Toughness Temperature Dependence

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Toughness temperature dependdencee

Temperature dependence of toughness

Describing the temperature dependence of toughness is a relevant evaluation-methodological problem in polymer testing [1–3]. In order to expand the areas of application for plastics and composite materials with a polymeric matrix, increasing demands are being placed on lowering the brittle-tough transition temperatures and improving temperature stability. For a materials science interpretation of the temperature dependence of toughness, parameters determined by a 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 and the modulus of elasticity [2, 3]. This influence on the characteristic values determined using various concepts of fracture mechanics is examined from a methodological perspective using two selected polypropylene materials (abbreviation: PP). The influence of the loading speed (see: strain rate basics) is also presented.

Static loading

The temperature dependence of toughness was investigated under quasi-static loading (see: quasi-static test methods) on 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 %.

Fig. 1:

Temperature dependence of the fracture toughness KIcLEFM, KIcE and the 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_Ic^LEFM and K_Ic^E, determined using the concept of linear-elastic fracture mechanics (LEFM) and the equivalent energy concept, as a function of temperature.

Hille [3] presented extensive structural investigations to explain the fundamental increase in 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 according to the 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 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 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 tip. Whilst the inclusion of a_s in K_Ic^LEFM does not yield higher fracture toughness values than for T = 193 K, the fracture toughness increases with rising temperature when the 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 LEFM concept, and only the application of the 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 is a parameter that qualitatively describes the toughness behaviour as temperature increases. In view of these aspects, it appears necessary to carry out fracture mechanical testing using such concepts of fracture mechanics and to describe the results using parameters that take into account the material’s deformability.

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

$K_{Ic}^{J}={\sqrt {J\cdot E}}\!$

(1)

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

Fig. 2:

Influence of temperature on the JIc and KIcJ values of two PP materials

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

$\delta _{Ic}={\frac {v_{c}}{1+n({\frac {a+z}{W-a}})}}\!$

(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_Ic^COD values using 'Eq. (3),

$K_{Ic}^{COD}={\sqrt {m\cdot R_{e}\cdot \delta _{Ic}\cdot E}}\!$

(3)

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

Fig. 3:

Influence of temperature on the critical crack opening δ and the KIcCOD values for two PP materials

The K_Ic^COD values decrease with increasing temperature, as the behaviour of the dynamic yield stress R_e – which is analogous to the temperature dependence of the modulus of elasticity – apparently has a greater effect than the increased deformability with rising temperature, as recorded by the crack opening measurement [1].

The increase in toughness determined for the J_Ic and δ_Ic parameters as a function of temperature occurs in the region of the 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 geometric criteria for fracture mechanics concepts leads to the conclusion that geometry-independent 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-specimens, whereby the type of test specimen removal from the rolled plates is shown in the left-hand section of Fig. 4.

Fig. 4:

Temperature dependence of dynamic fracture toughness and 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 dynamic loading.

Dynamic fracture toughness decreases when calculated according to the 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 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 does not provide a better description of the increase in deformability, as shown by the example of highly oriented PP. Here, the K_Id^E-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) exhibit significantly lower values.

Fig. 5:

Effect of temperature on the JId and KIdJ 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, as is the case with 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 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) 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 loading (see also: impact loading plastics) following verification of the geometric criteria.

Just as with the J-values, the critical 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.

Fig. 6:

Temperature dependence of the critical crack opening δId and the dynamic fracture toughness KIdCOD for unoriented and highly oriented PP

At the same time, the left-hand sub-figure shows that the K_Id^COD values are not suitable for describing the increased deformability. The dynamic fracture toughness values decrease much more significantly compared with the K_Ic^COD values determined under static loading, suggesting that the temperature dependence of the modulus of elasticity and 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 and the CTOD concept, as these reflect the increase in deformability particularly clearly. It is less advantageous to use the equivalent energy concept or the K_Ic^COD and K_Ic^J 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 using fracture mechanics parameters are given in [1].

See also

• Toughness
• Crack toughness
• Levels of knowledge in fracture mechanics
• Fractography
• Instrumented Charpy impact test
• J-Integral evaluation methods (overview)
• Crack resistance (R) curve

References

[1]	Grellmann, W.: Beurteilung der Zähigkeitseigenschaften von Polymerwerkstoffen durch bruchmechanische Kennwerte. Habilitation (1986), Technische Hochschule Leuna-Merseburg, Wiss. Zeitschrift TH Merseburg 28 (1986), No. 6, pp. 787–788 (Content, Summary)
[2]	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
[3]	Hille, E.: Untersuchungen zum Bruchverhalten des orientierten isotaktischen Polypropylen. Ph.D. Dissertation, Technische Hochschule Leuna-Merseburg (1983)
[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
[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
[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
[7]	Williams, J. G.: Fracture mechanics of polymers. Polymer Engng. and Sci. 17 (1977) 144–149; https://doi.org/10.1002/pen.760170303
[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)