Fluid dynamics and thermodynamics numerical modelling of self-healing fibre reinforced laminated composites

Abstract

Inspired by the bleeding mechanism in living organisms to heal injury for survival, such capability has been integrated into a damaged laminate composite for autonomous internal repairing to extend its service life. The main healing mechanisms include infiltration of healing liquid into the crack plane, resulted from the breaching of pre-embedded vessels, which is triggered by a damage event. The later polymerization of the healant serves to restore the strength of the crack plane and hence inhibits further crack growth. The best healing performance is generally governed by both infiltration and polymerization rates of healing liquid at the crack tip. In ensuring assessment of these rates without excessive computational burden but free from the companion numerical stability-consistency-accuracy issues, in-house hydrodynamic and thermodynamic models based on the weak form Galerkin finite element (FE) method have been developed in this study. To simulate the micro-scale isothermal hydrodynamics of the Newtonian liquid, one-dimensional (1D) incompressible Stokes equations have been solved using the penalty function method. Computational matters, such as the feasible penalty parameter (γp) for multiple flow geometries of single straight micro-channel, are discussed and numerically addressed. Meanwhile, the polymerization mechanics of healing liquid in a straight crack channel is obtained by solving the heat conduction formulation coupled with the phenomenological Arrhenius’s rate equation and Crank-Nicolson time scheme. It is observed that the iterative Uzawa’s technique, which employs forcing term correction in terms of the previous velocity solution, coupled with another forcing term correction in terms of the previous divergence of velocity solution is capable of eliminating the instability of axial pressure distribution and inconsistency of the conventional penalty model setting. Additionally, implementing termination criterion by equalizing the order of both maximum elemental divergence of velocity (EDVmax) and penalty parameter ensures stability, consistency, and accuracy of solution for 1 x 101 ≤ γp ≤ 1 x 1011. Adopting similar termination technique for the Crank-Nicolson predictor-corrector time integration scheme with the penalty formulation, the proposed model is capable of capturing the flow front motion in micro-channel by electing the temporal mesh size (Δt) from a function of hydraulic diameter (Dh) and spatial mesh size (Δx). Parametric study for temperature and cure degree evolution by varying pre-exponential factor ( ˜ A), activation energy (˜E ), ˜n-th order of reaction, and ultimate enthalpy of cure ( ˜H ) has been performed thoroughly where an optimal coupling between ˜ A and ˜E is identified as the dominating factor in achieving the most favored repairing behavior. While the order of reaction imparts less significance in the evaluation, it is observed that polymeric healant with a higher numerical value of ˜H is not beneficial either. The principal contribution of the present study includes the construction of a series of FE Eulerian frameworks that are reliable, without excessive computational burden, in assessing key diffusive mechanistic variables of extrinsic self-healing mechanisms in achieving optimal strength recovery of straight crack geometry in polymeric materials.