- Email: [email protected]
Overinjection of thermoplastic composites
Journal of Materials Processing Technology 182 (2007) 21–27
Overinjection of thermoplastic composites II. Numerical simulation A.M. Harte a,∗ , J.F. Mc Namara b a
b
Department of Civil Engineering, National University of Ireland, Galway, Ireland Department of Mechanical and Biomedical Engineering, National University of Ireland, Galway, Ireland Received 7 July 2005; received in revised form 14 June 2006; accepted 20 June 2006
Abstract During many forming processes, gaps open and close along the interface between the cooling part and the tool or mould. The influence of the gaps on the rate of heat transfer between the cooling part and the mould may be significant. In these cases, it is necessary to use a fully coupled analysis approach in modelling the process due to the two-way coupling between temperature and displacement. This phenomenon is investigated for the case of the overinjection process. Coupled finite element modelling of each step of the manufacturing process is performed. Results show very close agreement with temperature measurements and process induced deformations of the finished part. © 2006 Elsevier B.V. All rights reserved. Keywords: Overinjection; Thermoplastic; Finite element analysis; Thermomechanical interface modelling
1. Introduction This paper addresses the finite element modelling of the thermomechanical behaviour of complex thermoplastic components during forming processes. In the present case, the overinjection of a short-fibre reinforced thermoplastic onto a preformed reinforced thermoplastic base is considered. The objective of the finite element modelling is to determine whether the distortion of a part during an overinjection process can be modelled successfully. The rib stiffener, shown in Fig. 1, is used in this study to measure the feasibility of the overinjection process itself. If the deformations of the test rib can be accurately predicted, then the process-induced distortions of real products can be predicted prior to manufacture using the same procedures. The overinjection process itself is quite complex involving a number of different processing stages. It is important that each stage in the process is accurately modelled as the thermal history of the part has a significant influence on the final distortion. Measurements of the temperature in the part during different stages of the manufacturing process indicate that the development of interface gaps between the mould and the part itself have an importance influence on the rate of cooling of the part in the
mould and as a result the part warpage. An uncoupled model [1] which failed to take this into account overestimated the rate of cooling of the part in the mould and resulted in the predicted warpage being overestimated by 29%. The primary focus of this paper is the modelling of the cooling of the part using a fully coupled heat transfer/thermal stress analysis of the process, in which the deformations and temperatures are determined at the same time. Features of the model include the use of element birth/death facilities to incorporate changes in the finite element mesh during different stages of the process, the inclusion of a lack of fit analysis of the base and mould, incorporation of the influence of the packing pressure on the interface gaps, gap width and temperature dependent gap properties and non-linear temperature dependent material properties. The results of the analysis provide a complete history of the temperature, deformations and stresses in the part at every stage of the manufacturing process. Results of this coupled analysis are presented and comparisons are made with results of an uncoupled model [1] and with experimental measurements of temperature and deformation in order to determine the optimal modelling approach. 2. Background
∗
Corresponding author. Fax: +353 91 570507. E-mail address: [email protected] (A.M. Harte).
0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.06.017
In the context of the modelling considerations involved in the overinjection process, the important issues relate to injection
22
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
Fig. 1. Overinjected part.
moulding, tool–part interaction with laminated composites and resistance heating. The injection moulding process involves filling, packing and holding and solidification in the mould followed by ejection. Many researchers have concentrated in the specific phases of the process. Manzione [2] developed a model for the filling stage of the injection moulding process, which predicts the temperature and pressure distributions at the end of filling. Himasekhar et al. [3] carried out a simultaneous heat transfer and fluid flow analysis of the cooling stage of the injection moulding process, treating the part as a purely viscous fluid. They developed a software package for the simulation of heat transfer in thin plastic parts during the cooling stage of the injection moulding process. Initial conditions for the model are the temperatures from a mould filling analysis. Perfect contact between the mould and the part are assumed. Santhanam et al. [4] used elastic shell finite elements in the filling/post-filling residual stress analysis based on a viscoelastic model for the polymer. Choi and Im [5] developed an integrated 3-D finite element analysis program for the calculation of residual stress, shrinkage and warpage coupled with the filling and post-filling stages. Zheng et al. [6] examined the issue of thermal and pressure-induced stresses during the injection moulding of fibre-reinforced thermoplastics. The model developed accounted for material anisotropy due to fibre orientation. Flow-induced residual stresses were determined and subsequently used to determine warpage and shrinkage caused by relaxation of the stresses after ejection. Processed induced distortions in FRP laminates have been considered by several researchers [7–10]. Hwang and Tucker [7] examined the thermal behaviour of APC-2 laminates being cooled in a large steel mould using a 2-dimensional finite element model. Cooling channels were modelled using fixed temperature boundary conditions. Gap elements were used to model small gaps between the two halves of the mould. Saigal et al. [8] conducted a study on the effect of interface gaps on the thermal performance of a blanket for a nuclear reactor using a 3dimensional coupled temperature-displacement model. Neglecting the effect of interface gaps on the heat conductance led to a serious underestimation of the maximum temperature and the temperature drop across the blanket. A number of researchers [11–15] have investigated the resistance welding of thermoplastic composites. Xiao et al. [11] and Jacobsen et al. [12] performed thermal analyses of the process of resistance heating of APC-2 composites with an APC-2 heating
element. Two-dimensional finite element models were used with the power input modelled as a uniformly distributed heat flux. Models to illustrate the effect of the process parameters on the void content and degree of interfacial bonding in thermoplastic laminates were developed by Pitchumani et al. [16]. Past research has demonstrated that finite element codes can be used successfully to model different aspects of the processing of reinforced thermoplastic components. In general, these studies have concentrated on the analysis of a single process or phase of a process and a single material type. The present problem involves a processing setup which is considerably more complex that those mentioned above. The mix of material types involved, including both short and long fibre reinforced composites, and the fact that the behaviour both inside and outside the mould must be considered requires a more demanding sequence of analysis steps and an advanced array of model features. The implementation of these advanced modelling procedures to track the manufacture through a multi-stage process is the major contribution of the present work. 3. Part definition and process description The part selected for this study, shown in Fig. 1, is intended to represent a typical rib stiffener. The overitem material is a short glass fibre reinforced PA-6. The base item material is a compatible woven glass fibre fabric reinforced PA-6. Layers of carbon fibre reinforced polyetherimide are placed at the top and bottom of the base stack prior to compression forming. The top layer forms a heating element for the resistance heating of the base as it is necessary to raise the temperature of the base in the bond area in order to promote fusion bonding of the base and overitem. The bottom layer is included to form a balanced laminate and therefore reduce warping during cooling. The processing cycle can be summarised as follows. The injection mould is heated to a temperature of about 100 ◦ C. The preformed base is then inserted in a cavity in one half of the mould. When the mould is closed, the base then forms part of the mould. The base is heated by passing a current through the carbon fibre layer until the desired base temperature is reached. The overitem is then injected into the mould cavity adjoining the base. A cross-section through the mould showing the location of the base and overitem is given is Fig. 2. At the end of the filling of the mould, the part is left to cool in the mould for a total duration of 330 s. For the first 30 s of mould cooling, the overitem is
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
Fig. 2. Cross-section through injection mould.
subjected to a packing or holding pressure. The mould is then opened and the part is ejected and allowed to cool in air until it reaches the ambient temperature. 4. Finite element modelling of process The analysis of the thermomechanical behaviour of the part during forming and subsequent cooling initially in the mould and then in air is carried out in a number of steps which correspond to the different stages of the process. These steps can be summarised as follows: • • • • •
Heating of the base Injection of the overitem Cooling of the part in the mould Ejection of the part from the mould Cooling of the part in air
23
In order to determine the coupled temperature-displacement history during these different stages, it was necessary to develop a modelling approach which takes into account the changes in the model domain, loading and boundary conditions as the process moves through the different stages. The history of loading applied to the model is defined using a series of analysis steps corresponding to the different processing stages. The loading and boundary conditions change from step to step to reflect the physical changes which take place during the different stages of the process. The different stages are linked automatically as the nodal temperatures and displacements at the end of one step are used as initial conditions for the next step. The 2-dimensional finite element model incorporating the mould, the base and overitem originally developed using [17] is extended here. The model domain is shown shaded in Fig. 2. As the process moves through the different stages, the region to be modelled changes. Initially, the base and mould are included, the overitem is added at the injection stage and the mould is removed for the final stages. The finite element mesh changes during the analysis to reflect this as shown in Fig. 3. This is achieved by using the element birth/death facility, which allows elements to be removed during an analysis step and reactivated during a later stage. An eight-noded biquadratic displacement, bilinear temperature, coupled temperature displacement plane strain element is used in the discretisation of the base, overitem and mould. The material properties of all elements are specified as functions of temperature. The characterisation of the thermomechanical behaviour of the base and overitem is a significant problem in itself involving the specification of 31 material constants for the three materials over the processing temperature range of 20 ◦ C–260 ◦ C. This has been addressed in a separate paper by the authors [18]. The mechanical properties of the steel mould are invariant over the temperature range experienced by the mould. Compatible coupled temperature-displacement interface elements are used to model the interaction between discrete parts of the model. The four different interfaces which must be characterised are between the two parts of the mould, the overitem and the overitem mould, the base and the base mould and finally
Fig. 3. Finite element mesh.
24
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
Fig. 4. Boundary conditions and interface.
the base and the overitem mould. The locations of the interface elements are shown in Fig. 4. The properties associated with the different interface elements have a significant influence the overall cooling regime in the mould. For these elements, the gap conductance is specified as a function of both temperature and gap width. For a given temperature, the gap conductance is assumed to vary linearly from a maximum value when the gap width is zero to a minimum when the gap width is greater than or equal to 0.05 mm. At a zero gap width, the gap conductance is assumed to be equal to the mimimum thermal conductivity of the two materials forming the interface. Once a gap has opened, the gap conductance of the interface is a value corresponding to the thermal conductivity of air [19]. The relevant values for the different interfaces are given in Table 1 as a function of gap width and temperature. Note that the gap conductivity value at zero gap width is different for the interface between base and the base mould and that between the base and the overitem mould. This is because a 5 m thick layer of an electrical insulating material is placed between the heating element on top of the base and the overitem mould. The gap conductivity value for this interface is the thermal conductivity of the insulating material. The gap radiation values for the different interfaces are tabulated in Table 2. These are assumed to be temperature invariant.
Table 1 Gap conductance in W/mK Interface
A zero friction value is associated with all interface elements as a mould release agent is used. 4.1. Modelling steps The modelling steps used correspond to the processing stages outlined above. The first of these is the heating of the base to the desired temperature. The finite element mesh for this analysis step comprises the mould, the base and the interface gap elements and is shown in Fig. 3(i). The location of the interface elements is shown in Fig. 4. A coupled temperaturedisplacement analysis with a duration of 100 s is performed. Power input to the base is modelled by specifying a distributed heat flux of 0.0762 W/mm3 for those elements in the top layer of the base, which corresponds to a current of 19 amps. In the finite element model, it is assumed that the electrical energy is converted with no losses. The boundary conditions for the analysis are shown in Fig. 4(i). The top and bottom of the mould are fixed along the surfaces shown. The sides of the mould and the exposed part of the top surface of the model are radiation and convection surfaces. The radiation coefficient for these surfaces is taken as 1.81 × 10−8 W/m2 K4 . This is based on an assumed value for the emissivity of steel with a ground finish of 0.32 [20] at a temperature of 100 ◦ C. A convective heat transfer coefficient of 10 W/m2 K is assumed. Radiation and convection are both to a sink temperature of the laboratory ambient value. The remaining surfaces of the mould are insulated and are adiabatic surfaces. Symmetry boundary conditions are applied along the axis of symmetry. The initial temperature distribution in the part for this analysis is found from a stand-alone heat transfer anal-
Gap width (mm)
Gap conductance T = 20 ◦ C
T = 100 ◦ C
T = 200 ◦ C
Mould–mould
0 ≥0.05
52 0.0251
52 0.0307
0.52 0.0370
Overitem–mould
0 ≥0.05
0.386 0.0251
0.403 0.0307
0.410 0.0370
Table 2 Gap radiation coefficients in W/m2 K4
Base–base mould
0 ≥0.05
0.43 0.0251
0.495 0.0307
0.495 0.0370
Interface
Gap radiation (×108 )
Base–overitem mould
0 ≥0.05
0.172 0.0251
0.172 0.0307
0.172 0.0370
Mould–mould Overitem–mould Base–mould
0.23 1.08 0.93
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
ysis of the preheating of the mould and the insertion of the base [1]. The injection of the overitem is modelled using a propriety mould filling software package [21]. The analysis provides the temperature and pressure distributions in the overitem at the end of the filling stage. The injection of the overitem is incorporated in the finite element analysis by activating the overitem elements together with the interface elements between the overitem and mould. The overitem elements are activated at the temperature predicted by the mould filling analysis and in a stress free state. This assumption is reasonable for the overitem since it is still in a viscous state and the measured pressure distribution in the overitem is found to be negligible. The mesh for this stage is shown in Fig. 3(ii) and the location of the interface elements are shown in Fig. 4(ii). Cooling of the part in the mould takes places with a duration of 330 s. The procedure used to model this stage is a coupled temperature-displacement analysis with a duration of 330 s. The coupled analysis of this stage is computationally very intensive due to the highly non-linear coupling between the temperature and the displacement. The opening and closing of interface gaps as the part cools results in changing interface element properties at each time step which are solved in an iterative fashion. The overitem is subjected to a packing pressure for part of this period and this is modelled by applied a pressure loading to the top surface of the base, having a magnitude of 55 MPa at the start of packing reducing linearly to 25 MPa at the end of the 30 s of packing. This residual pressure is reduced linearly to zero over the next 30 s. These values are taken from pressure transducer measurements of the melt pressure during actual processing runs. It is assumed that the packing pressure does not affect the temperature distribution. After the period of cooling in the mould, the part is ejected from the mould and allowed to cool in air. This is done by removing the interface elements between the part and the mould so that there is no interaction between the two. The procedure used in this step is a geometrically nonlinear static analysis. Additional
25
radiation and convection boundary conditions are imposed on the exterior surfaces of the base and overitem. The final stage in the process, the cooling of the part in air, continues until the part cools to the ambient laboratory temperature. The procedure used in this step is a geometrically nonlinear coupled temperature-displacement analysis with a duration determined by the model reaching the ambient temperature. 5. Results and discussion 5.1. Resistance heating of base Experimental work was carried out on a large number of bases. Thermocouples were embedded in the top surface of the bases and heat-up curves for a range of current settings were recorded. Results are shown in Fig. 5 for a current setting of 19 amps since this is found to be the optimum for the processing of parts. The coupled model results compare very well with the temperature measurements from a thermocouple, which is located on the top surface of the base along the centreline. Using an uncoupled model [1], in which the influence of interface gaps is neglected, the temperature of the top surface of the base along the centreline is underestimated by 22 ◦ C after 120 s of heating. 5.2. Cooling of part in mould Measurements of the temperature in the part while it is cooling in the mould are not available. Comparing the results of the present model with an uncoupled model shows that the part cools more quickly and the shrinkage in the mould is greater for the uncoupled model. At the end of cooling the maximum temperature in the part is 184.4 ◦ C for the uncoupled model compared to 208.1 ◦ C for the coupled case. 5.3. Cooling of part in air Temperature measurements on the surface of number of parts during the initial period of cooling in air were made using an
Fig. 5. Base heating.
26
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
Fig. 6. Cooling of part in air.
Fig. 7. Deformation of part (i) at end of mould cooling and (ii) on ejection from mould.
Fig. 8. Residual deformation of part after overinjection.
infrared sensor. There was very little variance between the cooling curves for these parts. The cooling curve for a point of the top of the overitem of one of the parts is shown in Fig. 6 together with the predictions from the numerical models. This shows that the coupled model correctly predicts the temperature of the part as it emerges from the mould whereas the uncoupled model values are low. Good agreement is found between the coupled model results and the temperature measurements over the 1000 s duration of the test with the uncoupled model giving significantly lower predictions in all cases.
The final deformation of the part after it has completely cooled to ambient conditions is shown in Fig. 8. The deformations in both figures are magnified by a factor of 10 for the purposes of illustration. The average deformations at the end of the process taken from five samples are given in Table 3 along with the
Deformation (mm)
Measured value
Coupled model
Uncoupled model [1]
5.4. Deformation of part
Warpage, W Shrinkage in Dimension A Shrinkage in Dimension B Shrinkage in Dimension H
0.90 0.10 0.10 0.59
0.96 0.13 0.13 0.56
1.16 0.18 0.11 0.55
The deformations of the part at the end of cooling in the mould and at the instant of release from the mould are shown in Fig. 7.
Table 3 Deformation of the part after cooling in air
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
predicted values from the numerical modelling. The coupled model shows a distinct improvement on the uncoupled model results, with the coupled model predicting the base warpage to within 6% compared to a 29% overestimate by the uncoupled model. Both models gave good prediction for the shrinkage of the overitem. 6. Conclusions An overinjection process involving the injection of a short fibre thermoplastic onto a long fibre thermoplastic base has been successfully modelled using a coupled thermomechanical numerical simulation. Excellent agreement is found between the temperature measurements and the coupled model predictions at every stage of the manufacturing process and the computed warpage of the base is within 6% of the measured value. An uncoupled analysis, on the other hand, has been found to be less satisfactory and underestimates the centreline base temperature at the end of baseheating stage by 22 ◦ C. Also, the overitem surface temperature at the end of cooling in the mould is found to be lower than the measured values by up to 12 ◦ C and the warpage of the base at the end of processing is about 29% greater than the measured value. It is important to account for the development of interface gaps between forming parts and the mould when modelling such processes. In the present case, and in many other forming processes, these gaps have a significant effect on the rate of cooling and on the residual deformation of the finished part. The coupled approach results in significantly increased computational times compared with the uncoupled or sequential analysis approach. References [1] A.M. Harte, J.F. Mc Namara, Overinjection of thermoplastic composites, I—processing and testing of components, J. Mater. Process.Technol., 2005,. Elsevier, submitted for publication. [2] L.T. Manzione, Applications of computer aided engineering in injection moulding, in: L.T. Manzione (Ed.), Computer-Aided Engineering for Polymer Processing Series, Macmillan, NY, 1986, pp. 1–15. [3] K. Himasekhar, K.K. Wang, J. Lottey, in: R.K. Shaw (Ed.), Mold-cooling simulation in injection molding of three-dimensional thin plastic parts, ASME HTD-110, 1989, pp. 129–136.
27
[4] N. Santhanam, H.H. Chiang, K. Himasekhar, P. Tuschak, K.K. Wang, Postmolding and load-induced deformation analysis of plastic parts in the injection molding process, Proc. ABAQUS Users’ Conference, Oxford, 1991, pp. 425–440. [5] D.-S. Choi, y.-T. Im, Prediction of shrinkage and warpage in consideration of residual stress in integrated simulation of injection moulding, Compos. Struct. 47 (1999) 655–665. [6] R. Zheng, P. Kennedy, N. Phan-Thien, X.-J. Fan, Thermoviscoelastic simulation of thermally and pressure-induced stresses in injection moulding for the prediction of shrinkage and warpage for fibre-reinforced thermoplastics, J. Non-Newtonian Fluid Mech. 84 (1999) 159–190. [7] S.J. Hwang, C.L. Tucker III, Heat transfer analysis of composite fiber/thermoplastic matrix composites during manufacture, J. Comp. Mater. 3 (1990) 41–51. [8] A. Saigal, R. Saigal S. Majumdar, Coupled temperature-displacement analysis of blankets for nuclear reactors, Proc. ABAQUS Users’ Conference, Newport, RI, 1992, pp. 433–444. [9] G. Twigg, A. Poursartip, G. Fernlund, Tool-part interaction in composites processing. Part II: numerical modelling, Compos.: Part A 35 (2004) 135–141. [10] M.T. Abadi, H.R. Daghyani, S. Fariborz, Finite element analysis of thermoplastic composite plates in forming temperature, Compos. Sci. Technol. 66 (2006) 306–313. [11] X.R. Xiao, S.V. Hoa, K.N. Street, Processing and modelling of resistance welding of APC-2 composite, J. Comp. Mater. 26 (1992) 1031–1049. [12] T.B. Jacobsen, R.C. Don, J.W. Gillespie Jr., Two-dimensional thermal analysis of resistance welded thermoplastics, Polym. Eng. Sci. 29 (1989) 1722–1729. [14] A. Fosbury, S. Wang, Y.F. Pin, D.L.L. Chung, The interlaminar interface of a carbon fiber polymer-matrix composite as a resistance heating element, Composites: Part A 34 (2003) 933–940. [15] M. Hou, M. Yang, A. Beehag, Y.-W. Mai, L. Ye, Resistance welding of carbon fibre reinforced thermoplastic composite using alternative heating element, Compos. Struct. 47 (1999) 667–672. [16] R. Pitchumani, S. Ranganathan, R.C. Don, J.W. Gillespie, M.A. Lamontia, Analysis of transport phenomena governing interfacial bonding and void dynamics during thermoplastic tow-placement, Int. J. Heat Mass Transport 39 (1996) 1883–1897. [17] ABAQUS Inc., ABAQUS Analysis User’s Guide, ABAQUS Inc., Providence, R.I., USA. [18] A.M. Harte, J.F. Mc Namara, Use of micromechanical modelling in the material characterisation of overinjected thermoplastic composites, J. Mater. Process. Technol. 173 (2006) 376–383. [19] F. Kreith, M.S. Bohn, Principles of Heat Transfer, Harper & Row, New York, 1986. [20] J.P. Holman, Heat Transfer, 5th ed., McGraw-Hill, Inc., New York, 1981. [21] C-Mold, Filling and Post-filling User’s Guide. C-Mold, Ithaca, NY, USA, 1996.
Overinjection of thermoplastic composites II. Numerical simulation A.M. Harte a,∗ , J.F. Mc Namara b a
b
Department of Civil Engineering, National University of Ireland, Galway, Ireland Department of Mechanical and Biomedical Engineering, National University of Ireland, Galway, Ireland Received 7 July 2005; received in revised form 14 June 2006; accepted 20 June 2006
Abstract During many forming processes, gaps open and close along the interface between the cooling part and the tool or mould. The influence of the gaps on the rate of heat transfer between the cooling part and the mould may be significant. In these cases, it is necessary to use a fully coupled analysis approach in modelling the process due to the two-way coupling between temperature and displacement. This phenomenon is investigated for the case of the overinjection process. Coupled finite element modelling of each step of the manufacturing process is performed. Results show very close agreement with temperature measurements and process induced deformations of the finished part. © 2006 Elsevier B.V. All rights reserved. Keywords: Overinjection; Thermoplastic; Finite element analysis; Thermomechanical interface modelling
1. Introduction This paper addresses the finite element modelling of the thermomechanical behaviour of complex thermoplastic components during forming processes. In the present case, the overinjection of a short-fibre reinforced thermoplastic onto a preformed reinforced thermoplastic base is considered. The objective of the finite element modelling is to determine whether the distortion of a part during an overinjection process can be modelled successfully. The rib stiffener, shown in Fig. 1, is used in this study to measure the feasibility of the overinjection process itself. If the deformations of the test rib can be accurately predicted, then the process-induced distortions of real products can be predicted prior to manufacture using the same procedures. The overinjection process itself is quite complex involving a number of different processing stages. It is important that each stage in the process is accurately modelled as the thermal history of the part has a significant influence on the final distortion. Measurements of the temperature in the part during different stages of the manufacturing process indicate that the development of interface gaps between the mould and the part itself have an importance influence on the rate of cooling of the part in the
mould and as a result the part warpage. An uncoupled model [1] which failed to take this into account overestimated the rate of cooling of the part in the mould and resulted in the predicted warpage being overestimated by 29%. The primary focus of this paper is the modelling of the cooling of the part using a fully coupled heat transfer/thermal stress analysis of the process, in which the deformations and temperatures are determined at the same time. Features of the model include the use of element birth/death facilities to incorporate changes in the finite element mesh during different stages of the process, the inclusion of a lack of fit analysis of the base and mould, incorporation of the influence of the packing pressure on the interface gaps, gap width and temperature dependent gap properties and non-linear temperature dependent material properties. The results of the analysis provide a complete history of the temperature, deformations and stresses in the part at every stage of the manufacturing process. Results of this coupled analysis are presented and comparisons are made with results of an uncoupled model [1] and with experimental measurements of temperature and deformation in order to determine the optimal modelling approach. 2. Background
∗
Corresponding author. Fax: +353 91 570507. E-mail address: [email protected] (A.M. Harte).
0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.06.017
In the context of the modelling considerations involved in the overinjection process, the important issues relate to injection
22
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
Fig. 1. Overinjected part.
moulding, tool–part interaction with laminated composites and resistance heating. The injection moulding process involves filling, packing and holding and solidification in the mould followed by ejection. Many researchers have concentrated in the specific phases of the process. Manzione [2] developed a model for the filling stage of the injection moulding process, which predicts the temperature and pressure distributions at the end of filling. Himasekhar et al. [3] carried out a simultaneous heat transfer and fluid flow analysis of the cooling stage of the injection moulding process, treating the part as a purely viscous fluid. They developed a software package for the simulation of heat transfer in thin plastic parts during the cooling stage of the injection moulding process. Initial conditions for the model are the temperatures from a mould filling analysis. Perfect contact between the mould and the part are assumed. Santhanam et al. [4] used elastic shell finite elements in the filling/post-filling residual stress analysis based on a viscoelastic model for the polymer. Choi and Im [5] developed an integrated 3-D finite element analysis program for the calculation of residual stress, shrinkage and warpage coupled with the filling and post-filling stages. Zheng et al. [6] examined the issue of thermal and pressure-induced stresses during the injection moulding of fibre-reinforced thermoplastics. The model developed accounted for material anisotropy due to fibre orientation. Flow-induced residual stresses were determined and subsequently used to determine warpage and shrinkage caused by relaxation of the stresses after ejection. Processed induced distortions in FRP laminates have been considered by several researchers [7–10]. Hwang and Tucker [7] examined the thermal behaviour of APC-2 laminates being cooled in a large steel mould using a 2-dimensional finite element model. Cooling channels were modelled using fixed temperature boundary conditions. Gap elements were used to model small gaps between the two halves of the mould. Saigal et al. [8] conducted a study on the effect of interface gaps on the thermal performance of a blanket for a nuclear reactor using a 3dimensional coupled temperature-displacement model. Neglecting the effect of interface gaps on the heat conductance led to a serious underestimation of the maximum temperature and the temperature drop across the blanket. A number of researchers [11–15] have investigated the resistance welding of thermoplastic composites. Xiao et al. [11] and Jacobsen et al. [12] performed thermal analyses of the process of resistance heating of APC-2 composites with an APC-2 heating
element. Two-dimensional finite element models were used with the power input modelled as a uniformly distributed heat flux. Models to illustrate the effect of the process parameters on the void content and degree of interfacial bonding in thermoplastic laminates were developed by Pitchumani et al. [16]. Past research has demonstrated that finite element codes can be used successfully to model different aspects of the processing of reinforced thermoplastic components. In general, these studies have concentrated on the analysis of a single process or phase of a process and a single material type. The present problem involves a processing setup which is considerably more complex that those mentioned above. The mix of material types involved, including both short and long fibre reinforced composites, and the fact that the behaviour both inside and outside the mould must be considered requires a more demanding sequence of analysis steps and an advanced array of model features. The implementation of these advanced modelling procedures to track the manufacture through a multi-stage process is the major contribution of the present work. 3. Part definition and process description The part selected for this study, shown in Fig. 1, is intended to represent a typical rib stiffener. The overitem material is a short glass fibre reinforced PA-6. The base item material is a compatible woven glass fibre fabric reinforced PA-6. Layers of carbon fibre reinforced polyetherimide are placed at the top and bottom of the base stack prior to compression forming. The top layer forms a heating element for the resistance heating of the base as it is necessary to raise the temperature of the base in the bond area in order to promote fusion bonding of the base and overitem. The bottom layer is included to form a balanced laminate and therefore reduce warping during cooling. The processing cycle can be summarised as follows. The injection mould is heated to a temperature of about 100 ◦ C. The preformed base is then inserted in a cavity in one half of the mould. When the mould is closed, the base then forms part of the mould. The base is heated by passing a current through the carbon fibre layer until the desired base temperature is reached. The overitem is then injected into the mould cavity adjoining the base. A cross-section through the mould showing the location of the base and overitem is given is Fig. 2. At the end of the filling of the mould, the part is left to cool in the mould for a total duration of 330 s. For the first 30 s of mould cooling, the overitem is
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
Fig. 2. Cross-section through injection mould.
subjected to a packing or holding pressure. The mould is then opened and the part is ejected and allowed to cool in air until it reaches the ambient temperature. 4. Finite element modelling of process The analysis of the thermomechanical behaviour of the part during forming and subsequent cooling initially in the mould and then in air is carried out in a number of steps which correspond to the different stages of the process. These steps can be summarised as follows: • • • • •
Heating of the base Injection of the overitem Cooling of the part in the mould Ejection of the part from the mould Cooling of the part in air
23
In order to determine the coupled temperature-displacement history during these different stages, it was necessary to develop a modelling approach which takes into account the changes in the model domain, loading and boundary conditions as the process moves through the different stages. The history of loading applied to the model is defined using a series of analysis steps corresponding to the different processing stages. The loading and boundary conditions change from step to step to reflect the physical changes which take place during the different stages of the process. The different stages are linked automatically as the nodal temperatures and displacements at the end of one step are used as initial conditions for the next step. The 2-dimensional finite element model incorporating the mould, the base and overitem originally developed using [17] is extended here. The model domain is shown shaded in Fig. 2. As the process moves through the different stages, the region to be modelled changes. Initially, the base and mould are included, the overitem is added at the injection stage and the mould is removed for the final stages. The finite element mesh changes during the analysis to reflect this as shown in Fig. 3. This is achieved by using the element birth/death facility, which allows elements to be removed during an analysis step and reactivated during a later stage. An eight-noded biquadratic displacement, bilinear temperature, coupled temperature displacement plane strain element is used in the discretisation of the base, overitem and mould. The material properties of all elements are specified as functions of temperature. The characterisation of the thermomechanical behaviour of the base and overitem is a significant problem in itself involving the specification of 31 material constants for the three materials over the processing temperature range of 20 ◦ C–260 ◦ C. This has been addressed in a separate paper by the authors [18]. The mechanical properties of the steel mould are invariant over the temperature range experienced by the mould. Compatible coupled temperature-displacement interface elements are used to model the interaction between discrete parts of the model. The four different interfaces which must be characterised are between the two parts of the mould, the overitem and the overitem mould, the base and the base mould and finally
Fig. 3. Finite element mesh.
24
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
Fig. 4. Boundary conditions and interface.
the base and the overitem mould. The locations of the interface elements are shown in Fig. 4. The properties associated with the different interface elements have a significant influence the overall cooling regime in the mould. For these elements, the gap conductance is specified as a function of both temperature and gap width. For a given temperature, the gap conductance is assumed to vary linearly from a maximum value when the gap width is zero to a minimum when the gap width is greater than or equal to 0.05 mm. At a zero gap width, the gap conductance is assumed to be equal to the mimimum thermal conductivity of the two materials forming the interface. Once a gap has opened, the gap conductance of the interface is a value corresponding to the thermal conductivity of air [19]. The relevant values for the different interfaces are given in Table 1 as a function of gap width and temperature. Note that the gap conductivity value at zero gap width is different for the interface between base and the base mould and that between the base and the overitem mould. This is because a 5 m thick layer of an electrical insulating material is placed between the heating element on top of the base and the overitem mould. The gap conductivity value for this interface is the thermal conductivity of the insulating material. The gap radiation values for the different interfaces are tabulated in Table 2. These are assumed to be temperature invariant.
Table 1 Gap conductance in W/mK Interface
A zero friction value is associated with all interface elements as a mould release agent is used. 4.1. Modelling steps The modelling steps used correspond to the processing stages outlined above. The first of these is the heating of the base to the desired temperature. The finite element mesh for this analysis step comprises the mould, the base and the interface gap elements and is shown in Fig. 3(i). The location of the interface elements is shown in Fig. 4. A coupled temperaturedisplacement analysis with a duration of 100 s is performed. Power input to the base is modelled by specifying a distributed heat flux of 0.0762 W/mm3 for those elements in the top layer of the base, which corresponds to a current of 19 amps. In the finite element model, it is assumed that the electrical energy is converted with no losses. The boundary conditions for the analysis are shown in Fig. 4(i). The top and bottom of the mould are fixed along the surfaces shown. The sides of the mould and the exposed part of the top surface of the model are radiation and convection surfaces. The radiation coefficient for these surfaces is taken as 1.81 × 10−8 W/m2 K4 . This is based on an assumed value for the emissivity of steel with a ground finish of 0.32 [20] at a temperature of 100 ◦ C. A convective heat transfer coefficient of 10 W/m2 K is assumed. Radiation and convection are both to a sink temperature of the laboratory ambient value. The remaining surfaces of the mould are insulated and are adiabatic surfaces. Symmetry boundary conditions are applied along the axis of symmetry. The initial temperature distribution in the part for this analysis is found from a stand-alone heat transfer anal-
Gap width (mm)
Gap conductance T = 20 ◦ C
T = 100 ◦ C
T = 200 ◦ C
Mould–mould
0 ≥0.05
52 0.0251
52 0.0307
0.52 0.0370
Overitem–mould
0 ≥0.05
0.386 0.0251
0.403 0.0307
0.410 0.0370
Table 2 Gap radiation coefficients in W/m2 K4
Base–base mould
0 ≥0.05
0.43 0.0251
0.495 0.0307
0.495 0.0370
Interface
Gap radiation (×108 )
Base–overitem mould
0 ≥0.05
0.172 0.0251
0.172 0.0307
0.172 0.0370
Mould–mould Overitem–mould Base–mould
0.23 1.08 0.93
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
ysis of the preheating of the mould and the insertion of the base [1]. The injection of the overitem is modelled using a propriety mould filling software package [21]. The analysis provides the temperature and pressure distributions in the overitem at the end of the filling stage. The injection of the overitem is incorporated in the finite element analysis by activating the overitem elements together with the interface elements between the overitem and mould. The overitem elements are activated at the temperature predicted by the mould filling analysis and in a stress free state. This assumption is reasonable for the overitem since it is still in a viscous state and the measured pressure distribution in the overitem is found to be negligible. The mesh for this stage is shown in Fig. 3(ii) and the location of the interface elements are shown in Fig. 4(ii). Cooling of the part in the mould takes places with a duration of 330 s. The procedure used to model this stage is a coupled temperature-displacement analysis with a duration of 330 s. The coupled analysis of this stage is computationally very intensive due to the highly non-linear coupling between the temperature and the displacement. The opening and closing of interface gaps as the part cools results in changing interface element properties at each time step which are solved in an iterative fashion. The overitem is subjected to a packing pressure for part of this period and this is modelled by applied a pressure loading to the top surface of the base, having a magnitude of 55 MPa at the start of packing reducing linearly to 25 MPa at the end of the 30 s of packing. This residual pressure is reduced linearly to zero over the next 30 s. These values are taken from pressure transducer measurements of the melt pressure during actual processing runs. It is assumed that the packing pressure does not affect the temperature distribution. After the period of cooling in the mould, the part is ejected from the mould and allowed to cool in air. This is done by removing the interface elements between the part and the mould so that there is no interaction between the two. The procedure used in this step is a geometrically nonlinear static analysis. Additional
25
radiation and convection boundary conditions are imposed on the exterior surfaces of the base and overitem. The final stage in the process, the cooling of the part in air, continues until the part cools to the ambient laboratory temperature. The procedure used in this step is a geometrically nonlinear coupled temperature-displacement analysis with a duration determined by the model reaching the ambient temperature. 5. Results and discussion 5.1. Resistance heating of base Experimental work was carried out on a large number of bases. Thermocouples were embedded in the top surface of the bases and heat-up curves for a range of current settings were recorded. Results are shown in Fig. 5 for a current setting of 19 amps since this is found to be the optimum for the processing of parts. The coupled model results compare very well with the temperature measurements from a thermocouple, which is located on the top surface of the base along the centreline. Using an uncoupled model [1], in which the influence of interface gaps is neglected, the temperature of the top surface of the base along the centreline is underestimated by 22 ◦ C after 120 s of heating. 5.2. Cooling of part in mould Measurements of the temperature in the part while it is cooling in the mould are not available. Comparing the results of the present model with an uncoupled model shows that the part cools more quickly and the shrinkage in the mould is greater for the uncoupled model. At the end of cooling the maximum temperature in the part is 184.4 ◦ C for the uncoupled model compared to 208.1 ◦ C for the coupled case. 5.3. Cooling of part in air Temperature measurements on the surface of number of parts during the initial period of cooling in air were made using an
Fig. 5. Base heating.
26
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
Fig. 6. Cooling of part in air.
Fig. 7. Deformation of part (i) at end of mould cooling and (ii) on ejection from mould.
Fig. 8. Residual deformation of part after overinjection.
infrared sensor. There was very little variance between the cooling curves for these parts. The cooling curve for a point of the top of the overitem of one of the parts is shown in Fig. 6 together with the predictions from the numerical models. This shows that the coupled model correctly predicts the temperature of the part as it emerges from the mould whereas the uncoupled model values are low. Good agreement is found between the coupled model results and the temperature measurements over the 1000 s duration of the test with the uncoupled model giving significantly lower predictions in all cases.
The final deformation of the part after it has completely cooled to ambient conditions is shown in Fig. 8. The deformations in both figures are magnified by a factor of 10 for the purposes of illustration. The average deformations at the end of the process taken from five samples are given in Table 3 along with the
Deformation (mm)
Measured value
Coupled model
Uncoupled model [1]
5.4. Deformation of part
Warpage, W Shrinkage in Dimension A Shrinkage in Dimension B Shrinkage in Dimension H
0.90 0.10 0.10 0.59
0.96 0.13 0.13 0.56
1.16 0.18 0.11 0.55
The deformations of the part at the end of cooling in the mould and at the instant of release from the mould are shown in Fig. 7.
Table 3 Deformation of the part after cooling in air
A.M. Harte, J.F. Mc Namara / Journal of Materials Processing Technology 182 (2007) 21–27
predicted values from the numerical modelling. The coupled model shows a distinct improvement on the uncoupled model results, with the coupled model predicting the base warpage to within 6% compared to a 29% overestimate by the uncoupled model. Both models gave good prediction for the shrinkage of the overitem. 6. Conclusions An overinjection process involving the injection of a short fibre thermoplastic onto a long fibre thermoplastic base has been successfully modelled using a coupled thermomechanical numerical simulation. Excellent agreement is found between the temperature measurements and the coupled model predictions at every stage of the manufacturing process and the computed warpage of the base is within 6% of the measured value. An uncoupled analysis, on the other hand, has been found to be less satisfactory and underestimates the centreline base temperature at the end of baseheating stage by 22 ◦ C. Also, the overitem surface temperature at the end of cooling in the mould is found to be lower than the measured values by up to 12 ◦ C and the warpage of the base at the end of processing is about 29% greater than the measured value. It is important to account for the development of interface gaps between forming parts and the mould when modelling such processes. In the present case, and in many other forming processes, these gaps have a significant effect on the rate of cooling and on the residual deformation of the finished part. The coupled approach results in significantly increased computational times compared with the uncoupled or sequential analysis approach. References [1] A.M. Harte, J.F. Mc Namara, Overinjection of thermoplastic composites, I—processing and testing of components, J. Mater. Process.Technol., 2005,. Elsevier, submitted for publication. [2] L.T. Manzione, Applications of computer aided engineering in injection moulding, in: L.T. Manzione (Ed.), Computer-Aided Engineering for Polymer Processing Series, Macmillan, NY, 1986, pp. 1–15. [3] K. Himasekhar, K.K. Wang, J. Lottey, in: R.K. Shaw (Ed.), Mold-cooling simulation in injection molding of three-dimensional thin plastic parts, ASME HTD-110, 1989, pp. 129–136.
27
[4] N. Santhanam, H.H. Chiang, K. Himasekhar, P. Tuschak, K.K. Wang, Postmolding and load-induced deformation analysis of plastic parts in the injection molding process, Proc. ABAQUS Users’ Conference, Oxford, 1991, pp. 425–440. [5] D.-S. Choi, y.-T. Im, Prediction of shrinkage and warpage in consideration of residual stress in integrated simulation of injection moulding, Compos. Struct. 47 (1999) 655–665. [6] R. Zheng, P. Kennedy, N. Phan-Thien, X.-J. Fan, Thermoviscoelastic simulation of thermally and pressure-induced stresses in injection moulding for the prediction of shrinkage and warpage for fibre-reinforced thermoplastics, J. Non-Newtonian Fluid Mech. 84 (1999) 159–190. [7] S.J. Hwang, C.L. Tucker III, Heat transfer analysis of composite fiber/thermoplastic matrix composites during manufacture, J. Comp. Mater. 3 (1990) 41–51. [8] A. Saigal, R. Saigal S. Majumdar, Coupled temperature-displacement analysis of blankets for nuclear reactors, Proc. ABAQUS Users’ Conference, Newport, RI, 1992, pp. 433–444. [9] G. Twigg, A. Poursartip, G. Fernlund, Tool-part interaction in composites processing. Part II: numerical modelling, Compos.: Part A 35 (2004) 135–141. [10] M.T. Abadi, H.R. Daghyani, S. Fariborz, Finite element analysis of thermoplastic composite plates in forming temperature, Compos. Sci. Technol. 66 (2006) 306–313. [11] X.R. Xiao, S.V. Hoa, K.N. Street, Processing and modelling of resistance welding of APC-2 composite, J. Comp. Mater. 26 (1992) 1031–1049. [12] T.B. Jacobsen, R.C. Don, J.W. Gillespie Jr., Two-dimensional thermal analysis of resistance welded thermoplastics, Polym. Eng. Sci. 29 (1989) 1722–1729. [14] A. Fosbury, S. Wang, Y.F. Pin, D.L.L. Chung, The interlaminar interface of a carbon fiber polymer-matrix composite as a resistance heating element, Composites: Part A 34 (2003) 933–940. [15] M. Hou, M. Yang, A. Beehag, Y.-W. Mai, L. Ye, Resistance welding of carbon fibre reinforced thermoplastic composite using alternative heating element, Compos. Struct. 47 (1999) 667–672. [16] R. Pitchumani, S. Ranganathan, R.C. Don, J.W. Gillespie, M.A. Lamontia, Analysis of transport phenomena governing interfacial bonding and void dynamics during thermoplastic tow-placement, Int. J. Heat Mass Transport 39 (1996) 1883–1897. [17] ABAQUS Inc., ABAQUS Analysis User’s Guide, ABAQUS Inc., Providence, R.I., USA. [18] A.M. Harte, J.F. Mc Namara, Use of micromechanical modelling in the material characterisation of overinjected thermoplastic composites, J. Mater. Process. Technol. 173 (2006) 376–383. [19] F. Kreith, M.S. Bohn, Principles of Heat Transfer, Harper & Row, New York, 1986. [20] J.P. Holman, Heat Transfer, 5th ed., McGraw-Hill, Inc., New York, 1981. [21] C-Mold, Filling and Post-filling User’s Guide. C-Mold, Ithaca, NY, USA, 1996.