The Stress-Strain Curve calculator allows for the calculation of the engineering stress-strain curve of a material using the Ramberg-Osgood equation. See the reference section for details on the methodology and the equations used.

### Material Property Inputs

Enter the material properties in either US or SI units:

### Points for Stress-Strain Curve

The points for the *engineering stress-strain curve* are shown below:

**Display Units:**

Yield Point | Ultimate Point | |||
---|---|---|---|---|

Yield Strength: | Ultimate Strength: | |||

Yield Strain: | Ultimate Strain: |

### Ramberg-Osgood Equation

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

$$ \varepsilon = { \sigma \over E } + 0.002 \left( { \sigma \over S_{ty} } \right) ^ { 1 / n } $$where \(\sigma\) is the value of stress, \(E\) is the elastic modulus of the material, \(S_{ty}\) 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.

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

n = | strain hardening exponent |

### Strain Values at Yield and Ultimate Strength Points

The strain value associated with the yield strength is:

$$ \varepsilon_{yield} = { S_{ty} \over E } + 0.002 = $$ |

__Reference Values__

S_{ty} |
= | |

E | = |

Note that a plastic strain of 0.002 is assumed. This is consistent with the 0.2% offset method, as described here.

The strain value associated with the ultimate strength is:

$$ \varepsilon_{ult} = { S_{tu} \over E } + \varepsilon_f = $$ |

__Reference Values__

S_{ty} |
= | |

E | = | |

ε_{f} |
= |

where \( \varepsilon_f \) is the plastic strain at failure and is simply the percent elongation expressed in decimal form:

$$ \varepsilon_f = { eL \over 100\% } = $$ |

__Reference Values__

eL | = |