Microstructural analysis of crack growth caused by static and dynamic loads in a carbon fiber reinforced cement paste

Abstract

By using a novel fiber-reinforced cement paste in a 3D-printing process, a material with vastly improved flexural and tensile strength can be created. The extrusion-based process leads to a high degree of fiber orientation. A fiber content of 3 vol. % results in static flexural strengths of above 100 MPa. High-strength fiber-reinforced materials have potential to be used in lightweight construction. Due to the susceptibility of lightweight structural members to oscillating dynamic loads, cyclic flexural and tensile tests with up to 10 million cycles are carried out. To characterize the complex (micro-)cracking behavior of the material, the tests are augmented by external deformation sensors (strain gauges, fiber-optic sensors, photogrammetry) and microstructural analysis (X-ray CT, acoustic emission sensors, coda-wave interferometry). The experimental data will serve as the basis for multiscale-modelling approach which uses representative volume elements created from high-resolution CT scans.

Homogenization of linearized elasticity in a two-component medium with slip displacement conditions

“…3 := {φ ∈ D(Ω) 3 : v is equal to 0 in a neighbourhood of Γ 1 }, w 0 , w 1 , v 0 ∈ [D(Ω)] 3 , ψ 0 (x) = ψ 0 x ε with ψ 0 ∈ H 1 (Y 0 ) 3 (Y-periodically extended to R 3 ), ψ 1 (x) = ψ 1 x ε with ψ 1 ∈ H 1 per (Y 1 ) 3 such that ∇ × ϕ ε 0 = 0. Then, ϕ ε ∈ W d (Ω ε ),…”

“…On the other hand, in the connected case, the composite consists of two globally connected materials. We choose a bounded connected Lipschitz-domain Ω ⊂ R 3 , which can be represented as a union of axis-parallel cuboids and which has corner coordinates in Q 3 .…”

“…for some u 1 ∈ H 1 (Ω, Γ 1 ) 3 and û1 ∈ L 2 (Ω, H 1 per,0 (Y 1 )) 3 . The definition of the linear strain tensor e(u ε 1 ) = 1 2 ∇u ε 1 + (∇u ε 1 ) T directly yields…”

“…The problem is motivated by recently proposed concretes reinforced with short carbon fibres, cf. [1], [2], [3]. Similarly to carbon-fibre-reinforced ceramics, the bonding of the fibres to the concrete matrix is rather weak, so that it cannot be modelled as a perfect bond.…”

“…The solutions u 1 ∈ H 1 (Ω, Γ 1 ) 3 and u 0 ∈ L 2 curl (Ω)3 of the macroscopic problem(21) are unique.…”