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1. Microstructure Variability and Macroscopic Composite Properties of High Performance Fiber Reinforced Cementitious Composites Victor C. Li and Shuxin Wang Advanced Civil Engineering Materials Research Laboratory The University of Michigan

2. High Performance Fiber Reinforced Cementitious Composites • High strength • High durability • Self-compacting • High tensile failure resistance

3. s HPFRCC FRC Concrete e , D HPFRCC Characteristics: Strain-Hardening

4. 20 mm Damage Engineered Cementitious Composites Composite response in uniaxial tension 5 100 Fiber volume fraction 2% ECC 4 80 3 60 Crack Width (m) Tensile Stress (MPa) 2 40 1 20 Concrete Strain 10 times expanded 0 0 0 1 2 3 4 5 6 Strain (%)

5. Mihara Bridge in Hokkaido Open to traffic: April, 2005 Length: 1000 m, span: 340 m Deck area: 20,000 sq. m.; ECC layer thickness: 38 mm Composite ECC-Steel Deck Super light-weight 40% reduction Expected service life: 100 yrs

6. Lspan Lspan Llink slab = 0.1 x Lspan Bridge-deck Link Slab RetrofitMichigan, 2005 Conventional Bridge Joint Durable ECC Link Slab ECC Link Slab

7. Variation of Tensile Behavior PVA fiber reinforced ECC, Vf = 2% Extreme variability case

8. Microstructure Inhomogeneity Matrix flaws 10 mm Fiber distribution

9. a   P   s s Le  z        Scale Linking Steady State Cracking Requirement Crack Saturation Requirement Single fiber pullout behavior Crack initiation at flaw Bridging stress vs. crack opening Multiple-cracking process Composite stress vs. strain

10. a   Le  Le Single Fiber Modeling Debonding Pullout  Fiber parameters Interface parameters

11. Modeling of Fiber Randomness

12. s s0 Jb’ complementary energy sss Jtip crack tip fracture energy  Conditions for Strain-hardening sss sss Variability of Jtip, Jb’ ? Matrix parameter

13. Effect of Initial Flaw Size on Cracking Strength(Computed) Matrix intrinsic tensile strength 5 MPa

14. Tailoring of Flaw Size Distribution for Saturated Multiple Cracking • Superimpose artificial flaws with prescribed sizes • Artificial flaws: plastic, bubbles, lightweight aggregates, etc. p(c) p(c) s s artificial flaw distribution natural flaw distribution activated flaws Activated flaws cmc cmc flaw size c flaw size c

15. lightweight aggregates size: 3.5 mm Flaw Size Tailoring in PVA-ECC 4mm plastic beads

16. Lightweight Aggregates as Artificial Flaws w/o lightweight aggr. lightweight aggr.: 7 vol% s/c = 0.8, fa/c = 0.8, w/b = 0.24, PVA Vf = 2.0%

17. Plastic Beads as Artificial Flaws w/ 7 vol% beads w/o beads s/c = 0.8, fa/c = 1.2, w/b = 0.24, PVA Vf = 2.0%

18. Open Issues • Further understand linkages between randomness of microstructures and variability in composite behaviors • Capture and quantify randomness of critical microstructures • Incorporate probabilistic models in ECC theoretical framework

19. Multiple Cracking Process

20. Conclusions • Microstructure variability significantly influences ductility of ECC materials • Control of key microstructure variability is critical to achieve robust strain-hardening behavior • Ensure enough margin between Jtip and Jb’ • Implantation of artificial flaws with controlled size • Further work in characterization and modeling of microstructure randomness is needed