21.4.1. Stress-Strain Behavior

Fiber-reinforced concrete displays a markedly different stress-strain behavior compared to plain concrete:

• Plain Concrete: Linear elastic until peak, then sudden brittle failure.
• FRC: Shows non-linear strain hardening after first crack. Fibers bridge cracks, allowing for energy dissipation and strain capacity beyond peak load.

The behavior of concrete under stress describes how it responds to being pushed or pulled. Plain concrete behaves in a linear manner meaning it stretches evenly until it reaches a peak strength and then fails suddenly, like a thin glass rod. In contrast, fiber-reinforced concrete (FRC) shows non-linear behavior. This means that after the first crack happens, the material doesn’t just fail; it can continue to bear weight because the fibers help to bridge the cracks. This bridging allows the material to absorb more energy, making it tougher and more durable.

Think of plain concrete as a balloon that pops suddenly once too much air is blown into it. Now, imagine fiber-reinforced concrete as a rubber band that, although it stretches and may break, can still hold onto some of the load due to its flexible fibers, allowing for more bending and energy absorption before ultimately failing.

Post-Cracking Behavior: Often categorized as:

• Deflection Hardening: Load continues to increase after first crack.
• Deflection Softening: Load decreases but concrete retains some post-crack load-carrying capacity.

After the initial cracking of the concrete, the way it behaves can be classified into two categories: deflection hardening and deflection softening. In deflection hardening, the material can take on even more load after the first crack occurs. This is beneficial because it means the structure can still function after it has experienced damage. On the other hand, in deflection softening, after the first crack, the load that the concrete can carry starts to decline but it can still carry some load, indicating it hasn’t totally failed yet. This behavior is significant in assessing how structures made with FRC will behave under stress.

Imagine a team of friends lifting a heavy box together. If one person pulls a muscle and could no longer help, the remaining friends may still be able to lift more weight (deflection hardening). However, if the load becomes too heavy, they may slowly start to drop more weight even after one person gets hurt (deflection softening).

Stress-Strain Curve Phases for FRC:

1. Elastic behavior up to matrix cracking.
2. Multiple cracking as fibers begin to engage.
3. Fiber pull-out or rupture depending on bond and length.
4. Final failure after loss of fiber effectiveness.

The stress-strain curve for fiber-reinforced concrete has distinct phases which highlight its performance under stress. Initially, FRC behaves elastically, meaning it stretches without permanent deformation. The next phase shows that as stress increases, multiple cracks begin to form due to the action of the fibers. Following this, we might see fibers pulling out of the matrix or breaking, which also depends on how well they're bonded to the concrete and their length. Finally, once the fibers are no longer effective, the material reaches total failure. This progressive failure is unlike plain concrete, which fails suddenly.

Think of this stress-strain curve like a video game where a character levels up. Initially, the character gains experience points (elastic phase), then as they face stronger enemies, they begin to collect multiple power-ups (multiple cracking phase) that provide added strength. However, as they continue facing challenges, some power-ups may be lost (fiber pull-out), and ultimately, when all abilities are exhausted, they can no longer continue the battle (final failure). This illustrates how FRC holds up under stress better than plain concrete.

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