.. _auto_math_lankford_coefficient:

*COMPUTE LANKFORD COEFFICIENT BASED ON 0,45 AND 90 DEG STRAINS*
===============================================================

Computes the Lankford coefficient (r-value) for sheet metal anisotropy from width and thickness strains measured at 0°, 45°, and 90° orientations relative to the rolling direction. Use this worker when characterizing plastic anisotropy of sheet materials as part of material characterization or forming analysis workflows.

When to use
-----------

Classification: **process**.

Tagged: ``"``, ``-``, ``a``, ``c``, ``d``, ``e``, ``f``, ``g``.

Inputs
------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20 20 20

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - R0 Strain
     - r0strain
     - scalar
     - —
     - ✓
     - Dimensionless width-to-thickness true plastic strain ratio (or raw strain scalar) measured from a tensile coupon oriented at 0° to the rolling direction; required to compute R0.
   * - R45 Strain
     - r45strain
     - scalar
     - —
     - ✓
     - Dimensionless width-to-thickness true plastic strain ratio (or raw strain scalar) measured from a tensile coupon oriented at 45° to the rolling direction; required to compute R45.
   * - R90 Strain
     - r90strain
     - scalar
     - —
     - ✓
     - Dimensionless width-to-thickness true plastic strain ratio (or raw strain scalar) measured from a tensile coupon oriented at 90° to the rolling direction; required to compute R90.

Outputs
-------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20

   * - Label
     - ID
     - Type
     - Description
   * - math_lankford_coefficient_output_1
     - math_lankford_coefficient_output_1
     - scalar
     - Computed normal anisotropy coefficient (r̄ or individual Lankford r-value), dimensionless; typically the average r-value r̄ = (R0 + 2·R45 + R90) / 4 unless a single directional value is derived.

Disciplines
-----------

- engineering.manufacturing
- engineering.material.characterization

Runnable example
----------------

A runnable example is registered for this worker. Open the example workflow on the d3VIEW canvas: `/api/workflow/example?id=math_lankford_coefficient <https://www.d3view.com/api/workflow/example?id=math_lankford_coefficient>`_

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   Auto-generated from <code>transformation</code> schema. Worker id: <code>math_lankford_coefficient</code>. Schema hash: <code>9b23b34b3d8c</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
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