Limitations on the properties of aggregate regarding water absorption, crushing and impact values, gradation, percent fines, and deleterious materials exsist for the selection of suitable aggregate for concrete work
Establishing relation between crushing strength of aggregate and hardened concrete is quite tedious because of following reasons.
1. Mix proportion of concrete depends on strength, density, exposure condition, durability, w/c ratio, cement type and their quality, compaction, air voids etc.,
2. Aggregate source,size, gradation and properties of parent rock
3. Method of mix proportion
However theoretically correlation maybe established, but on field/ laboratory conditions results may vary due to above mentioned variables.
Perhaps question is very interesting. Thank you for good question.
I think surface characteristics, shape and, size are more dominant rather than crushing value. Crushing value should be according to permissible limit but it is not always true that higher crushing value will provide a higher compressive strength. Compressive strength of concrete is influenced by a lot of factors such as water cement ratio, binder content, mix design etc. Although your question is also very interesting and to the answer to your question is 'Yes" you are right. According to best of my knowledge until now there is no any paper explaining the relation between crushing value of aggregate and compressive strength of concrete.
Crushing value of aggregate (One of the model in which pavement material can fail is by crushing under compressive stress. A test is standardized by IS:2386 part-IV and used to determine the crushing strength of aggregates. The aggregate crushing value provides a relative measure of resistance to crushing under gradually applied crushing load. Please ref https://nptel.ac.in/courses/105101087/22-Ltexhtml/p4/p.html) is an indirect measure of strength of aggregate as reflected in its resistance to disintegration under load. Neither is a factor in ordinary concrete as explained below -
"The aggregate strength is usually not a factor except in lightweight and high strength concrete. However, aggregate characteristics other than strength, such as the size, shape, surface texture, grading and mineralogy are known to affect concrete strength in varying degrees."
Aggregate crushing can be done by crushing testing machine as per IS: 2386-4 and aggregate compressive strength can be done with round aggregates (Artificial aggregates) with CBR testing machine where failure load can be calculated.
The cement paste usually fails before failing the aggregates in the concrete matrix. But yes if the quality of aggregates ( coarse) taken is very low or below the standards, then it has impacts on the concrete comprehensive strength. Research should be focused on taking a range of coarse aggregates ( having different crushing value) and then having a similar mix design the compressive strength should be checked.