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Simulation of solidification and the resulting mechanical properties of polypropylene
COMPUTATIONAL MATERIALS SCIENCE Computational Materials Science 7 ( 1996) 253-256
Simulation of solidification and the resulting mechanical properties of polypropylene W. Michaeli Institutfir Kunststoflerarbeitung,
*, H. Keller D-52056 Aachen. Germany
Abstract During the processing of thermoplastics the macromolecules undergo several influences due to the local flow direction and shear stresses. Accordingly, in the final part a wide distribution of molecular orientation and degree of crystallinity can be found, which both have a significant influence on the mechanical properties of semicrystalline polymers. This non-isotropic behavior is to be simulated with a specifically adjusted deformation model, consisting of a parallel circuit of Maxwell-elements. Keywords:
Thermoplastics; Deformation model; Molecular orientation; Crystallization
1. Introduction During the macromolecules
processing of thermoplastics the undergo several influences due to
the local flow direction and shear stresses. Accordingly in the final part depending on the local flow history and cooling process a wide distribution of molecular orientation and degree of crystallinity can be found, which both have a significant influence on the mechanical properties of semicrystalline polymers, as Young’s modulus, elongation-at-break and yield stress [II.
2. Morphologic characteristics Molecular orientation can be judged by two characteristics namely direction and value. The direction
* Corresponding author. Tel.: + 49-241- 1802750; fax: -t 49241-1802752.
of the molecular orientation is determined by the direction of the velocity vectors. Its value results from the stresses at the point of freezing. These stresses can be derived from the local velocity field which causes shear and strain deformations. The calculation is different for two areas of the flow field. In the area of the flow front the fountain flow effect has a big influence on the velocity field. Elongational deformations cause the molecular orientation close to the cavity walls. Behind the flow front shear stresses have the major influence on molecular orientation. The calculation is made for different layers. The orientation of each layer is the result of the integration over the processing time until the complete solidification of the layer is reached (Fig. 1). During the cooling phase crystals occur and grow to globular spherolites (Fig. 2). In the quiescent melt their size and fraction of the total volume mainly depends on the cooling rate. A second important factor that strongly influences the emerging spherolites’ shape and size is the shear stress close to the
Copyright 0 1996 Elsevier Science B.V. All rights reserved. PII SO927-0256(96)00089-4
0927-0256/%/$15.00
254
W. Michaeli.
H. Keller/
Compututionul
mould walls during the filling phase, the flow induced stress. As a result, spherolites near the surface of the mould are much smaller than those in the central layer and are highly oriented and the degree of crystallinity is significantly higher close to the surface than it is in the center. The boundary layers’ thickness depends mainly on flow path and flow history. Therefore the simulation model is divided into two cases: melt in motion and quiescent conditions. During the filling and holding phase when melt movement is possible, the crystallization is calculated with a modified Avrami equation. In this equa-
Matrrrds
Science
7 (1996) 253-256
tion a stress-proportional factor is added. The stresses are calculated the same way as for the molecular orientation. There is also a distinction between the areas of flow front and behind the flow front for the calculation of shear-induced crystallization. The increase of temperature because of crystallization kinetics is also incorporated into the model. The orientational anisotropy causes an anisotropy of major mechanical properties both elastic and plastic as Young’s modulus, elongation-at-break and yield stress or rather creep behavior in general. On the other hand the mechanical behavior of boundary layers and central layers differ considerably, so the
Calculation of the Flow Process
Shear Flow at the Flow Front
Extensional Flow at the Flow Front
Simulation of Microstructure Boundary Layer
Calculated Orientation Profile
5
Morphological Analysis
Fig.
I. Modelling of molecular orientation.
W. Michaeli, H. Keller/
Computational Materials Science 7 (1996) 253-256
boundary layer
melt flow direction
al Fig. 2. Cross-sectional view of the microstructure.
boundary layers’ share of the overall thickness is also an important value.
3. Deformation
255
can be determined and it is possible to calculate the material’s response to external loads up to periods of 10.000 hours. The deformation model has been implemented in the FEA system ABAQUS as a usersubroutine @MAT). Up to now anisotropy of material behavior in injection moulded parts had been neglected in mechanical finite element analysis. This is not longer acceptable since designers have to exploit material’s potential as good as possible to increase the chances for plastic parts to be used in highly demanding technical fields and to lower costs for research and development. To adjust the deformation model to this aim IKV is working on an extension to orthotropy mechanical behavior. This restriction to general anisotropy in all three dimensions is permissible, because injection moulded parts generally consist mainly of flat, two-dimensional basic geometries as wall or rib sections. To consider of orthotropic material behavior in the deformation model Hill’s equations will be implemented as an anisotropic flow condition. Therefore it is necessary to know the stiffness tensor (spring stiffness of the Maxwell elements) and the coefficients of the Hill equations for every integration point during the simulation. With the Hill equations the creep rate of each damper unit can be determined.
model
At IKV the deformation model was developed, which is a numerical model for the simulation of nonlinear-viscoelastic material behavior. It has been tested during the last 10 years on different polymers and showed good results for the simulation of static and dynamic loads under variable boundary conditions, for example changing temperatures [2]. The deformation model consists of 20 Maxwell springdamper elements with different stiffness values and flow functions for each element. These Maxwell elements are arranged in a parallel way. By superposing the separate element’s stress-strain curves the material characteristics can be approximated properly (Fig. 3). The deformation model has to be calibrated by several tensile tests under variation of temperature and tensile velocity which needs about one week. After applying the time-temperature shift principle to the acquired data the model parameters
i = const.
Strain E Fig. 3. Approximation of stress-strain behaviour with the deformation model (elements stress-strain curves: u,. 0; and a,; superposed stress-strain curve: Lri).
256
W. Michuelr, H. Kelkr/
Compururiod
From this procedure the FE program gets a specific distribution of element strain into elastic and plastic components for the two main directions in every element of the FE net. The orthotropic stressstrain behavior of thermoplastics can be simulated this way with much higher accuracy than before. The different behavior of layer near the surface of the mould and those inside the mould is to be simulated by an approach that defines the part as consisting of single layers forming a laminate. The respective layers’ properties have to be determined by a combination of tensile and bending tests. Furthermore the central layer’s properties are to be verified with specimens for which the boundary layers have been removed subsequently.
Matrriu1.s Science 7 (1996) 253-256
Acknowledgements The described work was supported by Deutsche Forschungsgemeinschaft (DFG) as a part of SFB 370 at RWTH Aachen. The investigated material is a polypropylene Vestolen P 7000 which was donated by Vestolen GmbH. We are very grateful for this contribution.
References
III A. Troost et al., Final Report, SFB 106, RWTH Aachen (1991). [2] E. Schmachtenberg, Die mechanischen Eigenschaften nichtlinear viskoelastischer Werkstoffe. Dissertation at the RWTH Aachen (1986).
Simulation of solidification and the resulting mechanical properties of polypropylene W. Michaeli Institutfir Kunststoflerarbeitung,
*, H. Keller D-52056 Aachen. Germany
Abstract During the processing of thermoplastics the macromolecules undergo several influences due to the local flow direction and shear stresses. Accordingly, in the final part a wide distribution of molecular orientation and degree of crystallinity can be found, which both have a significant influence on the mechanical properties of semicrystalline polymers. This non-isotropic behavior is to be simulated with a specifically adjusted deformation model, consisting of a parallel circuit of Maxwell-elements. Keywords:
Thermoplastics; Deformation model; Molecular orientation; Crystallization
1. Introduction During the macromolecules
processing of thermoplastics the undergo several influences due to
the local flow direction and shear stresses. Accordingly in the final part depending on the local flow history and cooling process a wide distribution of molecular orientation and degree of crystallinity can be found, which both have a significant influence on the mechanical properties of semicrystalline polymers, as Young’s modulus, elongation-at-break and yield stress [II.
2. Morphologic characteristics Molecular orientation can be judged by two characteristics namely direction and value. The direction
* Corresponding author. Tel.: + 49-241- 1802750; fax: -t 49241-1802752.
of the molecular orientation is determined by the direction of the velocity vectors. Its value results from the stresses at the point of freezing. These stresses can be derived from the local velocity field which causes shear and strain deformations. The calculation is different for two areas of the flow field. In the area of the flow front the fountain flow effect has a big influence on the velocity field. Elongational deformations cause the molecular orientation close to the cavity walls. Behind the flow front shear stresses have the major influence on molecular orientation. The calculation is made for different layers. The orientation of each layer is the result of the integration over the processing time until the complete solidification of the layer is reached (Fig. 1). During the cooling phase crystals occur and grow to globular spherolites (Fig. 2). In the quiescent melt their size and fraction of the total volume mainly depends on the cooling rate. A second important factor that strongly influences the emerging spherolites’ shape and size is the shear stress close to the
Copyright 0 1996 Elsevier Science B.V. All rights reserved. PII SO927-0256(96)00089-4
0927-0256/%/$15.00
254
W. Michaeli.
H. Keller/
Compututionul
mould walls during the filling phase, the flow induced stress. As a result, spherolites near the surface of the mould are much smaller than those in the central layer and are highly oriented and the degree of crystallinity is significantly higher close to the surface than it is in the center. The boundary layers’ thickness depends mainly on flow path and flow history. Therefore the simulation model is divided into two cases: melt in motion and quiescent conditions. During the filling and holding phase when melt movement is possible, the crystallization is calculated with a modified Avrami equation. In this equa-
Matrrrds
Science
7 (1996) 253-256
tion a stress-proportional factor is added. The stresses are calculated the same way as for the molecular orientation. There is also a distinction between the areas of flow front and behind the flow front for the calculation of shear-induced crystallization. The increase of temperature because of crystallization kinetics is also incorporated into the model. The orientational anisotropy causes an anisotropy of major mechanical properties both elastic and plastic as Young’s modulus, elongation-at-break and yield stress or rather creep behavior in general. On the other hand the mechanical behavior of boundary layers and central layers differ considerably, so the
Calculation of the Flow Process
Shear Flow at the Flow Front
Extensional Flow at the Flow Front
Simulation of Microstructure Boundary Layer
Calculated Orientation Profile
5
Morphological Analysis
Fig.
I. Modelling of molecular orientation.
W. Michaeli, H. Keller/
Computational Materials Science 7 (1996) 253-256
boundary layer
melt flow direction
al Fig. 2. Cross-sectional view of the microstructure.
boundary layers’ share of the overall thickness is also an important value.
3. Deformation
255
can be determined and it is possible to calculate the material’s response to external loads up to periods of 10.000 hours. The deformation model has been implemented in the FEA system ABAQUS as a usersubroutine @MAT). Up to now anisotropy of material behavior in injection moulded parts had been neglected in mechanical finite element analysis. This is not longer acceptable since designers have to exploit material’s potential as good as possible to increase the chances for plastic parts to be used in highly demanding technical fields and to lower costs for research and development. To adjust the deformation model to this aim IKV is working on an extension to orthotropy mechanical behavior. This restriction to general anisotropy in all three dimensions is permissible, because injection moulded parts generally consist mainly of flat, two-dimensional basic geometries as wall or rib sections. To consider of orthotropic material behavior in the deformation model Hill’s equations will be implemented as an anisotropic flow condition. Therefore it is necessary to know the stiffness tensor (spring stiffness of the Maxwell elements) and the coefficients of the Hill equations for every integration point during the simulation. With the Hill equations the creep rate of each damper unit can be determined.
model
At IKV the deformation model was developed, which is a numerical model for the simulation of nonlinear-viscoelastic material behavior. It has been tested during the last 10 years on different polymers and showed good results for the simulation of static and dynamic loads under variable boundary conditions, for example changing temperatures [2]. The deformation model consists of 20 Maxwell springdamper elements with different stiffness values and flow functions for each element. These Maxwell elements are arranged in a parallel way. By superposing the separate element’s stress-strain curves the material characteristics can be approximated properly (Fig. 3). The deformation model has to be calibrated by several tensile tests under variation of temperature and tensile velocity which needs about one week. After applying the time-temperature shift principle to the acquired data the model parameters
i = const.
Strain E Fig. 3. Approximation of stress-strain behaviour with the deformation model (elements stress-strain curves: u,. 0; and a,; superposed stress-strain curve: Lri).
256
W. Michuelr, H. Kelkr/
Compururiod
From this procedure the FE program gets a specific distribution of element strain into elastic and plastic components for the two main directions in every element of the FE net. The orthotropic stressstrain behavior of thermoplastics can be simulated this way with much higher accuracy than before. The different behavior of layer near the surface of the mould and those inside the mould is to be simulated by an approach that defines the part as consisting of single layers forming a laminate. The respective layers’ properties have to be determined by a combination of tensile and bending tests. Furthermore the central layer’s properties are to be verified with specimens for which the boundary layers have been removed subsequently.
Matrriu1.s Science 7 (1996) 253-256
Acknowledgements The described work was supported by Deutsche Forschungsgemeinschaft (DFG) as a part of SFB 370 at RWTH Aachen. The investigated material is a polypropylene Vestolen P 7000 which was donated by Vestolen GmbH. We are very grateful for this contribution.
References
III A. Troost et al., Final Report, SFB 106, RWTH Aachen (1991). [2] E. Schmachtenberg, Die mechanischen Eigenschaften nichtlinear viskoelastischer Werkstoffe. Dissertation at the RWTH Aachen (1986).