Thermosetting Polymers Part 13 potx

13 Yielding and Fracture of Toughened Networks 13.1 INTRODUCTION In the previous chapter, the relationships between structure and mechanical and fracture properties of neat thermosets were analyzed. It was shown that an increase in thermal resistance (T g or HDT, heat deflection temperature) and yield stress leads to a decrease in toughness (K Ic ), and in impact or fatigue resistance. So the challenge is how to increase toughness without sacrificing thermal and mechanical properties? The two methods of improving the macroscopic toughness of thermo- sets are similar to those used for amorphous or semicrystalline thermoplas- tics: (i) plasticization and (ii) amplification of deformation mechanisms via the generation of a heterogeneous structure. The plasticizer addition is a relatively simple technique. A miscible low-T g compound is added to the formulation, so as to produce a decrease in both the glass transition temperature and the yield stress, and a corre- sponding improvement in the fracture resistance. These drawbacks are very severe for thermosets, and generally this method is not used for toughening purposes. The most frequently applied methods for improving toughness are the addition of preformed particles or the in-situ formation of dispersed rubbery or thermoplastic particles in the thermoset matrix (Chapter 8). In Secs. 13.2–13.3 the principles of toughening of thermosets by rub- ber particles, and the role of morphologies, interfacial adhesion, composi- tion, and structural parameters on the toughening effect are analyzed. Section 13.4 is devoted to the use of initially miscible thermoplastics for toughening purposes. The effect of core-shell rubber particles is discussed in Sec. 13.5 and, in Sec. 13.6, miscellaneous ways of toughening thermosets (liquid crystals, hybrid composites, etc.), are analyzed. 13.2 TOUGHENING OF THERMOSETS Epoxy networks are the most widely studied materials, due to their well- known chemistry. Consequently, many studies are devoted to epoxy net- works as model networks, although the principles and models developed can be applied to other thermosets. The principles of toughening have been described by Kinloch (1989), Mu ¨ lhaupt (1990), Huang et al. (1993b), and McGarry (1996). The roles of particles during both the initiation and propagation of the crack may be analyzed separately. 13.2.1 Role of the Inclusions in the Initiation Step (Before the Appearance of an Intrinsic Defect or Crack) a. Modification of the Stress Field For a single rubber particle in an infinite uniaxial tensile stress field, it was demonstrated that there is a stress concentration effect with a factor around 2, at the particle equator (Fig. 13.1). This is only valid for particles with a modulus lower than the matrix. On the other hand, in the case of glass beads in polymers the stress con- centration occurs at the poles. If the particle is bonded firmly to the matrix (we will discuss this point later), the initial uniaxial tension stress is changed into a triaxial tension stress field, due to the low rubber incompressibility. The stress field around rubbery particles is not the same as that around a void. Increasing the concentration of particles (roughly for a volume frac- tion approaching 10%), the stress concentration effects of neighboring par- ticles can overlap (Fig. 13.2). Therefore, a large volume fraction of the matrix supports an average load higher than the applied load and can yield. This stress concentration effect increases when the volume fraction of dispersed particles increases or the interparticle distance decreases. As shear yielding is the main deformation mechanism of the network, it is clear that the presence of rubber particles favors the yielding of the 390 Chapter 13 matrix. But also, due to incomplete phase separation (Chapter 8), a fraction of rubber remains dissolved in the matrix and contributes to the decrease of T g and  y . Yielding can then occur at lower applied loads. The introduction of rubber particles increases the fracture energy of the networks at room temperature, but also decreases the temperature of the ductile–brittle transition (Van der Sanden and Meijer, 1993). This ductile– brittle transition is strongly dependent on the nature (and T g ) of the rubber- rich phase and the amount of rubber dissolved in the matrix. The lowest ductile–brittle transition is obtained with butadiene-based copolymers (T g $À80  C), compared with butylacrylate copolymers (T g $À40  C). b. Internal Cavitation and Debonding Due to the difference of expansion coefficients between the particles and the matrix, different kinds of stress fields may be developed (Raghava, 1987). Rubbery and thermoplastic particles are placed in a hydrostatic tension Yielding and Fracture of Toughened Networks 391 FIGURE 13.1 Stress concentration around a single rubber particle. FIGURE 13.2 Stress field overlap between rubber particles. stress field (8–12 MPa) (Sec. 13.3.2 d), while glass beads are placed in a compressive stress field (15–20 MPa). The ratio of the bulk modulus, K ¼ E=3ð1 À 2Þ, over the shear modulus, G, is around 1000 for a rubber and close to 1 for a glassy polymer. If the adhesion between particles and matrix is good, rubber particles internally cavitate when a load is applied. If the adhesion is low, debonding at the rubber particle–matrix inter- face can occur. In both cases voids are formed and this reduces the degree of stress triaxiality in the surrounding matrix and favors the further growth of shear bands. Internal cavitation was proved by comparison of the initial particle diameter with the diameter measured on a fracture surface (Huang et al., 1993b). An increase of about 20–70% of the initial volume was found, depending on the temperature. This voiding process participates in the energy consumption and is the cause of the stress whitening effect observed on deformed samples. In the case of thermoplastic particles, because the bulk modulus is equivalent to that of the matrix, no cavitation is observed. c. Initiation of Matrix Shear Yielding As discussed in Chapter 12, crazing does not occur in thermosets; therefore, the only possible response of the matrix to a load is to promote localized shear yielding between particles. A considerable amount of energy is stored in the sample before the appearance of the first crack. In this step, the rubbery particles act – after cavitation or debonding – as triggers for the generation of shear bands in the matrix (Huang and Kinloch, 1992b). Using finite element stress analysis, Huang et al. (1993b) demonstrated that shear bands must appear at 45  , between voids formed in a previous step. As there are many particles, a network of shear bands is generated in the deformed sample (Yee and Pearson, 1986). Their growth generates the appearance of the first crack. 13.2.2 Role of the Particles during Crack Propagation As a result of the increase in stress and/or strain, shear bands develop in a large fraction of the sample but, at a certain point, a crack appears and starts to propagate. Several mechanisms for energy absorption, associated with the presence of particles, become active during crack propagation. 392 Chapter 13 a. Crack-Bridging Mechanism The crack-bridging mechanism is illustrated in Fig. 13.3. The particles are stretched between the edges of the propagating crack, increasing the fracture energy. This mechanism needs a good adhesion between matrix and parti- cles. However, because of the very low modulus of rubber, and in spite of the high failure strain, the dissipated energy in such a mechanism is low: $ 5–10% of the total energy (Kunz-Douglass et al., 1980). In the case of thermosets toughened with thermoplastics particles (Sec. 13.4), this mechanism may be of a considerable importance because of the intrinsic toughness and/or ductility of these particles. b. Increase of the Fracture Surface The presence of particles can modify the fracture surface from a mirror-like surface (for a brittle material), to a rough stress-whitened surface. The roughness can act as a multiplication factor for the absorbed energy. Sometimes, steps of height (h) are created when the crack jumps over a particle. This leads to the presence of tails issuing from particles, on fracture surfaces. The fracture energy may be expressed by  ¼  matrix 1 À   ÀÁ þ k h d c ð13:1Þ where d c is the interparticle distance (center to center), k is a constant, and   is the volume fraction of particles. Furthermore, the particle–matrix decohesion gives an additionnal surface and increases the fracture energy. Yielding and Fracture of Toughened Networks 393 FIGURE 13.3 Illustration of crack-bridging mechanism. c. Crack-Front Pinning This mechanism, very often mentioned in metallic alloys and in filled poly- mers, can also be considered in the case of low-modulus particles (Fig. 13.4). The particles, arranged in lines, act as obstacles for the crack front, in the same way as a line of trees constitutes a good protection against the wind. The crack front has to bow locally between particles in order to pass through the line of particles, slowing down the propagation rate. Lange (1970) gives a quantitative description of the critical energy release rate supplied by this mechanism: G Ic ¼ G Ic matrix þ 2 T L d p ð13:2Þ where T L is a constant (called the line tension) and d p is the interparticle distance (surface to surface). For particles with the same diameter, an increase in their volume fraction leads to a decrease in d p and an increase in G Ic . On fracture surfaces observed by SEM (scanning electron micro- scopy), the presence of a crack-pinning mechanism is revealed by features such as river markings. The crack-pinning mechanism is not very efficient with low-modulus particles such as rubbers. But with stiff thermoplastics (Sec. 13.4), or with high-modulus particles such as inorganic fillers, this mechanism may have an important contribution. d. Crack Blunting During crack propagation, macromolecular chains in the vicinity of the crack tip are stretched and broken. The initially sharp crack becomes 394 Chapter 13 FIGURE 13.4 Scheme of the crack-pinning mechanism: d p , interparticle dis- tance. more and more blunted as a result of the formation of a plastic zone and the decohesion of particles. The stress concentration effect at the crack tip becomes lower, and the crack is slowed down and even stopped, for the case of stick-slip propagation (Fig. 12.4). e. Crack Deflection During a fracture-mechanical test performed in mode I, the crack propa- gates in this mode from a macroscopic point of view. But the crack can be deflected locally by the rubbery particles and can also propagate in mode II. As for isotropic materials, G IIc is generally higher than G Ic ; an artificial increase of the macroscopic G Ic value will be then evidenced. f. Conclusion An improvement in the toughness of thermosets can be favored by rubber or thermoplastic particles, which operate both in crack initiation and propaga- tion mechanisms. The different toughening mechanisms can act simulta- neously and can be modeled quantitatively. 13.3 RUBBER TOUGHENING OF THERMOSETS 13.3.1 Fracture Modeling of Rubber-Modified Epoxy Networks The fracture modeling of rubber-modified thermosets was developed by Huang and Kinloch (1992a), Kinloch and Guild (1996), Huang et al. (1993b), and Yee et al. (2000). Huang et al. (1993b) proposed a two-dimensional plane strain model, which was successfully used to identify the stress field around the rubbery particles and to simulate the initiation and growth of shear bands between rubbery particles. A model was proposed to quantify the different mechan- isms. G Ic of the rubber-modified network was written as G Ic ¼ G Icn þ ð13:3Þ where G Icn is the fracture energy for the neat network and is the additional energy dissipated per unit area due to the presence of rubber particles. It is given by ¼ ÁG r þ ÁG s þ ÁG v ð13:4Þ where ÁG r is the contribution of particle bridging, ÁG s is the contribution from plastic shear banding, and ÁG v is due to plastic-void growth in the matrix. The other possible contributions were not taken into account. Yielding and Fracture of Toughened Networks 395 According to Kunz-Douglass et al. (1980), ÁG r may be calculated as ÁG r ¼ 4À t   ÁG r is proportional to the tearing energy ðÀ t Þ multiplied by the rubber volume fraction   . ÁG s may be expressed as proportional to   ,  yc (compressive yield stress),  f (fracture strain), the plastic zone size, and the square of the con- centration factor, K 2 m . The influence of hydrostatic pressure was taken into account with a modified von Mises criterion (Chapter 12). ÁG v is proportional to the void growth and plasticity parameters of the matrix. The model was successfully applied to rubber-modified epoxy net- works, taking into account both the test temperature and the rate effect (Fig. 13.5). Furthermore, the model makes it possible to separate the contribu- tions of the three toughening mechanisms as a function of temperature (Fig. 13.6). At high temperatures, the crack-bridging mechanism plays a minor role; the void-growth mechanism is very sensitive to temperature and can be completely suppressed at low temperatures. Shear yielding is the main mechanism, except at very high test temperatures where cavitation plays the major role. The contribution of shear yielding depends on the difference between the test temperature and T g , as discussed in Chapter 12. 396 Chapter 13 FIGURE 13.5 Comparison between theoretical predictions of Kinloch’s model (&) and the experimental results (&) at different test rates and temperatures of a rubber-toughened epoxy. (Huang and Kinloch, 1992a, with kind permis- sion from Kluwer Academic Publisher.) 13.3.2 Influence of Network Structure and Morphology on Fracture Properties of Epoxy Networks As discussed in the previous section, the toughening effect depends both on the matrix, where the shear bands are propagating, and the rubbery phase, which induces cavitation and crack bridging. In this section, the influence of in-situ formed rubber particles is dis- cussed, while the influence of preformed particles is analyzed in Sec. 13.5. For epoxy networks modified by liquid reactive rubbers, it is not so easy to discuss these parameters separately, because they are interdependent. For example, an increase in the acrylonitrile content of the carboxy-termi- nated butadiene acrylonitrile rubber (CTBN) induces a size reduction of the rubbery domains but also a higher miscibility with the epoxy-rich phase, leading to a higher amount remaining dissolved in the matrix at the end of cure (Chapter 8). It is not possible to separate the influence of these two effects on toughness. Yielding and Fracture of Toughened Networks 397 FIGURE 13.6 Relative contributions (%) of the different toughening mechan- isms in epoxy networks versus temperature: (&) rubber bridging; (*) shear yielding; and (~) cavitation. (From the results of Huang et al:, 1993b.) a. Influence of the Volume Fraction of Rubber In a first approximation, G Ic depends linearly on the amount of dispersed phase up to a 20–25% volume fraction (Yee and Pearson, 1986; Verche ` re et al., 1993; McGarry, 1996). The use of an in-situ phase-separated rubber produces a decrease in both the Young’s modulus and the yield stress (Fig. 13.7). Therefore, high rubber volume fractions cannot be used for structural applications (high stresses, long-time creep, etc.). A stiffness–toughness compromise has to be considered. But, in any case, the initial volume fraction of rubber cannot be higher than  crit , to avoid phase inversion, leading to a rubbery matrix with thermoset inclusions (Chapter 8). Another limiting factor may be the cost of the liquid reactive rubbers. b. Influence of Particle Size and Particle Size Distribution It is generally observed that rubber particles are effective for toughening purposes when their sizes are in the 0.1–10 m diameter range. For a given volume fraction of the rubbery phase, there is a critical particle size below which toughening occurs and above which there is no significant effect. The critical size is related to the interparticle distance, which, in fact, is the main parameter affecting the toughening effect for both thermoplastics (Wu, 1985) and thermosets (Van der Sanden and Meijer, 1993). To keep the 398 Chapter 13 FIGURE 13.7 Variation of yield stress ( y ) and Young’s modulus (E) for rubber- modified epoxy networks. Rubber ¼ CRBN: carboxy-terminated butadiene acrylonitrile random copolymer. (Reprinted with permission from Pearson, 1993, Copyright 2001. American Chemical Society.) [...]... Fracture of Toughened Networks 407 13. 5.1 Design of the Core-Shell Rubber Particles The emulsion free-radical polymerization carried out in different steps ensures a precise control of the particle size and particle size distribution The particle diameter can be adjusted between 100 nm and 1000 nm, with a low polydispersity (generally less than 1.1) (Chapter 8) Rubber particles with sizes lower than 100... order to avoid particle coalescence 13. 5.6 Conclusions A high degree of toughening may be attained by the use of CSR particles as modifiers of thermosetting polymers This is because several adjustable parameters – the chemical structure and size of the core; the number, chemical structure, and thickness of shells; and the possibility of crosslinking 412 Chapter 13 FIGURE 13. 11 Paris diagrams for fatigue... Influence of Particle Size and Particle Size Distribution It is generally observed that rubber particles are effective for toughening purposes when their sizes are in the 0.1–10 m diameter range For a given volume fraction of the rubbery phase, there is a critical particle size below which toughening occurs and above which there is no significant effect The critical size is related to the interparticle... transparent, toughened materials, which is not generally possible with the use of rubbers or TP particles 408 Chapter 13 13.5.2 Specific Toughening Mechanisms with CSR Particles Sue (1992, 1996a,b) studied the fracture behavior of high-performance epoxies and thermosets toughened with acrylic core-shell particles Using the technique of four-point bending test with two notches, together with microscopy... systems modified with CSR particles, there is no reason why it should not be present in systems modified with rubber particles The sequence of events arising during croid formation is summarized in Fig 13. 9 At the crack tip, due to a high triaxial stress field, internal FIGURE 13. 9 Sequence of events in a croid formation (a) Initial state at the crack tip (b) Cavitation of the rubber particles due to loading... mechanisms induce a significant toughening effect Should matrix yielding precede the cavitation of CSR particles, the croiding mechanism would be suppressed 13. 5.3 Influence of CSR Structural Parameters As a result of their highly versatile chemical structures and morphologies, thermosetting polymers toughened with CSR particles allow us to obtain a very large improvement in fracture resistance The addition of... Particles It is not possible to produce a dispersion of rubber particles in the thermoset precursors due to their agglomeration It is possible, however, to synthesize a stable emulsion or suspension of rubber particles in one of the monomers These particles, stabilized by copolymers and surfactants, may be considered as a limiting case of CSR particles when the shell thickness tends to zero The use of... us to increase the volume fraction of dispersed TP particles with a corresponding toughness increase 13. 5 TOUGHENING BY CORE-SHELL RUBBER (CSR) PARTICLES Core-shell rubber (CSR) particles are prepared by emulsion polymerization, and typically exhibit two or more alternating rubbery and glassy spherical layers (Lovell 1996; Chapter 8) These core-shell particles are widely used in thermoplastics, especially... be used to obtain good dispersions in the thermoset precursors The main drawback is the possibility of producing agglomerates of particles during storage or processing 13. 6 MISCELLANEOUS TOUGHENING AGENTS 13. 6.1 Use of Liquid-Crystalline Polymers (LCP) Liquid-crystalline polymers (LCP) can be used in thermoset systems as initially miscible modifiers that phase-separate during cure Carfagna et al (1992)... phase-separated particles But other studies showed that increasing the amount of HBP led to a decrease in both the Young’s modulus and the glass transition temperature; 402 Chapter 13 moreover, a linear polyester of the same chemical structure as the HPB produced a similar toughening effect (Gopala et al., 1999; Wu et al., 1999) Particles with lower sizes than 1 m gave no increase in toughness, while particles . Chapter 13 13.5.1 Design of the Core-Shell Rubber Particles The emulsion free-radical polymerization carried out in different steps ensures a precise control of the particle size and particle. core-shell rubber particles is discussed in Sec. 13. 5 and, in Sec. 13. 6, miscellaneous ways of toughening thermosets (liquid crystals, hybrid composites, etc.), are analyzed. 13. 2 TOUGHENING OF. thermoplastic particles are placed in a hydrostatic tension Yielding and Fracture of Toughened Networks 391 FIGURE 13. 1 Stress concentration around a single rubber particle. FIGURE 13. 2 Stress