April 25, 2008
The Process and Microstructure Modeling of Long-Fiber Thermoplastic Composites
By Vaidya, U K Chawla, K K; Thattaiparthasarthy, K Balaji; Goel, A
Interest in thermoplastic matrix composites has increased in recent years due to several advantages of these materials, including high volume process ability, recyclability, superior damage tolerance and fracture toughness, and ability to produce complex shapes. Among thermoplastic composites, long-fiber thermoplastics (LFTs) are finding increased use in the automotive and transportation sector. Predictive process and material characterization tools are much needed in industry to minimize expensive tooling/process trials and to improve the design avenues for parts produced using LFTs. The current work focuses on finite element simulation of LFT materials for two scenarios: first, process modeling of LFTs to evaluate the flow of fiberfilled viscous charge during compression molding and the resulting fiber orientation prediction and, second, modulus prediction of LFT materials accounting for fiber orientation and distribution. Together these tools provide insight into the process and performance characteristics of LFT materials. (ProQuest: ... denotes formulae omitted.)INTRODUCTION
Long-fiber thermoplastics (LFTs) are being used increasingly in the automotive and transportation industries due to their superior specific strength and modulus resulting in substantial weight savings, combined with their relative ease of fabrication and handling.1 The resultant weight reduction of vehicles increases their overall efficiency, thereby reducing the maintenance costs of vehicles and assembled structures.3 The advantages of using LFTs over metals include high impact resistance, superior toughness, improved damping, and corrosion resistance. Other benefits are ease of shaping, recyclability, high-volume processing, high end-use properties, and lower system costs.1-5
The mechanical properties of a part made of fiber-reinforced composite are governed by the matrix system, type of fibers, fiber content, fiber aspect ratio (length-to-diameter ratio), and orientation of the reinforcing fibers. The orientation and length of the fibers are influenced by the processing method and process parameters. The most distinctive characteristic of an LFT is its initial fiber length, which ranges from 10 mm to 50 mm. Short-fiber thermoplastic composites typically have fiber lengths of 0.5 mm or less.6 The full strength of the reinforcement is utilized because the fiber length is above the critical fiber length for effective load transfer.5 The critical fiber length is given by 1^sub c^ = sigma^sub max^ r/tau, where 1^sub c^ is the critical fiber length, r is the fiber radius, sigma^sub max^ is the tensile stress acting on the fiber, and tau is the interfacial shear strength. The use of long fibers enhances the elastic modulus and tensile strength of the material approximating 90% of continuous fibers.7
Long-fiber thermoplastics, unlike continuous-fiber reinforced composites, can be processed using traditional plastic-molding equipment and therefore parts can be manufactured at medium volume rates with a high degree of consistency and repeatability. The processing of LFT materials through extrusion-compression molding involves three steps. First, continuous fiber (glass, carbon, and/ or aramid) tows are pultruded through a heated die during which the individual filaments are wet-out with thermoplastic resin. The cooled impregnated tows are then chopped into pellets of average length 12-38 mm. Next, the pellets are fed into a plasticator (low shear extruder), heated above the melting point, and extruded in the form of a molten charge of desired length. Finally, the molten charge is quickly transferred to a heated mold where it is compressed. The part is then removed after sufficient cooling. Figure 1 illustrates the changes in material form between each of the three processing steps, from the pellets to molten charge to molded plate.
PROCESS MODELING OF LFTs
Several authors have either implemented models or used commercially available software packages to verify injection molding of short-fiber composites.8,9 In the current work, Cadpress Thermoplastic(R) (EXPRESS),10 a finite element simulation approach for fiber-filled polymer, was used to simulate the flow pattern, fiber orientation, and process-induced shrinkage/warpage of compression-molded geometries.
The process simulation in this study was limited to the flow through the cavity and fiber orientation studies. A representative case study considered a 40% weight fraction E-glass/PP LFT composite battery access door for a mass transit bus. The battery box access door functions to protect and house several batteries needed for the regular operation of the electrical systems in the vehicle. The LFT door is ribbed on the inner side and smooth on the exterior side. The door is located at the rear part of the bus, adjacent to the wheel housing, and measures approximately 95.25 cm x 49.5 cm x 0.5 cm. Details of the material and process modeling parameters are given in Reference 11.
A solid model of the LFT battery door was meshed using three- noded finite element mesh in Hypermesh(R). The shell element is considered a 2.5 dimension membrane element with the thickness specified. For the simulation of compression molding, charge placement is defined by selecting an area on the finite element mesh which corresponds to an extruded charge placed on a mold maintained at a lower temperature than the charge. The flow analysis in compression molding is modeled as non-Newtonian, non-isothermal flow in three-dimensional (3-D) cavities using finite elements. This technique, commonly called a control volume approach (CVA), requires that the 3-D molding surface be divided into flat shell elements. The cells or control volumes are generated by connecting the element centroid with element midsides. When applying the mass balance to each cell, the resulting equations are identical to those arising from a Galerkin method for finite elements.12 The influence of the effect of temperature on the local viscosity of the material is captured by the Carreau-Williams Landel Ferry (WLF) model. This model is used to capture the temperature and deformation rate dependency of the viscosity10 as given by Equation 1, where: ... corresponds to the shear rate, a^sub T^ is the temperature shift coefficient which accounts for variation of viscosity at various temperature, P^sub 1^ is the zero shear viscosity, P^sub 2^ is the time constant, and P^sub 3^ is the exponent index. (Note: all equations are shown in the Equations table.
Compression molding of LFT involves placing a heated charge in a cold mold. The material that comes into contact with the mold walls is rapidly cooled; the local viscosity increases and the material in these regions will no longer flow. The filling stages of the compression molding process are temperature dependant, and the calculation of the temperature distribution is an integral step of the overall simulation. The simplified form of the energy Equations 2-4 used in the simulation of the heat transfer is as Equations 2, 3, and 4,10 where rho is the density; c is specific heat capacity; lambda is the thermal conduction coefficient; tau^sub xz^ and tau^sub yz^ are the shear stresses in xz and yz plane, respectively; and v^sub z^, v^sub y^, and z are velocity components in x, y, and z, respectively.
There are several assumptions made in calculating the energy transport during the filling stage. Conduction heat transfer occurs only in the throughthickness direction. Convection occurs only in the direction of flow, temperature profile is symmetric, and heat transfer between material and mold is ideal. Once the mold has been filled completely, the convection and diffusion terms in the energy equation are neglected and only the conduction term is considered. The fiber distribution model accounts for the fiber volume content, aspect ratio, and a fiber interaction coefficient that depends on the number of fiber contacts that occurred during the flow. The fiber distribution plot represents the fiber orientation in an element with respect to the XY plane of the element.
The state of particle orientation at a point is described by an orientation distribution function and is defined such that the probability of a particle located at coordinates (x, y) at time t, oriented between two angles are given by Equations 5 and 6. The orientation distribution function changes constantly as the fibers travel within a deforming fluid element. Assuming the fiber density is homogenous throughout the fluid and remains that way during processing, the continuity equation can be written as shown in Equations 7-9, where psi is the orientation distribution function; phi^sub 1^, phi^sub 2^ are the orientation angles;
... is the change in orientation
angle with respect to time; ... is the magnitude of the strain rate tensor; C^sub 1^ is the phenomological coefficient which models the interaction between the fibers; and v^sub x^ , v^sub y^, v^sub z^ are the velocity component in x, y, and z, respectively.
Flow Fronts of Molten Charge
The flow patterns for four different charge locations and configurations for the battery box access door are represented in Figure 2. Types 1 to 3 (Figure 2a-c) have two small charges placed in different configurations, and these show the presence of knit lines when the two molten charges are compressed inside the mold. Hence, a charge parallel to the longer edge was adopted to mold the battery door. For the mold to fill completely without any voids or premature freezing of the melt, the approximate charge dimensions were deemed to be 650 mm in length and 170 mm in diameter and the force required to flow the molten charge inside the tool was predicted to be approximately 350 tonnes. The top tool temperature was maintained at 80[degrees]C and the bottom tool at 90[degrees]C. The flow front of the charge is seen to progress from the geometric center to the edges of the mold. The flow simulation shows that the four corners of the mold fill at the very end of the molding process. Figure 2d illustrates the simulation corresponding to the charge placement along the long axis of the battery box access door. A short shot of the LFT charge was used to verify the flow simulation result as illustrated in Figure 3. A short shot consists of placing a smaller volume dosing of the mold than is required to completely fill the cavity. The part produced using a short shot provides information about the actual flow fronts developed inside the mold. The flow pattern of the model, which is 85% filled, is compared to a short shot of a charge. In both the described cases the four corners did not fill and the flow pattern was accurately predicted.
The fiber orientation in each element is represented by a plot of fiber distribution function versus fiber angle as illustrated in Figure 4 for a random element. This scale is derived for five layers through half the thickness, from the top surface to the mid-plane. For a randomly oriented layer there will be an equal number of fibers in each sector or direction. On the other hand, for a preferential orientation, the fibers align along a preferred direction and so most fibers will lie in just a few sectors. Simulation results show areas where the top surface has random orientation compared to a preferential orientation at the center. From the fiber orientation distribution plots shown in Figure 4, the selected area shows that the degree of orientation increases through the thickness as opposed to the random orientation on the surface. This graph represents the fiber orientation in an element with respect to the local XY plane of the element.
The degree of orientation that occurred as the melt flowed through the cavity is predicted by a fiber orientation scale. This scale is derived for five virtual layers through half the thickness, from the top surface to the mid-plane.10 The value on the scale that represents no orientation is derived by dividing 1 by 25 (the total number of sectors considered for the simulation), which yields the value 0.04. For a preferential orientation, the fibers will tend to align in one direction and so most fibers will lie in just a few sectors. The more oriented the fibers become, the fewer sectors. Hence the fiber orientation scale value is greater than 0.04.
During compression molding, the fibers tend to align preferentially along the transverse (width) direction of the part. X- ray radiographie studies were done to verify the fiber orientation of the final molded part using a tungsten target x-ray source at 40 RV. The x-ray radiograph in Figure 5a represents the preferential fiber orientation in the entire battery access door. Selected areas compared with the modeling results indicate that range of fiber orientation predicted and observed lies between 50[degrees] and 90[degrees].
Simulation results in Figure 5b show typical areas where the top surface has random orientation compared to a preferential orientation at the center. It can be seen that for a majority of the elements, there is well-defined fiber orientation for layers 2, 3, 4, and 5, and more random orientation for the surface layer. This is explained as follows. The viscous E-glass/PP charge begins to flow during the compression process; the cavity thickness begins to reduce (i.e., due to mold closure). The shear forces generated help in the flow of the material, which manifests in the form of preferential fiber orientation in the direction of the flow. The charge placement in the case of the battery access door was along the long axis of the part, as illustrated in Figure 1d. Although a precise orientation at each layer is not possible to predict with existing tools, the simulation provides adequate measure of the fiber orientation, particularly for thin parts, where the out-of- plane fiber rotation is minimal.
MODULUS DETERMINATION USING FINITE-ELEMENT MODELING
One of the major advantages of LFTs is their superior mechanical properties vis-a-vis short glass fiber composites. In particular, for a given fiber/matrix system and fiber volume fraction, the Young's modulus of LFTs is higher than that for SFTs. In this study an image-based object oriented finite element method (OOF, National Institute of Standards and Technology) was used to predict the Young's modulus and investigate the microstructural effects on the local stress state in an LFT composite. This tool has been shown to be highly effective in incorporating the actual microstructure in the finite element model to predict elastic and thermal constants of materials.13-16
A representative microstructure of the glass-fiber-reinforced LFT taken from the surface of the plate is shown in Figure 6. A significant amount of alignment of the fibers along the extrusion axis is observed. Note that fibers are not randomly distributed; in fact, the fibers show a distinct alignment along the extrusion axis. For the OOF study a thin plate (3 mm) was considered to ensure that most fibers are oriented along the extrusion axis. This simplified the problem of quantifying the microstructure. For thicker parts (such as the battery door face), the fiber orientation is a function of the thickness. The OOF study was limited to a thin plate. The volume fraction of the fibers determined from image analysis was approximately 21% and was confirmed by matrix burn-off, which is a procedure by which matrix is removed by burning, leaving fibers as the residue. The mean value of the experimentally determined Young's modulus from the linear elastic portion of the stress strain curve was 7.92 +-1 GPa.
Object-Oriented Finite Element Method The object-oriented finite element
method is image-based. Thus, one starts with a representative image of the microstructure, which can be somewhat subjective. The size of the image used for simulation is iteratively increased until the simulated response does not vary from image to image. The next step in the analysis is segmentation of the images, which involves separation of each of the constituents of the microstructure into distinct gray levels, which is used later to assign materials properties. A total of five representative micrographs similar to that shown in Figure 5 were modeled.
After image segmentation, material properties are assigned. The material properties of the fiber (E-glass) and matrix (polypropylene) are taken from the literature17,18 and are shown in Table I. Fibers and matrix are both elastic, which is a reasonable assumption since both fiber and matrix behave as elastic material within the strain limits used to calculate the modulus.
After the assignment of material properties, the microstructure is meshed following an adaptive meshing algorithm. The main focus of the adaptive meshing process is to conform the boundaries of the triangular mesh to the actual microstructure. The mesh generation process begins with the superposition of a uniform and symmetric grid of right triangular elements over the microstructure. This mesh is then made to conform to the actual microstructure by following a series of steps leading to a mesh which conforms very closely to the boundaries of the element present in the microstructure. After this step, the material and group properties are transferred to the mesh and the mesh is imported to OOF for further analysis. A mesh is considered sufficiently refined, or saturated, when subsequent refinements yield essentially unchanged values when virtual experiments are performed.
The following boundary conditions were used: the displacement on the left edge was set to zero, and the displacement of the lower left node in both x and y directions was also zero. A force in the x- direction was applied to the right side of the microstructure (see Figure 7a). The analysis was conducted in plane stress condition since OOF does not take the thickness of the samples into consideration. Several iterations of mesh refinement were conducted. The microstructure of the LFT composite after the assignment of the material properties and meshing is shown in Figure 1b. Note that a higher density of elements is present within the fiber and at the fiber/matrix interface.
The modulus value predicted from OOF was 7.28+0.4 GPa, very close to the experimental value. Some discrepancy could be due to the fact that OOF is a two-dimensional analysis and does not take into account the 3-D fiber orientation that develops during the processing of LFT. This indicates the need for a 3-D finite element modeling effort wherein a 3-D representation of the structure of the composite can be obtained.19
How would you...
...describe the overall significance of this paper?
This paper contributes to the prediction of process-induced fiber orientation and properties of long-fiber thermoplastic composite materials. There is a limited understanding of microstructure evolution as a function of flow of viscous fiber containing thermoplastic polymers. The position and orientation of the fibers influence mechanical properties.
...describe this work to a materials science and engineering professional with no experience in your technical specialty? Long- fiber thermoplastics refer to glass, carbon, Kevlar, or other types of reinforcing fibers thai are impregnated with thermoplastic polymers such as polypropylene, polyethylene, poly phenylene sulfide, etc. These fibers have lengths of 3 mm to 25 mm,- hence their aspect ratio (fiber length to diameter) is very high and they possess very high mechanical properties. With a predictive tool that determines fiber distribution and orientation, the process/design engineer has the knowledge to position and orient the fiber melt (charge) to maximize performance and minimize processing cycle/ time.
...describe this work to a layperson?
The automotive industry likes to use Long fiber thermoplastics (LFTs) because they can produce body, floor, and instrument panels with a compression molding process, where an extruder produces a molten charge from the LFT pellets. The charge is compression molded at rapid cycle times-30 seconds to 1 minute for automotive applications.
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U.K.Vaidya, K.K. Chawla, K. Balaji Thattaiparthasarthy, and A. Goel are with the University of Alabama at Birmingham, Department of Materials Science & Engineering, 1530 3rd Avenue South, Birmingham, AL 35294-4461. Dr.Vaidya can be reached at (205) 934-9199; e-mail email@example.com.
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