Simulation of fiber restraint during free shrinkage of cement composites

The irregular lattice model, and discrete modeling of individual fibers, have been used to simulate the restraining effects of fibers during free shrinkage of a cement-based matrix (Bolander and Li, 2004; Bolander, 2004). The experimental work of Mangat and Azari (1988) serves to define the example problem. Results are also compared with those given by the micro-mechanical model of Zhang and Li (2001), which is based on elastic shear lag theory and accounts for the random nature of the fiber distribution.

In the experimental work of Mangat and Azari (1988), various fiber types and fiber volume fractions were placed within 500x100x100 mm specimens made of either mortar or concrete. The tests involving the crimped steel fibers are considered here. The material parameters relevant to simulating the FRCC specimens are: fiber elastic modulus, Ef = 210 GPa; fiber length, l = 48.7 mm; fiber diameter, d = 1.14 mm; elastic modulus of the mortar at 28 days, Em = 20 GPa; the volume fraction of coarse aggregate in the concrete specimens, Va = 0.175; and ultimate shrinkage strain of the mortar, eSU = 825 microstrain. For direct comparison with the analyses of Zhang and Li (2001), the effective fiber length is set to 58.7 mm and the concrete is assumed to shrink uniformly throughout the domain according to

where time t is measured in days. Also, the time dependent variation of the mortar elastic modulus is as described by Zhang and Li (2001). Two types of fiber distributions are considered: 1) fibers aligned in the long direction of the specimen, and 2) randomly oriented fibers. These distributions are shown in the following figure (for Vf = 1%), along with the Voronoi discretization of the specimen used for analysis. Fiber positions and orientations within the domain are determined using a pseudo-random number generator.

Figure 2 shows the shrinkage strains developed in the fiber reinforced concrete over time for a volume fraction of fibers Vf = 2%. The uniform shrinkage strain is introduced into each lattice element, resulting in uniform shrinkage throughout the domain when no fibers are present. When fibers are included, the individual fibers restrict shrinkage of the concrete, which causes tension in the matrix and compression in the fibers. The fiber distributions used for the lattice simulations are constrained by the specimen dimensions, so that there is directional alignment near the boundaries. The amount of shrinkage predicted for the random fiber composite is therefore slightly less than that given by Zhang and Li (2001), which assumed a uniformly at random distribution of fiber orientations. Agreement with the experimental values is good, considering the simplified, uniform representation of shrinkage. In actuality, drying shrinkage is highly nonuniform through the cross-section of cement composite members and such behavior is being considered elsewhere within this project.

References

1. Bolander, J.E. and Li, Z., "The effects of fiber restraint on the shrinkage of cement composites." In Advancing Concrete through Science and Engineering, RILEM Spring Meeting, Center for Advanced Cement Based Materials, Northwestern University, March 2004 (on CD-ROM).
2. Bolander, J.E., "Numerical modeling of fiber reinforced cement composites: Linking material scales." In Proceedings of the Sixth International RILEM Symposium on Fibre-Reinforced Concretes - BEFIB 2004, eds. M. di Prisco, R. Felicetti and G.A. Plizzari, RILEM, 2004, pp. 45-60.
3. Mangat, P.S. and Azari, M.M., "Shrinkage of steel fiber reinforced cement composites." Mat. Structures 21, 1988, 163-171.
4. Zhang, J. and Li, V.C., "Influences of fibers on drying shrinkage of fiber-reinforced cementitious composite."ASCE J. Engrg. Mech. 127(1), 2001, 37-44.