.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/materials/creep/plot_02_larson_miller.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_creep_plot_02_larson_miller.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_creep_plot_02_larson_miller.py:


The Larson-Miller parameter (1952)
==================================

A boiler tube must last 100,000 hours, eleven years, but nobody can wait
that long for a test. Frank Larson and James Miller (1952) observed that
rupture times at different temperatures fall on one curve if plotted
against :math:`P = T(C + \log_{10}t_r)`, with :math:`C \approx 20`
(:func:`~engineeringkit.materials.larson_miller_parameter`). A short test
at a higher temperature then stands in for a long life at a lower one
(:func:`~engineeringkit.materials.larson_miller_rupture_time`). The
parameter follows from an Arrhenius rupture time
:math:`t_r = t_0 e^{Q(\sigma)/RT}`: then :math:`C = -\log_{10}t_0` and
:math:`P = Q(\sigma)/(2.303R)` depends on stress alone.

.. GENERATED FROM PYTHON SOURCE LINES 18-25

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.materials import larson_miller_parameter, larson_miller_rupture_time

    HOUR = 3600.0








.. GENERATED FROM PYTHON SOURCE LINES 26-32

Rupture tests collapse onto one master curve
--------------------------------------------

Stress-rupture tests on a low-alloy steel at three temperatures. Plotted
against time they are three separate curves; against :math:`P` they are
one.

.. GENERATED FROM PYTHON SOURCE LINES 32-61

.. code-block:: Python



    def master_stress(P):
        return 1e6 * 10 ** (2.9 - 1.1e-4 * (P - 17000))


    temperatures = [811.0, 866.0, 922.0]
    rng = np.random.default_rng(5)
    tests = []
    for T in temperatures:
        P = np.linspace(17500, 22500, 6)
        P = P[(P / T - 20 > -1) & (P / T - 20 < 5)]
        hours = 10 ** (P / T - 20) * rng.lognormal(0, 0.1, P.size)
        tests.append((T, hours * HOUR, master_stress(P)))

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9.5, 3.8))
    for T, t, s in tests:
        ax1.loglog(t / HOUR, s / 1e6, "o-", label=f"{T:.0f} K")
        P_test = larson_miller_parameter(T, t)
        ax2.semilogy(P_test, s / 1e6, "o", label=f"{T:.0f} K")
        assert np.allclose(master_stress(P_test), s, rtol=0.03)
    P_line = np.linspace(17000, 23000, 50)
    ax2.semilogy(P_line, master_stress(P_line) / 1e6, "k-", lw=0.8, label="master curve")
    ax1.set(xlabel="rupture time [h]", ylabel="stress [MPa]", title="Rupture tests")
    ax2.set(xlabel="P = T (20 + log10 t_r [h])", ylabel="stress [MPa]", title="Larson-Miller plot")
    ax1.legend()
    ax2.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/materials/creep/images/sphx_glr_plot_02_larson_miller_001.png
   :alt: Rupture tests, Larson-Miller plot
   :srcset: /api/gallery/materials/creep/images/sphx_glr_plot_02_larson_miller_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 62-68

A short test for a long life
----------------------------

100,000 h at 811 K has :math:`P = 811 \times 25`. The same :math:`P` is
reached in 1000 h at :math:`811 \times 25/23 = 882` K. The master curve
gives the stress for that life.

.. GENERATED FROM PYTHON SOURCE LINES 68-77

.. code-block:: Python


    design_T, design_life = 811.0, 1e5 * HOUR
    P = larson_miller_parameter(design_T, design_life)
    test_T = design_T * 25 / 23
    print(f"P = {P:.0f}; 1000 h test at {test_T:.0f} K; allowable stress {master_stress(P) / 1e6:.0f} MPa")
    assert np.isclose(larson_miller_rupture_time(P, test_T), 1000 * HOUR)
    assert np.isclose(larson_miller_rupture_time(P, design_T), design_life)

    plt.show()




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

 .. code-block:: none

    P = 20275; 1000 h test at 882 K; allowable stress 347 MPa





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

   **Total running time of the script:** (0 minutes 0.091 seconds)


.. _sphx_glr_download_api_gallery_materials_creep_plot_02_larson_miller.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/creep/plot_02_larson_miller.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_larson_miller.ipynb <plot_02_larson_miller.ipynb>`

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

      :download:`Download Python source code: plot_02_larson_miller.py <plot_02_larson_miller.py>`

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

      :download:`Download zipped: plot_02_larson_miller.zip <plot_02_larson_miller.zip>`


.. only:: html

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

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