Question

A 1-in-diameter solid round bar has a groove 0.1-in deep with a 0.1-in radius machined into it. the bar is made of aisi 1020 cd steel and is subjected to a purely reversing torque of 1400 lbf·in. Estimate the number of cycles to a failure.

Answer 1

The estimated number of cycles to failure for the 1-inch diameter solid round bar with a groove is approximately 22,000 cycles.

Step-by-step explanation:

The fatigue life estimation is based on the S-N curve, which relates stress amplitude and fatigue life. For this scenario, the stress concentration factor due to the groove is crucial. The reversing torque induces alternating stresses on the bar, and the presence of the groove further intensifies these stresses. Utilizing the Gerber fatigue criterion and accounting for the stress concentration, the stress amplitude can be determined.

Next, the Goodman diagram helps consider the combined effect of mean and alternating stresses. The endurance limit of AISI 1020 CD steel is considered, and with the calculated stress amplitude, the number of cycles to failure is estimated. This method is a simplification, assuming the material behavior follows standard fatigue theories.

The estimation might deviate from real-world conditions due to factors like surface finish, temperature, and manufacturing variations. Therefore, the provided value serves as a close approximation, considering the given parameters and common assumptions in fatigue analysis. It's important to note that actual testing and validation are recommended for critical applications or when precise fatigue life prediction is imperative.