Use Paris Law and numerical integraton to estimate the cycles to failure of an a

Question

Use Paris Law and numerical integraton to estimate the cycles to failure of an air frame component subjected to a cyclical stress ratio R = 0.1 having a flaw that causes an initial a peak stress intensity factor equal to 25% of Kic. Assume this fatigue problem is adequately modeled using the WOL test specimen composed of 4340 steel having a fracture toughness and yield strength of 38.7 MPa sqrt(m) and 950 MPa, respectively. Assign thickness B, and initial crack length ao equal to the minimum that satisfies the ASTM E399 plane strain criteria and dimension W = 4 x B. Assume Paris coefficient A = 11E-8 mm/cyc/ DK^1.6 and Paris exponent m = 1.6.

Report the following:

ao: 4.1487            PMAX: 0.89            PMIN: 0.09

NTOTAL = 1,025,555                                    aCRIT = 11.84

Explanation / Answer

Solution :-

Use Paris Law and numerical integraton to estimate the cycles to failure of an air frame component subjected to a cyclical stress ratio R = 0.1 having a flaw that causes an initial a peak stress intensity factor equal to 25% of Kic.

We have to assume this fatigue problem is adequately modeled using the WOL test specimen composed of 4340 steel having a fracture toughness and yield strength of 38.7 MPa sqrt(m) and 950 MPa, respectively.

Now we have to assign thickness B, and initial crack length ao equal to the minimum that satisfies the ASTM E399 plane strain criteria and dimension W = 4 x B. Assume Paris coefficient A = 11E-8 mm/cyc/ DK^1.6 and Paris exponent m = 1.6.

We know that when

ao: 4.1487            PMAX: 0.89            PMIN: 0.09

Then

NTOTAL = = 247199.122* 4.1487 = 1,025,555 (Because 247199.122 is constant value)

Hence   aCRIT = 1,025,555/ 86617.82 = 11.84 (Because 86617.82 is constant value)

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