The fatigue data for a brass alloy are given The fatigue dat

The fatigue data for a brass alloy are given as follows. Make an S-N plot (stress amplitude versus logarithm cycles to failure\') using these data. Use the attached graph paper. Label the axes with proper units. Determine the fatigue strength at 6.0 times 10^6 cycles. Determine the fatigue life for 95 MPa. Show all the information in the attached graph paper.

Solution

a) The S-N curve is a plot of the relation given by,

N1 = N2 (S1/S2)^1/b

The plot for the data is as follows,

The slope of the curve is given by,

b = -( logS1 - logS2 )/ logN2 - log N1

The slope of the above curve is,

b = - ( log 170 - log 144 ) / log 5 - log 4.2 = (-) 0.095

b) Fatigue strength at 6 x 10^6 cycles,

log N2 = log 6 x 10^6 = 6.77

Assuming log N1 = 6 and S1 = 144 and solve for S2,

log S2 = b (log N2 - log N1 ) + log S1

log S2 = - 0.095 (6.77 - 6) + log 144

S2 = 120 MPa

c) Cycles at 95 MPa,

S1 = 95Mpa, log N2 = 7, S2 = 92MPa

Using the above relation find the value of N1,

log N1 = 1/b [log S1 - log S2] + log N2

N1 = 0.78 x 10^7 cycles