Can you please explain the effect on hardenability by chromium in medium-carbon steels?  

As you most likely know, carbon, and to a lesser extent manganese, have the greatest effect on hardenability in steels. Still, chromium does have an influence, which can be summarized below:

“Chromium (Cr) is one of the most versatile and widely used alloying elements in steel. It is considered a mild hardenability agent, improves wear resistance (generally via hard and stable chromium carbides), promotes the retention of strength at elevated temperatures, provides resistance to softening during tempering and, depending on amount, provides resistance to corrosion and oxidation. It is not as strong a hardenability agent as either manganese (Mn) or molybdenum (Mo).”[1] 

It is less cost effective (hardenability gain/cost) than Mn but more cost effective than Mo. This may be seen in Table 1, which collectively provides important information on the effect of carbon, the primary alloying elements and the significant effect of grain size (which is often overlooked).[2]

“Due to the strengthening effect at higher temperatures and the resistance to softening during tempering, Cr-containing steels will require higher tempering temperatures and/or times than for plain-carbon steels. These effects increase with increasing Cr content.”[1]

Chromium and chromium–nickel steels are susceptible to both temper embrittlement and tempered-martensite embrittlement.[1]

When comparing steels from two different heats of the same or essentially the same grade of steel, caution must be exercised to evaluate all of the following: relative carbon contents; relative levels and associated hardenability effects of the various primary and residual alloying elements; and the grain sizes of the two materials. If one heat has a coarser grain size, via killing method and/or processing history, it will have an innate hardenability advantage. This is readily seen by studying Table 1.