mean_stress#

The mean_stress module contains all the functions and classes related to the mean stress, such as mean stress correction.

MeanStress#

py_fatigue.mean_stress.mean_stress#

alias of <module ‘py_fatigue.mean_stress.mean_stress’ from ‘/home/runner/work/py_fatigue/py_fatigue/py_fatigue/mean_stress/mean_stress.py’>

corrections#

The py_fatigue.msc.corrections module collects all the mean stress corrections implemented in py_fatigue. classes.

py_fatigue.mean_stress.corrections.dnvgl_mean_stress_correction(mean_stress: ndarray, stress_amplitude: ndarray, detail_factor: float | int = 0.8, plot: bool = False) → ndarray#

Calculates the mean stress correction according to par. 2.5 of`DNVGL-RP-C203 <https://bit.ly/3dUZ1OY>`_ which includes an attenuation factor \(p\) for the stress ranges if the following cases:

  • base material without significant residual stresses \(\rightarrow p = 0.6\). This option neglects fully compressive cycles.

  • welded connections without significant residual stresses \(\rightarrow p = 0.8\). This option multiplies the stress range of fully compressive cycles by p.

Given that the stress ranges are \(\Delta \sigma\), the corrected stress ranges are:

\[\Delta \sigma_{corr} = f_m \cdot \Delta \sigma\]

where:

\[f_m = \frac{\sigma_{max} + p \cdot \vert \sigma_{min} \vert}{\sigma_{max} + \vert\sigma_{min} \vert}\]

with:

\[\frac{\sigma_{amp}}{\vert \sigma_m \vert} \leq 1, \quad \sigma_{amp} = \frac{\sigma_{max} - \sigma_{min}}{2} \,\land \, \sigma_m = \frac{\sigma_{max} + \sigma_{min}}{2}\]
Parameters:

  • mean_stress (np.ndarray) – The mean stress of the fatigue test (\(\sigma_m\)).

  • stress_amplitude (np.ndarray) – The stress amplitude of the fatigue test (\(\sigma_{amp}\)).

  • detail_factor (float, optional) – mean stress attenuation factor (\(p\)), defaults to 0.8 in welded connections without significant residual stresses.

  • plot (bool, optional) – If True, the mean stress correction is plotted, defaults to False.

Returns:

The mean stress corrected ranges (\(\Delta \sigma_{corr}\)).

Return type:

np.ndarray

py_fatigue.mean_stress.corrections.walker_mean_stress_correction(mean_stress: ndarray, stress_amplitude: ndarray, gamma: float = 0.5, plot: bool = False) → ndarray#

Calculates the mean stress correction according to Walker model.

The correction is given by:

\[\Delta \sigma_{corr} = {\sigma_{max}} ^ {(1 - \gamma)} \, \sigma_{amp} ^ {\gamma}\]

with:

\[\sigma_{max} = \sigma_{mean} + \sigma_{amp}\]
Parameters:

  • mean_stress (np.ndarray) – The mean stress of the fatigue test (\(\sigma_{mean}\)).

  • stress_amplitude (np.ndarray) – The stress amplitude of the fatigue test (\(\sigma_{amp}\)).

  • gamma (float, optional) – The gamma Walker exponent (\(\gamma\)), defaults to 0.5.

  • plot (bool, optional) – If True, the mean stress correction is plotted, defaults to False.

Returns:

The mean stress corrected ranges (\(\Delta \sigma_{corr}\)).

Return type:

np.ndarray

py_fatigue.mean_stress.corrections.swt_mean_stress_correction(mean_stress: ndarray, stress_amplitude: ndarray, plot: bool = False) → ndarray#

Calculates the mean stress correction according to Smith-Watson-Topper model. It is equivalent to the Walker model with gamma = 0.5.

The correction is given by:

\[\Delta \sigma_{corr} = \sqrt{\sigma_{max} \cdot \sigma_{amp}}\]

with:

\[\sigma_{max} = \sigma_{mean} + \sigma_{amp}\]
Parameters:

  • mean_stress (np.ndarray) – The mean stress of the fatigue test (\(\sigma_{mean}\)).

  • stress_amplitude (np.ndarray) – The stress amplitude of the fatigue test (\(\sigma_{amp}\)).

  • plot (bool, optional) – If True, the mean stress correction is plotted, defaults to False.

Returns:

The mean stress corrected ranges (\(\Delta \sigma_{corr}\)).

Return type:

np.ndarray

py_fatigue.mean_stress.corrections.goodman_haigh_mean_stress_correction(amp_in: ndarray | list[float], mean_in: ndarray | list[float], r_out: float | ndarray | list[float], ult_s: float, correction_exponent: float, initial_guess: ndarray | None = None, plot: bool = False, logger: Logger | None = None) → tuple[ndarray, ndarray]#

This function extends the standard Goodman-Haigh correction formula which computes the corrected stress amplitude at zero mean stress (\(R=-1\)) for a given set of input stress amplitudes and mean stresses.

\[\sigma_{amp, \text{out}} =  \frac{\sigma_{amp, \text{in}}} {1 - \left(\frac{\sigma_{mean, \text{in}}}{\sigma_{ult}} \right)^{n}}\]

The correction exponent \(n\) is a material property that can be obtained from experimental data.

The current implementation extends the standard Goodman-Haigh formula by correcting the stress amplitude from an initial load ratio \(R_{in}\) to any other load ratio \(R_{out}\), as long as the material’s ultimate strength is known. The corrected stress amplitude \(\sigma_{amp, \text{out}}\) is computed using the following implicit nonlinear equation:

\[\sigma_{amp, \text{out}} =  \frac{1}{ \frac{1 - \left( \frac{(1 + R_{\text{in}}) \cdot \sigma_{amp, \text{in}}} {(1 - R_{\text{in}}) \cdot \sigma_{ult}} \right)^{n}}{\sigma_{amp, \text{in}}} + \sigma_{amp, \text{out}}^{n-1} \cdot \left( \frac{(1 + R_{\text{out}})}{(1 - R_{\text{out}}) \cdot \sigma_{ult}} \right)^{n}}\]

where:

  • \(R\)in = \(\sigma_{min} / \sigma_{max} = (\sigma_{mean} - \sigma_{amp}) / (\sigma_{mean} + \sigma_{amp})\) is the input stress ratio,

  • \(R\)out is the output stress ratio,

  • \(\sigma_{amp}\)in is the input amplitude,

  • \(\sigma_{amp}\)out is the output amplitude,

  • \(\sigma_{ult}\) is the ultimate strength of the material, and

  • \(n\) is the correction exponent.

The solver is based on the Newton-Raphson method, which is implemented internally at py_fatigue.utils.numba_newton(), py_fatigue.utils.compile_specialized_newton(), and py_fatigue.mean_stress.corrections.__goodman_equation().

Parameters:

  • amp_in (np.ndarray | list) – Input amplitude values.

  • mean_in (np.ndarray | list) – Input mean stress values.

  • r_out (float | np.ndarray) – Output stress ratio values.

  • ult_s (float) – Ultimate strength of the material.

  • correction_exponent (float) – Mean stress correction exponent (n).

Returns:

Computed amp_out values, and corresponding mean_out values.

Return type:

tuple[np.ndarray, np.ndarray]

See also

py_fatigue.utils.numba_newton(), py_fatigue.utils.compile_specialized_newton(), :func:`py_fatigue.mean_stress.corrections.__goodman

Raises:

  • ValueError – If the input arrays have different shapes or if there are negative stress amplitude values in amp_in.

  • Warning – If the number of points in the input arrays is too large for plotting.

Examples

>>> import numpy as np
>>> from py_fatigue.mean_stress.corrections import (
...     goodman_haigh_mean_stress_correction
... )
>>> amp_in = np.array([100, 200, 300])
>>> mean_in = np.array([0, 0, 0])
>>> r_out = np.array([-1, 0, 0.5, 0.75, 0.9])
>>> ult_s = 1000
>>> correction_exponent = 9
>>> amp_out, mean_out = goodman_haigh_mean_stress_correction(
...     amp_in, mean_in, r_out, ult_s, correction_exponent, plot=True
... )