The RambergOsgood class

class pylife.materiallaws.RambergOsgood(E, K, n)

Represent an elastic-plastic Ramberg-Osgood material law.

The material law describes total strain as the sum of an elastic part and a plastic power-law part. Stresses and the Young’s modulus must use the same stress unit, typically MPa.

Parameters:

• E (float) – Young’s modulus in MPa or another consistent stress unit.

• K (float) – Cyclic strength coefficient in the same stress unit as E. This value is often written as K' or K_prime in FKM nonlinear formulas.

• n (float) – Cyclic strain hardening exponent, dimensionless. This value is often written as n' or n_prime in FKM nonlinear formulas.

Notes

The implemented relation follows the alternative Ramberg-Osgood form with Hollomon parameters:

\[\varepsilon = \frac{\sigma}{E} + \operatorname{sign}(\sigma) \left|\frac{\sigma}{K}\right|^{1/n}\]

property E

Return Young’s modulus.

property K

Return the cyclic strength coefficient.

delta_strain(delta_stress)

Calculate cyclic Masing strain span for a stress span.

Parameters:

delta_stress (array_like) – Stress span in MPa or another unit consistent with E and K.

Returns:

Strain span, dimensionless.

Return type:

numpy.ndarray

Notes

The calculation assumes Masing material behavior as used in the notch strain concept (Kerbgrundkonzept). It evaluates twice the monotonic strain at half the stress span.

delta_stress(delta_strain)

Calculate cyclic Masing stress span for a strain span.

Parameters:

delta_strain (array_like) – Strain span, dimensionless.

Returns:

Stress span in MPa or another unit consistent with E and K.

Return type:

numpy.ndarray

Notes

The calculation assumes Masing material behavior as used in the notch strain concept (Kerbgrundkonzept). It inverts twice the monotonic strain at half the strain span.

elastic_strain(stress)

Calculate elastic strain for a stress.

Parameters:

stress (array_like) – Stress in MPa or another unit consistent with E.

Returns:

Elastic strain, dimensionless.

Return type:

array_like

lower_hysteresis(stress, max_stress)

Calculate the lower hysteresis branch from maximum stress.

Parameters:

• stress (array_like) – Stress values on the lower branch in MPa or another unit consistent with E and K. Values must not exceed max_stress.

• max_stress (float) – Maximum stress of the hysteresis loop in the same unit as stress.

Returns:

Strain values on the lower hysteresis branch from max_stress to stress, dimensionless.

Return type:

numpy.ndarray

Raises:

ValueError – Raised if any value in stress is greater than max_stress.

property n

Return the cyclic strain hardening exponent.

plastic_strain(stress)

Calculate plastic strain for a stress.

Parameters:

stress (array_like) – Stress in MPa or another unit consistent with K.

Returns:

Plastic strain, dimensionless.

Return type:

array_like

strain(stress)

Calculate elastic-plastic strain for a stress.

Parameters:

stress (array_like) – Stress in MPa or another unit consistent with E and K.

Returns:

Total elastic-plastic strain, dimensionless.

Return type:

numpy.ndarray

Examples

>>> from pylife.materiallaws import RambergOsgood
>>> rg = RambergOsgood(210000.0, 1000.0, 0.2)
>>> round(float(rg.strain(300.0)), 6)
0.003859

stress(strain, *, rtol=1e-05, tol=1e-06)

Calculate stress for an elastic-plastic strain.

Parameters:

• strain (array_like) – Total elastic-plastic strain, dimensionless.

• rtol (float, optional) – Relative tolerance passed to scipy.optimize.newton(). Default is 1e-5.

• tol (float, optional) – Absolute tolerance passed to scipy.optimize.newton(). Default is 1e-6.

Returns:

Stress in MPa or another unit consistent with E and K.

Return type:

numpy.ndarray

tangential_compliance(stress)

Calculate tangential compliance for a stress.

Parameters:

stress (array_like) – Stress in MPa or another unit consistent with E and K.

Returns:

Derivative of strain with respect to stress, in reciprocal stress units.

Return type:

array_like

tangential_modulus(stress)

Calculate tangential modulus for a stress.

Parameters:

stress (array_like) – Stress in MPa or another unit consistent with E and K.

Returns:

Derivative of stress with respect to strain, in stress units.

Return type:

array_like