.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/materials/fatigue/plot_02_basquin_sn_curve.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_materials_fatigue_plot_02_basquin_sn_curve.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_materials_fatigue_plot_02_basquin_sn_curve.py:


Basquin's S-N law (1910)
========================

August Wöhler's railway-axle tests of the 1860s showed that steel breaks
under repeated stresses far below its static strength, and that below an
endurance limit it may never break. Olin Basquin (1910) noticed that on
log-log axes the finite-life part of Wöhler's curves is a straight line,
:math:`\sigma_a = \sigma_f'(2N)^b`
(:func:`~engineeringkit.materials.basquin_cycles`). The example fits the
line to scattered test results with
:func:`~engineeringkit.materials.utils.power_law_fit` and recovers the
constants that produced them.

.. GENERATED FROM PYTHON SOURCE LINES 17-24

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.materials import basquin_cycles
    from engineeringkit.materials.utils import power_law_fit
    from engineeringkit.materials.visualizers import plot_sn_curve








.. GENERATED FROM PYTHON SOURCE LINES 25-31

Simulated endurance tests
-------------------------

A steel with :math:`\sigma_f' = 1000` MPa and :math:`b = -0.085` is tested
at six amplitudes, three specimens each. Fatigue lives scatter by a
factor of a few, so each life gets a lognormal error.

.. GENERATED FROM PYTHON SOURCE LINES 31-42

.. code-block:: Python


    sigma_f, b = 1000e6, -0.085
    amplitudes = np.repeat(np.array([300, 340, 380, 420, 460, 500]) * 1e6, 3)
    rng = np.random.default_rng(7)
    lives = basquin_cycles(amplitudes, sigma_f, b) * rng.lognormal(0, 0.4, amplitudes.size)

    A, p = power_law_fit(lives, amplitudes)
    b_fit, sigma_f_fit = p, A / 2**p
    print(f"fitted b = {b_fit:.4f} (true {b}), sigma_f' = {sigma_f_fit / 1e6:.0f} MPa (true {sigma_f / 1e6:.0f})")
    assert abs(b_fit - b) < 0.01 and abs(sigma_f_fit / sigma_f - 1) < 0.15





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    fitted b = -0.0832 (true -0.085), sigma_f' = 975 MPa (true 1000)




.. GENERATED FROM PYTHON SOURCE LINES 43-49

The S-N diagram
---------------

One decade of life costs a fixed fraction of strength,
:math:`10^{b}`, about 18% here. Wöhler's endurance limit, the flat tail
of a steel's curve, is not part of Basquin's law.

.. GENERATED FROM PYTHON SOURCE LINES 49-61

.. code-block:: Python


    N = np.geomspace(1e3, 1e7, 50)
    fitted = sigma_f_fit * (2 * N) ** b_fit
    print(f"strength lost per decade of life: {100 * (1 - 10**b_fit):.1f}%")
    assert np.allclose(basquin_cycles(fitted, sigma_f_fit, b_fit), N)

    ax = plot_sn_curve(lives, amplitudes, style="o", label="tests")
    plot_sn_curve(N, fitted, ax=ax, label="Basquin fit")
    ax.set_title("Stress-life curve")
    ax.figure.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/materials/fatigue/images/sphx_glr_plot_02_basquin_sn_curve_001.png
   :alt: Stress-life curve
   :srcset: /api/gallery/materials/fatigue/images/sphx_glr_plot_02_basquin_sn_curve_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    strength lost per decade of life: 17.4%





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.121 seconds)


.. _sphx_glr_download_api_gallery_materials_fatigue_plot_02_basquin_sn_curve.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/materials/fatigue/plot_02_basquin_sn_curve.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_basquin_sn_curve.ipynb <plot_02_basquin_sn_curve.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_basquin_sn_curve.py <plot_02_basquin_sn_curve.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_basquin_sn_curve.zip <plot_02_basquin_sn_curve.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_