Stress-strain behaviour and microcracks

Concrete has three phases (aggregate, paste and the weak interfacial transition zone). Even before loading, bond microcracks exist at the interface because of bleeding, shrinkage and thermal strain. Their growth with load controls the shape of the curve.

 stress
   |
 f_c |                      _.---'''---._
     |                   .-'      IV      '-._
 0.75|----------------.-'                     '-._  post-peak
     |             .-'    III                      '-. (softening)
 0.50|-----------.-'
     |         .'     II
 0.30|-------.-'
     |     .'    I
     |   .'
     | .'
     +--------------------------------------------- strain

Stage I: up to about 30% of $f_c$

Stress-strain is nearly linear. Pre-existing interface cracks stay stable; no new cracks form. The energy is stored elastically.

Stage II: 30% to about 50%

Curve starts to bend. Bond cracks at the aggregate-paste interface begin to grow in number and length. Mortar cracks are still absent; the system remains stable.

Stage III: 50% to about 75%

Cracks start to appear in the mortar (matrix) and link with the bond cracks. Crack growth is still stable, but it only continues while the stress is increased; the curve flattens. About 75% of $f_c$ is called the critical stress or onset of unstable crack propagation, also the long-term strength.

Stage IV: 75% to 100%

Crack propagation becomes unstable; the matrix cracks join the bond cracks into continuous crack paths. Volumetric strain reverses (the concrete starts to dilate), strain rises quickly and the peak stress is reached.

Post-peak

Strain softening: the curve falls along the descending branch, and failure occurs by shear or splitting along a continuous crack surface at a strain of about 0.003 to 0.004.

Result: the curve is non-linear even in the early part because progressive microcracking and gel creep increase the strain faster than the stress.