A machine component is composed of 1045 steel One run of a p

A machine component is composed of 1045 steel. One run of a process exposes the critical region of the component to I cycle at 480 MPa and 4 Cycles at 400 MPa. What is the accumulated damage per run? According to Miner\'s rule, how many runs are expected before failure?

Solution

1 cycle at 480 Mpa

It requires 10^4 cycle at this stress level for failure

Similarly 4 cycles at 400 Mpa

At this stress level the steel can with stand 10^5 cycles before failure

1 cycle at 480 Mpa will reduce the life of the componentby 1-10^4 i.e .9999% life is available

4 cycles at 400 Mpa will reduce the life of the component by 1-4×10^5=.99996%of life

Hence in one cycle the net reduction in life is life after one cycleof 480 mpa - life after 4 cycles of 400 Mpa cycle=.9999-.99996=.99986% of life is available after one cycle of loading

ACCORDING to miners rule % of life consumed is n1/N1+n2/N2=1 where n1 is no of pf cycle at one stress value and n2 the next stress value.N1 and N2 are the fatigue life of the element for the two stress values i.e.1/10^4+4/10^5=1.hence the remaining life is .999756% is available

IN ONE CYCLE THE THE TOTAL CYCLE CONSUMED IS .0001+.00004=.00014 THEREFORE CYCLES TO FAILURE =1/.00014=7142 CYCLES