what is the correlation between the erosion resistance and depth of crater ( indentation) that resulted from single particle impact ( steel ball ) test at normal incidence ( in case of target is ductile material such as al-alloys)
How do you define erosion resistance? Is it the failure strength (UTS)? In that case, we can find the correlation by carrying out finite element (FE)simulations and/or experiments. We can have plate material with different material properties, stress-strain curve, UTS etc. The size of the plate/target and indenter/particle and its material can be kept constant. Based on the outcome of FE results (depth of crater), a correlation coefficient can be obtained between erosion resistance and depth of crater.
Other parameters that can affect are initial velocity of the particle, mass and size of the particle, impedance mismatch between plate and particle, thickness of the plate, material properties of the particle etc.