Towards a numerical modeling of the coupling between RTM process and induced mechanical properties for rigid particle-filled composites

Abstract

In this work, a method is proposed for modeling RTM process and the associated mechanical behavior of composites filled with mono-sized spherical Alumina particles. This method combines (i) a numerical model (RTM model) that allows the simulation of the RTM process during the injection of particle filled resins and (ii) a computational strategy of mechanical properties based on the homogenization methods. These proposed models have already been validated with experimental results. The RTM model is based on 3 sub-models: the first one to describe the suspension flow, the second one to simulate the advance of the flow front, and the last one to model the particles filtration by the fibrous medium. The distribution result of the concentration of particles in the fibrous medium obtained at the end of the simulation of the injection is used as input data for mechanical models of homogenization. The homogenization numerical model was constructed from a representative volume element of the microstructures using the Poisson process. The idea here is to couple these two steps (RTM simulation + mechanical property computation) in a complete model which allows at the same time and in a single operation: to simulate the process of the manufactured composites loaded with particles and to deduce their induced mechanical properties. The pertinence of the proposed method is confirmed by the simulation of nine elastic properties of composites with the finite element method. The influence of post-filling on the induced mechanical properties has been studied.

Appendix

Constant for analytical model

$$\begin{array}{c}A=8(\frac{{G}_{i}}{{G}_{m}}-1)(4-5{\nu }_{m}){\eta }_{1}{p}^\frac{10}{3}-2(63(\frac{{G}_{i}}{{G}_{m}}-1){\eta }_{2}+2{\eta }_{1}{\eta }_{3}){p}^\frac{7}{3}+252(\frac{{G}_{i}}{{G}_{m}}-1){\eta }_{2}{p}^\frac{5}{3}\\ -50(\frac{{G}_{i}}{{G}_{m}}-1)(1-12{\nu }_{m}+8{\nu }_{m}^{2}){\eta }_{2}p+4(7-10{\nu }_{m}){\eta }_{2}{\eta }_{3}\end{array}$$

$$\begin{array}{c}B=-4(\frac{{G}_{i}}{{G}_{m}}-1)(1-5{\nu }_{m}){\eta }_{1}{p}^\frac{10}{3}+4(63(\frac{{G}_{i}}{{G}_{m}}-1){\eta }_{2}+2{\eta }_{1}{\eta }_{3}){p}^\frac{7}{3}-504(\frac{{G}_{i}}{{G}_{m}}-1){\eta }_{2}{p}^\frac{5}{3}\\ +150(\frac{{G}_{i}}{{G}_{m}}-1)(3-{\nu }_{m}){\nu }_{m}{\eta }_{2}p+3(15{\nu }_{m}-7){\eta }_{2}{\eta }_{3}\end{array}$$

$$\begin{array}{c}{C}=4(\frac{{G}_{i}}{{G}_{m}}-1)(5{\nu }_{m}-7){\eta }_{1}{p}^\frac{10}{3}-2(63(\frac{{G}_{i}}{{G}_{m}}-1){\eta }_{2}+2{\eta }_{1}{\eta }_{3}){p}^\frac{7}{3}+252(\frac{{G}_{i}}{{G}_{m}}-1)(5{\nu }_{m}-1){\eta }_{1}{p}^\frac{10}{3}\\ +25(\frac{{G}_{i}}{{G}_{m}}-1)({\nu }_{m}^{2}-7){\eta }_{2}p-(7+5{\nu }_{m}){\eta }_{2}{\eta }_{3}\end{array}$$

$$\begin{array}{c}{\eta }_{1}=(\frac{{G}_{i}}{{G}_{m}}-1)(49-50{\nu }_{i}{\nu }_{m})+35\frac{{G}_{i}}{{G}_{m}}({\nu }_{i}-2{\nu }_{m})+35(2{\nu }_{i}-{\nu }_{m})\\ {\eta }_{2}=\frac{{G}_{i}}{{G}_{m}}(7+5{\nu }_{i})+4(7-10{\nu }_{i})\\ {\eta }_{3}=\frac{{G}_{i}}{{G}_{m}}(8-10{\nu }_{m})+7-5{\nu }_{m}\end{array}$$