Stress-strain of paste, aggregate, concrete

Concrete is a three-phase system: aggregate, hydrated cement paste and the interfacial transition zone (ITZ) between them. The stress-strain behaviour of the composite is different from that of its parts.

 stress
   |     /  aggregate: steep, linear, brittle
   |    /
   |   /          _.--'''--.   concrete: curved,
   |  /       _.-''          '.  slope between the two
   | /    _.-'
   |/  .-'     paste: gentler slope, linear, brittle
   |.-'     _____--------
   | _____---
   +----------------------------- strain

Aggregate

Linear elastic up to brittle failure; high strength and high modulus (typically 50 to 100 GPa), small strain at failure.

Hydrated cement paste

Also nearly linear up to failure and brittle, but of lower modulus (10 to 30 GPa) and strength; large strain capacity compared to aggregate.

Concrete

Although aggregate and paste each behave almost linearly, concrete gives a curved, non-linear curve. Its stiffness lies between that of paste and aggregate, and its strength is lower than that of the aggregate:

• The ITZ is porous and contains oriented Ca(OH)2 crystals and microcracks formed by bleeding water and shrinkage. It is the weakest link.
• Under load the elastic mismatch between the stiff aggregate and the softer paste causes stress concentration at the interface, so bond cracks grow from about 30% of $f_c$ and matrix cracks from about 50 to 75%.
• This progressive cracking gives the curved shape; the strain at the peak is about 0.002, and the descending branch shows that the failure is governed by the matrix and the ITZ, not by the strength of aggregate.

So the modulus of concrete lies between that of aggregate and paste, and the strength depends on the paste and ITZ quality rather than on the aggregate.