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Minimization of surface friction effect on scratch-induced deformation in polymers.

INTRODUCTION

Scratch research in thermoplastics has drawn significant attention in recent years due to its relevance in high-gloss plastics that demand aesthetic appearance. A popular method to evaluate polymer scratch resistance uses a rigid spherical tip to scratch across a polymer surface with increasing normal load. The resulting scratch-induced deformation features, such as scratch depth, shoulder height, crack, and fish-scale greatly influence the scratch visibility resistance of polymers. The development of shoulder height and surface roughness along the scratch groove during scratch process are primarily responsible for the observed scratch visibility (1). Increase in surface roughness along the scratch groove is due to localized plastic deformation, crazing, microcracking, fish-scale formation, plowing developed during the scratch process and can be correlated with the scratch depth for some polymers (2). Extensive research work has been carried out to correlate these scratch-induced damage features with the bulk mechanical properties (3-8) in hope of establishing guidelines for improving scratch resistance of polymers. Surface friction is also known to greatly influence the scratch-induced deformation features as changes in coefficient of surface friction can alter the stress state polymer substrate experiences near the surface during the scratch process. An increase in coefficient of surface friction shifts and localizes the stress field toward the surface (9), (10), which in turn causes substantial changes in scratch-induced deformation features. It is thus of great interest to learn how the combination of surface friction coefficient and constitutive behavior affect scratch-induced deformation. It is hoped that, through the current finite element method (FEM) parametric study and experimental work, one can determine how the effect of surface friction on scratch behavior of polymers can be minimized by altering their constitutive behavior.

As the scratch tip moves with an increasing normal load, the material in front and beneath the scratch tip experiences a complex stress state where a quick transformation from compressive to tensile stress state takes place (3). As a result, the scratch-induced deformation mechanisms are expected to be dependent on polymer type, that is, constitutive behavior of the polymer. In an earlier attempt, Browning et al. (4) used ASTM/ISO standard scratch test (11) to investigate the effect of acrylonitrile (AN) content and molecular weight ([M.sub.w]) on scratch behavior of styrene AN (SAN) random copolymers. As the compressive properties of the model SAN systems were essentially the same, the correlation between the tensile properties and critical load for onset of scratch groove formation, periodic microcracking, and plowing has been established. The study concluded that, as the tensile strength and ductility increases with the AN content or [M.sub.w], an increase in AN content or Mw delays the onset of microcracking and plowing. Hadal and Misra (12) carried out scratch experiments to establish correlation between scratch behavior and tensile properties and concluded that an increase in both modulus and yield strength improves the scratch resistance in polypropylene (PP). Hossain et al. (7) performed FEM parametric study along with experimental work following the ASTM D7027-05 scratch testing protocol (11) to investigate the effect of asymmetric tension-compression constitutive behavior on scratch-induced deformation of polymers. Based on the FEM simulation and experimental work on a set of model SAN and polycarbonate (PC) systems, they concluded that the compressive behavior dominates scratch depth and shoulder height formation during the scratch process. Tensile behavior has little influence on scratch depth and shoulder height formation but affects the surface roughness along the scratch groove which is primarily due to crack formation and plowing for the polymers investigated. Bucaille et al. (8) used experimental work and FEM to study the effect of compressive strain hardening slope on piling-up phenomena during scratch. They concluded that a larger strain hardening led to greater elastic deformation, thus less plastic strain, which improves the scratch resistance.

Parametric studies on scratch behavior of polymers using FEM have also been used to study the effect of various material and surface properties on scratch-induced deformation. In an earlier attempt, by using elastic-perfectly-plastic model in the FEM parametric study, Jiang et al. (5) showed that an increase in coefficient of adhesive friction induces deeper scratch depth with all other parameters kept the same. They concluded that yield stress and coefficient of adhesive friction are the two most important parameters that can significantly influence the scratch depth of a polymer. The study used a simplified material constitutive model that did not consider the strain softening--strain hardening phenomena. Hossain et al. (6) later performed FEM parametric study by incorporating strain softening and strain hardening phenomena to investigate the effect of different material constitutive parameters on scratch depth and shoulder height formed during the scratch process. The simulation results showed that yield stress and strain at stress recovery are the two most important parameters that influence the scratch depth and shoulder height. The study (6) provided limited information due to the fact that true stress--strain relationship used in describing the material behavior was inappropriate due to larger than expected deformation involved in the scratch process. In other words, although strain softening--strain hardening phenomena were incorporated in the model, the material behavior was in essence elastic-perfectly-plastic after the strain exceeded a finite value. As a result, the simulation results beyond a certain scratch length became exaggerated which might affect the final outcome. By eliminating this unintended error, an extensive study (13) was carried out later. This extensive study showed that, strain hardening slope beyond the strain at stress recovery also influence scratch-induced deformation in addition to yield stress and strain at stress recovery reported earlier (6).

The effect of surface friction on scratch-induced deformation has long been studied using analytical, experimental, and FEM approaches. Hamilton and Goodman (9), (10) derived equations for quasi-static stress field due to a circular sliding contact by assuming hemispherical Hertzian normal pressure and proportionally distributed shearing traction. Their analysis showed that the region of maximum yield intensifies and moves toward the surface with an increase in surface friction. Also, a maximum tensile stress developed primarily on the rear edge of the circular scratch tip as the coefficient of surface friction increases. Browning et al. (14) performed ASTM/ISO standard scratch test (11) on different thermoplastic olefin samples and showed improvements in scratch performance with the reduction in coefficient of adhesive friction. Pelletier et al. (15) used FEM for elastic-plastic contact and showed that the shape of the residual groove is related to the plastic strain field in deformation beneath the indenter during scratching. Using the FEM simulation, they also showed that an increase in surface friction increases and shifts the maximal equivalent plastic strain along the scratch path.

In this study, attempts are made to analyze the effect of surface friction on scratch-induced deformation and investigate how this effect can be altered by varying the polymer yield and postyield behaviors, namely, yield stress, strain hardening slope, and strain at stress recovery. The parameters chosen are consistent with our previous FEM parametric studies (6), (13), where it has been shown that these constitutive parameters strongly influence the scratch-induced deformation mechanisms. The FEM simulation was carried out based on a set of hypothetical piece-wise linear true stress--strain plots taking into account the strain softening--strain hardening phenomena (16). In addition to the FEM simulation, scratch tests on a set of model polymers were conducted according to the ASTM/ISO scratch test standard to validate the FEM findings. It is hoped that this study will provide insights toward designing scratch-resistant polymers for engineering applications.

FEM MODELING

A commercial finite element package ABAQUS[R] (17) (V. 6.9) was used to perform the numerical analysis. The dimensions of the FEM computational domain for the substrate along with the boundary conditions imposed are shown in Fig. 1. The detailed description of the FEM model used in this study can be found elsewhere (6). It is worth noting that, mechanisms involving node or element separation during the scratch process and viscoelasticity of polymers were not included in this study. The present simulation also assumed no heat generation during the scratch process.

The FEM simulation of scratch process was divided into two steps: (1) indentation process and (2) scratch process. A linearly increasing normal load of 1-30 N was applied on the scratch tip during the scratch process following the ASTM standard (11). To save computation time, scratch tip moving over a length of 12 mm at a constant speed of 10 m/s during the scratch process was prescribed. The difference between instantaneous scratch depth and the amount of scratch depth recovered due to elastic recovery is denoted as scratch depth in this FEM parametric study.

Table 1 shows the simulated piece-wise linear true stress--strain plots along with the material parameters used to describe the constitutive behavior of polymer substrate in the FEM parametric study. Similar behavior in tension and compression was considered in this simulation work. Four different categories of systems were considered with variations in yield stress and strain hardening slope; namely, low yield stress system (LYSS), high yield stress system (HYSS), low strain hardening system (LSHS), and high strain hardening system (HSHS). It should be noted that the strain at stress recovery is also changed when strain hardening slope is varied between the systems (e.g., LSHS vs. HSHS). The coefficient of adhesive friction, [mu] based on the Coulomb's friction law, was varied from 0-0.9 with an increment of 0.3 in these systems to investigate the effect of surface friction on scratch depth and shoulder height along the scratch path.

EXPERIMENTAL

Model Systems

SAN, in the form of reactor-grade random copolymers polymerized by free-radical reactions, and PC (Makrolon 2800 from Bayer MaterialScience) systems were provided by BASF SE (Ludwigshafen, Germany). The SAN model system contained 19% AN by weight. Molecular weight information of the model systems was provided by BASF SE and is summarized in Table 2. The resins were produced into injection-molded plaques with dimensions of 150 X 150 X 6 [mm.sup.3]. The surface finish of the plaques was smooth (RMS Roughness = 37 nm).

TABLE 2. Molecular weight information of the model systems
investigated.

                                               SAN    PC

Acrylontrile content (wt%)                      19    --

Weight average molecular weight, [M.sub.w]     134    67
(kg/mol)

Polydispersity                                 4.1   2.6


Mechanical Property Characterization

As scratch depth and shoulder height formed along the scratch path are greatly influenced by compressive behavior rather than tensile (7), only uniaxial compression test was performed following the ASTM D695 standard (18). A screw-driven MTS[R]. Insight load frame equipped with a 30 kN capacity load cell was used for the test. MTS[R] Testworks 4 was used as the software interface for data collection.

Prismatic uniaxial compression specimens (12.7 x 6 x 6 [mm.sup.3]) were prepared from the injection-molded plaques by precision-cutting using a diamond saw. After cutting the samples, the surfaces were polished using P2400 first, and, then P4000 grit silicone-carbide abrasive paper to ensure that all the edges were flat and square. A crosshead speed of 2.5 mm/min was used in conducting the compression test. An MTS[R] extensometer was used to monitor the displacement for strain calculation. Sufficient lubrication was provided by using lithium grease to minimize contact friction between the fixture and sample surfaces.

Scratch Tests

Scratch tests were carried out according to ASTM D7027-0511S0 19252:08 (11) standard by using a linearly progressive normal load of 1-70 N. A constant scratch speed of 100 mm/s was used for the scratch tests with a scratch length of 100 mm. A stainless steel spherical scratch tip of 1 mm diameter was used to conduct the tests. To reduce surface friction in SAN and PC, Teflon spray was applied on the surface of the plaques before conducting the scratch tests. Three scratch tests were performed on the same plaque. All tests were performed in such a way that the tip movement was in the direction of melt flow.

Measurement of Surface Friction Coefficient

To determine the coefficient of surface friction, [mu] at the interface between the model systems (Neat and Teflon coated) and scratch tip, a flat smooth stainless steel tip with 10 x 10 [mm.sup.2] square area was used. The flat tip was installed on the scratch machine and tests were conducted under 5 N constant normal load for a distance of 40 mm at a velocity of 100 mm/s. Three tests were conducted for each system to obtain an average value of [mu]. The procedure to measure the coefficient of surface friction was comparable with the method described in literature (19).

Microscopic Observation

After completing the scratch tests, all the samples were stored for over 48 hr to allow for sufficient viscoelastic recovery of the scratch-induced deformation. Afterward, the samples coated with Teflon were sonicated for 2 hr in a water bath. Then, the samples were dried using compressed air. A Keyence[R] VK9700 violet laser scanning confocal microscope (VLSCM) was used for high-resolution analysis of the scratch-induced damage mechanisms. The microscope has a height resolution of ~1 nm. A 408 nm wavelength violet laser was used to perform the microscopy. The VK Analyzer software provided with the microscope was used to obtain optical images as well as topographical information. The raw images were processed using the software to remove noise and correct tilt for precise measurement. The scratch depth and shoulder height at different locations on the scratch path were measured using the VK Analyzer software. Shoulder heights and scratch depths measured for three scratches at the same location are reported in this study to obtain mean value and standard deviation.

RESULTS AND DISCUSSION

FEM Findings

Figures 2 and 3 show the plots of variation in scratch depth and shoulder height as a function of scratch normal load obtained via FEM simulation for LYSS and HYSS, with and without friction, respectively. As shown, higher [[sigma].sub.y] induces shallower scratch depth and lower shoulder height, which is consistent with our previous findings (5-7), (13). Increase in surface friction intensifies the stress field, thus induces deeper scratch depth and higher shoulder height in both systems. This finding is also consistent with the literature (5), (15).

To further elucidate the effect of surface friction on scratch-induced deformation, initial portion of the scratch depth is shown in Fig. 4. As shown, the onset of groove Formation is delayed in HYSS (point A) compared to that of LYSS (point B) without friction. As [[sigma].sub.y] is higher in HYSS, the plastic strain is lesser and elastic recovery is higher in HYSS compared with that of LYSS. As a result, the onset of groove formation is delayed in HYSS compared with LYSS. As surface friction intensifies the stress gradient and magnitude, for a frictional value of 0.9, the onset of groove formation occurs at a lower load than that of the frictionless case for both systems. For HYSS, the onset of groove formation is near point B, whereas for LYSS the onset occurs at the very beginning of scratch. Thus, increase in surface friction can significantly affect the onset of groove formation.

To further our understanding, the scratch depth profiles for cases with friction are divided by the corresponding no friction case within the scratch normal load of 8-24 N. This normalization allows for direct assessment of relative frictional effect on scratch depth. As scratch depth denotes the nodal displacement along the scratch path, whereas shoulder height is measured at different points on the scratch, it is more practical to evaluate the relative frictional effect based on scratch depth as it provides continuous data points throughout the scratch path for analysis. As shown in Fig. 5, an increase in surface friction increases the relative frictional effect in both HYSS and LYSSs. At lower coefficient of friction (COF; [mu] = 0.3, 0.6), the relative frictional effect is similar for both HYSS and LYSSs. When the frictional value is 0.9, the relative frictional effect is higher at the beginning in HYSS, which diminishes later on and falls below LYSS. This high relative frictional effect in HYSS at the beginning of scratch can be attributed to the high elastic recovery and low plastic strain in no friction case compared to that of high friction case. As the plastic strain continues to increase with the scratch normal load in no friction case, the relative frictional effect begins to diminish as the scratch progresses. This phenomenon is more pronounced in HYSS compared to LYSS. The relative frictional effect is higher in LYSS compared with that of HYSS toward the end of the scratch. Thus, yield stress has no significant impact on relative frictional effect on scratch depth.

Figures 6 and 7 show the scratch depth profile and variation in shoulder height for LSHS and HSHS, with and without friction, respectively. As shown, both smaller strain at stress recovery and higher strain hardening slope beyond the strain at stress recovery induce shallower scratch depth and lower shoulder height, which is again consistent with our previous findings (6), (13). Similar to the previous case, increase in surface friction induces deeper scratch depth and higher shoulder height in both systems.

Similar to the previous case, initial portion of the scratch depth is shown in Fig. 8. As shown, the onset of groove formation is similar for both systems without friction (point A). This similarity in onset of groove formation can be attributed to the similarities in their Young's modulus and yield stress. Thus, postyield behavior has no influence on onset of groove formation. Analogous to the previous case, increase in coefficient of surface friction induces an earlier onset of groove formation. For a frictional value of 0.9, the onset of groove formation is at the starting point of the scratch for both systems (point B). Again, it shows that surface friction significantly affects the onset of groove formation.

As described earlier, the scratch depth profiles with friction cases are divided by the corresponding no friction case within the scratch normal load of 8-24 N. As shown in Fig. 9, increase in surface friction increases the relative frictional effect in both systems. Overall, the relative frictional effect is more severe in LSHS compared with HSHS. It is interesting to note that there is almost no relative frictional effect on scratch depth when COF value is 0.3 for the HSHS. This reduction in relative frictional effect on scratch depth in the HSHS can be attributed to its higher resistance against further plastic deformation. Thus, although surface friction intensifies the stress gradient and magnitude for both systems, the relative frictional effect is less in HSHS.

According to the FEM simulation results, effect of surface friction on scratch-induced deformation can be reduced by increasing the strain hardening slope. Increase in yield stress has no significant influence on relative frictional effect on scratch depth. It should be noted that, increasing the strain hardening slope will reduce the strain at stress recovery if all the other material parameters kept the same.

Experimental Validation

Mechanical and Frictional Properties of the Model Systems. Figure 10 shows the uniaxial compression plot for SAN and PC model systems. As shown, the compressive yield stress of SAN is higher compared to that of PC. Conversely, PC has higher strain hardening slope (lower strain at stress recovery) than SAN. Figure 11 shows the COF, [mu] measurement for both SAN and PC, with and without Teflon sprayed. As shown, the system with Teflon sprayed on the surface (denoted as LCF) has lower COF compared to their respective neat counterpart (denoted as HCF). The reduction in COF, [mu] is ~51% in SAN and ~48% in PC. Thus, similar reduction in COF for both systems is achieved. It should be noted that, the scratch COF, which is the ratio of tangential load to normal load during the scratch process, of both systems follow the same trend.

SAN-HCF  0.29
SAN-LCF  0.14
PC-HCF   0.35
PC-LCF   0.18

FIG. 11. COF measured for the model systems.

Note: Table made from bar graph.


Correlation to FEM Findings. Figure 12 shows the plot of onset of groove formation for the model systems obtained via VLSCM. The detailed procedure for the measurement of onset of groove formation can be found elsewhere (4). The onset load for groove formation in SAN-HCF system is higher compared with PC-HCF system. As the compressive yield stress of SAN is higher than that of PC (Fig. 10), the onset of groove formation is delayed in SAN, which matches well with the FEM findings. Also, for both systems, reduction in COF delays the onset of groove formation, which is also consistent with the FEM findings. Although not shown, the onset of plowing in SAN is also delayed with the reduction in coefficient of surface friction.

SAN-HCF   9.84
SAN-LCF  14.91
PC-HCF    7.62
PC-LCF    8.68

FIG. 12. Onset load for scratch groove formation in the model systems.

Note: Table made from bar graph.


Figures 13 and 14 show the plots of scratch depth and shoulder height obtained via VLSCM following the procedure described in Microscopic Observation Section, respectively. As SAN has higher compressive yield stress compared with PC, it has lower shoulder height and shallower scratch depth, which is consistent with the literature (6), (7), (13). Reduction in COF induces shallower scratch depth and lower shoulder height for both systems, but the percent reduction in scratch-induced deformation in SAN (dotted lines) is much higher compared with that of PC (solid lines). Although the reduction in COF for both systems is comparable, SAN shows higher relative frictional effect compared with that of PC. As, according to the FEM simulation, increase in yield stress has negligible influence on relative frictional effect up to a COF value of 0.6, this higher relative frictional effect in SAN can be attributed to the lower strain hardening slope compared with that of PC. Although not presented here, PP, with and without slip agent, which has lower yield stress and strain hardening slope compared to that of PC, also showed higher relative frictional effect compared to PC. As fish-scales form at a very low load in PP, there were not enough consistent data points for scratch depth measurement. However, the shoulder height data were more reliable and showed higher relative frictional effect in PP compared with that of PC. Scratch tests at 1 mm/s scratching speed also showed similar behavior.

According to the FEM simulation and experimental results, the onset of groove formation is primarily affected by yield stress, which is influenced by coefficient of surface friction. Up to a certain value of COF, increase in yield stress alone has no significant influence on frictional effect on scratch-induced deformation. According to the present study, frictional effect on scratch-induced deformation can be reduced by increasing the strain hardening slope. It should be noted that, strain at stress recovery is reduced when the strain hardening slope increases with all the other parameters kept the same. The present findings suggest that the effect of COF on scratch-induced deformation can be altered by modifying the constitutive behavior of polymers. More importantly, if the strain hardening slope is high enough, there is no need to use slip agent or other surface treatment process to reduce the friction as the frictional effect on scratch-induced deformation would be minimal.

Finally, it should be noted that the present findings will only hold true for ductile polymers, not for brittle polymers where possible tensile stress-induced premature crazing or cracking is most likely to occur. Therefore, care should be taken to address the friction coefficient effect on brittle polymers. Also, uniaxial compressive behavior of the model polymers at a constant crosshead speed has been used to draw the conclusion, which may be oversimplified as the stress state during scratch is generally triaxial. Furthermore, polymer mechanical behavior is known to be sensitive to the rate of testing. These aspects of study will be subjected to our future investigation.

CONCLUSIONS

Using FEM parametric study and experimental work, the effect of surface friction on scratch-induced deformation and its correlation with the constitutive behavior were sought in this study. By varying material constitutive parameters and coefficient of surface friction, the frictional effect on scratch depth and shoulder height formed during the scratch process was investigated. The results indicate that the onset of scratch groove formation is strongly related to the yield stress of the polymer, which is influenced by surface friction. Postyield constitutive parameters have no influence on onset of scratch groove formation. Although surface friction has an adverse effect on scratch-induced deformation, the frictional effect can be reduced by increasing the strain hardening slope, which also reduces the strain at stress recovery with all other constitutive parameters kept the same. This work provides useful guidelines on whether or not slip agents are needed for preparation of scratch-resistant polymers based on the respective constitutive behavior.

Correspondence to: Hung-Jue Sue; e-mail: hjsue@tamu.edu

Contract grant sponsors: Texas A&M Scratch Behavior Consortium, Styrolution GmbH, and BASF SE.

DOI 10.1002/pen.23394

Published online in Wiley Online Library (wileyonlinelibrary.com).

[c] 2012 Society of Plastics Engineers

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Mohammad Motaher Hossain, (1) Rolf Minkwitz, (2) Hung-Jue Sue (1)

(1.) Polymer Technology Center, Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843-3123

(2.) Styrolution GmbH, Ludwigshafen, Germany
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Author:Hossain, Mohammad Motaher; Minkwitz, Rolf; Sue, Hung-Jue
Publication:Polymer Engineering and Science
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Geographic Code:1USA
Date:Jul 1, 2013
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