.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/materials/fatigue/plot_04_coffin_manson.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_04_coffin_manson.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_04_coffin_manson.py:


Coffin and Manson: low-cycle fatigue (1954)
===========================================

Nuclear plant and jet-engine parts heated and cooled a few thousand times
fail by cycles of plastic strain, where Basquin's stress-life law is
useless because the stress hardly changes. Louis Coffin (1954) and Samson
Manson (1953-1954) independently found that the plastic strain amplitude
follows its own power law, :math:`\Delta\varepsilon_p/2 = \varepsilon_f'(2N)^c`
(:func:`~engineeringkit.materials.coffin_manson_cycles`). Added to
Basquin's elastic line it gives the strain-life curve
(:func:`~engineeringkit.materials.strain_life_amplitude`) used for notched
parts today.

.. GENERATED FROM PYTHON SOURCE LINES 17-23

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy.optimize import brentq

    from engineeringkit.materials import basquin_cycles, coffin_manson_cycles, strain_life_amplitude








.. GENERATED FROM PYTHON SOURCE LINES 24-30

The strain-life curve
---------------------

For a quenched and tempered steel, :math:`\sigma_f' = 1100` MPa,
:math:`b = -0.09`, :math:`\varepsilon_f' = 0.6`, :math:`c = -0.6`. Below the
transition life plastic strain dominates; above it, elastic.

.. GENERATED FROM PYTHON SOURCE LINES 30-39

.. code-block:: Python


    E, sf, b, ef, c = 200e9, 1100e6, -0.09, 0.6, -0.6
    N = np.geomspace(10, 1e7, 300)
    total, elastic, plastic = strain_life_amplitude(N, E, sf, b, ef, c)
    Nt = 0.5 * (ef * E / sf) ** (1 / (b - c))
    _, e_t, p_t = strain_life_amplitude(Nt, E, sf, b, ef, c)
    print(f"transition life {Nt:.0f} cycles, where both strains are {e_t:.5f}")
    assert np.isclose(e_t, p_t)





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

 .. code-block:: none

    transition life 4950 cycles, where both strains are 0.00240




.. GENERATED FROM PYTHON SOURCE LINES 40-46

Life at a given strain
----------------------

A part strained to :math:`\pm 0.8\%` fails in about 1300 cycles. Its
plastic part alone, put through Coffin-Manson, and its elastic part, put
through Basquin, give the same life.

.. GENERATED FROM PYTHON SOURCE LINES 46-64

.. code-block:: Python


    target = 0.008
    life = brentq(lambda n: strain_life_amplitude(n, E, sf, b, ef, c)[0] - target, 1, 1e8)
    _, e_life, p_life = strain_life_amplitude(life, E, sf, b, ef, c)
    print(f"strain amplitude {target}: {life:.0f} cycles (plastic {p_life:.5f}, elastic {e_life:.5f})")
    assert np.isclose(coffin_manson_cycles(p_life, ef, c), life) and np.isclose(basquin_cycles(e_life * E, sf, b), life)

    fig, ax = plt.subplots(figsize=(6, 3.8))
    ax.loglog(2 * N, total, label="total")
    ax.loglog(2 * N, elastic, "--", label="elastic (Basquin)")
    ax.loglog(2 * N, plastic, "--", label="plastic (Coffin-Manson)")
    ax.axvline(2 * Nt, color="0.6", ls=":", label="transition")
    ax.plot(2 * life, target, "ko")
    ax.set(xlabel="reversals to failure 2N", ylabel="strain amplitude", title="Strain-life curve")
    ax.legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/materials/fatigue/images/sphx_glr_plot_04_coffin_manson_001.png
   :alt: Strain-life curve
   :srcset: /api/gallery/materials/fatigue/images/sphx_glr_plot_04_coffin_manson_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    strain amplitude 0.008: 1327 cycles (plastic 0.00529, elastic 0.00271)





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

   **Total running time of the script:** (0 minutes 0.085 seconds)


.. _sphx_glr_download_api_gallery_materials_fatigue_plot_04_coffin_manson.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_04_coffin_manson.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_04_coffin_manson.ipynb <plot_04_coffin_manson.ipynb>`

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

      :download:`Download Python source code: plot_04_coffin_manson.py <plot_04_coffin_manson.py>`

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

      :download:`Download zipped: plot_04_coffin_manson.zip <plot_04_coffin_manson.zip>`


.. only:: html

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

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