Concept of Yield Point or Elastic Limit?

A similar discussion on this forum raised many interesting point about- Stress or strain: which one is more fundamental?

http://imechanica.org/node/1001 

On a similar note I would like to address this decade old fundamental question on how do we define yield point of a material?  

Plasticity in coarse grain alloys deformed at room temperature is controlled by dislocation motion induced primarily by activation of intragranular sources and subsequent multiplication processes [1]. At the same time, the concept of a yield stress is sometimes difficult to define because plastic deformation due to dislocation generation and movement is often a diffuse process rather than a singular event [2-4]. As a result, obtaining a clearly discernible transition from elastic to plastic strain within the flow curve, defining the concept of a “yield point”, has proven elusive. The gradual transition from reversible strain to the irreversible strain associated with permanent dislocation movement in the stress-strain response has necessitated the common use of a 0.2% offset strain definition of yield stress [4]. The 0.2% offset definition is favored for most engineering design applications [5-7], and in particular, those applications that are not sensitive to the small plastic strains that occur at stresses below the 0.2% offset definition. In classical and advanced plasticity theories, the plastic behavior of a material in a general stress state is defined by an initial yield criterion (i.e. specifying the state of stress for the beginning of plastic flow), a kinetics of flow rule, and a hardening law. The onset of plasticity is often described by a definition of the elastic limit or yield point. These definitions are divided into small-scale (deviation from linearity, small offset, etc.) and more commonly used largescale definition of yield (0.2% offset, extrapolation, etc.) [8]

Recent studies employing microscale test specimens have adopted alternate definitions of yield stress, which are applied as a matter of necessity when large initial strain bursts are present [18- 22]. These reports cite yield point values that range from apparent 0.2% offset strain values, drawn from data showing large strain bursts, to values greater than 1% offset strain, where plastic deformation has been arrested following an initial burst. However, these definitions are primarily used for material characterization or rough engineering purposes, and may not address the true elastic limit or true onset of plastic flow and irreversible deformation. In routine mechanical testing, forces are measured using some form of load sensor and most of the recent advancements in such testing have been in strain measurement. This progress has been driven by better strain resolution in time and/or length scales [23- 24], testing conditions and material geometry. At the same time, the existing definitions of the elastic limit/onset of yield remain subjective in nature, requiring determination of Young’s modulus and/or strain level, or the assumption that some quantifiable deviation from the linear response implies yielding. These existing definitions make the definition of yield subjective, particularly for materials with high work hardening response which display non-linearity in the stress-strain response from an early stage [14]. Inaccuracies associated with such a subjective definition of yield could obscure relative contributions of the elastic and plastic deformation in the overall response. Many strain measurement techniques such as Electron Backscatter Diffraction, neutron diffraction or X-ray can be used to obtain improved local strain resolution within the gage section [12] of specimens. However, these techniques either lack sensitivity for the smallest of strains or are costprohibitive and/or challenging to implement, especially for testing under elevated temperatures and complex test conditions. As an alternative to these strain-based measurements, a stress-based probe of plasticity affords a highly sensitive window on the presence of dislocation activity.

 http://link.springer.com/article/10.1007/s11340-016-0152-3  

References-

1. Rajagopalan, J., Han, J. H., & Saif, M. T. A. (2007). Plastic deformation recovery infreestanding nanocrystalline aluminum and gold thin films. Science, 315(5820), 1831- 1834.

2. Hull, D., & Bacon, D. J. (1984). Introduction to dislocations (Vol. 257). Oxford: Pergamon Press. 3. Dieter, G. E., & Bacon, D. (1986). Mechanical metallurgy (Vol. 3). New York: McGraw-Hill.

4. H. Kuhn, M. Dana, ASM Handbook Mechanical Testing and Evaluation, 8 (2000).

5. Christensen, R. M. (2008). Observations on the definition of yield stress. Acta Mechanica, 196(3-4), 239-244.

6. Ashby, M. F., & Cebon, D. (1993). Materials selection in mechanical design. Le Journal de Physique IV, 3(C7), C7-1.

7. Zhou, M. (2013). Exceptional properties by design. Science, 339(6124), 1161-1162.

8. Michno, M. J., & Findley, W. N. (1976). An historical perspective of yield surface investigations for metals. International Journal of Non-Linear Mechanics, 11(1), 59-82.

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18. Uchic, M. D., Shade, P. A., & Dimiduk, D. M., (2009). Plasticity of micrometer-scale single crystals in compression. Ann Rev Mat Res 39, 361-386 (2009) 

19. Miguel, M.C., Zapperi, S.: Fluctuations in plasticity at the microscale. (2006) Science 312, 1151–1152.

20. Uchic, M. D., Dimiduk, D. M., Florando, J. N., & Nix, W. D. (2004). Sample dimensions influence strength and crystal plasticity. Science, 305(5686), 986-989.

21. Dimiduk, D. M., Woodward, C., LeSar, R., & Uchic, M. D. (2006). Scale-free intermittent flow in crystal plasticity. Science, 312(5777), 1188-1190.

22. Csikor, F. F., Motz, C., Weygand, D., Zaiser, M., & Zapperi, S. (2007). Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale. Science, 318(5848), 251-254.

23. Legros, M., Gianola, D. S., & Motz, C. (2010). Quantitative in situ mechanical testing in electron microscopes. MRS bulletin, 35(05), 354-360.

24. Liu, H. H., Schmidt, S., Poulsen, H. F., Godfrey, A., Liu, Z. Q., Sharon, J. A., & Huang, X. (2011). Three-dimensional orientation mapping in the transmission electron microscope. Science, 332(6031), 833-834.