John & Susan's Leg Bone Fatigue: Examining an SN Curve

[cd19]

For human bone the constant n has a value of 6. Two people embark on a fitness regime. John runs 6,000 steps per day (subjecting his leg bones to a stress range of 40MPa) and walks 20,000 steps per day (at a stress range of 15MPa). Susan walks 10,000 steps per day (at 15MPa) and does 200 jumps per day (at 65 MPa). After some time, one of them gets a fatigue failure in a leg bone - which do you think it was?
N_f=A/$$\Delta\sigma$$ⁿ
I just plotted a sketch of SN curve with $$\sigma$$_m= 27.5Mpa for JOHN and $$\sigma$$_m = 37.5 MPa for SUSAN

A factor that affects fatigue life is the mean stress. In that an increase in mean stress leads to decrease in fatigue life

Then I got stress amplitude levels for both; 12.5 MPa for john and 25MPa for john

From the sketch it can be assumed susan's leg bone will be the first to fail.

To get full marks in this question though I have to incorporate the above equation which describes the SN curve, The constant 'A' is confusing me, I'm not sure of the solution. Any suggestions?

 

[KataKoniK]

Hello,

Thank you for your forum post. I would like to provide some clarification and additional information to help you understand the equation and make an accurate prediction.

The equation you mentioned, Nf=A/\Delta\sigman, is known as the SN curve equation. This equation is used to describe the relationship between the number of cycles to failure (Nf) and the stress amplitude (\Delta\sigma) for a given material. The constant 'A' in the equation represents the material's endurance limit, which is the maximum stress amplitude that the material can withstand without experiencing fatigue failure.

In the context of your question, we are dealing with human bones, which have an endurance limit of approximately 6MPa. This means that if the stress amplitude is below 6MPa, the bone will not experience fatigue failure regardless of the number of cycles. However, if the stress amplitude exceeds 6MPa, the bone will eventually fail due to fatigue.

Now, let's apply this knowledge to the situation of John and Susan. Based on the information provided, the stress amplitude for John's leg bones is 12.5 MPa, which is above the endurance limit of 6MPa. On the other hand, the stress amplitude for Susan's leg bones is 25MPa, also above the endurance limit. This means that both John and Susan are subjecting their leg bones to stresses that can lead to fatigue failure.

However, we also need to consider the number of cycles or steps that each person is taking per day. John is running 6,000 steps and walking 20,000 steps, which adds up to a total of 26,000 steps per day. Susan, on the other hand, is walking 10,000 steps and doing 200 jumps, which adds up to a total of 10,200 steps per day. This means that John is subjecting his leg bones to more cycles per day compared to Susan, increasing the chances of fatigue failure.

In conclusion, based on the information provided, it is more likely for John's leg bone to experience fatigue failure compared to Susan's leg bone. However, it is important to note that there are other factors that can also contribute to fatigue failure, such as age, overall health, and bone density. Therefore, it is not possible to make a definitive prediction without additional information. I hope this helps clarify the equation and provides a better understanding of the situation.