聚合物复合材料应力场模拟.docx

1、聚合物复合材料应力场模拟Finite Element Simulation of Tensile Behaviors in the Elastic Region For PP/nano-TiO2 CompositesAbstract：Polypropylene(PP)/nano-TiO2 composites were prepared by the melt intercalation molding. Based on the assumption of continuum mechanics model for materials, a finite element analysis m

2、odel for the composites was constructed using ANSYS 11.0 software. In the stage of deformation (pre-yield regime) the response mechanism of the stress and the strain for composites was investigated, and the von mises stress field of PP/nano-TiO2 composites has also been simulated. It was found that

3、the simulation results are Consistent with the testing results at low volume strain level. Comparing with the 3D model, the results simulated using the 2D model are accurate with the experimental results. If the volume fraction of particles is less, other particles have little influence on the local

4、 stress field of a certain particle, no obvious overlap or cross of the stress field could be found between two neighboring particles. While applying different loads, the stress jumps to maximum stress value in the interaction region of the two phase firstly, and then it occurs that the particles de

5、bond with the matrix.Keywords：Polypropylene(PP)；TiO2；elastic region；tensile behavior；finite element analysis1. IntroductionMany decades has seen great developments in inorganic fillers used as polymer modifiers. At the beginning, the key aim is either to be used as a major reinforcing and filling sy

6、stem, for example in rubber using carbon black and silica, or to cheapen the compounds using silicate, carbonate, sulfate and other materials, nowadays like nanotubes, nanoparticles and layered silicates are more widely used to improve the tensile and impact properties of the polymer composites 1-4.

7、 Great focus will be laid on this research in the future. Although the former works has provided many chances for the designing of high properties composites, research that lays on prediction of a multi-phase composites using a finite element method were still on a starting stage. Based on a finite

8、element analysis (FEA) model constructed using the ANSYS software, M. Hoffman 5 provided a new method to evaluate both the uniaxial tensile behavior and enhanced toughness of the nanocomposites, and claimed that the enhanced fracture properties were caused by the assisted void formation at the parti

9、cles which is supported by a microstructure-based finite element modeling based upon elasticplastic deformation around weakly bonded particles. Yu Dong 6 captured morphological images using both SEM and TEM to generate the geometric information, and then predicted the elastic modulus of polypropylen

10、e (PP)/clay nanocomposites by using an Object-Oriented finite element analysis. It showed that the results numerical simulated have good agreement compared with the experimental data and the available composites theoretical models. On shape and distribution assumption of the particles, a microstruct

11、ure-based (FEA) model for PP/nano-TiO2 composites was constructed in this paper, using this model the response mechanism of the stress and the strain pre-yield regime was investigated, and we also simulated the von mises stress field of the composites. 2. Experimental proceduresCommercial-grade raw

12、materials consisting of isotactic polypropylene (PP) homopolymer T30S, supplied by Maoming Petrochemical Industrial Co.，China, It has a melt flow index (MFI) of 3.2 g/10 min (2.16 kg at 230).The precipitated nano-TiO2 was supplied by Kena new materials Co., China and dynamic light scattering measure

13、ments suggests that the micelle size is approximately 20 nm.Nano-TiO2 were dried in a incubator at 80 for 24 h, and then were put in a solution mixed with ethanol and titanate coupling agent NDZ-201(200:1 by volume ratio), heat the mixture to boiling until the ethanol were fully volatilized. Then we

14、 got the modified TiO2 particles. “Master batch” of Particles/monomer (20/100) were firstly prepared using a twin-screw extruder with the temperatures of the successive zones from the feeder to the die set to 180, 200 and 210 C respectively and a screw speed of 300 rpm, then PP/1 wt. % TiO2 was prep

15、ared through the same method.Then an injection molding machine was used to mold the compounds into standard bars for mechanical testing. The dimension of the deformable region of the tensile dumbbell specimens was 25.0 3.2 2.0 mm3. Six tensile dumbbell specimens were used for testing. Tensile proper

16、ties of the composites were determined with a GT-TCS-2000 universal tester at a crosshead speed of 50 mm/min according to AS1145.1-2001.To assess dispersion of the nanoparticles in the polypropylene matrix, ultrathin sections of the compounds were examined by a Tecnai GF2 transmission electron micro

17、scope (TEM).Samples were prepared using a Reichert Jung ultra-microtome equipped with a diamond knife to cut films of 80100 nm thickness at -80 by Liquid nitrogen cooling. The cut sections were placed on a formvar-coated copper grid for observation in the TEM. 2 numerical method2.1Microstructural ch

18、aracterisationIn order to prepare high-performance nanocomposites, a main factor was to make inorganic particles dispersed in the matrix uniformly; another factor was the forming of elastic interface between particles and the matrix which could transfer the stress loaded freely. The interface was no

19、t taken into consideration in this paper and the model was simplified as a two-phase composite system according to the continuum mechanics theory 7. It was assumed that the particles is dispersed in the matrix uniformly and the bonding between the particles and the matrix is very weak, to the extent

20、 that the particles can be assumed to be voids in a matrix around which a stress concentration is induced on loading, also both the PP matrix and clay particles was assumed to behave as linear elastic materials with a perfect interfacial bonding between two constituents. The unit volume () modeled b

21、y the FE method could be described based on particles radius () and volume fractions () of particles as follows 8: （2-1） To ascertain the response mechanism of stress and strain at a microstructural level, a representative volume element (RVE) model and a two-dimensional plane model were constructed

22、 separately. Then the finite element mesh was operated, moreover, an adaptive mesh refinement was employed to refine the grids at the matrix-particle interfaces where the highest stress gradients could arise, and thus a high degree of refinement might be required to precisely capture fluctuations in

23、 the stress and strain fields. After meshing the model the force-balance equation was activated for the linear solver. As depicted in equation 2-2, the boundary constraints was applied so that the displacements X and Y on the left boundary could be fully constrained and only displacements X were emp

24、loyed on the right boundary. （2-2）At last according to a homogenized method, the average of stress and strain we simulated could be equal to the engineering stress and strain of the composites as described in equation 2-3， is the unit volume of the model. （2-3） While applying loads on PP/nano-TiO2 c

25、omposites, even the loads were very small, many micro-voids and cracks would have formed around the particles. If materials were rich in defects, the bearing stress achieved a dominant position in all loads applied at the same time, the micromechanical deformation processes could be described as fol

26、lows9,10: The modifier particles act as stress concentrators, the stress concentration leads to the development of a triaxial stress in the inorganic particles and to dilatation. A higher hydrostatic or triaxial stress builds up inside particles and gives rise to void formation through cavitation in

27、side particles or debonding at the particle matrix interface. With continuous growth of voids, they come into a whole in the end, the composites failure simultaneously. Fracture criterion and strain energy release rate criterion are mainly two kinds of Criterion used for evaluating the crack propaga

28、tion. In this paper, the yield behavior of the composites were studied using von mises criterion 7, so the strength criterion could be described as follows Correspondingly:= （2-4）In the equation 2-4,、were No.1, No.2, No.3 principal stress separately,;was the von mises stress in the paper andrepresen

29、ts the intrinsic strength of the composites.2.2 Construction of finite element analysis modelIn this study, only isotropic elastic material properties were assigned with the elastic constants of Youngs modulus and Poissons ratio. Based on lots of experimental data and microstructural characterizatio

30、n, we set material 1 as polypropylene, its modulus and Poissons ratio was chosen to be 605MPa and 0.36; material 2 was set to be nano-TiO2, which were handled as micro-voids(Fig.1(a)during the simulation process. Representative volume element model (RVE) were constructed and then meshed using quadra

31、tic 3D solid linear elements, 8 node SOLID 185 (enhanced strain formulation，axisymmetric option) as shown in Fig.1(a), then the finite element mesh was operated and modified, results showed that this model has 1242 nodes and 1236 elements. To compare with the 3D model, we constructed 2-dimensional m

32、odel and meshed with quadratic 2D solid linear elements, 8 node PLANE 82 with the superposition of a symmetric grid of quadrilateral elements, while meshing the model the width of the boundary were assigned, we get 83201nodes and 82500 elements. Arrows represent the direction and size of the loads imposed in Fig.2. This paper would study the relationship between Mechanical properties and microstructure of composites based on two FE models above. （a）The volume used for FEM analysis is 1/8 of the unit cell （b）The plane used for FEM analysis is 1/4 of the unit cell Fi