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Fatigue solution

Fatigue solution - Fatigue solution

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Total Life Given: A high cycle fatigue power law, with the coefficients A and b obtained from experiments on the alloy. b f n N A S ) ( = a) Engineers run S-N tests (in repeated loading, periodically from 0 to S n ) to find that N f =1 x 10 5 cycles for S n =800 MPa, N f =1 x 10 7 cycles for S n =510 MPa. What are the coefficients A and b ? N f = # of cycles to failure, S n = Stress range. Given the equation above, a and b are as follows: MPa a E a b b E A MPa E A MPa b b 2463 ) 5 1 ( 800 0977 . 0 2 510 800 log ) 7 1 ( 510 ) 5 1 ( 800 0977 . 0 = = - = - = = = - b) Find the stress life for an unetched neck (no stress concentration). Assume that the neck is cyclically loaded during daily activity to the maximum stress computed in part (b) above. Choose (justify) an appropriate minimum stress. In Part. 1, Static Analysis, you were told that the force is some multiple of the body weight, α. As determined from gait analysis, the maximum load that occurs is about 4x body weight. Hence, you solve for the maximum load (P maz ) with α=4. The maximum stress at point A and point B are tensile and compressive, respectively. Since the stresses at point B are compressive, we are not concerned with the stress range there. What remains to be determined is the minimum stress at point A. The minimum could be tensile or zero. Generally, during walking α is about zero. I accepted either of these two assumptions, but for simplicity, the solutions here assume α=0). From Part I, ∆σ @ A = 348 MPa. Substituting back into the equation:

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Cycles E Nf Nf 8 0977 . 0 10 9 . 4 ) ( 2463 348 = = - c) If the device is required to survive for 3 x 10 7 cycles (assuming an unetched surface and no endurance limit), will the device fail? Since the number of cycles to failure is greater than 3 x 10 7 cycles, the device will not fail. d) As given in the case study, the device failed after 43 months post- operatively. If the patient loaded the implant for 1 x 10 6 cycles/year, what was the total number of cycles to failure? What would the stress concentration factor from the laser etching have to have been to cause failure at 43 months? Total number of cycles to failure: 62 . 1 348 564 564 ) 6 58 . 3 ( 2463 6 58 . 3 ) 6 1 ( 12 43 0977 . 0 = = = = = - SCF MPa E S year cycles E year cylces E months Months etched e) If laser etching has to be included in the design, how might the neck design (geometry, materials, implantation) be changed to allow the etching but still meet the 3 x 10 7 cycles life requirement?
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Fatigue solution - Fatigue solution

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