A cylindrical rod of diameter 91 mm and fabricated from a re

A cylindrical rod of diameter 9.1 mm and fabricated from a red brass alloy is subjected to reversed tension-compression load cycling along it axis. If the maximum and minimum loads are +7850 N and -3860 N, respectively, determine its fatigue life (in cycles).

Solution

solution:

1) here cylindrical rod has material=red brass alloy and diameter d=9.1 mm

Sut=240 MPa

Syt=70 MPa

Nf=1

here rod subjected to fluctuating stress as mean stress not eual to zero

here Fmax=7850N

Fmin=-3860 N

2) here tensile and compressive stress are given as

max.stress=Fmax*4/(pi*d2)=120.697143 N/mm2

min.stress=Fmin*4/(pi*d2)=-59.3491 N/mm2

3) here mean stress

mean stress=(max.stress+min stress)/2=120.697-59.34/2=30.6739 N/mm2

4) amplitude stress

amplitude stress=(max.stress-min.stress)/2=120.697+59.34/2=90.02 N/mm2

5) here to convert it to completely reversed stress fatigue stress acting is given by

fatigue stress=Sut*(amplitude stress/(Sut-mean stress)=240(90.02/(240-30.67))=103.2148 N/mm2

here fatigue strength isSxf=fatigue stress*Nf=103.2148 N/mm2

6) here by goodman line we get

logSxf-logSe/(6-logNxf)=log(.9Sut-logse)/6-3

on putting value we get fatigue finite life as

Nxf=5875596.011 cycle