Modelling of oxidation gradients of epoxy-diamine networks on both sides of the glass transition temperature: Towards the prediction of degradation of thermo-mechanical properties
Topic(s) : Material and Structural Behavior - Simulation & Testing
Co-authors :
Juan-Pablo MARQUEZ-COSTA (FRANCE), Xavier COLIN (FRANCE)Abstract :
Carbon/epoxy composites present risks when they are exposed to temperatures close to their glass transition temperature (Tg). Those linked to thermo-oxidative aging phenomena of the matrix prove to be particularly critical [1]. Indeed, the appearance of a thin oxidized layer on the part surface induces local weakening and the development of stress gradients with potential danger of premature failure [2]. In this context, it is crucial to establish a link between the oxidation kinetics of epoxy matrices and the evolution of their thermomechanical properties and those of their composites. A compilation of thicknesses of oxidized layers (TOLs) measured by experimental technics on epoxy-diamine networks after thermal aging, clearly shows a break in the Arrhenius graph (Fig. 1) in the vicinity of the Tg, when the material reaches the rubber state.
Fig. 1. Variation of the TOLs with the exposure temperature in air for epoxy-diamine networks (data from 15 bibliographic references)
To verify the TOL jump in Fig. 1, numerical modelling is necessary to simulate the propagation of the oxidation front, which is directly linked to local oxidation gradients. For it, we propose a 1D semi-numerical finite element approach which couples, in an oxygen (O2) balance equation, the two main involved mechanisms: the diffusion of O2 and its consumption by the chemical reaction with the epoxy matrix. In the case of 1D through-thickness diffusion, this equation (Eq. 1) is:
(∂C(x,t))/∂t=D (∂^2 C(x,t))/(∂^2 x)-r(C(x,t)) (Eq. 1)
C(x,t) being the local concentration of O2, r(C) the chemical consumption rate, D the diffusion coefficient of O2, x the through-thickness coordinate, and t the time. A recent kinetic analysis of the so-called closed-loop oxidation reaction made it possible to establish a general analytical expression for r(C) [3]:
r(C)=2r_0 βC/(1+βC) (1-βC/2(1+βC) ) (1/(1+be^(-Kt) ))^2 (Eq. 2)
The integration of r(C) will then allow direct access to the oxidation consumption gradients Q(C), and to propose a criterion for estimating the TOL. As an example, simulations carried out in air at 200°C for an epoxy-diamine network (TACTIX(123+742)-DDS) are shown in Fig. 2.
Fig. 2. Calculation of the gradients C(x,t) (left) and the evolution of Q(x,t) at different depths with the TOL criterion (right) in air at 200°C for an epoxy-diamine network
The comparison of numerical simulations with experimental TOL values should make it possible to: (i) highlight the predominant influence of O2 diffusion on the dispersion of TOL and (ii) to explain the jump in TOL in the vicinity of Tg (Fig. 1) by a sudden increase in D by a factor of 10^2 when the material passes into the rubber state, in agreement with the permeation results of O2 from the literature [4]. Finally, the impact of oxidation gradients on the thermomechanical properties (Tg and Young modulus) of epoxies and/or their composites will be analysed with a view to predicting their durability.
Fig. 1. Variation of the TOLs with the exposure temperature in air for epoxy-diamine networks (data from 15 bibliographic references)
To verify the TOL jump in Fig. 1, numerical modelling is necessary to simulate the propagation of the oxidation front, which is directly linked to local oxidation gradients. For it, we propose a 1D semi-numerical finite element approach which couples, in an oxygen (O2) balance equation, the two main involved mechanisms: the diffusion of O2 and its consumption by the chemical reaction with the epoxy matrix. In the case of 1D through-thickness diffusion, this equation (Eq. 1) is:
(∂C(x,t))/∂t=D (∂^2 C(x,t))/(∂^2 x)-r(C(x,t)) (Eq. 1)
C(x,t) being the local concentration of O2, r(C) the chemical consumption rate, D the diffusion coefficient of O2, x the through-thickness coordinate, and t the time. A recent kinetic analysis of the so-called closed-loop oxidation reaction made it possible to establish a general analytical expression for r(C) [3]:
r(C)=2r_0 βC/(1+βC) (1-βC/2(1+βC) ) (1/(1+be^(-Kt) ))^2 (Eq. 2)
The integration of r(C) will then allow direct access to the oxidation consumption gradients Q(C), and to propose a criterion for estimating the TOL. As an example, simulations carried out in air at 200°C for an epoxy-diamine network (TACTIX(123+742)-DDS) are shown in Fig. 2.
Fig. 2. Calculation of the gradients C(x,t) (left) and the evolution of Q(x,t) at different depths with the TOL criterion (right) in air at 200°C for an epoxy-diamine network
The comparison of numerical simulations with experimental TOL values should make it possible to: (i) highlight the predominant influence of O2 diffusion on the dispersion of TOL and (ii) to explain the jump in TOL in the vicinity of Tg (Fig. 1) by a sudden increase in D by a factor of 10^2 when the material passes into the rubber state, in agreement with the permeation results of O2 from the literature [4]. Finally, the impact of oxidation gradients on the thermomechanical properties (Tg and Young modulus) of epoxies and/or their composites will be analysed with a view to predicting their durability.