June 23, 2013
June 23, 2013
June 26, 2013
23.678.1 - 23.678.12
Illustrating Rotating Principal Stresses in a Materials Science Course Somnath Chattopadhyay Georgia Southern University Rungun Nathan Pennsylvania State University ABSTRACTThis work constitutes a laboratory component with a junior level materials science course andillustrates the importance of rotating principal stresses in design of components such as theautomotive crankshaft. The activity is centered on Mohr’s circle for a biaxial stress situationsinvolving time varying normal and shear stresses. A number of dynamic situations have beenconsidered, namely, (a) sinusoidally varying normal and shear stresses that are in phase, (b)sinusoidally varying normal and shear stresses that are 90° out of phase, (c) constant normalstress and sinusoidally varying shear stress, and (d) sinusoidally varying normal stress andconstant shear stress. Employing a graphical approach, the diameter of Mohr’s circle (theabsolute difference between the two principal stresses) as well as the principal stress directions ismonitored. The students see that for certain stress situations the principal stress directionsremain unchanged while for others the principal stress directions keep changing with time(rotating principal stresses). In general, the size of Mohr’s circle changes with time. The plottingoption of the Matlab code has been employed to construct three-dimensional plots for theindicated stress situations with the normal and shear stresses respectively in the x and ydirections and the time in the z-direction. The plots show how the principal directions changewith time, along with the size of Mohr’s circle. The students are made aware of the fact thatrotating principal stresses play a very important role in designing components that are subjectedto biaxial or mutiaxial fatigue, such as the crankshaft. Also the diameter of Mohr’s circle can bedirectly related to the Tresca or von-Mises theory of failure.
Chattopadhyay, S., & Nathan, R. (2013, June), Illustrating Rotating Principal Stresses in a Materials Science Course Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. https://peer.asee.org/19692
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