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Abstract

The automotive industry has great interest in designing and producing lightweight high-performance components using fiber-reinforced polymers (FRPs), primarily due to their high specific strengths. Injection molding of FRP is one of the preferred processes to meet low-cost, high-volume objectives. It is imperative to account for shrinkage and warpage while designing the tools for injection molding. However, predicting shrinkage and warpage of injection-molded FRP parts remains a challenge. This is because both the structural and thermal properties depend on the condition of the fibers in the resin, that is, variation in the orientation, length, and concentration throughout the part. Additional challenges come from the fact that the material properties of polymers are a function of temperature, which varies as the parts cool. In this study, we are presenting a finite element-based semiempirical approach to address both these challenges and predict warpage due to cooling for a fiber-reinforced resin component in solid phase. The approach is demonstrated to predict warpage of an injection-molded flat plaque made of glass fiber-reinforced polypropylene, cooled from 160°C to room temperature of 23°C. First, the fiber orientation in the plaque is estimated. Next the material properties for the combined material, that is, glass and resin, are measured as a function of temperature. Then the combined material properties and calculated fiber orientations are used to estimate the ‘in-mold’ condition resin properties using reverse engineering. Finally, the warpage of the plaque is predicted using the estimated resin properties and fiber orientations. Warpage predictions using this method compare well with the measured experimental results. Our study demonstrates that valid predictions for shrinkage and warpage of injection-molded fiber-reinforced thermoplastic parts in solid phase can be made if accurate material properties are used.

Keywords

Fiber reinforced warpage anisotropy prediction measurements

Introduction

There is a growing importance placed on vehicle weight reduction in the automotive industry, primarily due to rising fuel efficiency standards. Weight reduction may be achieved through the design of efficient parts/components as well as by switching from conventional steel to lightweight materials. Fiber reinforced polymers (FRPs) are a subset of lightweight material and have become increasingly popular due to their high strength-to-weight ratios. Many different combinations of fibers, polymers, and manufacturing processes are being considered for this purpose. Among these options, injection molding of glass fibers (GFs) with thermoplastic materials is of great interest because it can be used to manufacture FRP parts at a higher volume and lower cost compared to other materials and methods.¹

In the injection molding process, the molten resin and discontinuous fibers are fed into the barrel via a mixing screw. This molten mixture is then injected into the mold cavity. As this mixture of molten resin and fiber flows to fill the cavity, the fibers tend to align along the flow, which can be oriented in different directions at different locations in the cavity.² When the mixture cools, the resin solidifies into a finished part with fibers dispersed and oriented based on the flow pattern throughout the part. The goal is to design the mold cavity such that once the part is ejected and cooled to operating temperature, it attains near net shape. Therefore, it is very important to accurately predict the processing deformation, that is, shrinkage and warpage, before a mold design is finalized for production.³

Warpage in an injection-molded part occurs due stresses that are generated within a part as it undergoes uneven shrinkage.^4
–6 At times, these stresses can be high enough to create cracks. Ideally, it is desired to predict the deformed shape of the part based on the process parameters and mold geometry. The warpage due to residual stresses of an injection-molded part results from various sources of heterogeneity in material and processing such as:

differential cooling of the mold cavity^7
–9;

variation in the pressure distribution^4,7,10
–12; and

anisotropic material properties through the part.^7,13
–15

Cooling always begins at the mold surface because cooling channels in the mold create a lower temperature to absorb heat. This generates a temperature variation, not only through the thickness but also throughout the part geometry, resulting in differential shrinkage, which ultimately leads to warpage. It has been seen that the pressure in the molten resin has a significant influence on the shrinkage. Higher fill pressure results in higher density for resin, which shows lesser shrinkage, while lower fill pressure results in lower density and higher shrinkage.¹⁰ During the fill-and-hold step of molding process, variation in the pressure throughout the mold cavity is possible. This can cause differential shrinkage, which may result in warpage. In the thermoplastic material as the melt flows, the polymer tends to align along the flow.³ As the material solidifies, the polymer stays aligned along the flow and therefore the properties along the flow and cross-flow direction could be slightly different, which also may cause warpage in the parts.

When the fibers are used with the polymer resin material, the complexities of warpage become orders of magnitude higher,¹⁴ as the fiber resin-combined material properties are highly dependent of the fiber conditions such as fiber length, volume fraction, and orientation. During the fill process, the fiber aligns along the flow of molten resin depending on the flow field, which depends on the fill process parameters and the shape of cavity, as a result the fiber conditions varies along the part.^13
–15 Also due to the fountain flow effect,¹⁶ the fiber alignment varies through the thickness, resulting in considerable material property variation through the part. Coefficient of linear thermal expansion (CLTE) is one of the key contributors to the warpage. The CLTE in the flow direction is usually much lower compared to cross-flow, as the fiber aligned along the flow makes significant reduction in the CLTE.

It has been also observed that the resin properties can be slightly anisotropic, as the semicrystalline materials tend to change with the fiber as the polymer chains tends to aligns along the fiber.^17,18 The resin property varies with the temperature, that is, the elastic modulus, CLTE, as well as other properties, such as thermal conductivity, for the material varies along with the temperature.

The current approach in the industry is to use the pressure–volume–temperature (PVT)-based method, which mainly accounts for shrinkage and warpage due to mold fill pressure and temperature differential in the material and cavity.^19,20 Additional efforts have been made by Kabanemi et al.²¹ and Pontes et al.²² to account for the effect of fiber in the shrinkage and warpage predictions using numerical methods, such as finite element model (FEM), but the material was assumed to be isotropic. To the best of our knowledge, very little literature is available in the area of FE analysis of fiber-filled polymers corresponding to shrinkage and warpage predictions.^13,23 Furthermore, most of the available literature considering anisotropy arising due to fibers assumes that the material properties are linear, elastic, and do not change with temperature.^19,20

Since most of the warpage in the fiber-filled injection-molded thermoplastic parts results from the anisotropy caused by the fibers,^13
–15 we decided to focus on the effect of fibers on the warpage. In this study, we are offering two unique improvements over the past studies,

The material properties are considered to be anisotropic, nonlinear, and expected to vary with the temperature, that is, CLTE, thermal conductivity, and elastic modulus are considered to be functions of temperature.

Since such properties were not readily available for the material of interest, we developed a unique method to estimate the resin properties. The combined, that is, fiber + resin material properties are experimentally measured and then using reverse engineering the resin only properties are estimated. This is important because when used with the fibers, resin properties are slightly different compared to just resin condition due to polymer alignment. The measured properties are called ‘effective’ properties.

The approach is demonstrated on a GF + polypropylene (PP) plaque. We choose a plaque because the stiffness against warpage is quite low and has tendency to warp a lot, which makes the warpage in the plate not only observable but also challenging.

Materials and methods

Experimental study

Three millimeter thick plaques measuring 300 × 300 mm² were manufactured by injecting 30% GF (by weight) and PP material in an edge-gated tool (Figure 1). This material was commercially available from Ticona in a long fiber thermoplastic (LFT; Florence, South Carolina, USA) form under the trade name of CELSTRAN PP-GF30-03 (Celanese, Irving, Texas, USA). The process parameters are listed in Mold fill process simulation section. Plaques were manufactured in three different configurations. The details of these three plaque configurations are shown in Table 1:

Figure 1.

Plaque details and warped shape.

Table 1.

Build configuration and physical layout of plaques.^a

Build configuration	Physical layout
1. Injection-molded LFT pallet material
2. Injection molding of LFT pallet material overmolded with sheet of UD fibers on one side
3. Injection molding of LFT pallet material overmolded with sheet of UD fibers on both the sides.

LFT: long fiber thermoplastic; UD: unidirectional; GF: glass fiber; PP: polypropylene.

^aThe UD sheets were 0.2 mm thick and made of 70% (by weight) continuous GFs-reinforced PP.

It is seen that all three types of the plaques warped significantly when they were ejected from the mold and cooled to room temperature of 23°C (Figure 1). However, when reheated and soaked at 160°C (i.e. less than melting temperature of the resin material, i.e. 180°C and T _g ∼130°C) for 4 h, we observed that the plaques became flat as shown in Figure 1. As the plaques were allowed to naturally cool back to the room temperature without constraint, they warped back to original shape. We repeated this cycle three to four times to confirm the repeatability of this condition, that is, warpage at room temperature and no warpage at 160°C. Based on these observations we assumed that the residual stresses in the plaque at 160°C are very low, and therefore, there is no warpage. Also we assumed that since the plate is already in the solid phase, the differential shrinkage, and hence warpage, observed at the room temperature is the result of material anisotropy. In the rest of the article, we will focus on developing FEM to predict warpage in the three different build configurations of the plaque.

We would like to point out that in general due to limited stiffness in ‘out-of-plane’ direction the warpage prediction for a flat plate is considered quite challenging. In practice, ribs are often added to flat plate-like parts to add stiffness and stabilize the warpage. Since the primary focus of this study was to understand and model warpage of fiber-reinforced materials, we decided to use a flat plaque since its warpage is highly observable.

Prediction method

The processing strain that causes residual stresses, which leads to warpage are composed of two components: (1) processing strains due to chemical shrinkage and crystallization and (2) processing strains due to thermal expansion. ^24
–26 Mathematical expression for the chemical shrinkage and crystallization is very complex, so a semiempirical approach is used in this study. The homogenized material properties for the composite material are measured as a function of temperature in the flow and cross-flow direction and then the resin properties are estimated using reverse engineering from the measured homogenized properties.

The key steps in the entire prediction methodology are shown in Figure 2. The warped shape is predicted at step 3, which is carried out in two stages.

Figure 2.

Key steps in prediction of warpage.

During the first stage of step 3, temperature distribution throughout the plaque is predicted as a function of time using transient heat transfer analysis. During the second stage, a thermomechanical analysis is used to estimate the thermal deformation in the plaque using the temperature history obtained from the first stage. These simulation steps can be easily performed using the commercial FE codes available in the market today, provided the material properties needed for these calculations are available. The first stage, that is, transient heat transfer, requires thermal conductivity, specific heat, and density. The second stage requires the coefficient of thermal expansion, elastic modulus, and material plastic properties. The key challenges include determining these properties and developing mathematical models to represent these materials in the FE models. These are the major challenges because:

The material properties of the fiber and resin composite depend on the fiber conditions such as fiber length, orientation, and concentration. Accurate knowledge of fiber condition, resin properties, and homogenized properties are difficult to obtain.

The material properties vary with the temperature. We observed that elastic modulus, thermal conductivity, coefficient of thermal expansion as well as specific heat varies significantly with the temperature.

Since fiber conditions are highly dependent on the manufacturing process, Moldex3D was used to simulate the mold filling process and obtain the fiber orientations throughout the plaque. Fiber length and fiber volume are not predicted as the software capability to predict them was not available at the time this work was done. Therefore, actual measurements are used for the fiber length and fiber volume fractions in this study. Also we assumed that fiber length distribution and volume fraction remains consistent in the whole plaque. The details of the mold fill process parameters are shown under the Mold fill process simulation section. The homogenized anisotropic material properties are estimated as a function of fiber orientation using Mori–Tanaka homogenization approach²⁷ in Digimat (Version 5.0),²⁸ a commercially available material modeling software. As the fiber orientation varies over the plaque through the thickness as well as from location to location, the homogenized material properties also vary throughout the part.

The GF properties used in the homogenization calculations are assumed to be linear elastic and constant at all the temperatures. The resin properties are considered to be nonlinear wherein the plastic behavior is defined by using J2-plasticity model.²⁸ We also assumed that the resin properties are function of temperature, that is, they vary over the range of temperature from 160°C to room temperature which was 23°C. We recognize that the resin properties are often influenced by the presence of fibers, as polymer chain tends to align along the fiber. Therefore, in order to determine the resin properties that are representative of “molded-in” condition, we reverse engineered the data obtained from various evaluations of composite material. The reverse engineering, essentially, is an iterative approach to estimate the resin properties from the known GF properties, fiber conditions such as orientation, length and volume fraction, and measured homogenized properties.

Once the resin material properties are estimated, a two-step warpage prediction is carried out using FE analysis in Abaqus. In the first step, plaque at uniform temperature of 160°C is cooled to room temperature (23°C) during which the temperature change at each location of the plaque is predicted and recorded as a function of time. In the second step, the temperature and time data predicted during first step are used to predict the mechanical stresses in the plaque. The material property such as thermal conductivity, specific heat, coefficient of thermal expansion, Young’s modulus, and nonlinear responses of the fiber-reinforced material in plastic stage are modeled using Mori–Tanka homogenization. This is accomplished using the material modeling software Digimat. The details of the prediction steps are described subsequently.

Mold fill process simulation to get the fiber orientation

The mold filling process is simulated using Moldex3D (Version 13 from Coretech). A detailed FEM of the plaque cavity is prepared, and the simulation is carried out using the process parameters listed in Figure 3. The material used for the process simulation is CELSTRAN PPGF30-03. The material properties used in the simulation are from the Moldex3D material library. The plaque is modeled using a combination of tetra and prism elements. In total, there are10 layers of elements through the thickness.

Figure 3.

Details of the mold fill simulation. Material used is Ticona PPGF30 from material library. PP: polypropylene; GF: glass fiber.

The calculated fiber orientation tensor’s component along the flow and cross-flow at two selected locations are shown in Figure 4. To verify the accuracy of the prediction, we measured the fiber orientation at the flow location and compared “A11” component of the orientation tensor with the predicted values as shown in Figure 4. We judge that the difference between the two is within the part to part variations range and therefore the predicted fiber orientation of plaque is considered acceptable. The samples around the location A and B, for which the fiber orientation is known, are cut using water-jet and used to measure material properties for further study. Details of measurement and their usage in obtaining resin properties are discussed in Material properties calculations section.

Figure 4.

Predicted fiber orientation for flow sample and cross flow samples, The measured fiber orientation is compared for flow sample at location A.

Fiber resin homogenization process

The fiber and resin properties at room temperature are shown in Table 2.

Table 2.

Physical and mechanical properties of GFs and PP at room temperature.

Property	GF	PP
Density (g cc⁻¹)	2.55	0.92
CLTE (K⁻¹)	5E−6	1E−4
Fiber length (mm)	0.3	N/A
Fiber weight percentage (%)	40	N/A
Young’s modulus (GPa)	70	2
Poisson’s ratio	0.2	0.3

GF: glass fiber; PP: polypropylene; CLTE: coefficient of linear thermal expansion.

The properties for the fiber-reinforced material in the plaque can be estimated using these properties and estimated fiber orientation using mean-field homogenization approach based on a model proposed by Mori and Tanaka.²⁷ The material properties are expected to be anisotropic and changing from location to location as the fiber orientation varies through the volume.

Material properties calculations using reverse engineering

Young’s modulus

The temperature-dependent Young’s modulus for the composite material is determined using Q800 dynamic mechanical analyzer system (TA Instruments, New Castle, Delaware, USA). Samples cut from two locations of the plaque are evaluated in compliance with ASTM E2769-13 standard. The sample location and measured Young’s modulus for flow and cross-flow direction are shown in Figure 5. It is seen that both the flow and cross-flow specimens show similar trend in the reduction of the Young’s modulus of the composite with increasing temperature.

Figure 5.

Sample locations and measured Young’s modulus.

Coefficient of linear thermal expansion

The CLTE calculated is a secant CLTE based on the reference temperature at 20°C. A Q400 series thermal mechanical analysis from TA instrument was used for this purpose. Tests carried out for CLTE determination were in compliance with ASTM E831-14 standard. The influence of temperature on the CLTE is shown in Figure 6. It is seen that the CLTE of the flow specimens remains almost unchanged when compared with the increasing CLTE seen with cross-flow specimens. This huge variation may be a result of the fact that the fibers exhibit almost no change in their CLTE, whereas the CLTE of resin is highly sensitive to temperature change.

Figure 6.

Sample location and measured CLTE. CLTE: coefficient of linear thermal expansion.

Thermal conductivity

The thermal conductivity was measured using a modulated differential scanning calorimeter (DSC) from TA Instruments. Samples from two locations were prepared and evaluated in compliance with ASTM E1225-13 standard. The effect of temperature on thermal conductivity is shown in Figure 7. The thermal conductivity of both flow and cross-flow specimens increase at almost same rate with the increase in the temperature.

Figure 7.

Locations for measuring thermal conductivity and results.

Specific heat

The temperature-dependent specific heat is determined using DSC Q2000 series from TA instruments ASTM standard E1269-11. The results are shown in Figure 8. Specific heat of the composite material appears to rise steadily till 115°C after which it increases rapidly.

Figure 8.

Measured specific heat results and location of the sample.

It is assumed that the density of the material in the solid phase is not changing significantly with temperature and the small change may not have significant impact on the structural performance of interest here. Also other properties, such as Poisson’s ratio, are assumed to be unaltered in the range of temperature considered for this study.

Reverse engineering to get the resin properties

The resin properties are estimated from the measured properties of FRP using reverse engineering as function of temperature. The process flow used in the reverse engineering is shown in Figure 9. The reverse engineering used here is essentially an iterative process where the resin properties are unknown, while the properties for GF and composite material are known. The reverse-engineered resin properties for Young’s modulus, CLTE, and thermal conductivity are shown in Figure 10. Note that these are isotropic properties, when homogenized with the fibers the combined properties are anisotropic, based on the fiber orientations. Other properties such as specific heat, density, and so on are not direction dependent, that is, the fiber orientation does not affect them; therefore, the measured values can be directly used in Abaqus separation of resin properties though reverse engineering is not necessary.

Figure 9.

Reverse engineering processes.

Figure 10.

Reverse engineered properties for resin: (a) Young’s modulus, (b) thermal conductivity, and (c) CLTE. CLTE: coefficient of linear thermal expansion.

Plastic material model properties

The constitutive model used for modeling resin nonlinearity is defined by J2 plasticity model in Digimat.²⁸ This model is based on the Von Misses equivalent stress δ _eq defined as:

δ_{eq} = \sqrt{J_{2} (σ)} = σ_{Y} + R (p),

where σ _Y is the yield stress, $R (p)$ is the hardening stress, and p is the accumulated plastic strain. The exponential and linear law is used for the hardening model:

R (p) = k_{p} + R_{\infty} [1 - \exp (- m p)],

where k_p is the linear hardening modulus, R _∞ is the hardening modulus, and m is the hardening exponent.

The nonlinear tensile stress–strain response of the resin is shown in Figure 11. At this time, for simplicity, we assume that the parameters (yield stress, linear hardening modulus, hardening exponent, and hardening modulus) for this J2-plasticity model material remain constant with temperature.

Figure 11.

Quasi-static stress–strain curve of PP. PP: polypropylene.

FE analysis to calculate warpage

Details of the FEM for the plaque, generated using prism elements, are shown in Figure 12. The key interest here is to represent the FRP as temperature-dependent, anisotropic, nonlinear material. This is accomplished using coupling Digimat to Abaqus through material user subroutine.²⁸ Digimat updates the material properties for each element at every time increment based on the fiber orientations as well as temperature at that time in Abaqus as shown in Figure 13. The FEM analysis for the warpage calculations involves two steps: first, calculation of temperature history at each elements and second, using the temperature history as input to estimate the warpage of the plaque.

Figure 12.

Finite element model details.

Figure 13.

Details of FE analysis steps. FE: finite element.

The plaques fabricated by over-molding LFT material on sheets of unidirectional (UD) fibers require additional FE modelings. The UD fibers are modeled as one layer (t = 0.2 mm) of solid element. The fiber content is assumed to be oriented along the flow direction and the fibers are modeled to have an aspect ratio of infinity.

Results

The temperature distribution in the plaque is shown in Figure 14(a) and temperature–time history at two selected locations is shown in Figure 14(b). At any given time the temperature at different locations is different in the transient stage. Eventually the temperature becomes steady.

Figure 14.

a) Temperature distribution plaque and b) temperature–time history at two locations.

The comparison of the warpage predicted using the current methodology and the actual warpage measured using a coordinate measuring machine is shown in Figure 15. It is seen that the predicted deformation mode as well as deformation magnitude for all the three type of plaques compares well with the measured.

Figure 15.

Warpage results comparison between measurement and Computer Aided Engineering (CAE).

Conclusions and discussions

The addition of fibers can help improve structural properties such as strength and stiffness of polymers, but they also add anisotropy, which may result in differential shrinkage, and hence, warpage in the parts. In this article, we have developed a FE-based semiempirical approach to predict the warpage for a fiber-reinforced plaque in solid phase, cooled from 160°C to room temperature of 23°C. Both the chemical shrinkage and thermal shrinkage are lumped together as temperature-dependent material properties. The predicted results show good correlation with the measured deformation as well as deformed shapes. We observe that the key to a successful prediction, in this case, is the use of accurate material properties and its representation in the FEMs. We also observed that the temperature-dependent resin properties are not always readily available; therefore, experimental measurement may be needed. The resin properties are strongly influenced by the fibers as well as process condition. The reverse engineering approach where material properties for resin can be estimated through an iterative process from the combined material properties can be a very useful in such conditions. In this study, we treated only some of the material properties to be changing with temperature. We recognize that other material properties may also be a function of temperature. We selected elastic modulus, CLTE, and thermal conductivity because we wanted to choose fewest temperature-dependent parameters while keeping a strong influence on the warpage.

Footnotes

Acknowledgment

We would like to thank Duane Emerson (formerly Ticona, now Celenese) for providing the fiber-reinforced plaques used in this study.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

References

Vaidya

Chawla

Balaji

. The process and microstructure modeling of long-fiber thermoplastic composites. JOM 2008; 60(4): 43–49.

Advani

. The use of tensors to describe and predict fiber orientation in short fiber composites. J Rheol 1987; 31(8): 751.

Osswald

. Material science of polymers for engineers. 3rd ed. Cincinnati: Hanser Publishers, 2012.

Fischer

. Handbook of molded part shrinkage and warpage. 2nd ed. Amsterdam: Elsevier/William Andrew, 2013.

Zoetelief

Douven

LFA

Housz

AJI

. Residual thermal stresses in injection molded products. Polym Eng Sci 1996; 36(14): 1886–1896.

Shen

. Numerical simulation for effects of injection mold cooling on warpage and residual stresses. Polym-Plast Technol Eng 2003; 42(5): 971–982.

Zheng

Kennedy

Phan-Thien

. Thermoviscoelastic simulation of thermally and pressure-induced stresses in injection moulding for the prediction of shrinkage and warpage for fibre-reinforced thermoplastics. J Non-Newton. Fluid Mech 1999; 84(2–3): 159–190.

Lee

Kwon

. Modeling and numerical simulation of residual stresses and birefringence in injection molded center-gated disks. J Mater Process Technol 2001; 111(1–3): 214–218.

Choi

D.-S

Y.-T

. Prediction of shrinkage and warpage in consideration of residual stress in integrated simulation of injection molding. Compos Struct 1999; 47(1–4): 655–665.

10.

Kikuchi

Koyama

. The relation between thickness and warpage in a disk injection molded from fiber reinforced PA66. Polym Eng Sci 1996; 36(10): 1317–1325.

11.

Osswald

. Experimental investigation into the effects of fountain flow on fiber-matrix. Paper presented at the 44th CIRP International Conference on Manufacturing Systems. Madison, Wisconsin, USA on 1-3 June 2011.

12.

Hine

Duckett

. Fiber orientation structures and mechanical properties of injection molded short glass fiber reinforced ribbed plates. Polym Compos 2004; 25(3): 237–254.

13.

Kamal

Lai-Fook

Hernandez-Aguilar

. Residual thermal stresses in injection moldings of thermoplastics: a theoretical and experimental study. Polym Eng Sci 2002; 42(5): 1098–1114.

14.

Kikuchi

Koyama

. Material anisotropy and warpage of nylon 66 composites. Polym Eng Sci 1994; 34(18): 1411–1418.

15.

Kikuchi

Koyama

. Warpage, anisotropy, and part thickness. Polym Eng Sci 1996; 36(10): 1326–1335.

16.

Wang

J. PVT

Properties of polymers for injection molding: Wang

(ed) Some Critical Issues for Injection Molding, Croatia. InTech, 2012, pp. 19–25.

17.

Tadmor

. Molecular orientation in injection molding. J Appl Polym Sci 1974; 18(6): 1753–1772.

18.

Bessell

Hull

Shortall

. Interface morphology and mechanical properties of unidirectional fibre reinforced nylon 6. Faraday Spec Discuss Chem Soc 1972; 2: 137.

19.

Shoemaker

Moldflow design guide: a resource for plastics engineers. Munich, Cincinnati and Hanser: Hanser Gardner Publications, 2006.

20.

Beaumont

. Successful injection molding: process, design, and simulation. Munich , Cincinnati and Hanser Publishers: Hanser Gardner Publications, 2002.

21.

Kabanemi

Vaillancourt

Wang

. Residual stresses, shrinkage, and warpage of complex injection molded products: numerical simulation and experimental validation. Polym Eng Sci 1998; 38(1): 21–37.

22.

Pontes

Oliveira

Pouzada

. Studies on the influence of the holding pressure on the orientation and shrinkage of injection molded parts. Paper presented at the ANTEC, San Francisco, 2002.

23.

Foss

. Coupling of flow simulation and structural analysis for glass-filled thermoplastics. Polym. Compos 2004; 25(4): 343–354.

24.

Ghasemi Nejhad

Gillespie

Jr Cope

. Prediction of process-induced stresses for in-situ thermoplastic filament winding of cylinders. In: Proceedings of Third International Conference CADCOMP, Computer Aided Design in Composite Material Technology. Netherlands: Springer, May 1992, pp. 225–253.

25.

Ghasemi Nejhad

Gillespie

Jr Cope

. Processing stresses for in-situ thermoplastic filament winding using the divergence method. In: Proceedings of ASME WAM, Heat Transfer Effects in Materials Processing, Anaheim, California, Vol. 233, November 1992, pp. 33–43.

26.

Eduljee

John

Gillespie

Mccullough

. Prediction of process induced thermal residual stresses in injection molded composites. J. Thermoplast. Compos. Mater 1989; 2(4): 319–333.

27.

Mori

Tanaka

. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 1973; 21(5): 571–574.

28.

Digimat 5.0.1 Users’ Manual.” e-Xstream Engineering, November 2013, http://www.e-xstream.com/sites/default/files/DIGIMAT_5.0.1_manual.pdf. pp. 663–820.

Semiempirical approach to predict shrinkage and warpage of fiber-reinforced polymers using measured material properties in finite element model

Abstract

Keywords

Introduction

Materials and methods

Experimental study

Prediction method

Mold fill process simulation to get the fiber orientation

Fiber resin homogenization process

Material properties calculations using reverse engineering

Young’s modulus

Coefficient of linear thermal expansion

Thermal conductivity

Specific heat

Reverse engineering to get the resin properties

Plastic material model properties

FE analysis to calculate warpage

Results

Conclusions and discussions

Footnotes

Acknowledgment

Declaration of Conflicting Interests

Funding

References