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 1 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

! cycle at 480 Mpa

it requires 10^4 cycle at this stress level for failure ( from Graph)

Similaly 4 cycles at 400MPa,

at this stress level the steelcan with stand 10^5 cycles before failure. ( from graph)

1 cycle at 480 Mpa will reduce the life of the component by 1-10^4 ie. ).9999 % life is available.

4 cycles at 400 MPa will reduce tthe life of the component by 1 - 4X10^5 = 0.99996 % of life

Hence in one cycle the net reduction in life is life after one cycle of 480 Mpa - life after 4 cycles of 400 MPa cycle

= 0.9999 - 0.99996 = ).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 the no pf cyle 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 given

ie. 1/10^4 + 4/10^5 =1 Hence the remaining life is 1-(  1/10^4 + 4/10^5) = 0.999756% is available

In one cycle the total cycle consumed is 0.0001 + 0.00004 = 0.00014

therefor cycles to failure = 1/ .00014 = 7142 cycles.