Materials Selection- Low and High Cycle Fatigue Flashcards
High-cycle fatigue (HCF)
It is stress controlled. The stress amplitude is held constant and we measure the number of cycle required to cause failure. The strain component is largely elastic. Fatigue failure occurs at a high number of cycles e.g 10^3 or 10^4
Basquin equation
Describes the S-N curve in the high-cycle regime
σa=ΔεeE/2=σf’(2Nf)^b
Where σa is stress amplitude
Δεe/2 is elastic strain amplitude (e subscript)
E is elastic modulus
Nf is cycle to failure
σf’ is fatigue strength coefficient
b is fatigue strength exponent or Basquin constant (-0.05 to -0.12)
Limitation of Basquin equation
Doesn’t allow for fatigue endurance limit
Low-cycle failure (LCF)
At higher cyclic stresses, the number of cycles to failure decreases. There is considerable plastic deformation. Nf<10^3 or 10^4. Tests are conducted with controlled strain.
In what areas must LCF be considered?
Nuclear reactor pressure vessels. Steam turbines. Most other types of power machinery.
Anything where cyclic stresses are thermal in origin because they arise from thermal expansion so fatigue results from cyclic strain.
Stress-strain graph for LCF testing
Line up straight diagonal then curved to point of chosen strain. Straight diagonal line down crossing x axis at roughly half the max strain applied. Keeps going down then curved and crosses y axis and keeps going to chosen point of negative strain. Straight diagonal line up crossing x axis at roughly half max negative strain. Then curved and crosses y axis and keeps going until point it was at with max positive strain.
Values determined on LCF stress vs strain graph
Height at maximum applied strain point is σa=Δ σ/2. Intersections with x axis at horizontal distance Δ σ/2E from point of maximum strain. For straight diagonal line down, continue gradient until stress at maximum negative strain point. Distance from here to max positive strain is Δεe (elastic strain range). Distance to max negative strain is Δεp (plastic strain range)
Cyclic hardening
Stress required to cause same strain increases with number of cycles. Stress vs strain graph is stretched vertically slightly after more cycles.
Cyclic softening
The stress required to cause the same strain decreases with more cycles. Stress vs strain graph is squashed vertically slightly after more cycles
What is the usual method to present LCF?
Plot plastic strain range Δεp against Nf. Both axes are on log scales
Coffin-Manson equation for LCF
Δεp/2=εf’(2Nf)^c
Where Δεp/2 is plastic strain amplitude
Nf is cycles to failure
εf’ is fatigue ductility coefficient (similar to true fracture strain)
c is fatigue ductility exponent of a Coffin constant (-0.5 to -0.7)
What does the graph of Coffin-Manson equation look like?
Straight line with negative gradient.
The strain-life equation
Combines Basquin and Coffin-Manson equations to give equation that can be used to estimate the entire range of fatigue lives.
ΔεT/2=(σf’/E)(2Nf)^b + εf’(2Nf)^c
T is subscript
Superposition of Basquin and Coffin-Manson graphs
Δε/2 vs Nf. Basquin line is for elastic and is straight with shallow negative gradient of b. Coffin-Manson line is for plastic and is straight with steeper negative gradient c. Summing them gives curved line like exponential decrease which is above both of them. Intersection between straight lines is transition from LCF to HCF.
Strain-life equation graphs for strong, tough and ductile materials
Curved lines all intersect at one point. Ductile has steepest gradient as they have the longest lives for LCF (highest to left of intersection). Strong has shallowest gradient as they have longest lives for HCF (highest right of intersection). Tough lies between them.
