Refer to the strain amplitude diagram below (established for a mean stress and strain of zero). i) Use the black circle on the diagram to determine the constant C1 in the Basquin equation for b = 0.2 and E = 150,000 MPa. Then ii) use the Basquin equation to establish the stress amplitude corresponding to a lifetime of 10^7 cycles (i.e. the 'endurance limit'). Then iii) use Goodman's equation to estimate the endurance limit expected for a mean stress of 150 MPa (assuming an ultimate tensile strength of 450 MPa). Then iv) use Miner's rule to establish if the component is likely to fail after 10^6 cycles for applied stress amplitudes of 70 MPa followed by 10^3 cycles at 100 MPa (all at a mean stress of 100 MPa).
Low-cycle fatigue
High-cycle fatigue
slope-c Coffin Log (strain amplitude, )
Bulk of sample plastic
= E
Basquin slope-b
Bulk of sample elastic
LY = 3.15 x 10^-4
10^10
1
10^2 10^4 10^6 Log (cycles to failure, Nf)