What is tensile strain-hardening?
1. One-sentence answer
Tensile strain-hardening means the material can carry increasing tensile stress even after the first crack forms.
2. Intuitive explanation
In ordinary concrete, the first crack is usually the beginning of failure. In ECC, the first crack is only the beginning of a controlled cracking process. More cracks form while the material continues to carry load.
3. Technical explanation
In ECC/SHCC, tensile strain-hardening occurs when fiber bridging across a crack can support a stress higher than the matrix cracking strength, and when the complementary bridging energy is sufficient for steady-state crack propagation. These are usually discussed as the strength criterion and energy criterion for pseudo-strain-hardening.
4. Why it matters
This behavior is the core reason ECC can achieve high tensile ductility, distributed damage, and small crack widths at relatively low fiber volume.
5. Representative evidence
- Core node:
02_concepts/strain_hardening_criteria.md. - Foundational evidence: Li & Wu 1992; Li & Leung 1992; Kanda & Li 2006 in
07_visualization/foundational_papers_claim_evidence_matrix.csv. - Teaching module:
08_teaching/lecture_modules/02_micromechanics_and_psh.md.
6. Common misunderstanding
Strain-hardening does not mean the cement matrix itself becomes ductile like steel. It is a composite-level pseudo-ductile behavior created by many fiber-bridged cracks.
7. Linked Atlas nodes
02_concepts/strain_hardening_criteria.md02_concepts/fiber_bridging_law.md02_concepts/flaw_design.md05_experiments/direct_tensile_test.md