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{{Language_sel|LANG=ger|ARTIKEL=Zähigkeit Temperaturabhängigkeit}}
{{PSM_Infobox}}
Toughness temperature dependdencee
__FORCETOC__

==Temperature dependence of toughness==

Describing the temperature dependence of [[Toughness|toughness]] is a relevant evaluation-methodological problem in [[Polymer|polymer]] [[Polymer Testing|testing]] [1–3]. In order to expand the areas of application for [[Plastics|plastics]] and [[Fibre-reinforced Plastics|composite materials]] with a [[Polymer|polymeric matrix]], increasing demands are being placed on lowering the [[Brittle-Tough Transition Temperature|brittle-tough transition temperatures]] and improving temperature stability. For a [[Materials Science|materials science]] interpretation of the temperature dependence of toughness, [[Material Parameter|parameters]] determined by a [[Fracture Mechanical Testing|fracture mechanics test]] are required. The strong temperature dependence of the secondary valence bonds in plastics leads to a pronounced temperature dependence of mechanical properties, such as the [[Yield Stress|yield stress]] and the [[Elastic Modulus|modulus of elasticity]] [2, 3]. This influence on the [[Material Value|characteristic values]] determined using various concepts of [[Fracture Mechanics|fracture mechanics]] is examined from a methodological perspective using two selected polypropylene materials ([[Plastics – Symbols and Abbreviated Terms|abbreviation]]: PP). The influence of the loading speed (see: [[Strain Rate Basics|strain rate basics]]) is also presented.

==Static loading==

The temperature dependence of toughness was investigated under quasi-static loading (see: [[Quasi-static Test Methods|quasi-static test methods]]) on [[CT-Specimen|compact tension (CT-) specimens]] for a non-oriented and a highly oriented PP material produced by cold rolling. The degree of orientation produced by subsequent cold rolling was ''f''x = 80 %.

[[File:Toughness-Temp-Fig1.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Temperature dependence of the fracture toughness ''K''IcLEFM, ''K''IcE and the [[Fracture Mirror|fracture mirror]] as for unoriented (''B'' = 10 mm) and highly oriented (''B'' = 4 mm) PP (WR = direction of rolling)
|}

'''Figure 1''' shows the fracture toughness values ''K''IcLEFM and ''K''IcE, determined using the concept of linear-elastic [[Fracture Mechanics|fracture mechanics]] (LEFM) and the [[Equivalent Energy Concept – Basics|equivalent energy concept]], as a function of temperature.

Hille [3] presented extensive structural investigations to explain the fundamental increase in [[Toughness|toughness]] of highly oriented PP compared to unoriented PP, whereby a reorientation of the crystallites (from a-texture to c-texture) in the rolling direction was demonstrated by X-ray textural measurements.

In describing the temperature dependence of [[Toughness|toughness]] according to the [[Fracture Mechanics|LEFM concept]], a decrease in toughness was experimentally determined, which is attributable to the reduction in fracture force. This behaviour, which does not correspond to the notion of increased deformability, was described early on in the literature [4−7] for other [[Plastics|plastics]] as well, without it ever being possible to clarify the causes.

From the left-hand sub-figure in '''Fig. 1''', the temperature dependence of the [[Fracture Mirror|fracture mirror]] ''a''s clearly shows that the scope of validity of the LEFM is apparently exceeded due to the energy-dissipative mechanisms occurring in front of the [[Crack|crack tip]]. Whilst the inclusion of ''a''s in ''K''IcLEFM does not yield higher fracture toughness values than for ''T'' = 193 K, the fracture toughness increases with rising temperature when the [[Equivalent Energy Concept – Basics|equivalent energy concept]] is applied.

'''Figure 1''' also clearly shows that the increased deformability of the material expected with rising temperature cannot be reflected by the [[Fracture Mechanics|LEFM concept]], and only the application of the [[Equivalent Energy Concept – Application Limits|equivalent energy concept]] leads to toughness values that are at least higher than those at lower temperatures, as is evident for the highly oriented PP material. At the same time, it can be seen that the [[Fracture Mirror|fracture mirror]] is a [[Material Parameter|parameter]] that qualitatively describes the toughness behaviour as temperature increases. In view of these aspects, it appears necessary to carry out [[Fracture Mechanical Testing|fracture mechanical testing]] using such concepts of [[Fracture Mechanics|fracture mechanics]] and to describe the results using [[Material Parameter|parameters]] that take into account the [[Material & Werkstoff|material’s]] deformability.

If the temperature dependence of the J-values is determined for both materials (see: [[J-Integral Concept|J-integral concept]]), the relationship shown in '''Fig. 2''' is obtained. To ensure consistency of the quantitative [[Material Value|characteristic values]] with [3], the [[RICE, PARIS and MERKLE – J-Integral Estimation Method|evaluation method according to RICE, PARIS and MERKLE]] was employed, which does not affect the methodological conclusion. If the fracture toughness values ''K''IcJ are determined in accordance with '''Eq. (1)''',

{|
|-
|width="20px"|
|width="500px" | <math>K^{J}_{Ic} = \sqrt{J \cdot E} \!</math>
|(1)
|}

the increase in toughness values with rising temperature is described accurately, and the simultaneous decrease in the static [[Elastic Modulus|modulus of elasticity]] with temperature does not have a significant effect.

[[File:Toughness-Temp-Fig2.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |Influence of temperature on the ''J''Ic and ''K''IcJ values of two PP materials
|}

The increased deformability of the two [[Polymer|polymer]] [[Material & Werkstoff|materials]] as the temperature rises is reflected in particular by the critical [[Crack Opening|crack opening]], whereby the critical crack opening is determined, according to the analysis carried out in [3] and based on [8], using '''Eq. (2)'''.

{|
|-
|width="20px"|
|width="500px" | <math>\delta_{Ic} = \frac{v_c}{1+n(\frac{a+z}{W-a})} \!</math>
|(2)
|}

(''z'' = distance between the COD sensor and the specimen surface).

If, on the other hand, one attempts to convert the ''δ''Ic values into ''K''IcCOD values using '''Eq. (3)'',

{|
|-
|width="20px"|
|width="500px" | <math>K^{COD}_{Ic} = \sqrt{m \cdot R_{e} \cdot \delta_{Ic} \cdot E} \!</math>
|(3)
|}

then, using the constraint factor (see also: [[J-Integral Concept|J-integral concept]]) ''m'' = 0.7 [3], one obtains the relationship shown in the left-hand panel of '''Fig. 3'''.

[[File:Toughness-Temp-Fig3.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 3''':
|width="600px" |Influence of temperature on the critical [[Crack Opening|crack opening]] ''δ'' and the ''K''IcCOD values for two PP materials
|}

The ''K''IcCOD values decrease with increasing temperature, as the behaviour of the dynamic [[Yield Stress|yield stress]] ''R''e – which is analogous to the temperature dependence of the [[Elastic Modulus|modulus of elasticity]] – apparently has a greater effect than the increased deformability with rising temperature, as recorded by the [[Crack Opening|crack opening]] measurement [1].

The increase in [[Toughness|toughness]] determined for the ''J''Ic and ''δ''Ic parameters as a function of temperature occurs in the region of the [[Glass Transition Temperature|glass transition temperature]]. The glass transition temperature for the unoriented PP material is 278 K, and for ''f''x = 80 %, ''T''g = 285 K [3].

Controlling the [[Geometry Criterion|geometric criteria]] for fracture mechanics concepts leads to the conclusion that geometry-independent [[Material Value|material values]] can only be assumed with certainty for the unoriented initial state [1, 3].

==Dynamic loading==

The investigation of the temperature dependence of the fracture mechanical values under dynamic loading is carried out on [[SENB-Specimen|SENB-specimens]], whereby the type of test specimen removal from the rolled plates is shown in the left-hand section of '''Fig. 4'''.

[[File:Toughness-Temp-Fig4.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 4''':
|width="600px" |Temperature dependence of dynamic fracture toughness and [[Fracture Mirror|fracture mirror]] for unoriented and highly oriented PP (''B'' = 4 mm; ''s''/''W'' = 7; ''a''/''W'' ~ 0.45; WR = rolling direction)
|}

The problem of describing toughness behaviour using fracture mechanics parameters becomes particularly apparent under [[Stress|dynamic loading]].

Dynamic fracture toughness decreases when calculated according to the [[Fracture Mechanics|LEFM concept]] in the temperature range under investigation, 123 ≤ ''T'' ≤ 293 K, whereby even the extension of LEFM to LEFM with small-scale yielding, taking into account the [[Fracture Mirror|fracture mirror]] indicated in the right-hand section, does not yield fracture toughness values above the initial values at ''T'' = 123 K.

In contrast to static loading, even the application of the [[Equivalent Energy Concept – Basics|equivalent energy concept]] does not provide a better description of the increase in deformability, as shown by the example of highly oriented PP. Here, the ''K''IdE-values increase for ''T'' > 273 K, but do not reach the initial values for ''T'' = 123 K.

A comparison with '''Fig. 1''' shows that both the fracture toughness and the stable crack growth (see: [[Crack Propagation|crack propagation]]) exhibit significantly lower values.

[[File:Toughness-Temp-Fig5.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 5''':
|width="600px" |Effect of temperature on the ''J''Id and ''K''IdJ values of unoriented and highly oriented PP
|}

Due to the increase in maximum deflection ''f''max and deformation energy ''A''G with rising temperature, the material’s increasing deformability is represented by the EPFM’s [[J-Integral Concept|J-integral concept]], as is the case with [[Quasi-static Test Methods|static loading]] (see '''Fig. 5'''). Whilst the fracture toughness values determined under static loading still increase slightly with rising temperature, a decrease in toughness is observed across the entire temperature range under dynamic loading. The reason for this is that the increase in the dynamic [[Elastic Modulus|modulus of elasticity]] ''E''d with decreasing temperature has a greater effect given the significantly smaller rise in the ''J''Id values compared to static loading. The ''E''d values were determined by Hille [3] in a tensile–strain oscillation test (see: [[Dynamic-mechanical Analysis (DMA) – Tensile Stress|dynamic-mechanical analysis (DMA) – tensile stress]]) at a test frequency of 1 Hz. The J-values and the dynamic fracture toughnesses are to be regarded as geometry-independent material properties under impact [[Stress|loading]] (see also: [[Impact Loading Plastics|impact loading plastics]]) following verification of the [[Geometry Criterion|geometric criteria]].

Just as with the J-values, the critical [[Crack Opening|crack openings]] ''δ''Id are suitable for describing the toughness behaviour; these primarily indicate the increased deformability with rising temperature and are approximately one order of magnitude lower than the ''δ''Ic values. This is particularly evident in '''Fig. 6''' for both polymer materials.

[[File:Toughness-Temp-Fig6.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 6''':
|width="600px" |Temperature dependence of the critical crack opening ''δ''Id and the dynamic fracture toughness ''K''IdCOD for unoriented and highly oriented PP
|}

At the same time, the left-hand sub-figure shows that the ''K''IdCOD values are not suitable for describing the increased deformability. The dynamic fracture toughness values decrease much more significantly compared with the ''K''IcCOD values determined under static loading, suggesting that the temperature dependence of the [[Elastic Modulus|modulus of elasticity]] and [[Yield Stress|yield stress]] – which is opposite to that of fracture toughness – has a greater effect under dynamic loading.

==Informative value of fracture mechanics parameters==

In summary, it should be noted that the toughness properties can be appropriately described in terms of temperature using the [[J-Integral Concept|J-integral concept]] and the [[Crack Tip Opening Displacement Concept (CTOD)|CTOD concept]], as these reflect the increase in deformability particularly clearly. It is less advantageous to use the [[Equivalent Energy Concept – Basics|equivalent energy concept]] or the ''K''IcCOD and ''K''IcJ values for characterisation, as these incorporate the dependence of the modulus and yield strength on temperature, which exhibit a temperature dependence opposite to that of the toughness behaviour [2]. Further examples of describing the temperature dependence of [[Toughness|toughness]] using fracture mechanics parameters are given in [1].

==See also==

* [[Toughness]]
* [[Crack Toughness|Crack toughness]]
* [[Levels of Knowledge in Fracture Mechanics|Levels of knowledge in fracture mechanics]]
* [[Fractography]]
* [[Instrumented Charpy Impact Test|Instrumented Charpy impact test]]
* [[J-Integral Evaluation Methods (Overview)|J-Integral evaluation methods (overview)]]
* [[Crack Resistance (R) Curve|Crack resistance (R) curve]]

==References==

{|
|-valign="top"
|[1]
|[[Grellmann,_Wolfgang|Grellmann, W.]]: Beurteilung der Zähigkeitseigenschaften von Polymerwerkstoffen durch bruchmechanische Kennwerte. Habilitation (1986), [https://de.wikipedia.org/wiki/Technische_Hochschule_Leuna-Merseburg Technische Hochschule Leuna-Merseburg], Wiss. Zeitschrift TH Merseburg 28 (1986), No. 6, pp. 787–788 ([https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Habil_Grellmann_Inhaltsverzeichnis.pdf Content], [https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Habil_Grellmann_Kurzfassung.pdf Summary])
|-valign="top"
|[2]
|[https://www.researchgate.net/profile/Wolfgang-Grellmann Grellmann, W.], Che, M.: Assessment of temperaturedependent fracture behaviour with different fracture mechanics concepts on example of unoriented and cold-rolled polypropylene. J. Applied Fracture Polymer Science 66 (1997) 1237−1249; [https://doi.org/10.1002/(SICI)1097-4628(19971114)66:7%3C1237::AID-APP4%3E3.0.CO;2-H https://doi.org/10.1002/(SICI)1097-4628(19971114)66:7%3C1237::AID-APP4%3E3.0.CO;2-H]
|-valign="top"
|[3]
|Hille, E.: Untersuchungen zum Bruchverhalten des orientierten isotaktischen Polypropylen. Ph.D. Dissertation, [https://de.wikipedia.org/wiki/Technische_Hochschule_Leuna-Merseburg Technische Hochschule Leuna-Merseburg] (1983)
|-valign="top"
|[4]
|Casiraghi, T.: The fracture mechanics of polymers at high rates. Polymer Engng. and Sci. 18 (1978) 10, 833; https://doi.org/10.1002/pen.760181016
|-valign="top"
|[5]
|Karger-Kocsis, J., Kiss, L., Kuleznev, V. N.: Mechanical loss peaks of polypropylene/EPDM blends in relation to their fracture toughness and impact strength. Acta Polymerica 33 (1982) 1,14–19; [https://doi.org/10.1002/actp.1982.010330103 https://doi.org/10.1002/actp.1982.010330103]
|-valign="top"
|[6]
|Savadori, A., Bramuzzo, M., Marega, C.: J-integral analysis of ductile fracture of PP/EP rubber blends. Polymer Testing 4 (1984) 73–89; https://doi.org/10.1016/0142-9418(84)90035-7
|-valign="top"
|[7]
|[[Williams, James Gordon|Williams, J. G.]]: Fracture mechanics of polymers. Polymer Engng. and Sci. 17 (1977) 144–149; [https://doi.org/10.1002/pen.760170303 https://doi.org/10.1002/pen.760170303]
|-valign="top"
|[8]
|Schwalbe, K. H.: Theoretische und experimentelle Untersuchungen zum COD-Konzept und J-Integral. Fortschritt-Berichte, VDI Zeitschrift Reihe 18, Nr. 10 VDI-Publing House (1981); (ISBN 978-3-1814-1018-9)
|}

[[Category:Fracture Mechanics]]

Toughness Temperature Dependence - Revision history