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Information content of fracture mechanical material parameters FORCETOC ==General remarks== When applying fracture mechanics working methods (see: fracture mechanics and fracture mechanical testing) to [[Plastics|plastics]..."

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{{Language_sel|LANG=ger|ARTIKEL=Erkenntnisniveauebenen der Bruchmechanik}}
{{PSM_Infobox}}
Levels of knowledge in fracture mechanics 
Information content of fracture mechanical material parameters
__FORCETOC__

==General remarks==

When applying fracture mechanics working methods (see: [[Fracture Mechanics|fracture mechanics]] and [[fracture Mechanical Testing|fracture mechanical testing]]) to [[Plastics|plastics]],

* on the one hand, a number of fundamental methodological findings and experimental procedures can be adopted that were gained during the evaluation of the [[Toughness|toughness]] of metallic [[Material & Werkstoff|materials]], and,
* on the other hand, the pronounced time and temperature dependencies of materials with a [[Polymer|polymer]] matrix must lead to plastic-specific methodological developments (see, for example: [[Toughness Temperature Dependence|toughness temperature dependence]]) [1, 2].

==Levels of knowledge in fracture mechanics==

From a methodological point of view, the fracture mechanical material parameters or fracture toughness parameters can be divided into three levels of knowledge [3‒5]:

# [[Crack Toughness|Crack toughness]] as resistance against unstable [[Crack Initiation|crack initiation]]
# Crack toughness as resistance against stable crack initiation and [[Crack Propagation|crack propagation]]
# Crack toughness as resistance against the rate of change of loading variables

==Fracture toughness as resistance against crack initiation==

Level I contains all fracture mechanics [[Material Parameter|material parameters]] that enable the determination of crack toughness as resistance against unstable crack initiation (see '''Table 1''').

Column 1 lists the respective fracture mechanics concept used to analyse the [[Material & Werkstoff|material]] behaviour. The second column lists the essential fracture mechanics parameters for characterising the stress and deformation field near the crack tip, and the last two columns list the respective crack failure criterion (see: [[Fracture Safety Criterion|fracture safety criterion]]) and describe the informative value of the [[Material Parameter|material parameters]].

The concept of [[Fracture Mechanics#Linear-elastic fracture mechanics|linear-elastic fracture mechanics (LEFM)]], [[Fracture Mechanics#Linear-elastic fracture mechanics with small-scale yielding|LEFM with small-scale yielding]] and the [[Equivalent Energy Concept – Basics|equivalent energy concept]] enable quantitative recording of failure on the basis of force- or stress-determined [[Fracture Mechanics|fracture toughness]], as only the force or stress measurements are included in the determination equations. Thus, based on their informative value, LEFM with small-scale yielding and the equivalent energy concept can be classified analogously to LEFM.

'''Table 1''': Level of knowledge I – Fracture mechanics material parameters as resistance against unstable crack initiation
{|border="1px" style="border-collapse:collapse"
|-
!width="200" style="text-align:center;|Fracture mechanics concept
!width="5" colspan="3"|Parameters for characterising the stress and deformation field near the crack tip
!width="200"|Fracture safety criterion
!width="200"|Practical relevance
|-
!colspan="6"|Crack toughness as resistance against unstable crack initiation
|-
|style="text-align:center"|linear-elastic fracture mechanics (LEFM)
|colspan="3"|stress intensity factors
|style="text-align:center;|static crack initiation
|rowspan="2"|force- or stress-determined
|-
|style="text-align:center"; rowspan="3"|LEFM LEFM with small scale yielding
 equivalent energy concept
|rowspan="3"|<math>K_{I}(a_{0})</math> <math>K_{I}(a_{eff})</math> <math>K_{I}(F_{Q}^{*},\,a_{eff})</math>
|rowspan="3"|<div style="font-size:200%;"><math>\Biggr\rbrace</math>
|rowspan="2"| critical values: <math>K_{Ic},\,K_{Id}</math>
|style="text-align:center;|<math>K_{I} \ge K_{Ic}</math>
|-
|style="text-align:center;|dynamic crack initiation
|rowspan="2"|fracture toughness (crack toughness)
|-
|Mode I, II, III: <math>K_{I},\,K_{II},\,K_{III}</math>
|style="text-align:center;| <math>K_{I} \ge K_{Id}</math>
|-
|colspan="6"| 
|-
|style="text-align:center"|elastic-plastic fracture mechanics (EPFM)
|colspan="5"| 
|-
|colspan="6"| 
|-
|style="text-align:center"|CTOD-concept
|colspan="3"|crack opening displacement <math>\delta_{Ic}, \delta_{Id}</math> Mode I, II, III, Mixed Mode
|style="text-align:center;|<math>\delta_{I} \ge \delta_{Ic}</math> <math>\delta_{I} \ge \delta_{Id}</math>
|deformation-determined crack opening displacement
|-
|colspan="6"| 
|-
|style="text-align:center"|J-integral concept
|colspan="3"|J-integral <math>J_{Ic}, J_{Id}</math> Mode I, II, III, Mixed Mode
|style="text-align:center;|<math>J_{I} \ge J_{Ic}</math> <math>J_{I} \ge J_{Id}</math>
|energy determined ''J''-integral
|}

The parameters of [[Extended CTOD Concept|crack opening displacement]] ''δ''Ic and ''δ''Id under static and dynamic loading, determined according to the [[Crack Tip Opening Displacement Concept (CTOD)]] of elastic-plastic fracture mechanics (EPFM), prove to be deformation-determined fracture mechanical material parameters, since only deformation values (crack expansion, [[Crack Opening|crack opening]] and maximum deflection) are taken into account.

In connection with the [[Composite Materials Testing|testing of composite materials]], i.e. the [[Toughness|toughness]] assessment of [[Fibre-reinforced Plastics|fibre composites]] but also [[Adhesive Joints – Determination of Characteristic Values|adhesive bonds]], the experimental methods and evaluation formalisms for Mode II, Mode III and [[Mixed-Mode Crack Propagation|mixed-mode]] stress (see: [[Fracture Modes|fracture modes]] and [[Crack Opening Modes|crack opening modes]]) have become increasingly important.

While the CTOD concept is deformation-determined and the LEBM concept is fracture force-determined, the [[J-Integral Concept|J-integral concept]] enables an energetic interpretation of the fracture behaviour, as both force and deformation measurements are taken into account. The J-integral concept thus plays a central role in the evaluation of [[Fracture Behaviour|fracture behaviour]].

==Fracture toughness as resistance against stable crack initiation and propagation==

When applying the J-integral concept to determine fracture mechanical [[Material Parameter|material parameters]], it should be noted that in most cases of mechanical [[Stress|stress]], the resulting [[Fracture|fracture]] is initiated by stable [[Crack Propagation|crack propagation]]. The evaluation of fracture toughness as resistance to stable [[Crack Initiation|crack initiation]] and propagation (see '''Table 2''') is based on the [[Crack Resistance (R) Curve|crack resistance (R) concept]].

'''Table 2''': Level of knowledge II – Fracture mechanics material parameters as resistance against stable crack initiation and propagation
{|border="1px" style="border-collapse:collapse"
|-
!width="150"|Fracture mechanics concept
!width="500" colspan="3"|Parameters for characterising the stress and deformation field near the crack tip
!width="100"|Fracture safety criterion
!width="100"|Practical relevance
|-
|colspan="6"| Crack toughness as resistance against stable crack initiation and propagation
|-
|crack resistance (R) concept
|style="text-align:center" |crack initiation
|style="text-align:center" |crack propagation
|style="text-align:center" |generalised crack propagation
|style="text-align:center" |crack initiation
| 
|-
|colspan="4"| 
|rowspan="2" style="text-align:center" | <math>\delta; J_{component} \ge \delta_{i}; J_{i\,resp.\,0.2}</math>
|rowspan="4" style="text-align:center" |<math>J \cdot T_{J}, \delta \cdot T_{\delta}</math>-controlled stable crack propagation
|-
|CTOD-resistance curve
|style="text-align:center" |<math>\delta_{/phys}, \delta_{0.2}</math>
|style="text-align:center" |<math>T_{\delta}=\frac{d\,\delta}{d(\Delta a)}\,\frac{E}{R_{e}}</math>
|style="text-align:center" |<math>\delta \cdot T_{\delta}</math>
|-
|colspan="4"| 
|style="text-align:center" |crack propagation
|-
|J-R-curve
|style="text-align:center" |<math>J_{/phys}, J_{0.2}</math>
|style="text-align:center" |<math>T_{J}=\frac{d\,J}{d(\Delta a)}\,\frac{E}{R_{e}^{2}}</math>
|style="text-align:center" |<math>J \cdot T_{J}</math>
|style="text-align:center" |<math>\frac{d\,J_{component}}{d(\Delta a)} \ge \frac{d\,J_{material}}{d(\Delta a)}</math>
|-
|colspan="6"| 
|-
|rowspan="2"|J-T-stability diagram
|style="text-align:center"; rowspan="2" colspan="3"|instability value <math>J_{50}</math>
|style="text-align:center" |Instability caused by advanced crack propagation
|rowspan="2" style="text-align:center" |energy determininated plastic instability
|-
|style="text-align:center" |<math>T_{component} \ge T_{material}</math>
|}

For the construction of [[Crack Resistance (R) Curve|crack resistance (R) curves]], the crack opening ''δ'' and the ''J''-integral value are preferred as loading parameters over the stress intensity factor ''K''I of the LEFM concept.

The resistance to actual crack initiation is denoted by ''J''iphys or ''δ''iphys, and the resistance to stable crack propagation by ''T''δ or ''T''J, which represent the rise of the R curve multiplied by ''E''/''R''e or ''E''/''R''e2, respectively.

Based on the energy balance at the [[Crack|crack]], Will and Michel [6, 7] introduced a practical model for evaluating stable crack growth (see: [[JTJ-Concept|JTJ-concept]]).

'''''After that, stable crack growth occurs when the energy dissipated in the plastic zone specific to the material compensates for the excess available energy caused by the crack growth.'''''

Crack growth is then controlled by the product ''JT''J or ''δT''δ and is referred to as ''JT''J- or ''δT''δ-controlled stable crack growth. Numerous examples of model systems provide experimental evidence for the existence of ''JT''J-controlled crack growth in the literature [3‒5].

Paris and Johnson [8] introduced the instability parameter ''J''50 as a further toughness criterion. A graphical method [9] is used to determine this experimentally, transforming ''J''-Δ''a''- into ''J''-''T''-stability diagrams.

Such diagrams make it possible to draw conclusions about the growth instability of cracks in [[Plastic Component|components]] without using the method for determining [[Crack Toughness|crack toughness]] as resistance to unstable [[Crack Propagation|crack propagation]].

==Fracture toughness as resistance against the rate of change of parameters==

For the determination of crack resistance as resistance to the rate of change of parameters based on knowledge level III, on the one hand, only limited experimental results are available, and on the other hand, decisive progress can be expected here in material-related toughness assessment [10‒13] (see '''Table 3''').

'''Table 3''': Level of knowledge III – Fracture mechanics material parameters as resistance against the rate of change of parameters by taking into account the temporal change in deformation
{|border="1px" style="border-collapse:collapse"
|-
!width="150"|Fracture mechanics concept
!width="400"|Parameters for characterising the stress and deformation field near the crack tip
!width="100"|Fracture safety criterion
!width="100"|Praktical relavance
|-
|colspan="4" style="text-align:center" |'''Crack toughness as resistace against rate of chance of parameters'''
|-
|
|style="text-align:center" |consideration of time-dependent changing of deformation energy
|colspan="2"|
|-
|modified CTOD- and J-concept
|style="text-align:center" |<math>\dot \delta_{Ic}=\frac{\delta_{Ic}}{t_{B}};\;\dot \delta_{Id}=\frac{\delta_{Id}}{t_{B}}</math> t B – time to fracture <math>\dot J_{Ic}=\frac{J_{Id}}{t_{B}};\;\dot J_{Id}=\frac{J_{Id}}{t_{B}}</math>
|style="text-align:center" |<math>\dot \delta_{I} \ge \dot \delta_{Ic};\;\dot \delta_{I} \ge \dot \delta_{Id}</math> <math>\dot J_{I} \ge \dot J_{Ic};\;\dot J_{I} \ge \dot J_{Id}</math>
|<math>\dot \delta</math>- bzw. <math>\dot J</math>-controlled crack propagation
 (energy-rate-determined plastic instability)
|-
|<math>\dot R</math>-concept
|colspan="3"|
|-
|<math>\dot \delta-\Delta a</math> <math>\dot J-\Delta a</math>
|style="text-align:center" |<math>\dot \delta_{i};\;\dot T_{\delta}\;\;\;\dot \delta_{i} \cdot \dot T_{\delta}</math> <math>\dot J_{i};\;\dot T_{J}\;\;\;\dot J_{i} \cdot \dot T_{J}</math>
|style="text-align:center" |<math>\dot T_{\delta_{component}} \ge \dot T_{\delta_{material}}</math> <math>\dot T_{J_{component}} \ge \dot T_{J_{material}}</math>
|
|}

The loading speed is known to have a significant influence on the [[Fracture Behaviour|fracture behaviour]] of [[Polymer|polymeric]] materials. When conducting fracture mechanics tests, the [[Crosshead Speed|crosshead speed]] of the [[Material Testing Machine|materials testing machine]], the impact velocity of a pendulum or drop hammer, or the impact velocity of projectiles in arrest tests are usually specified. However, the data on the impressed [[Velocity|velocity]] are not comparable, as different test [[Specimen|specimen]] types cause different conversions of the load-line displacement into the [[Deformation|deformation]] of the crack tip area (see also: [[Fracture Process Zone|fracture process zone]]).

The crack opening displacement velocity appears to be a suitable measure for describing [[Toughness|toughness]] as resistance to the rate of change, as it is a comparable [[Material Parameter|parameter]] that compensates for the influence of different test specimen geometries. Analogous to this description of crack growth, the [[J-Integral Concept|J-integral]] and the [[Crack Resistance (R) Curve|R-curve concept]], as well as the [[Fracture Mechanics|LEFM concept]], can be used to assess the [[Material & Werkstoff|material]] based on the change in loading over time. The parameter ''J'' can thus be understood as a change in energy rate, and this is referred to as J-controlled crack growth.

==Assessment of the state of development of fracture mechanics values determination and the automation of stable crack growth detection==

With the classification of fracture mechanics material parameters, the transition to the next higher level of knowledge increases the theoretical demands regarding knowledge of fracture mechanics concepts, the degree of difficulty in experimental methodology, and also the effort required for automation, e.g., in determining the length of stable crack growth ('''Table 4''').

'''Table 4''': State of development in fracture mechanics material testing, problems in determining characteristic values and objectives
{|border="1px" style="border-collapse:collapse"
|-
!width="150"|
!colspan="3"|Characteristic values as resistance against crack initiation and propagation
|-
!style="text-align:center"|Level
|width="200"; style="text-align:center"|I
|width="200"; style="text-align:center"|II
|width="200"; style="text-align:center"|III
|-
!style="text-align:center"|State
|style="text-align:center"|for unstable crack growth
|style="text-align:center"|for stable crack growth
|style="text-align:center"|as function of the rate of change
|-
|effort required to determine the values
|style="text-align:center"|relatively low, easy to automate
|style="text-align:center"|relatively high, very difficult to automate to date
|style="text-align:center"|very high
|-
|current distribution of toughness values
|style="text-align:center"|widespread use in industrial practice
|style="text-align:center"|limited distribution to specialised testing institutes and knowledge carriers
|style="text-align:center"|still a current research topic
|-
|target objectives
|style="text-align:center"|fully automated value determination
|style="text-align:center"|automated crack length determination
|style="text-align:center"|distribution in practice, development of evaluation procedures, standardisation
|-
|information content
|style="text-align:center"|single-parameter description of fracture behaviour
|style="text-align:center"|multi-parameter description of fracture behaviour
|style="text-align:center"|comprehensive assessment of crack propagation kinetics
|}

==See also==

* [[Fracture Mechanics|Fracture mechanics]]
* [[Fracture Mechanical Testing|Fracture mechanical testing]]
* [[Fracture Safety Criterion|Fracture safety criterion]]
* [[J-Integral Concept|J-integral concept]]
* [[Crack Tip Opening Displacement Concept (CTOD)|Crack Tip opening displacement concept]]
* [[JTJ-Concept|JTJ-concept]]
* [[Fracture Behaviour of Plastics Components|Fracture behaviour of plastic components]]

==References==

{|
|-valign="top"
|[1]
|[[Blumenauer,_Horst|Blumenauer, H.]], Pusch, G.: Technische Bruchmechanik. Deutscher Verlag für Grundstoffindustrie, Leipzig Stuttgart (2003), 3rd Edition, (ISBN 3-342-00659-5; see [[AMK-Library]] under E 29-3)
|-valign="top"
|[2]
|Anderson, T. L.: Fracture Mechanics ‒ Fundamental and Applications. CRC Press, Boca Raton (2005) (ISBN 978-0849342608; see AMK-Library under E 8-2), DOI: [https://doi.org/10.1201/9781315370293 https://doi.org/10.1201/9781315370293]
|-valign="top"
|[3]
|[[Grellmann,_Wolfgang|Grellmann, W.]], [[Seidler,_Sabine|Seidler, S.]]: Anwendung des instrumentierten Kerbschlagbiegeversuches in der Werkstoffentwicklung von Kunststoffen. DVM-Tagung „Werkstoffprüfung 1990“, December 6 and 7, 1990, Bad Nauheim Proceedings. pp. 79‒88
|-valign="top"
|[4]
|[https://www.researchgate.net/profile/Wolfgang-Grellmann Grellmann, W.]: Aussagefähigkeit bruchmechanischer Werkstoffkenngrößen bei der Werkstoffentwicklung von Polymerblends. Proceedings 3. Erlanger Kunststoff-Tage, Erlangen, April 21‒23, 1993, Neue polymere Werkstoffe, Zahradnik, F., Kaschta, J. (Eds.), Self-Publishing (1993), Erlangen, Proceedings pp. 175‒195
|-valign="top"
|[5]
|[https://de.wikipedia.org/wiki/Wolfgang_Grellmann Grellmann, W.]: Neue Entwicklungen bei der bruchmechanischen Zähigkeitsbewertung von Kunststoffen und Verbunden. In: Grellmann, W., Seidler, S. (Eds.): Deformation und Bruchverhalten von Kunststoffen. Springer Berlin Heidelberg (1998) pp. 3‒26 (ISBN 3-540-63671-4, see [[AMK-Library]] under A 6), DOI: [https://link.springer.com/chapter/10.1007/978-3-642-58766-5_1#citeas https://link.springer.com/chapter/10.1007/978-3-642-58766-5_1#citeas]
|-valign="top"
|[6]
|Will, P.; Michel. B., Zerbst, U.: JTJ-gesteuertes Risswachstum und die Energiebilanz am duktilen Riss. Technische Mechanik 7 (1986) 58‒60
|-valign="top"
|[7]
|Will, P.: JTJ-Konzept und dissipative Energien am Riss. In: Grellmann, W., Seidler, S. (Eds.) Deformation und Bruchverhalten von Kunststoffen. Springer Berlin Heidelberg (1998) pp. 27‒34 (ISBN 3-540-63671-4; see [[AMK-Library]] under A 6)
|-valign="top"
|[8]
|Paris P. C., Johnson R. E.: Fracture Resistance Curves and Engineering Applications. ASTM STP 803 Vol II: 5 (1983)
|-valign="top"
|[9]
|[https://researchgate.net/profile/Ralf-Lach Lach, R.], Grellmann, W.: JTJ- und δTδ -Stabilitätsdiagramme als Grundlage einer alternativen Methode zur Ermittlung von Instabilitätswerten aus Risswiderstandskurven. In: Grellmann, W., [https://de.wikipedia.org/wiki/Sabine_Seidler Seidler, S.] (Eds.) Deformation und Bruchverhalten von Kunststoffen. Springer Berlin Heidelberg (1998) 145‒154 (ISBN 3-540-63671-4; see AMK-Library under A 6), DOI: https://link.springer.com/chapter/10.1007/978-3-642-58766-5_11#citeas
|-valign="top"
|[10]
|Seidler, S. (1998): Anwendung des Risswiderstandskonzeptes zur Ermittlung strukturbezogener bruchmechanischer Werkstoffkenngrößen bei dynamischer Beanspruchung. Fortschritt-Berichte, VDI-Reihe 18: Mechanik/Bruchmechanik No. 231, VDI-Publishing Düsseldorf (ISBN 3-18-323118-2; see [[AMK-Library]] under B 2-1)
|-valign="top"
|[11]
|Lach, R., Grellmann, W.: Time-dependent Fracture Behaviour of Polymers at Impact and Quasi-Static Loading Conditions. In: Grellmann, W., Langer, B. (Eds.): Deformation and Fracture Behaviour of Polymer Materials. Springer, Berlin (2017) 3‒21 (ISBN 978-3-319-41877-3; see [[AMK-Library]] under A 19), DOI: [https://link.springer.com/chapter/10.1007/978-3-319-41879-7_1#citeas https://link.springer.com/chapter/10.1007/978-3-319-41879-7_1#citeas]
|-valign="top"
|[12]
|Lach, R., Seidler, S., Grellmann, W.: Resistance Against the Intrinsic Rate of Fracture Mechanics Parameters for Polymeric Materials under Moderate Impact Loading. Mechanics of Time-Dependent Materials 9 (2005) 103‒119, DOI: [https://doi.org/10.1007/s11043-005-1084-y https://doi.org/10.1007/s11043-005-1084-y]
|-valign="top"
|[13]
|Lach, R., Grellmann, W.: Time- and Temperature-dependent Fracture Mechanics of Polymers: General Aspects at Monotonic Quasistatic and Impact Loading Conditions. Macromolecular Materials and Engineering 273 (2008) 555‒567, DOI: [https://doi.org/10.1002/mame.200700417 https://doi.org/10.1002/mame.200700417]
|}

'''Additional literature on assessing the toughness of polymers using the JTJ concept'''

* Grellmann, W., Seidler, S.: Risszähigkeit von Kunststoff-Messungen bei dynamischer Beanspruchung. Materialprüfung 33 (1991) 7-8, pp. 213–218

* Grellmann, W., Seidler, S., Oberbach, K.: Ermittlung dynamischer Risswiderstandskurven von Polymerblendes mit Hilfe des instrumentierten Kerbschlagbiegeversuches, 23. Vortragsveranstaltung, DVM Arbeitskreis "Bruchvorgänge", Berlin, Februar 26‒ 27, 1991, Proceedings, pp. 401‒412

* Seidler, S., Grellmann, W.: Bruchverhalten und Morphologie von PC/ABS Blends ‒ Anwendung moderner Konzepte der Fließbruchmechanik zur Optimierung der Zähigkeit. 2nd Erlanger Kunststoff Tage, Erlangen, April 17‒19, 1991, Werkstoffcharakterisierung und Qualitätssicherung, Zahradnik, F., Kaschta, J. (Eds.), Self-Publishing (1991), Erlangen, pp. 125‒145

* Grellmann, W., Seidler, S., Oberbach, K.: Dynamische Risswiderstandskurven von Polymerblends. 14. Gesa Symposium "Experimentelle Mechanik in Forschung und Praxis", Berlin, April 25‒ 26, 1991, VDI Berichte Nr. 882 (1991), pp. 433‒443

* Seidler, S., Grellmann, W.: Charakterisierung des Risswiderstandsverhaltens von Kunststoffen mit dem JTJ-Konzept. "Werkstoffprüfung 1992", Bad-Nauheim, December 3 and 4, 1992, Proceedings pp. 387‒393

* Seidler, S., Grellmann, W.: Anwendung bruchmechanischer Werkstoffkenngrößen in der Kunststoffentwicklung. Plaste und Kautschuk 40 (1993) 8., pp. 263‒269 [https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Anwendung_bruchmechanischer_Werkstoffkenngroessen_in_der_Kunststoffentwicklung.pdf Download as pdf]

* Grellmann, W., Seidler, S., Langer, B.: J-Integral-Analyse von Kurzfaser-Verbundwerkstoffen. "Werkstoffprüfung 1993", Bad Nauheim, December 2 and 3, 1993 Proceedings pp. 317‒325

* Grellmann, W., Seidler, S., Jung, K.: Stand und Entwicklungstendenzen bei der Anwendung des Risswiderstandskonzeptes in der Kunststoffprüfung. Werkstoffprüfung 1994, Bad-Nauheim, December 1 and 2, 1994, Proceedings pp. 273‒281

* Seidler, S., Grellmann, W.: Application of the Instrumented Impact test to the Toughness Characterization of High Impact Thermoplastics. Impact and Dynamic Fracture of Polymers and Composites, ESIS Publication 19 (Edited by [[Williams, James Gordon|J. G. Williams]] and A. Pavan), Mechanical Engineering Publications, London, 1995 pp. 171‒178

* Seidler, S., Grellmann, W., Langer, B.: Anwendbarkeit des Risswiderstandskonzeptes zur Zähigkeitsbewertung von kurzfaserverstärktem Polyamid. 27. Vortragsveranstaltung, DVM Arbeitskreis "Bruchvorgänge" Köln, Februar 14 and 15, 1995, Proceedings pp. 63‒72

* Seidler, S., Grellmann, W.: Application of the Instrumented Impact Test to the Toughness Characterization of High Impact Thermoplastics. Polymer Testing 14 (1995) 453‒469; https://doi.org/10.1016/0142-9418(95)00003-B

* Grellmann, W.: Morphologie-Zähigkeits-Korrelation polymerer Mehrphasenwerkstoffe ‒ Aussagefähigkeit und strukturelle Empfindlichkeit bruchmechanischer Werkstoffkenngrößen. Tagung "Gefüge und Bruch", Leoben, March 20‒22, 1996, Proceedings pp. 1‒8

* Grellmann, W., Seidler, S., Jung, K., Gahleitner, M., Fiebig, J.: Bruchverhalten und Morphologie von PP-Reaktorblends. Werkstoffwoche`96, Stuttgart, May 28‒31, 1996, Symposium 7 "Materialwissenschaftliche Grundlagen", Proceedings pp. 933‒938

* Seidler, S., Grellmann, W.: Fracture Behaviour and Morphology of Polymers. Ninth International Conference on Fracture, ICF 9 Sydney, April 1‒5, 1997, Proceedings Volume 2, pp. 1021‒1027

* Seidler, S., Grellmann, W.: Application of the Instrumented Impact Test to the Toughness Characterization of High Impact Thermoplastics. Polymer Testing 14 (1995) 453‒469 DOI: [https://doi.org/10.1016/0142-9418(95)00003-B https://doi.org/10.1016/0142-9418(95)00003-B]

[[Category:Fracture Mechanics]]

Levels of Knowledge in Fracture Mechanics - Revision history