Answer:
the life (N) of the specimen is 46400 cycles
Explanation:
given data
ultimate strength Su = 1600 MPa
stress amplitude σa = 900 MPa
to find out
life (N) of the specimen
solution
we first calculate the endurance limit of specimen Se i.e
Se = 0.5× Su .............1
Se = 0.5 × 1600
Se = 800 Mpa
and we know
Se for steel is 700 Mpa for Su ≥ 1400 Mpa
so we take endurance limit Se is = 700 Mpa
and strength of friction f = 0.77 for 232 ksi
because for Se 0.5 Su at [tex]10^{6}[/tex] cycle = (1600 × 0.145 ksi ) = 232
so here coefficient value (a) will be
a = [tex]\frac{(f*Su)^2}{Se}[/tex]
a = [tex]\frac{(0.77*1600)^2}{700}[/tex]
a = 2168.3 Mpa
so
coefficient value (b) will be
a = -[tex]\frac{1}{3}[/tex]log[tex]\frac{(f*Su)}{Se}[/tex]
b = -[tex]\frac{1}{3}[/tex]log[tex]\frac{(0.77*1600)}{700}[/tex]
b = -0.0818
so no of cycle N is
N = [tex](\frac{ \sigma a}{a})^{1/b}[/tex]
put here value
N = [tex](\frac{ 900}{2168.3})^{1/-0.0818}[/tex]
N = 46400
the life (N) of the specimen is 46400 cycles
