I am only interested in part 6-27(a). I see that Bartleby has answered this question before but I have a question regarding the yielding factor of safety. Why is the yielding factor of safety calculated as ( n=Sy/sigma_max), but not as ( n=Sy/Kt*sigma_max )? Since there is a stress concentration factor and the sigma_max is technically considered the nominal stress. My understanding is that when a ductile material is subjected to a static load the effects of stress concentration near the discontinuity are reduced to local yielding and for this reason not considered in the yielding factor of safety? Because under the static load, when the stress near the discontinuity reaches the yield point, local plastic deformation takes place and increases the yield strength hence sustaining higher loads. Here the the ductile material is subject to a dynamic load, Would the yielding factor of safety be the same reasoning as for static load?
I am only interested in part 6-27(a). I see that Bartleby has answered this question before but I have a question regarding the yielding factor of safety. Why is the yielding factor of safety calculated as ( n=Sy/sigma_max), but not as ( n=Sy/Kt*sigma_max )? Since there is a stress concentration factor and the sigma_max is technically considered the nominal stress.
My understanding is that when a ductile material is subjected to a static load the effects of stress concentration near the discontinuity are reduced to local yielding and for this reason not considered in the yielding factor of safety? Because under the static load, when the stress near the discontinuity reaches the yield point, local plastic deformation takes place and increases the yield strength hence sustaining higher loads.
Here the the ductile material is subject to a dynamic load, Would the yielding factor of safety be the same reasoning as for static load?
You're absolutely right. The yielding factor of safety for a ductile material subjected to a static load does not account for the stress concentration factor Kt, due to the reasons you mentioned.
However, for a dynamic or fluctuating load, the situation is different. Here are the key points:
Under cyclic/fluctuating loads, localized yielding at the stress concentration region can gradually propagate cracks over time due to fatigue.
The cyclic plastic deformation that helps alleviate static stress concentrations now contributes to fatigue damage accumulation.
So for dynamic loads, the peak stresses with the Kt multiplier need to be considered for yielding failure.
The yield factor of safety should be based on the maximum stress with the stress concentration effect factored in.
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