There are some data available about the relation of hardness and strength for wrought aluminium alloys. However, I need a relation or tabulated data for cast alloys, specially eutectic Al-Si for automotive pistons.
I suggest you to have a look at the following, interesting paper:
-Determination of hardness-strength and -flow behavior relationships in bulged aluminum alloys and verification by FE analysis on Rockwell hardness test
Amir Asgharzadeh, Sobhan Alah Nazari Tiji, Rasoul Esmaeilpour, Taejoon Park & Farhang Pourboghrat
The International Journal of Advanced Manufacturing Technology volume 106, pages315–331(2020)
Available at: https://link.springer.com/article/10.1007/s00170-019-04565-6?shared-article-renderer
There is no exact equation that relates these two properties, but there are approximate methods. For example: Datzco et al, have found a method for predicting the ultimate tensile strength (Su) of a material from Brinell-type hardness tests is described for several metals including steel, aluminum, and copper alloys. The prediction of Su is based on a consistent relationship between Su and amaterial’s hardness coefficient, Kd. The relationship between Su and Kd is found to be 1/3 for all cubic metals.
There is no definate relationship exist. It variers from casting to casting depending the chemical constituent elements, heat treatment, grain size, etc. Best thing is take the samples from the castings and carry experiment
Hardness varies even point to point along the surface of the alloy, based on the density of the regions. This variation starts and exists right from the casting process itself. But, tensile strength may be uniform along the axis of the sample, due to uniformity of the grains within the surface of the alloy, which may not be the case as for indentation is concerned.