Fracture toughness enhancement of thermoplastic/epoxy blends by the plastic yield of toughening agents: A multiscale analysis
Introduction
A highly crosslinked epoxy system has excellent properties such as good thermal stability, creep resistance, excellent adhesion properties, and relatively high modulus. However, the high crosslink density leads to low fracture toughness, and inferior impact strength, which limit their application in high performance areas such as the automotive, aerospace, and defense industries. Therefore, it has been a challenging issue to improve the fracture toughness of an epoxy by modifying the resin with a secondary phase such as rubber [1], [2], thermoplastic [3], [4], [5], [6], [7], and inorganic particles [8], [9], [10]. In particular, thermoplastic/epoxy blends are widely employed, because the high toughness enhancement through modification by the thermoplastic was not accompanied by critical reduction in the elastic modulus [3], [5]. Despite the importance of thermoplastic-toughened epoxy systems in various sectors, there have been insufficient studies to predict the toughness enhancement by thermoplastic polymers as the secondary phase [6].
Based on the experimental observations, it was reported that the ductile thermoplastic particle plays two key roles in toughening mechanisms of thermoplastic/epoxy blends (the plastic deformation in the material near the macroscopic crack tip and the particle bridging in the crack wake [11], [12]), as shown in Fig. 1. For the first mechanism, multiscale approach [8], [9], [10] is useful when developing an analytical model with an infinite number of particles embedded in the matrix domain. The density of energy dissipated by the damage mechanism of the representative volume element (RVE) near the crack tip can be described by micromechanics models. The fracture toughness enhancement of the composites can be obtained quantitatively through the J-integral near the macroscopic crack tip [13]. However, multiscale models for the toughness enhancements of thermoplastic/epoxy blends have not been reported, unlike rigid nanoparticles [8], [9], [10]. For this reason, we focused on the development of a model to describe the fracture toughness improvement by thermoplastic particle yield near the crack tip. The main objective of the present paper is to quantify the toughness enhancement due to the plastic yield of the thermoplastic particle.
With this motivation, we conducted the formulation to quantify the plastic dissipation energy of thermoplastic particles near the macroscopic crack tip. To quantify the plastic dissipation energy of thermoplastic particles, molecular dynamics (MD) simulation was then conducted to obtain the curve of nonlinear hydrostatic stress versus volumetric strain. The proposed multiscale model is validated through the reported experimental data. Based on results obtained using the multiscale model, design guidelines regarding the proper selection of toughening agents are proposed for enhancing the fracture toughness of thermoplastic/epoxy blends.
Section snippets
Review of multiscale strategy to describe fracture toughness enhancement by microscopic damage mechanisms near the macroscopic crack tip
A multiscale strategy to calculate the dissipated energy by considering the damage mechanism on the nanoscale near the crack tip of macroscopic structures has been developed [2], [10]. Through the theory of linear fracture mechanics under the assumption of plane strain conditions, hydrostatic components of macroscopic stress fields, Σh, are described as follows:where KI and νcomp are the stress intensity factor of the macroscopic stress field and the Poisson's ratio of
Mechanical description of the thermoplastic/epoxy blends system
It is assumed that the thermoplastic particles are well phase-separated from the epoxy domain as a continuous and homogeneous phase, as shown in the SEM image in Fig. 1 [6]. Reportedly, the spherical particulate diameter of the thermoplastic polyethersulfone (PES) phase, which is employed as toughening agent in this study, of the epoxy-rich composites is set as 0.1–1.5 μm [6].
General solutions of displacement and stress fields of the particle and matrix
The hardening behavior of the matrix was simplified as the following linear elasto-power law [15], [16]:
Thermoplastic particle bridging-induced toughness enhancement
Douglass et al. [2] proposed the toughness enhancement due to rubbery particle bridging mechanism. We quantified the thermoplastic particle bridging-induced toughness enhancement in a similar way. Even though the fracture toughness of PES has not been reported, the elongation limit (εl,p) and tensile strength (σY,p) were reported as 6–80% and 67.6–95.2 MPa, respectively [18]. Here, the Young's modulus (Ep) is determined by MD simulation results (Table 1). Using the linear elasto-perfect plastic
Molecular modeling of bulk PES
For the molecular modeling and relaxation simulation, commercial molecular simulation software Material Studio 5.5 was used [20], and the polymer consistent force-field (PCFF) [21] was employed to describe both the inter- and intra-atomic interactions. The chemical structure of PES is given in Fig. 2. In this study, a PES chain containing 60 repeating units was used as an end group. The initial target density of the unit cell containing five PES chains was set to 0.01 g/cm3 for modeling of a
Molecular dynamics simulation results of bulk PES
To validate the unit cell model of PES, we compared the Young's modulus (E), density (ρ), and glass-transition temperature (Tg) of PES obtained by MD simulation with experimental data reported in the literature [19], as shown in Table 1. Here, the Young's modulus and the glass transition temperature are obtained from the “Unreinforced PES” of Table 2 and “PES +0% CNF” of Table 6 in Ref. [19]. The obtained nonlinear hydrostatic stress-volumetric strain curve is as shown in Fig. 3, which shows
Conclusion
A multiscale model was developed to describe the fracture toughness enhancement of thermoplastic/epoxy blends by the plastic yield of toughening agents. As the main mechanisms of toughness enhancement of thermoplastic/epoxy blends, we considered plastic deformation in the material near the macroscopic crack tip, and particle bridging in the crack wake. The proposed multiscale model shows a satisfactory agreement with experimental data. From the viewpoint of the plastic yield of toughening
Acknowledgements
This work was supported by the Defense Acquisition Program Administration and Agency for Defense Development under the contract UE135112GD, and the National Research Foundation of Korea Grant funded by the Korea government (MSIP) (No. 2012R1A3A2048841).
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