Yang, Wang, Yang & Li 2008 - Fiber-bridging constitutive law of ECC

Citation

Yang, E.-H., Wang, S., Yang, Y., Li, V.C. (2008). Fiber-bridging constitutive law of engineered cementitious composites. Journal of Advanced Concrete Technology, 6(1), 181-193.

• DOI: 10.3151/jact.6.181 (verified via Crossref API, batch 2)

Source paths

• PDF: 00_sources/foundational_papers/originals/yang-2008-fiber-bridging-constitutive-law-of.pdf
• Extracted full text: 00_sources/foundational_papers/extracted_text/yang-2008-fiber-bridging-constitutive-law-of.md
• Source note: 00_sources/foundational_papers/source_notes/yang-2008-fiber-bridging-constitutive-law-of.md

Why the paper matters for the Atlas

• Delivers the current-generation analytical fiber-bridging constitutive law sigma(delta) used for ECC design, extending Lin et al. (1999) with three new mechanisms: fiber two-way debonding and pullout, matrix micro-spalling around inclined fibers, and Cook-Gordon interface effects.
• Provides the sigma(delta) whose complementary energy J_b' and peak strength sigma_0 feed both PSH criteria (J_b' > J_tip; sigma_c < sigma_0) used throughout the Atlas.
• Experimentally validates the analytical sigma(delta) against measured fiber-bridging response.
• Direct upstream reference for the Atlas nodes fiber_bridging_law, strain_hardening_criteria, scale_linkage, and for tight-crack-width benefits used in the durability chapters.

Direct evidence extracted from source note / full text

• Analytical sigma(delta) constructed by modeling single-fiber pullout, then averaging across fiber embedment length and orientation distributions (source note Sections 2, 3).
• Adds mechanisms not in Lin et al. (1999): fiber two-way debonding and pullout, matrix micro-spalling, and Cook-Gordon effects (source note Section 3).
• Validated by direct measurement of sigma(delta) on a single-crack specimen (source note Section 4).
• Reports self-controlled tight crack widths on the order of 60 um in ECC (source note Section 4).
• States both criteria that must be satisfied for tensile strain hardening: energy criterion J_b' > J_tip and strength criterion sigma_c < sigma_0 (source note Section 4).

Key equations and parameters

• Fiber-bridging constitutive law sigma(delta) is the central output. Exact analytical form, parameter list, equation numbers, and figure numbers: needs verification against the original PDF.
• Derived quantities used elsewhere: complementary energy J_b' (bounded area between sigma_0 and sigma(delta)), peak bridging strength sigma_0. Exact definitions and equation numbers: needs verification.

Atlas node links

• Concept nodes: 02_concepts/fiber_bridging_law.md, 02_concepts/strain_hardening_criteria.md, 02_concepts/micromechanics_based_design.md, 02_concepts/scale_linkage.md.
• Experiment nodes: 05_experiments/direct_tensile_test.md, 05_experiments/crack_width_distribution.md.
• Related paper cards: lin_li_1997_crack_bridging_slip_hardening.md (previous sigma(delta) with slip-hardening interface), redon_etal_2001_pva_interface_properties.md (interface inputs), li_wang_wu_2001_pva_ecc_tensile_strain_hardening.md (composite-level demonstration), li_wu_wang_etal_2002_interface_tailoring_pva_ecc.md (interface tailoring), kanda_li_2006_practical_design_criteria_psh.md (robust PSH thresholds), li_wang_2006_microstructure_variability.md (variability layer on top of sigma(delta)).

Graph implications

• Confirms candidate edge fiber_bridging_law -> strain_hardening_criteria (sigma(delta) determines both J_b' and sigma_0).
• Confirms candidate edge fiber_bridging_law -> distributed_microcracking (sigma(delta) shape controls saturated cracking / tight crack width around 60 um).
• Supports promoting scale_linkage -> micromechanics_based_design toward confirmed (single fiber pullout to composite sigma(delta) averaging is the scale bridge).
• Adds candidate edges: matrix_micro_spalling -> fiber_bridging_law, cook_gordon_effect -> fiber_bridging_law, two_way_debonding -> fiber_bridging_law (future concept nodes).

Verification status

• Source note: present.
• Full-text extraction: present.
• Original PDF: present.
• DOI: needs verification.
• Exact analytical form of sigma(delta), equation numbers, figure numbers, and reported crack width value (60 um) as it appears in the original PDF: needs verification.