Lin & Li 1997 - Crack bridging in fiber reinforced cementitious composites with slip-hardening interfaces

Citation

Lin, Z., Li, V.C. (1997). Crack bridging in fiber reinforced cementitious composites with slip-hardening interfaces. Journal of the Mechanics and Physics of Solids, 45(5), 763-787.

• DOI: 10.1016/S0022-5096(96)00095-6 (verified via Crossref API, batch 2)

Source paths

• PDF: 00_sources/foundational_papers/originals/lin-1997-crack-bridging-in-fiber-reinforced-cementitious.pdf
• Extracted full text: 00_sources/foundational_papers/extracted_text/lin-1997-crack-bridging-in-fiber-reinforced-cementitious.md
• Source note: 00_sources/foundational_papers/source_notes/lin-1997-crack-bridging-in-fiber-reinforced-cementitious.md

Why the paper matters for the Atlas

• Establishes the crack bridging model for randomly oriented discontinuous flexible fibers with a slip-hardening interfacial shear law, extending the earlier constant-tau (Li 1992) model.
• Introduces the two-parameter linear slip-hardening interface constitutive relation (initial frictional sliding shear stress r0, hardening parameter beta) that underlies the modern ECC sigma(delta) fiber-bridging law.
• Provides the micromechanics-based criterion for existence of a post-debonding rising branch on the sigma(delta) curve, which is a necessary structural feature for strain hardening in ECC.
• Direct upstream reference for the Atlas nodes fiber_bridging_law, strain_hardening_criteria (energy criterion via complementary energy J_b'), and micromechanics_based_design.

Direct evidence extracted from source note / full text

• New crack bridging model derived from micromechanics of single fiber pullout with linear slip-hardening interface (source note Section 2, 3).
• Slip hardening in synthetic fiber / cement matrix composites is attributed to fiber surface abrasion at the fiber / matrix interface (source note Section 4).
• The constant-tau model of Li 1992 is shown to under-predict crack opening and ultimate strain critical for ECC design; the slip-hardening model resolves this (source note Section 2).
• A closed-form micromechanics-based criterion governs the existence of the post-debonding rising branch of the composite sigma(delta) curve (source note Sections 2 and 4).
• Model is validated against single-fiber pullout data for polyethylene Spectra 900 fibers (source note Section 3).

Key equations and parameters

• Linear slip-hardening interface constitutive relation with parameters (r0, beta), where r0 is the initial frictional sliding shear stress at zero local slip and beta is a nondimensional hardening parameter. Exact functional form and equation numbers: needs verification against the original PDF.
• Composite bridging stress vs crack opening relation sigma(delta) with random fiber orientation, snubbing effect, and slip-hardening interface. Exact form: needs verification.
• Existence criterion for a rising post-debonding branch of sigma(delta): needs verification of the exact inequality against the original PDF.

Atlas node links

• Concept nodes: 02_concepts/fiber_bridging_law.md, 02_concepts/strain_hardening_criteria.md, 02_concepts/micromechanics_based_design.md.
• Experiment nodes: 05_experiments/direct_tensile_test.md (indirect, through sigma(delta)-driven prediction).
• Related paper cards: li_leung_1992_steady_state_multiple_cracking.md (constant-tau predecessor), redon_etal_2001_pva_interface_properties.md (measurement of r0, beta for PVA), yang_etal_2008_fiber_bridging_constitutive_law.md (later extension with two-way debonding, Cook-Gordon, micro-spalling), kanda_li_2006_practical_design_criteria_psh.md (practical PSH thresholds built on this sigma(delta)).

Graph implications

• Confirms candidate edge fiber_bridging_law -> strain_hardening_criteria (sigma(delta) drives energy and strength criteria).
• Confirms candidate edge micromechanics_based_design -> fiber_bridging_law.
• Adds a new candidate edge interface_properties (r0, beta) -> fiber_bridging_law (slip-hardening interface is the input to the bridging law).

Verification status

• Source note: present.
• Full-text extraction: present.
• Original PDF: present.
• DOI: needs verification.
• Exact page numbers, figure numbers, equation numbers, and numerical claims: needs verification against the original PDF before quoting into higher-order Atlas nodes.