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


Crack size and fracture threshold
=================================

With a fixed tensile stress and geometry factor, stress intensity rises with
the square root of crack length. Inverting the toughness threshold recovers
the critical crack length. Small-scale yielding is assumed.

.. GENERATED FROM PYTHON SOURCE LINES 9-28



.. image-sg:: /api/gallery/materials/images/sphx_glr_plot_materials_benchmark_001.png
   :alt: plot materials benchmark
   :srcset: /api/gallery/materials/images/sphx_glr_plot_materials_benchmark_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.materials import critical_crack_length, stress_intensity

    sigma, Y, Kic = 100e6, 1.12, 50e6
    critical = critical_crack_length(Kic, sigma, Y)
    a = np.linspace(1e-6, 1.5 * critical, 201)
    K = np.array([stress_intensity(Y, sigma, ai) for ai in a])
    assert np.isclose(stress_intensity(Y, sigma, critical), Kic)
    fig, ax = plt.subplots()
    ax.plot(a * 1000, K / 1e6)
    ax.axhline(Kic / 1e6, color="black", linestyle="--", label="toughness")
    ax.axvline(critical * 1000, color="gray", linestyle=":", label="critical crack")
    ax.set(xlabel="crack length [mm]", ylabel="stress intensity [MPa sqrt(m)]")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.078 seconds)


.. _sphx_glr_download_api_gallery_materials_plot_materials_benchmark.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/plot_materials_benchmark.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

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

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

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


.. only:: html

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

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