Mechanical properties and volume dilatation of HDPE/CaC[O.sub.3] blends with and without impact modifier.
Adding inorganic particles to polymers is an efficient and cheap method to enhance their mechanical properties and make them suitable for engineering applications as structural materials . For this reason, particle-filled polymers have been the subject to increasing interest in industrial and academic research. The most commonly employed fillers for this purpose are calcium carbonate, talc, kaolin, mica, and glass. Among them, the former (CaC[O.sub.3]) is widely utilized to reinforce polyethylene (PE), often in conjunction with a compatibilizing agent. Mechanical properties of CaC[O.sub.3]-filled binary or ternary composites are strongly dependent upon the microstructural features, such as volume fraction, particle size distribution, and interface structure [2-5].
The development of strong microcomposites requires to disperse homogeneously the particles in the material and to improve their bonding with the polymer matrix. One method to fulfill the latter condition is to introduce a rubbery phase into the composite with a morphology that is a rubber interphase forming core-shell structure . Previous studies have shown that ethylene-octene copolymers (POE) have high tear resistance, which makes them good candidates as packaging materials [7, 8]. POE copolymers are widely used for modifying nonpolar polymers [9, 10]. In addition, they can be functionalized or grafted with some unsaturated low molecular compounds containing polar functional groups. Maleic anhydride is one of the functional monomers that have been most widely used [11-13]. Such a modification is generally aimed at obtaining single monomer grafts or short length grafts that substantially change the polymer reactive properties but not the mechanical properties. In this work, POE grafted by maleic anhydride (POEg) was used in the HDPE/CaC[O.sub.3] system.
In recent years, structural damage has got more and more attention in the determination of the mechanical behavior of polymers. However, it was difficult until recently to determine quantitatively the contribution of damage mechanisms to the overall strain in the plastic range, especially because available techniques were inefficient to measure volume strain after the initiation of necking. Fortunately, a novel system (VideoTraction[c]) was invented by two of us (C.G' and J.M.H.) that gives access in real time to true stress, true strain, and volume strain in a representative volume element (RVE) located in the center of the neck during plastic deformation under uniaxial tension [14-17].
[FIGURE 1 OMITTED]
In this work, the binary blends of HDPE/CaC[O.sub.3] and the ternary blends of HDPE/POEg/CaC[O.sub.3] were studied experimentally. The mechanical behavior of these particle-filled polymers will be presented shortly, with particular attention on volume changes during tensile tests. The experimental results will be discussed in terms of the microscopic damage processes revealed by scanning electronic microscopy (SEM).
MATERIALS AND TECHNIQUES
The matrix material upon which this study is based is high-density polyethylene (HDPE for short). The HDPE under investigation is a commercial grade supplied by Pan-jin Petrochemical Company (brand name: HDPE 5070EA, MFI = 23 g/10 min). This polymer was added with an impact modifier, namely poly (ethylene-co-octene), belonging to the family of polyolefin elastomers (POE). This rubber-like material was supplied by the DuPont-Dow Company (Brand name: Engage 8445, MFI = 3.5 g/10 min). It contains 9.5 wt% of octene radicals. It was subsequently grafted with 1 wt% maleic anhydride in the Institute of Chemistry, Chinese Academy of Science. The grafted copolymer is noted as POEg.
Two kinds of fillers were used. The first one was made of plain calcium carbonate (untreated CaC[O.sub.3]), supplied by Heshan Chemical Industrial Company (Liaoning, China). The average diameter of particles was about 0.70 [micro]m. The second one was the same CaC[O.sub.3], but with particle surface treated with an amino acid provided by Nanjing Chemical Industrial University (brand name: JL GD02) in order to improve adhesion with the polymer matrix. The acid treatment was performed at 100[degrees]C in a high-speed mixing machine for 15-30 min. The layer introduced by this treatment on the surface of CaC[O.sub.3] particles represents about 2% of the filler weight. Figure 1 indicates interfacial reaction that presumably occurs between the maleic radicals attached to the grafted POE macromolecules and the N[H.sub.2] radicals at the surface of treated CaC[O.sub.3] particles.
The materials investigated in this study were obtained by mixing two or three of the ingredients (HDPE, POEg, untreated or treated CaC[O.sub.3]) in a high speed mixing blender for 10 to 20 min and then pelletized by means of a twin-screw extruder ([phi] = 30 mm) at about 210[degrees]C. Their formulation was summarized in Table 1. Specimens for mechanical characterization were finally molded in an injection machine.
Tensile Tests With the VideoTraction[c] System
Mechanical testing in tension was performed by means of the VideoTraction system (developed by the Apollor company, Vandoeuvre, France). This system is able not only to record the true stress/true strain behavior of the materials, but also to assess the volume strain in real time during the tensile test. Since the details of this technique were previously published , we only recall its main features here.
The type of specimens utilized is depicted in Fig. 2a. The calibrated portion was 30 mm long, 8 mm wide, and 4 mm thick. To impose the location of the neck, the width of the samples was slightly reduced down to 7.7 mm in the central zone. Seven dot markers were printed on the front face with a fluorescent paint specially developed to provide high contrast under video observation when illuminated with ultraviolet light. Real-time treatment of the video images gave access to the two-dimensional position of the gravity centers of the markers, so that the distances between dots pairs could be monitored (with a frequency of about 50 images per second) while the specimen was stretched.
Here we adopt the Hencky definition for strains ("true" strains) and we measure them in the "representative volume element" (RVE) constituted by a thin slice of material in the central zone of the sample, where the cross-section is at minimum. Because of the symmetry of the neck, it is assumed that the strain tensor is diagonal in the RVE (no shear strains along the [x.sub.1], [x.sub.2], and [x.sub.3] directions) and that the principal true strains are constant over the cross-section. The latter are determined directly from the marker positions. The transverse true strain along the [x.sub.1] direction is simply given by [[epsilon].sub.11] = ln (FG/[F.sub.o][G.sub.o]), where FG and [F.sub.o][G.sub.o] represent the initial and current distances between markers F and G aligned along the transverse axis [x.sub.1] (Fig. 2b). Also we take benefit of the verified property that deformation is transversally isotropic to write [[epsilon].sub.22] = [[epsilon].sub.11]. Finally, we assess the axial true strain by the following relation: [Int.sub.RVE] [ln ([A.sup.i][A.sup.i + 1]/[A.sub.o.sup.i][A.sub.o.sup.i + 1])] that represents the interpolated value at the RVE of the "partial" strains determined from the distances of the marker pairs aligned along the tensile axis [x.sub.3] (in the latter equation, [A.sup.i][A.sup.i+1] holds for AB, BC, CD, and DE).
[FIGURE 2 OMITTED]
Subsequently we defined stresses according to the Cauchy definition ("true" stresses), which is associated to the Hencky definition of strains. In the present state of the method, triaxial effects in the RVE are ignored so that we suppose for simplification that transverse stresses are negligible ([[sigma].sub.11] = [[sigma].sub.22] = 0) and that axial true stress is uniform over the cross-section. It is important to remark that true axial stress is larger than the nominal stress since the cross-section progressively decreases. It is given by [[sigma].sub.33] = (F/[S.sub.o]) exp(-2[[epsilon].sub.11]), where F and [S.sub.o] are the tensile load and the initial area of cross-section, respectively.
The most original feature of the VideoTraction system is that it also gives access in real time to volume changes. Since the three principal components [[epsilon].sub.11], [[epsilon].sub.22], and [[epsilon].sub.33] are available, the trace ([[epsilon].sub.11] + [[epsilon].sub.22] + [[epsilon].sub.33]) measures the volume strain in the Hencky's formalism [[epsilon].sub.v] = ln (V/[V.sub.o]), where [V.sub.o] and V represent the initial and current volumes of the RVE, respectively.
The overall system implementing all the earlier-mentioned operations was composed of a servo-hydraulic testing machine (MTS 810) and three digital or analog interfaces (load, video and actuator). Strain rate was dynamically controlled by the system and kept constant at [[epsilon].sub.33] = [10.sup.-3][s.sup.-1]. All the tests were run at room temperature (T = (23 [+ or -] 1)[degrees]C).
Positive volume strain in tension is due to damage mechanisms, involving the formation of various forms of cavitation (voids, crazes, etc.). For seeking the completeness, it is important to corroborate the VideoTraction measurements of [[epsilon].sub.v] with other methods based on density variations. X-Ray densitometry, thoroughly used in medicine, was applied here to characterize damage in deformed specimens.
After being deformed to prescribed amount of strain ([[epsilon].sub.33] = 1.0), specimens were unloaded to zero stress and maintained in the relaxed state for 12 h. Then they were carefully polished on front and rear faces until a slab of uniform thickness was obtained, slightly smaller than the central thickness in the center of the neck. This slab was irradiated for 20 s in the wide beam produced by an X-ray generator equipped with a tungsten anticathode (Inel XRG3000). The incident intensity of the beam was approximately constant on the sample surface. The two-dimensional intensity distribution of X-ray transmitted through the sample thickness was measured by means of a high definition image-plate system (Fujifilm BAS-5000). The through-thickness density distribution of the specimen was assessed from the X-ray intensity profile (see Fig. 3) by virtue of the Beer-Lambert absorption law. Volume strain at the level of the RVE was thus obtained through the equation [[epsilon].sub.v] = ln[ln([I.sub.o]/[I.sub.nd])] - ln[ln([I.sub.o]/[I.sub.d])], where [I.sub.o], [I.sub.nd], and [I.sub.d] represented the transmitted X-ray intensity outside the sample, in a nondeformed part of the sample and at the level of the RVE, respectively.
Scanning Electron Microscopy
For SEM observation, an environmental scanning electron microscope, E-SEM (Quanta 200F, FEI Co.), was used for three tasks. To estimate the particle size distribution, CaC[O.sub.3] particles were scattered by an ultrasonic instrument and the size of the particle inclusions was then determined by image analysis of the SEM micrographs of dispersed particles. To study the morphology of the blends, a nondeformed specimen was cryofractured and one of the two surfaces exposed via this technique was etched in normal heptane in order to dissolve POE. Subsequently, the surfaces of both halves (etched and not etched) were examined by E-SEM to check whether a core-shell structure was formed in the blends. The E-SEM was also used to study the microstructure of deformed specimens. The specimens were all stretched to prescribed amount of true axial strain ([[epsilon].sub.33] = 1.0), then unloaded to zero stress, and maintained in the relaxed state for 12 h. After that, the samples were cryofractured precisely at the location of the RVE. Finally the cryofractured surfaces were observed under E-SEM. No other treatment was applied to the surfaces prior to the observation.
[FIGURE 3 OMITTED]
RESULTS AND DISCUSSION
Particle Size Distribution and Morphology of Blends
The shape and average size distribution of the particles being acknowledged as major factors in the control of polymer blends properties [19, 20], we have examined under E-SEM the untreated and treated particles in our samples. The small diameter particles are roughly spherical while those of larger diameters possess irregular shapes with sharp edges. The size distributions of two kinds of particles, shown in Fig. 4a and 4b respectively, are quite broad, the diameters of most particles being in the range from 0.5 [micro]m to 1.0 [micro]m. Compared with the pure particles, the percentage of the treated particles is lower for diameters between 0.5 and 0.75 [micro]m and higher for those between 0.75 and 1.0 [micro]m (Fig. 4b). Consequently the average diameter of treated particles is slightly higher than that of untreated particles.
The micrographs in Fig. 5a and 5b, corresponding to cryo-fractured surfaces without or with subsequent etching by normal heptane, respectively, show the morphology of fillers within the BP30-1 blend that contains 30 wt% CaC[O.sub.3] and 3.6 wt% POEg. It can be seen that, compared with nonetched blend, a narrow void layer appears at the surface of the particle in the etched specimen, which indicates that a POEg shell is formed at the interface between the CaC[O.sub.3] particles and the HDPE matrix. Also it is remarked that no isolated void is visible (the hole at the right part of the figure is considered to be caused by a detached particle), which proves that the POEg is not present elsewhere than at the CaC[O.sub.3] surface. A study by Xie et al. . also revealed such a "core-shell" structure in ternary blends by etching the CaC[O.sub.3] particles with hydrochloric acid and proved that almost all the CaC[O.sub.3] particles are coated by POEg when POEg content is 10.8 wt%.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
Influence of CaC[O.sub.3] Content
The response of HDPE/treated CaC[O.sub.3] samples (A-series) under uniaxial tension at room temperature is displayed in Fig. 6. The tests were stopped when the true axial strain reached 1.0. The true stress/true strain behavior of the material shows important evolutions as the amount of CaC[O.sub.3] increases: (i) significant increase of the elastic modulus, (ii) dramatic decrease of the yield stress and, (iii) transition from a continuous plastic hardening to a large strain softening (Fig. 6a). However, it is remarkable that the HDPE/CaC[O.sub.3] blends keep significant ductility. Except for the ones with highest filler content (A50), all materials undergo a strain at least equal to 1.0, which corresponds to an extension ratio larger than [lambda] = 2.7. By contrast to experiments reported by others [2, 22], the results presented here gives access to the constitutive behavior in the large strain region since the VideoTraction testing system corrects automatically the variations of the actual cross-section area. Consequently, the effect of particle filling can be characterized even after the onset of necking. As such, the dramatic strain softening observed after yielding in highly filled materials is not an artifact but corresponds to the true plastic response of the materials.
The most striking feature in the behavior of the filled materials is the important volume strain undergone while they are stretched (Fig. 6b). By contrast with neat HDPE that experiences relatively low volume change, HDPE with higher CaC[O.sub.3] content exhibits dramatic dilatation. The most pronounced effect is for material A40 with 40 wt% CaC[O.sub.3], which experiences a volume strain as high as 0.7 (i.e. V/[V.sub.o] [approximately equal to] 2) when true strain is equal to 1.0. Also, it is remarkable that the variation of volume with true axial strain is nearly linear at large true stain. The much larger dilatation of the blends is caused by the occurrence of the debonding between the matrix and the fillers due to the poor interface adhesion and then the appearance of voids. The onset of debonding can be determined from the volume strain measurement at small true axial strain when the slopes of the curves begin to change. When debonding occurs and voids form, the contribution of cavitation to the overall strain is higher than that of the matrix deformation itself.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
The curves in Figs. 7 and 8 show the response of the materials of the AP- and BP-series compatibilized with POEg. In all these blends, the POEg/CaC[O.sub.3] ratio is fixed at a value of 0.45. The AP- and BP-series differ each other by the fact that the CaC[O.sub.3] particles are treated or untreated, respectively. Both series exhibit the same evolution when the amount of CaC[O.sub.3] increases: (i) modulus decreases, (ii) yield stress decreases, (iii) strain softening disappears, and (iv) strain hardening increases (Figs. 7a and 8a). Compared with A-series, volume strain for these two series is much lesser (Figs. 7b and 8b). The time when the onset of debonding occurs is not easy to determine. Also, an unexpected influence of filler content is noted: volume strain first increases until CaC[O.sub.3] content reaches 20%, and then it decreases at higher concentrations.
It is interesting to analyze the respective effects of formulation and particle treatment on the elastic modulus and the yield stress of blends from the graph in Fig. 9a. It can be seen that for the A-series, the CaC[O.sub.3] filler greatly improves the modulus, while the opposite effect is observed for the AP- and BP-series. This prominent difference between the blends with and without POEg is obviously due to the much smaller modulus of POEg with regards to HDPE and CaC[O.sub.3]. Also, the yield stress of A-series is higher than that of the series containing POEg. As for the CaC[O.sub.3] treatment, it appears to have no significant influence on the modulus. On the other hand, yield stress of AP-series is a little higher than that of BP-series. It is deduced that the surface treatment of CaC[O.sub.3] provides a moderate improvement of the interfacial adhesion between particles and matrix, and consequently the resistance to debonding at the interface is increased.
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
As for the volume strain, Fig. 9b shows that dilatation at [[epsilon].sub.33] = 1.0 is globally much lesser in the AP- and BP-series (0.12 < [[epsilon].sub.v] < 0.24) than in the A-series without compatibilizer (0.1 < [[epsilon].sub.v] < 0.7). Furthermore it is noted that in AP- and BP-series the evolution of volume strain with CaC[O.sub.3] content is not monotonous: it increases below 20% CaC[O.sub.3] and decreases at higher concentrations. This evolution should be related with the antagonist effects of CaC[O.sub.3] and POEg in the development of volume strain. In the work of Xie et al.  who analyzed blends in which the POEg/CaC[O.sub.3] ratio was 0.36 and CaC[O.sub.3] content was as high as 30 wt%, it was found that almost all the mineral particles were coated with POEg. Although in our ternary blends the POEg/CaC[O.sub.3] ratio is somewhat higher (0.45), the formation of the core-shell structure might be incomplete for the blends with the lowest POEg contents. Since the blends were obtained by mixing the three ingredients at the same time, it was likely that, at low CaC[O.sub.3] fraction (hence at low POEg content), a certain fraction of the filler might lack elastomer coating and consequently effect of the filler would be similar to that in the A-series. Conversely above 20% CaC[O.sub.3], due to the increase of POEg, the core-shell structure is fully formed and effect of the compatibilizer, which favors plastic deformation with less dilatation, becomes predominant. Furthermore, though it is found that the formulations with treated CaC[O.sub.3] (AP-series) are characterized by very slightly higher volume strain than those with untreated CaC[O.sub.3] (BP-series), it is considered that the treatment of CaC[O.sub.3] has little influence on the volume dilatation at large true axial strain, which will be interpreted in the following section. These differences of volume strain among A-, AP-, and BP-series come probably from the different mechanisms of deformation and damage, which will be revealed in the section Investigation of damage mechanisms from SEM observation.
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
Influence of POEg Content
Now we will study specifically the influence of POEg with a fixed amount of CaC[O.sub.3] (30 wt%). The results obtained with AP30 (treated particles) and BP30 series (untreated) are shown in Figs. 10 and 11, respectively. Both graphs show that strain hardening becomes more and more important as POEg content increases, except with AP30-1 and BP30-1, which show slight strain softening. On the other hand, volume strain at true axial strain ([[epsilon].sub.33] = 1.0) increases progressively with true axial strain.
The characterization of elastic modulus and yield stress is displayed in Fig. 12a for the AP30 and BP30 materials. While POEg content is increased, modulus drops very rapidly at small concentrations (more than twofold reduction for less than 4% POEg), due to the relatively small modulus of POEg, and then stabilizes somehow at larger concentrations. By the same time, yield stress decreases markedly, yield stress of AP30-series being always higher than that of BP30-series. Also it is noted that, for a given composition, the modulus and, to a lesser extent, the yield stress are not influenced very much by the treatment of the CaC[O.sub.3] particles.
Also, for both AP30 and BP30 series, volume strain follows similar exponential decay with POEg content, as shown in Fig. 12b (63% reduction in [[epsilon].sub.v] when POEg content is increased from 0-18% POEg). The rapid drop in volume strain at small POEg content and the relatively slow decrease after 10.8 wt% POEg content can be explained by the fact that the core-shell structure is fully formed for this composition. For POEg content lower than this critical value, the CaC[O.sub.3] particles lacking of elastomer coating induce large volume strain. By contrast above this value, the soft shell covering the particles actively prevents cavitation. Again, the surface treatment of CaC[O.sub.3] has little influence on the dilatation behavior. This rather unexpected result indicates that the stress concentration shielding provided by the elastomer layer at the reinforcing particles overrides the variation of adhesion at the CaC[O.sub.3] surface.
[FIGURE 12 OMITTED]
Comparison of Video Traction and X-Ray for Volume Strain Measurements
Five specimens with different formulations were selected in view of comparing the values of volume dilatation provided by VideoTraction (noted [[epsilon].sub.v]) and X-ray densitometry (noted [[epsilon].sub.v]*). The protocol for this investigation is the following: (i) the specimens were stretched up to the same true axial strain, [[epsilon].sub.33] = 1.0, (ii) the specimens were unloaded to zero stress, (iii) load was kept at zero for 12 h while continuously assessing strain and volume strain, and (iv) samples were rapidly machined for getting a constant thickness slab and transferred to the X-ray tomography unit. The data displayed in Table 2, corresponding to the five selected blends, show that the two methods are in reasonable agreement, since the discrepancy between [[epsilon].sub.v] and [[epsilon].sub.v]* is never more than 25% and, in most cases, less than 10%. Having critically investigated the possible causes of these discrepancies, we estimate that the error comes mostly from the X-ray densitometry and, to a lesser extend, from the VideoTraction technique. For the former, error on [[epsilon].sub.v]* is particularly important when the signal/noise ratio is insufficient, that is for low values of [[epsilon].sub.v]* when the density variations are small in the slab. For what is concerned with the VideoTraction measurements, the error is larger when the specimen undergoes more acute necking. Special analysis of triaxiality effects showed that, under such circumstances, the simple algorithm presently used for determining volume strain in the center of the neck does not fully take into account the local curvature of the specimen profile. Consequently, the values of [[epsilon].sub.v] obtained are somewhat overestimated when the neck is marked. The influence of specimen curvature on strain (and stress) distribution in the neck is now in progress and will be the object of a forthcoming paper.
Investigation of Damage Mechanisms from SEM Observation
The micrographs in Fig. 13, obtained from samples stretched to [[epsilon].sub.33] = 1.0, show some specific features of deformation damage at CaC[O.sub.3] particles in three selected blends. For the blend of the A-series (Fig. 13a), large interfacial debonding is clearly visible at the two poles of the fillers and the voids also occurs in the matrix. This cavitation process is responsible for the large volume dilatation measured macroscopically for this series. Much less cavitation is observed in the samples of AP- and BP-series in which the POEg compatibilizer was added (Fig. 13b and 13c). It is seen that as POEg content increases, and debonding becomes difficult to occur and mostly happens at the interface of large particles. This is interpreted by the effect of the rubber-like coating around CaC[O.sub.3] particles, which forms a kind of core-shell microstructure. This result agrees with the results of a detailed study performed by three of the authors (S.L.B, J.M.H., and C.G.) on the morphology and plastic damage of ternary blends of the PP/PA6/POE system . However, like in the latter system, it is difficult here to correlate quantitatively the microscopic void fraction observed by SEM in the cryofractured specimens and the macroscopic volume strain measured in the mechanical tests. Implementing this task would require more sophisticated techniques (including statistical treatment of TEM micrographs).
[FIGURE 13 OMITTED]
Experimental results presented in this paper definitely show that the constitutive behavior of polymers reinforced with hard particles results in the concurrence of two phenomena: (i) plastic deformation resulting from shear banding in the matrix and, (ii) nucleation and growth of voids at the interface between the polymer and the particles. Because of macromolecular orientation, the former mechanism causes strain-induced hardening, while the latter is responsible for damage-induced softening. Also, the presence of a ternary element (rubber-like compatibilizer segregated at the interface) influences the relative importance of both processes. Detailed modeling of this complex competition is in progress and will be published separately.
At this point, we just point out some relevant results obtained with the five series of materials under investigation. For example, comparing Figs. 7 and 8 with Fig. 6 reveals that, with the same CaC[O.sub.3] content, the AP- and BP-series show more strain hardening than the A-series due to the addition of POEg, which indicates that the compatibilizer has changed the balance between deformation mechanisms. Although the influence of blend formulation is complex, microscopic observation shows that the compatibilizer definitely lowers void size and density with reference to the blends with particles simply dispersed within the polymer matrix. It is interesting to remark that the novel testing technique utilized in this work provided valuable information on the efficiency of the compatibilizer, since it makes possible to determine very simply the extensive decrease of the volume strain with increasing amounts of POEg. A more systematic, multiparametric study would be necessary to determine the complete relationship between ternary composition and the mechanical properties of the blends, possibly leading to material optimization in view of predefined structural applications.
True stress-strain behavior and volume strain evolution were assessed for several series of HDPE/CaC[O.sub.3] blends with and without POEg compatibilizer. For selected systems, microscopic characterization of cavitation processes was also performed.
For binary blends, mechanical properties are considerably influenced by an increase of CaC[O.sub.3] concentration: (i) elastic modulus increases, (ii) yield stress decreases, (iii) strain hardening decreases and even strain softening appears, (iv) strain-induced dilatation increases.
For ternary blends, the core-shell structure was formed in the blends when POEg content was high. Increasing amount of POEg leads to decrease in modulus and yield stress, increase in strain hardening, and importantly, decrease in volume strain. For a fixed POEg/CaC[O.sub.3] composition ratio (45/100), volume strain moderately varies with CaC[O.sub.3] content. For a fixed CaC[O.sub.3] content (30 wt%), volume strain decreases extensively with POEg content. For all blends containing POEg, the treatment of CaC[O.sub.3] has some influence on the yield stress but little on modulus and volume strain.
The results obtained in this study reveal that the competition between cohesive plasticity and noncohesive damage processes at particle interface. The overall behavior depends on the balance of these two mechanisms. Systematic exploitation of such data is likely to help optimizing the materials.
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Yu-Lin Yang, Shu-Lin Bai
Center for Advanced Composite Materials, Department of Advanced Materials and Nanotechnology, College of Engineering, Peking University, 100871 Beijing, People's Republic of China
Christian G'Sell, Jean-Marie Hiver
Laboratoire de Physique des Materiaux, Ecole des Mines de Nancy (INPL), Parc de Saurupt, 54042 Nancy Cedex, France
Correspondence to: S.-L. Bai; e-mail: firstname.lastname@example.org or C. G'Sell; e-mail: email@example.com
Contract grant sponsor: National Natural Science Foundation of China; contract grant number: 10472002; contract grant sponsor: PRA Program between China and France.
TABLE 1. Formulation of the materials used in the present work (weight fractions). HDPE/POEg/treated HDPE/POEg/untreated HDPE/treated CaC[O.sub.3] CaC[O.sub.3] CaC[O.sub.3] A-Series AP-Series BP-Series No. Composition No. Composition No. Composition A0 100/0 A10 90/10 AP10 85.5/4.5/10 BP10 85.5/4.5/10 A20 80/20 AP20 71/9/20 BP20 71/9/20 A30 70/30 AP30 56.5/13.5/30 BP30 56.5/13.5/30 A40 60/40 AP40 42/18/40 BP40 42/18/40 A50 50/50 AP50 27.5/22.5/50 BP50 27.5/22.5/50 HDPE/POEg/treated HDPE/POEg/untreated CaC[O.sub.3] AP30-Series CaC[O.sub.3] BP30-Series No. Composition No. Composition AP30-1 66.4/3.6/30 BP30-1 66.4/3.6/30 AP30-2 62.8/7.2/30 BP30-2 62.8/7.2/30 AP30-3 59.2/10.8/30 BP30-3 59.2/10.8/30 AP30-4 55.6/14.4/30 BP30-4 55.6/14.4/30 AP30-5 52/18/30 BP30-5 52/18/30 TABLE 2. The comparison of results by two different methods ([[epsilon].sub.33]r is the residual axial strain after 12 h recovery at zero stress). [[epsilon].sub.33]r Material [[epsilon].sub.33] (after 12 h) A20 1.0 0.670 AP20 1.0 0.524 BP20 1.0 0.555 AP30-2 1.0 0.614 BP30-1 1.0 0.643 [[epsilon].sub.v] [[epsilon].sub.v]* Material (VideoTraction after 12 h) (X-ray densitometry after 12 h) A20 0.259 0.243 AP20 0.089 0.070 BP20 0.079 0.062 AP30-2 0.174 0.157 BP30-1 0.322 0.354
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|Author:||Yang, Yu-Lin; Bai, Shu-Lin; G'Sell, Christian; Hiver, Jean-Marie|
|Publication:||Polymer Engineering and Science|
|Date:||Nov 1, 2006|
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