Curve

Units of Measurement

The quantities that the El Haddad curve necessitates must be provided complying with the following units of measurement:

  • \([\sqrt{\text{area}}] = \mu\text{m}\)

  • \([\Delta\sigma] = \text{MPa}\)

  • \([\Delta K] = \text{MPa}\sqrt{\text{m}}\)

  • \([\Delta\sigma_w] = \text{MPa}\)

  • \([\Delta K_{th,lc}] = \text{MPa}\sqrt{\text{m}}\)

Implemented Variables

As concerns the practical implementation of MAP for EH curves, please note that:

  • \(\Delta K_{th,lc}\) is represented as dk_th

  • \(\Delta\sigma_w\) is represented as ds_w

  • \(Y\) is represented, obviously, as Y.

Having shorter names, yet sufficiently explanatory, helps contract the code.

Instantiation

The implementation of the El Haddad curve is given by subclassing from bfade.abstract.AbstractCurve and defining a concrete method for bfade.abstract.AbstractCurve.equation, i.e. bfade.abstract.ElHaddadCurve.equation, according to the prior section.

To instantiate an El Haddad curve, we do:

eh = ElHaddadCurve(metrics=aCallable, dk_th=aFloat, ds_w=aFloat, Y=aFloat, name=aStringName)

So, we instantiate the curve via \(\Delta K_{th, lc}\), and \(\Delta\sigma_w\), whilst \(\sqrt{\text{area}_0}\) is computed accordingly. The choice of metrics shall be discussed later.

Preliminary Inspection

We can graphically inspect the curve with:

eh.inspect(np.linspace(aFloatStart, aFloatEnd, aIntStep), scale="log")