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{{Language_sel|LANG=ger|ARTIKEL=Kunststoffbauteil}}
{{PSM_Infobox}}
Plastic component, Dimensioning
__FORCETOC__

==General==

For designers of [[Plastics|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.

{|
|-
|width="20px"|
|width="500px" | <math>\sigma_{zul}\,=\,\frac{\sigma_y}{p}</math>
|}

where p represents a safety factor that includes uncertainties in the [[Material & Werkstoff|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|toughness]] are not taken into account here. This procedure is shown schematically in the left part of the '''Figure'''.

[[File:Plastic Component Fig.jpg|600px]]
{|
|- valign="top"
|width="50px"|'''Fig. ''':
|width="600px" |Diagram for evaluating toughness properties of polymer-based products
|}

==Toughness verification==

The first approaches to taking into account aspects of material [[Failure Analysis – Basics|failure]] due to brittle fracture (see: [[Fracture Types|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 [[Material Parameter|parameter]] and no stress and strain values can be specified, i.e. notch impact strength values only allow a qualitative evaluation of the [[Material & Werkstoff|materials]], as it is not possible to transfer the results obtained from the test [[Specimen|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|Instrumented Charpy impact test]] and [[ICIT – Types of Impact Load–Deflection Diagrams|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|fracture types]]) occurs in the elastic and [[Viscoelastic Material Behaviour|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: [[Strain Rate Basics|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 Value|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 d''σ''/d''t'' from the strain rate d''ε''/d''t'' (see: [[Strain Rate Applications|deformation rate applications]]), taking into account the [[Velocity|speed]]-induced shift in the elastic modulus–temperature curve, and to compare it with stress rates such as those occurring in [[Puncture Impact Test|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 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|fracture mechanics]] concepts. For functional or manufacturing-related [[Notch|notches]] (grooves, cross-sectional changes, etc.) in the moulded part (see: [[Moulding Compound|moulding compound]]), a [[Fracture Mechanics|stress intensity factor]] [11] or, in the case of larger plastic deformations, such as those generally occurring in plastics, a [[J-Integral Evaluation Methods (Overview)|''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|geometry criterion]]) according to the equations

{|
|-
|width="20px"|
|width="500px" | <math>K_{Izul}\,=\,\frac{K_{Id}}{q_1}</math> 
|}
{|
|-
|width="20px"|
|width="500px" | <math>J_{Izul}\,=\,\frac{J_{Id}}{q_2}</math>
|}

where ''q''1 and ''q''2 represent safety factors that take into account uncertainties in modelling and [[Material Parameter|material]] properties [4].

To ensure a high level of technical safety and reliability, evaluation methods based on [[Fracture Mechanics#Elastic–plastic fracture mechanics (EPFM)|yield fracture mechanics (YFM)]] will be used to a greater extent in [[Material & Werkstoff|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 [[Material Value|mechanical values]] determined on small test [[Specimen|specimens]] (standard test specimens) [5, 6, 12], further investigations are necessary to evaluate the fracture behaviour (see: [[Geometry Criterion|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|Levels of knowledge in fracture mechanics]]).

==See also==

* [[Component Testing|Component testing]]
* [[Fracture Behaviour of Plastics Components|Fracture behaviour of plastic components]]
* [[Fracture Mechanics|Fracture mechanics]]
* [[Fracture Mechanical Testing|Fracture mechanical testing]]
* [[Composite Materials Testing|Composite materials testing]]
* [[Puncture Impact Test|Puncture impact test]]
* [[Levels of Knowledge in Fracture Mechanics|Levels of knowledge in fracture mechanics]]

==References==

{|
|-valign="top
|[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)
|-valign="top
|[2]
|[[Ehrenstein, Gottfried W.|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)
|-valign="top
|[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)
|-valign="top
|[4]
|May, M., Hoffmann, H., [[Grellmann, Wolfgang|Grellmann, W.]]: Anwendungen der dynamischen Bruchzähigkeit zur Beurteilung der Zähigkeitseigenschaften. Plaste und Kautschuk 31 (1984) 1, pp. 26–30 [https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/May_Anwendung_der_dynamischen_Bruchzaehigkeit.pdf Download as pdf]
|-valign="top
|[5]
|[https://www.researchgate.net/profile/Wolfgang-Grellmann 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)
|-valign="top
|[6]
|[https://de.wikipedia.org/wiki/Wolfgang_Grellmann Grellmann, W.], [[Seidler,_Sabine|Seidler, S.]] (Eds.): Deformation and Fracture Behaviour of Polymers. Springer, Berlin Heidelberg (2001) (ISBN 978-3540412472; see [[AMK-Library]] under A 7)
|-valign="top
|[7]
|Jungbluth, M.: Untersuchungen zum Verformungs- und Bruchverhalten von PVCC-Werkstoffen. PhD thesis, TH Leuna-Merseburg (1987) (see [[AMK-Library]] under B 1-1) ([https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Jungbluth_Untersuchungen_zum_Verformungs-_und_Bruchverhalten_von_PVCC-Werkstoffen.pdf Short summary/Content)]
|-valign="top
|[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
|-valign="top
|[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
|-valign="top
|[10]
|Rossmanith, H.-P. (Hrsg.): Finite Elemente in der Bruchmechanik. Springer, Berlin Heidelberg (1982) (ISBN 978-3-7091-2297-6)
|-valign="top
|[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
|-valign="top
|[12]
|Grellmann, W., Seidler, S., [https://researchgate.net/profile/Ralf-Lach 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;
|}

[[Category:Damage Analysis_Component Failure]]

Plastic Component - Revision history