatigue is a phenomenon associated with variable loading or more precisely to 
cyclic stressing or straining of a material. Just as we human beings get fatigue 
when a specific task is repeatedly performed, in a similar manner metallic 
components subjected to variable loading get fatigue, which leads to their 
premature failure under specific conditions.
Fatigue loading is primarily the type of loading which causes cyclic variations in the 
applied stress or strain on a component. Thus any variable loading is basically a 
fatigue loading. In reality, most mechanical components experience variable 
loading due to
• Change in the magnitude of applied load Example: punching or shearing 
operations
• Change in direction of load application Example: a connecting rod -
• Change in point of load application Example: a rotating shaft.
There are different types of fatigue/variable loading. The worst case of fatigue 
loading is the case known as a fully-reversible load. One cycle of this type of 
loading occurs when a tensile stress of some value is applied to an unloaded part 
and then released, then a compressive stress of the same value is applied and 
released.
The fatigue behaviour of a specific material, heat-treated to a specific strength 
level, is determined by a series of laboratory tests on a large number of apparently 
identical samples of that specific material.
Fatigue Failure
• Machine elements subjected to fluctuating stresses usually fail at stress 
levels much below their ultimate strength and in many cases below the yield 
point of the material too. These failures occur due to a very large number of 
stress cycle and are known as fatigue failure.
• A fatigue failure resembles to a brittle fracture and occurs without any 
noticeable plastic deformation or necking.
• It's sudden occurrence, without any noticeable warning, makes it dangerous. 
The fracture surfaces are flat and perpendicular to the stress axis.
• Fatigue failure begins with a microscopic crack that occurs due to some 
discontinuity (oil holes, keyways, screw threads etc.), surface irregularities 
due to machining (scratches, stamp marks, inspection marks etc.) or material 
defects. This crack propagates due to fluctuating stresses, grows continually 
and finally, sudden fracture takes place.
Types of Cyclic Stress
• For design purpose, only maximum and minimum value of stress is important 
and not the waveform
• Important types of cyclic stresses depending upon the level of minimum and 
maximum stress between which the stress fluctuates.
Completely Reversed Stress
• Extreme values of stress are of equal magnitude and opposite nature with 
mean equal to zero
Repeated Stress
• Stress varies from zero to certain maximum value (nature of stress does not 
change)
Fluctuating Stress
• The minimum value and maximum value of stress is of same nature (tensile 
or compressive)
Alternating Stress
• Stress changes its nature and magnitude of extreme values of tensile and 
compressive stress is not same.
Note: All variable stresses can be considered to be made of two components - 
static component called mean stress (sm ) and a variable component called stress 
amplitude (sa ).
• Mean Stress =
^m.ax ^ m in 
2
• Stress Amplitude =
®max ^m in 
° a ~ 2
• Stress Range=
^ r ®m ax ®m in
• Stress Ratio=
^ ax
^ min
• Amplitude Ratio,
Fatigue Curve (S-N Curve) & Endurance Limit
• Specimen subjected to constant bending moment is rotated at a very high­
speed due to which fibres of the specimen (except those on neutral axis) 
undergo repeated stress reversals (maximum tensile stress to maximum 
compressive stress).
• Stress-time plot is repeated for a number of similar specimens, subjecting 
them to different values of stress and number of stress reversals that the 
specimen survives before fracture are counted.
• First test is performed by subjecting the specimen to stress, below ultimate 
tensile strength and subsequent tests are performed at decreased levels of 
stress.
S-N Diagram
The S-N Diagram Tests on several specimens are conducted under identical 
conditions with varying levels of stress amplitude.
Page 4


Fatigue Strength and The S-N Diagram 
Fatigue is a phenomenon associated with variable loading or more precisely to 
cyclic stressing or straining of a material. Just as we human beings get fatigue 
when a specific task is repeatedly performed, in a similar manner metallic 
components subjected to variable loading get fatigue, which leads to their 
premature failure under specific conditions.
Fatigue loading is primarily the type of loading which causes cyclic variations in the 
applied stress or strain on a component. Thus any variable loading is basically a 
fatigue loading. In reality, most mechanical components experience variable 
loading due to
• Change in the magnitude of applied load Example: punching or shearing 
operations
• Change in direction of load application Example: a connecting rod -
• Change in point of load application Example: a rotating shaft.
There are different types of fatigue/variable loading. The worst case of fatigue 
loading is the case known as a fully-reversible load. One cycle of this type of 
loading occurs when a tensile stress of some value is applied to an unloaded part 
and then released, then a compressive stress of the same value is applied and 
released.
The fatigue behaviour of a specific material, heat-treated to a specific strength 
level, is determined by a series of laboratory tests on a large number of apparently 
identical samples of that specific material.
Fatigue Failure
• Machine elements subjected to fluctuating stresses usually fail at stress 
levels much below their ultimate strength and in many cases below the yield 
point of the material too. These failures occur due to a very large number of 
stress cycle and are known as fatigue failure.
• A fatigue failure resembles to a brittle fracture and occurs without any 
noticeable plastic deformation or necking.
• It's sudden occurrence, without any noticeable warning, makes it dangerous. 
The fracture surfaces are flat and perpendicular to the stress axis.
• Fatigue failure begins with a microscopic crack that occurs due to some 
discontinuity (oil holes, keyways, screw threads etc.), surface irregularities 
due to machining (scratches, stamp marks, inspection marks etc.) or material 
defects. This crack propagates due to fluctuating stresses, grows continually 
and finally, sudden fracture takes place.
Types of Cyclic Stress
• For design purpose, only maximum and minimum value of stress is important 
and not the waveform
• Important types of cyclic stresses depending upon the level of minimum and 
maximum stress between which the stress fluctuates.
Completely Reversed Stress
• Extreme values of stress are of equal magnitude and opposite nature with 
mean equal to zero
Repeated Stress
• Stress varies from zero to certain maximum value (nature of stress does not 
change)
Fluctuating Stress
• The minimum value and maximum value of stress is of same nature (tensile 
or compressive)
Alternating Stress
• Stress changes its nature and magnitude of extreme values of tensile and 
compressive stress is not same.
Note: All variable stresses can be considered to be made of two components - 
static component called mean stress (sm ) and a variable component called stress 
amplitude (sa ).
• Mean Stress =
^m.ax ^ m in 
2
• Stress Amplitude =
®max ^m in 
° a ~ 2
• Stress Range=
^ r ®m ax ®m in
• Stress Ratio=
^ ax
^ min
• Amplitude Ratio,
Fatigue Curve (S-N Curve) & Endurance Limit
• Specimen subjected to constant bending moment is rotated at a very high­
speed due to which fibres of the specimen (except those on neutral axis) 
undergo repeated stress reversals (maximum tensile stress to maximum 
compressive stress).
• Stress-time plot is repeated for a number of similar specimens, subjecting 
them to different values of stress and number of stress reversals that the 
specimen survives before fracture are counted.
• First test is performed by subjecting the specimen to stress, below ultimate 
tensile strength and subsequent tests are performed at decreased levels of 
stress.
S-N Diagram
The S-N Diagram Tests on several specimens are conducted under identical 
conditions with varying levels of stress amplitude.
F jtig w s t n f f l g t f i - S r
• The cyclic stress level of the first set of tests is some large percentage of the| 
Ultimate Tensile Stress (UTS), which produces failure in a relatively small 
number of cycles. Subsequent tests are run at lower cyclic stress values until 
a level is found at which the samples will survive 10 million cycles without 
failure.
• Results of the tests are plotted between stress (S) and the number of cycles 
(N), generally on a log-log scale. S-N Curve is shown In figure below:
• The ordinate of the S-N curve is called Fatigue Strength (Sf), which can be 
defined as the maximum stress that the material can withstand for a specified 
number of stress reversals.
• For ferrous metals and their alloys, S-N curve becomes horizontal after 106 to 
107 cycles, which means that the material can survive an infinite number of 
stress reversals if the induced stress is below this level.
• Stress corresponding to this horizontal line is called endurance limit or 
fatigue limit.
o The zone below 103 cycles is considered as low cycle fatigue 
° the zone between 103 and 106 cycles is high cycle fatigue with a finite 
life and
° beyond 106 cycles, the zone is considered to be high cycle fatigue with 
infinite life.
• Fatigue or Endurance Limit (S'e ) can be defined as the maximum amplitude of 
completely reversed stress that the standard specimen can sustain for an 
unlimited number of cycles without fatigue failure.
• Low Cycle Fatigue: The body of knowledge available on fatigue failure from 
N=1 to N=1000 cycles is generally classified as low-cycle fatigue.
Page 5


Fatigue Strength and The S-N Diagram 
Fatigue is a phenomenon associated with variable loading or more precisely to 
cyclic stressing or straining of a material. Just as we human beings get fatigue 
when a specific task is repeatedly performed, in a similar manner metallic 
components subjected to variable loading get fatigue, which leads to their 
premature failure under specific conditions.
Fatigue loading is primarily the type of loading which causes cyclic variations in the 
applied stress or strain on a component. Thus any variable loading is basically a 
fatigue loading. In reality, most mechanical components experience variable 
loading due to
• Change in the magnitude of applied load Example: punching or shearing 
operations
• Change in direction of load application Example: a connecting rod -
• Change in point of load application Example: a rotating shaft.
There are different types of fatigue/variable loading. The worst case of fatigue 
loading is the case known as a fully-reversible load. One cycle of this type of 
loading occurs when a tensile stress of some value is applied to an unloaded part 
and then released, then a compressive stress of the same value is applied and 
released.
The fatigue behaviour of a specific material, heat-treated to a specific strength 
level, is determined by a series of laboratory tests on a large number of apparently 
identical samples of that specific material.
Fatigue Failure
• Machine elements subjected to fluctuating stresses usually fail at stress 
levels much below their ultimate strength and in many cases below the yield 
point of the material too. These failures occur due to a very large number of 
stress cycle and are known as fatigue failure.
• A fatigue failure resembles to a brittle fracture and occurs without any 
noticeable plastic deformation or necking.
• It's sudden occurrence, without any noticeable warning, makes it dangerous. 
The fracture surfaces are flat and perpendicular to the stress axis.
• Fatigue failure begins with a microscopic crack that occurs due to some 
discontinuity (oil holes, keyways, screw threads etc.), surface irregularities 
due to machining (scratches, stamp marks, inspection marks etc.) or material 
defects. This crack propagates due to fluctuating stresses, grows continually 
and finally, sudden fracture takes place.
Types of Cyclic Stress
• For design purpose, only maximum and minimum value of stress is important 
and not the waveform
• Important types of cyclic stresses depending upon the level of minimum and 
maximum stress between which the stress fluctuates.
Completely Reversed Stress
• Extreme values of stress are of equal magnitude and opposite nature with 
mean equal to zero
Repeated Stress
• Stress varies from zero to certain maximum value (nature of stress does not 
change)
Fluctuating Stress
• The minimum value and maximum value of stress is of same nature (tensile 
or compressive)
Alternating Stress
• Stress changes its nature and magnitude of extreme values of tensile and 
compressive stress is not same.
Note: All variable stresses can be considered to be made of two components - 
static component called mean stress (sm ) and a variable component called stress 
amplitude (sa ).
• Mean Stress =
^m.ax ^ m in 
2
• Stress Amplitude =
®max ^m in 
° a ~ 2
• Stress Range=
^ r ®m ax ®m in
• Stress Ratio=
^ ax
^ min
• Amplitude Ratio,
Fatigue Curve (S-N Curve) & Endurance Limit
• Specimen subjected to constant bending moment is rotated at a very high­
speed due to which fibres of the specimen (except those on neutral axis) 
undergo repeated stress reversals (maximum tensile stress to maximum 
compressive stress).
• Stress-time plot is repeated for a number of similar specimens, subjecting 
them to different values of stress and number of stress reversals that the 
specimen survives before fracture are counted.
• First test is performed by subjecting the specimen to stress, below ultimate 
tensile strength and subsequent tests are performed at decreased levels of 
stress.
S-N Diagram
The S-N Diagram Tests on several specimens are conducted under identical 
conditions with varying levels of stress amplitude.
F jtig w s t n f f l g t f i - S r
• The cyclic stress level of the first set of tests is some large percentage of the| 
Ultimate Tensile Stress (UTS), which produces failure in a relatively small 
number of cycles. Subsequent tests are run at lower cyclic stress values until 
a level is found at which the samples will survive 10 million cycles without 
failure.
• Results of the tests are plotted between stress (S) and the number of cycles 
(N), generally on a log-log scale. S-N Curve is shown In figure below:
• The ordinate of the S-N curve is called Fatigue Strength (Sf), which can be 
defined as the maximum stress that the material can withstand for a specified 
number of stress reversals.
• For ferrous metals and their alloys, S-N curve becomes horizontal after 106 to 
107 cycles, which means that the material can survive an infinite number of 
stress reversals if the induced stress is below this level.
• Stress corresponding to this horizontal line is called endurance limit or 
fatigue limit.
o The zone below 103 cycles is considered as low cycle fatigue 
° the zone between 103 and 106 cycles is high cycle fatigue with a finite 
life and
° beyond 106 cycles, the zone is considered to be high cycle fatigue with 
infinite life.
• Fatigue or Endurance Limit (S'e ) can be defined as the maximum amplitude of 
completely reversed stress that the standard specimen can sustain for an 
unlimited number of cycles without fatigue failure.
• Low Cycle Fatigue: The body of knowledge available on fatigue failure from 
N=1 to N=1000 cycles is generally classified as low-cycle fatigue.
• High Cycle Fatigue: High-cycle fatigue, then, is concerned with failure 
corresponding to stress cycles greater than 103 cycles.(Note that a stress 
cycle (N=1) constitutes a single application and removal of a load and then 
another application and removal of load in the opposite direction. Thus N= V 2 
means that the load is applied once and then removed, which is the case with 
the simple tensile test.)
Note: In the absence of experimental fatigue data, following relations are 
sometimes used:
• For Steel, S'e = 0.5 Su t
• For Cast Iron, S'e = 0.4 Su t
Endurance Limit Modifying Factors
• The endurance limit of any machine element cannot match the values 
obtained from test due to variation in material, quality of manufacture, 
environmental conditions and design.
• Therefore, the endurance limit obtained by the test is modified using some 
factors to obtain more reasonable results.
• Endurance Limit of a particular machine part can then be estimated using 
following relation:
„ _ L T f o a d ^rel •
~ T jr
K f
where Se= Endurance Limit of the specimen
• Ksu rf = Surface Finish Factor
• Ksize = Size Factor
• K|0 a C j = Load Factor
• Kre | = Reliability Factor
• Ktem p = Temperature Factor
• Kf = Fatigue Stress Concentration Factor
Surface Finish Factor (Ksu rf)
• The surface of the rotating beam specimen is highly polished but most of the 
machine members don’t have that kind of surface finish requiring a 
modification in the endurance limit obtained by rotating beam experiment.
• Surface finish factor depends upon the manufacturing process used and 
ultimate tensile strength of the material. Its value can be selected with the 
help of chart shown in figure below