Plastic Component

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Plastic component, Dimensioning

General

For designers of plastic products, the task increasingly involves selecting materials, dimensioning and designing components using scientifically based, plastics-specific working methods.

Strength and deformation verification

The current approach to dimensioning plastic components is characterised by the fact that permissible stresses σ_zul or permissible deformations ε_zul are used as decision criteria when determining the cross-sections and their geometry. The stress state of the design, which is usually multiaxial, is compared with a permissible material-dependent stress using a comparative stress hypothesis [1–3]. This permissible stress is obtained, for example, when dimensioning with respect to the yield stress σ_y.

\sigma _{zul}\,=\,{\frac {\sigma _{y}}{p}}

where p represents a safety factor that includes uncertainties in the material properties, e.g. batch influences and inadequacies in the calculation methods (load assumptions, etc., risk to people and property). An analogous procedure is possible for dimensioning with respect to elongation. Taking into account the requirements for technological implementation and their control during production monitoring, which are assumed in the design, it is then possible to execute the design, whereby aspects of toughness are not taken into account here. This procedure is shown schematically in the left part of the Figure.

Fig. :

Diagram for evaluating toughness properties of polymer-based products

Toughness verification

The first approaches to taking into account aspects of material failure due to brittle fracture (see: fracture types) in dimensioning exist for the toughness assessment of pipes [4–8]. However, the use of notch impact strength acN to determine fracture energy does not provide any significant improvement in terms of informative value [5, 6]. The most significant disadvantage of notch impact strength is that it is an integral parameter and no stress and strain values can be specified, i.e. notch impact strength values only allow a qualitative evaluation of the materials, as it is not possible to transfer the results obtained from the test specimen to designs. An additional problem is associated with the crack propagation energies that occur in impact load–deflection diagrams for filled and reinforced plastics (see: Instrumented Charpy impact test and ICIT types of impact load–deflection diagrams) [5].

Since brittle fracture sensitivity is influenced not only by the stress state but also by temperature and loading speed, and since brittle fracture (see: fracture types) occurs in the elastic and viscoelastic range, concepts have been developed to estimate the changes in properties that can be expected in the elastic parameters E and G as a result of the high strain rates (see: deformation rate basics) occurring due to impact or shock. This is achieved with the help of the time–temperature displacement law [9]. This law involves a correlation between the stress time and temperature and allows the measured values obtained at defined temperatures or stress times to be transferred to other times and temperatures.

This method then makes it possible, for example, to determine the stress rate dσ/dt from the strain rate dε/dt (see: deformation rate applications), taking into account the speed-induced shift in the elastic modulus–temperature curve, and to compare it with stress rates such as those occurring in puncture impact test. In this way, it is possible to make better use of the information available for assessing brittle fracture susceptibility (see: brittle fracture promoting factors).

Brittle fracture safety verification with fracture mechanics parameters

A brittle fracture safety verification, which can be carried out in analogy to the strength or deformation verification, is possible with the help of fracture mechanics concepts. For functional or manufacturing-related notches (grooves, cross-sectional changes, etc.) in the moulded part (see: moulding compound), a stress intensity factor [11] or, in the case of larger plastic deformations, such as those generally occurring in plastics, a J-value must be calculated by numerical integration from the expected load using finite element method (FEM) [10]. This stress intensity factor or J-value must be less than the permissible stress intensity factor K_Izul or the permissible value J_Izul. The permissible characteristic values for toughness are calculated from the determined geometry-independent material characteristics K_Id and J_Id (see: geometry criterion) according to the equations

K_{Izul}\,=\,{\frac {K_{Id}}{q_{1}}}

J_{Izul}\,=\,{\frac {J_{Id}}{q_{2}}}

where q₁ and q₂ represent safety factors that take into account uncertainties in modelling and material properties [4].

To ensure a high level of technical safety and reliability, evaluation methods based on yield fracture mechanics (YFM) will be used to a greater extent in material selection and dimensioning due to the elastic-plastic fracture behaviour.

Transferability of test specimens – components

Despite the generally accepted knowledge regarding the transferability of geometry-independent fracture mechanical values determined on small test specimens (standard test specimens) [5, 6, 12], further investigations are necessary to evaluate the fracture behaviour (see: geometry criterion) of semi-finished products and finished parts in order to confirm the validity of the failure concepts of yield fracture mechanics (see also: Levels of knowledge in fracture mechanics).

References

[1]	Erhard, G.: Konstruieren mit Kunststoffen, Carl Hanser, Munich Vienna (1993) 1st Edition, pp. 99–108 (ISBN 3-446-17397-8; see AMK-Library under G 33)
[2]	Ehrenstein, G. W.: Mit Kunststoffen konstruieren – Eine Einführung. Carl Hanser, Munich Vienna (2007) (ISBN 978-3-446-41322-1; see AMK-Library under G 42)
[3]	Michaeli, W., Brinkmann, T., Lessenich-Henkys, V.: Kunststoff-Bauteile werkstoffgerecht konstruieren. Carl Hanser, Munich Vienna (1995) (ISBN 3-446-17535-0; see AMK-Library under G 130)
[4]	May, M., Hoffmann, H., Grellmann, W.: Anwendungen der dynamischen Bruchzähigkeit zur Beurteilung der Zähigkeitseigenschaften. Plaste und Kautschuk 31 (1984) 1, pp. 26–30 Download as pdf
[5]	Grellmann, W.: Bewertung der Zähigkeitseigenschaften durch bruchmechanische Kennwerte. In: Schmiedel, H. (Eds.): Handbuch der Kunststoffprüfung. Carl Hanser, Munich Vienna (1992) pp. 139–183, (ISBN 978-3446163362; see AMK-Library under A 3)
[6]	Grellmann, W., Seidler, S. (Eds.): Deformation and Fracture Behaviour of Polymers. Springer, Berlin Heidelberg (2001) (ISBN 978-3540412472; see AMK-Library under A 7)
[7]	Jungbluth, M.: Untersuchungen zum Verformungs- und Bruchverhalten von PVCC-Werkstoffen. PhD thesis, TH Leuna-Merseburg (1987) (see AMK-Library under B 1-1) (Short summary/Content)
[8]	Brown, N., Lu, X.: The Dependence of Rapid Crack Propagation in Polyethylene Pipes on the Plane Stress Fracture Energy of the Resin. Polymer Engng. and Science 41 (2001) 1140–1145, https://doi.org/10.1002/pen.10815
[9]	Menges, G., Schlüter, H., Jonas, R.: Ermittlung von Werkstoff- sowie Festigkeitskennzahlen für die Konstruktion und Dimensionierung von spritzgegossenen Kunststofferzeugnissen. Forschungsbericht des Landes Nordrhein-Westfalen No. 2892 Köln/Opladen, Westdeutscher Verlag, 1979
[10]	Rossmanith, H.-P. (Hrsg.): Finite Elemente in der Bruchmechanik. Springer, Berlin Heidelberg (1982) (ISBN 978-3-7091-2297-6)
[11]	Tada, H., Paris, P. C., Irwin, G. R.: The Stress Analysis of Cracks Handbook. 3th Ed., ASME Press, New York (2000) (ISBN 978-1-8605-8304-9); https://doi.org/10.1115/1.801535
[12]	Grellmann, W., Seidler, S., Lach, R.: Geometrieunabhängige bruchmechanische Werkstoffkenngrößen – Voraussetzung für die Zähigkeitscharakterisierung von Kunststoffen. Materialwissenschaften und Werkstofftechnik 32 (2001) pp. 552–561, DOI: https://onlinelibrary.wiley.com/doi/10.1002/1521-4052(200106)32:6%3C552::AID-MAWE552%3E3.0.CO;2-O;