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Ramberg-Osgood relationship From Wikipedia, the free encyclopedia Ju mp to: nav igation, search The Ramberg-Osgood equation was created to describe the non linear relationship between stress and strain— that is, the stress-strain curve— in materials near their yield points. It is especially useful for metals that harden with plastic deformation (see strain hardening), showing a smooth elastic-plastic transition. In its original form, it says that ,[1] where ε is strain, σ is stress, E is You ng's modu lu s, and K and n are constants that depend on the material being considered. The first term on the right side, , is equal to the elastic part of the strain, while the second term, , accounts for the plastic part, the parameters K and n describing the hardening behavior of the material. Introducing the yield strength of the material, σ0, and defining a new parameter, α , related to K as , it is convenient to rewrite the term on the extreme right side as follows: Replacing in the first expression, the Ramberg-Osgood equation can be written as [edit] Hardening behavior and Yield offset In the last form of the Ramberg-Osgood model, the hardening behavior of the material depends on the material constants and . Due to the power-law relationship between stress and plastic strain, the Ramberg-Osgood model implies that plastic strain is present even for very low levels of stress. Nevertheless, for low applied stresses and for the commonly used values of the material constants α and n, the plastic strain remains negligible compared to the elastic strain. On the other hand, for stress levels higher than σ0, plastic strain becomes progressively larger than elastic strain. The value can be seen...