Weave geometry generation avoiding interferences for mesoscale RVEs

doi:10.1016/j.jmst.2018.12.027

Abstract

Abstract:

An algorithm which allows the generation of representative volume elements (RVEs) for complex woven and warp-interlaced fiber-reinforced composite topologies while avoiding unphysical tow intersections is presented. This is achieved by extending an existing RVE generation strategy in two significant ways: (1) the local cross section shape of the tow is adjusted depending on the local tow curvature in a way that preserves the cross sectional area of the tow, and (2) the elementary crimp interval is separated into a planar and a transition region. The modifications facilitate the generation of a wide range of elaborate textile topologies without tow intersections, which are present without the proposed modifications unless complex tow to tow contact models are introduced. The mechanical properties of plain weaves were predicted based on the topology generated with the proposed algorithm as well as based on RVEs which were constructed based on actual micrographs, i.e. a “digital twin” of the actual microstructure. A comparison of the predicted mechanical properties based on finite element and Multiscale Generalized Method of Cells techniques shows close agreement. However, some differences exist with respect to experimentally determined material parameters due to the finite dimensions of the specimens. Lastly, mechanical properties of multilayered weaves are predicted with the finite element method. The considered material systems are carbon fiber in epoxy matrix as well as C/C-SiC. However, the procedure is applicable to a wide range of material systems.

Key words: RVE generation, Multiscale analysis, Composites

Daniel Höwer, Shengkai Yu, Trenton M. Ricks, Brett A. Bednarcyk, Evan J. Pineda, Bertram Stier, Stefanie Reese, Jaan-Willem Simon. Weave geometry generation avoiding interferences for mesoscale RVEs[J]. J. Mater. Sci. Technol., 2019, 35(12): 2869-2882.

Figures/Tables 30

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RVE thickness	Crimp length p	Tow r₁₀
0.464?mm	4.34?mm	0.228?mm
RVE width	Crimp height h	Tow r₂₀
8.68?mm	0.227?mm	4.2?mm
Contact length l
3.475?mm
Tow bending rigidity B	Correction factor A [13]
1?N/mm²	3.5

RVE thickness	Crimp length p	Tow r₁₀
0.464?mm	4.34?mm	0.228?mm
RVE width	Crimp height h	Tow r₂₀
8.68?mm	0.227?mm	4.2?mm
Contact length l
3.475?mm
Tow bending rigidity B	Correction factor A [13]
1?N/mm²	3.5

Epoxy matrix	E_m [MPa]	ν_m [-]	Volume fraction tow ϕ_tow
Epoxy matrix	3200	0.37	0.74
Tow (implicitly ϕ_C?=?0.66 within tow)	E_1,tow [MPa]	E_2,tow?=?E_3,tow [MPa]	G_12,tow?=?G_13,tow [MPa]
	200,790	9100	4655
	G_23,tow [MPa]	ν_12,tow?=?ν_13,tow [-]	ν_23,tow [-]
	3065	0.2473	0.485

Epoxy matrix	E_m [MPa]	ν_m [-]	Volume fraction tow ϕ_tow
Epoxy matrix	3200	0.37	0.74
Tow (implicitly ϕ_C?=?0.66 within tow)	E_1,tow [MPa]	E_2,tow?=?E_3,tow [MPa]	G_12,tow?=?G_13,tow [MPa]
	200,790	9100	4655
	G_23,tow [MPa]	ν_12,tow?=?ν_13,tow [-]	ν_23,tow [-]
	3065	0.2473	0.485

SiC matrix [55]	E_1,_m [MPa]	E_2,_m?=?E_3,_m [MPa]	G_12,_m?=?G_13,_m?=?G_23,_m
	0.001	15,000	5769
	ν_12,_m?=?ν_13,_m [-]	[MPa]ν_23,_m [-]	volume fraction SiC matrix ϕ_m_,_meso
	0.3	2?·?10^-8	0.35
“Inner tow” [55]	E_1,_tow [MPa]	E_2,_tow?=?E_3,_tow [MPa]	G_12,_tow?=?G_13,_tow [MPa]
	238,300	25,050	11,400
	G_23,_tow [MPa]	ν_12,_tow?=?ν_13,_tow [-]	ν_23,_tow [-]
	9947	0.2355	0.2592