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Stages of Fatigue
1: Crack Initiation
happens on a micro-structural level
causes the start fatigue cracks
persistent slip bands form at the surface
- they are the result of dislocations moving along crystallographic planes
- leads to slip band intrusions and extrusions on the surface
- act as stress concentrations, leading to crack initiationA
- crystallographic slip is controlled by shear stresses rather than normal stresses
- therefore cracks tend to initially grow in a plane of maximum shear stress range
- this leads to short cracks, usually on the order of a few grains
2: Crack Propagation
- the fatigue cracks tend to join together with more cycles
- they grow along planes of maximum tensile stress
3: Final Fracture
occurs when crack reaches critical length
results in either
- ductile tearing (plastic collapse)
- cleavage (brittle fracture)
Total Life Approach (Estimating Lifetime of a Part)
based on lab tests
- carried out under controlled loading conditions
- either stress or strain controlled loading conditions
- performed on idealised specimens
- specimens usually have finely polished defects (minimises surface roughness effects, affecting stage 1 crack initiation)
tests give number of loading cycles to the initiation of a measurable crack as a function of applied stress or strain parameters
measurability is dictated by the accuracy of the crack detection method used
this is typically between 0.75 mm to 1.00 mm
the challenge of fatigue design is to then relate the tests to actual component lives under real loading conditions
traditionally, most fatigue testing was based stress controlled conditions with mean stress, , which is known as a fully reversed load
the data was presented in the form of S-N curves (either semi-log or log-log plots) of alternating stress, , against cycles to failure, (failure defined as fracture)
- figure contains schematic representations of two typical S-N curves
- part (a) shows a continuously sloping curve
- part (b) shows a discontinuity (“knee”) in the curve—this is only found in a few materials (notably low strength steels) between and cycles under non-corrosive conditions
the curves are normally drawn through the median life value
therefore represent 50 percent expected failure
fatigue strength, , is a hypothetical value of stress range at failure for exactly cycles as obtained from an S-N curve
fatigue limit (or endurance limit) is the limiting value of the median fatigue strength as becomes very large ()
Effect of Mean Stress
- mean stress has a significant effect on fatigue behaviour in cyclically loaded components
- in figure you can see tensile mean stresses reduce fatigue life
- compressive stresses increase fatigue life
- effect of mean stress commonly represented as a plot of against for a given fatigue life
- attempts have been made to generalise the relationship, as shown in figure
modified Goodman line assumes linear relationship, where gradient and intercept are defined by fatigue life, , and material UTS, , respectively
Gerber parabola employs same intercepts but relationship is a parabola
Soderberg line assumes linear relationship but the x intercept (mean axis end point) is taken as yield stress,
these curves can be extended into the compressive mean stress region to give increasing allowable alternating stress with increasing compressive mean stress
this is normally taken to be horizontal for design purposes and conservatism
Effect of Stress Concentrations
fatigue failure is most commonly associated with notch-type features
stress concentrations associated with notch-type features typically leads to local plastic strain and eventually fatigue cracking
the estimation of stress concentration factors (SCFs) are typically expressed in terms of an elastic SCF, :
the fatigue strength of a notched component can be predicted with the fatigue notch factor, , which is defined as the ratio of the fatigue strengths:
i thought is alternating stress and is fatigue strength but the uni slides (slide 18) say otherwise :sob: TODO: find out what it’s meant to be for sure
- however is found to vary with both alternating stress level and mean stress level and thus number of cycles
figure shows the effect of a notch, with , on the fatigue behaviour of wrought aluminium alloy
S-N Design Procedure for Fatigue
- constant life diagrams plotted as against (also known as Goodman diagrams) (figure ) can be used in design to give safe estimates of fatigue life and loads
the fatigue strength for zero mean stress is is reduced by the fatigue notch factor,
is used if is not known
for static loading of a ductile component with a stress concentration, failure still occurs when mean stress, , is equal to UTS
failure at intermediate values of mean stress is assumed to be given by the dotted line
in order to avoid yield of whole cross-section of component, maximum nominal stress must be less than the yield stress, :
Safety Factor,
determined from the position of the point relative to the safe/fail boundary:
Derivation
from similar triangles we get
Failure Examples
Bicycle Crank Arm
D.H.-106 Comet Failure
- 1st production jet liner (debut in 1952)
- several crashed in 1954 led to an inquiry
- water tank testing and examination of a recovered fuselage showed that failure originated at a square corner window
- future designs used oval windows
Glossary (of Symbols)
- notch stress concentration factor,
- stress concentration factor,
- alternating stress,
- fatigue strength, — hypothetical value of stress range at failure for exactly cycles
- mean stress,
- ultimate tensile stress,
- yield strength,
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