Stress-Strain Curve Ramberg-Osgood Equations and Calculator

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Stress-Strain Curve Ramberg-Osgood Equations and Calculator

Structural Deflections, Stress, Strain Analysis Calculators

Stress-Strain Calculator and Plotted Curve Approximation using Ramberg-Osgood Equation:

The Ramberg–Osgood equation is used to approximate the non linear relationship between stress and strain, the stress–strain curve in materials near their yield points. It is especially applicable to metals that harden with plastic deformation, showing a smooth elastic-plastic transition.

The stress-strain curve may be approximated using the Ramberg-Osgood equation, which calculates the total strain (elastic and plastic) as a function of stress:

Preview example: Stress-Strain Curve Calculator Results and Plotted Stress-Strain Curve

ε = σ / E + o_s ( σ / σ_y )^1/n

where σ is the value of stress, E is the elastic modulus of the material, σ_y is the tensile yield strength of the material, and n is the strain hardening exponent of the material which can be calculated based on the provided inputs. o_s is the % offset of the yield stress which is can be assumed to be 0.2% of 0.002..

Based on the specified material properties, the value of the strain hardening exponent, n, is:

n = log (σ₂ / σ₁ ) / log (ε₂ /ε₁ ) strain hardening exponent

n = log(S_tu / S_ty ) / log(ε_f /ε_p )

ε_p = .002

Strain Values at Yield and Ultimate Strength Points
The strain value associated with the yield strength is:

ε_yield = σ_y / E + o_s

Note that a plastic strain of o_s = 0.002 is assumed. This is consistent with the 0.2% offset method.

The strain value associated with the ultimate strength is:

ε_ult = S_tu / E + ε_f

where e_f is the plastic strain at failure and is simply the percent elongation expressed in decimal form:

e_f = eL / 100%

References:

Ramberg, W., & Osgood, W. R. (1943). Description of stress–strain curves by three parameters. Technical Note No. 902, National Advisory Committee For Aeronautics, Washington DC.
Description of Stress Strain Curves by Three Parameters, Walter Ramburg and William R. Osgood. Techncail Note 902: NASA
Hollomon, J. R. (1945). "Tensile Deformation". Transaction of AIME. 162: 268–277.
Gadamchetty, Geethanjali; Pandey, Abhijeet; Gawture, Majnoo (2016-01-05). "On Practical Implementation of the Ramberg-Osgood Model for FE Simulation". SAE International Journal of Materials and Manufacturing. 9 (1): 200–205. doi:10.4271/2015-01-9086. ISSN 1946-3987.
Hill, H. N. (1944). Determination of stress-strain relations from "offset" yield strength values. National Advisory Committee for Aeronautics. OCLC 647978489.

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