Analysis of a stress-strain diagram

In tensile tests, force-displacement curves are measured. Using the original cross-sectional area So, the nominal stress a AL) is calculated from the force F AL), and the nominal strain e(AL) is calculated by dividing the extension AL by the initial gauge length Lq (see equations (3.9) and (3.10)). 

Young s modulus can also be determined in other ways. One possibility is to measure the resonant frequency of a vibrating beam because this frequency is determined by the sonic speed c = JW[q. Two advantages of this method are that very small amplitudes are sufficient and that frequencies can be measured electronically with high precision. 

During plastic deformation, the specimen s cross-sectional area changes significantly. Therefore, the nominal stress differs from the true stress that is defined as the quotient between the external load F Al) and the current 

During plastic deformation, the true stress in the material is the stress required to cause further plastic flow in the material. Therefore, it is called the flow stress (j-p. 

The current cross-sectional area S AL) can be calculated approximately if we assume that the volume of the specimen remains unchanged during plastic deformation and that the volume change due to elastic deformation is small. If the volume is constant, we can write 

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