Piano Wire Fatigue Experiment: Calculating Stress and Modulus"

[Gianelle]

Hi All

I am the new at the forum and would be very grateful for help about my Lab.

I am doing the postgraduate course of Biomedical Engineering. We had a Lab about the fatigue of piano wire, as a part of materials science module.

During the experiment, high strength piano wire was tested by rotating a bent wire around its axis using a drill and a bearing. As the wire rotated the stress at a point in the surface alternated from tension to compression, the degree being a function of the bend in the wire.

Elastic Modulus of wire is 200GPa and the Tensile strength about 2000MPa. The stress in the wire as it was bent can be calculate by Ey/R. (All the variables were provided)

Where E _ is Elastic Modulus
y_ Radius of the wire (=0,5mm)
R- Radius of curvature (110mm, 130mm, 150mm, 170mm and 190mm)

I will attach the excel file with all the data obtained during the lab.

Finally here comes the question:

I am supposed to calculate the minimum stress, mean stress, stress ratio, stress range, and alternating stress for different radius of curvature.

I guess the stress ratio is -1, due to the reverse cycle. Also, as I understand the minimum and the maximum stress applied to the wire during testing is the same (it changes from tensions to compression). However, according to that task get quite simple, which arises my doubts about the correctness of my thinking. Thanks in advance

 

[Valkarie]

!The stress ratio is not always -1; it depends on the ratio of the maximum and minimum stresses. You can calculate the minimum and maximum stress using the formula E_y/R, where E_ is the elastic modulus, y is the radius of the wire, and R is the radius of curvature. To calculate the stress ratio, divide the maximum stress by the minimum stress. To calculate the mean stress, take the average of the maximum and minimum stresses. To calculate the stress range, subtract the minimum stress from the maximum stress. To calculate the alternating stress, take the difference between the maximum and minimum stresses and divide it by two.