J.L. Thomason et aL/Composites: Part A 61(2014) 201-208 Measured 20 months earlier(Ref xx) Silane sized23° 三5 300400 Treatment Temperature('C) 0.5 average modulus(▲ water sized,● APS sized) than that of the silane coated fibres after elevated temperature conditioning. Hence it appears that the silane coating impedes sis of the data from all fibres and conditions as all sample strength the mechanism that leads to an increase in modulus of the fibres data produced Weibull plots similar in form to one of these two during the hot conditioning. Results for the unconditioned fibre examples. At higher strength values the data for the 600C condi modulus for both samples from a previous investigation measured tioned fibres mainly follow a linear relationship typical of a uni- approximately 20 months prior to the current measurements are modal flaw distribution. However, at lower strengths the data also presented in Fig. 5. It is noted that the modulus values for both exhibit a downward deviation in curvature that is a symptom of fibre samples are significantly lower in this investigation. the experimental inability to access very low strength values as discussed above. Consequently the data are poorly fitted by a 3.3. Discussion of fibre strength results straight line (indicative of the simplest two parameter Weibull dis- tribution but can be well fitted, as shown, by a more general three Data from single fibre strength measurement are commonly parameter Weibull distribution. Nevertheless, it has been shown subjected to further detailed analysis using Weibull methods that it is actually more accurate to fit the data with a two-param- 20. These details of the Weibull method are well documented eter model where the calculated values below the lower experi and will not be reproduced here[17, 20. In some cases, experimen- mental limit L have been removed [17 The data for the APs tal single fibre tensile strength data can be well described using a sized fibres without any heat conditioning exhibited a more com wo parameter unimodal Weibull analysis. However, curvature in plex fibre strength distribution and appear to exhibit three distinct the Weibull plot of experimental single fibre data is frequently ob- regions in Fig. 6. This could be interpreted as indicating that the served at low strength values [ 17]. A recent study has demon- failure of silane coated glass fibres is controlled by two, or more strated that this deviation can be well explained by the existence distinct types of flaw population. The overall failure distribution of an experimental lower strength limit(or)below which the fibre is then the result of the interaction of these flaw populations. is not strong enough to survive the pretest sample preparation and which may be described by the multimodal Weibull distribution [17. Consequently, the lowest strength values of the esti- and precludes the use of the simple linear fitting to obtain the wei- Weibull distribution do not appear in the experimental bull parameters. It is possible to fit the results for the APS sized fi- data In such cases it is necessary to revert to the original three bres using a partially concurrent bimodal Weibull distribution 12 parameter form of Weibull distribution 17. Unfortunately this where the lower strength part of the distribution also includes a phenomenon seriously complicates attempts to use Weibull anal- non-zero value of oT. However, it bears commenting that this re- ysis of single fibre strength data to distil useful information about quires the reliable estimation of six adjustable parameters. the materials science of the tested single fibres. The experimentally Although further discussion and analysis of all fibre strength data reflected lower strength limit is operator sensitive, sample prepa- is certainly possible, one has to question whether all of the exper Ition dependent, and test procedure dependent as well as being imental and theoretical uncertainties discussed above warrant any related to the material properties. Consequently, although average attempts at interpretation of this type of Weibull analysis in terms values for or can be obtained the value of or is not a constant of real material parameters but can be different for each individual fibre test this A more robust analysis method that requires a less complex situation can become even more complex when further structure theoretical background is simply to plot the cumulative probability is observed in a Weibull plot, often interpreted as evidence for of fibre failure(Pf)as a function of fibre strength as shown in Figs multiple flaw populations in the fibres under test [12, 16, 17. This and 8 for the two fibre types in this investigation. Fig. 7 shows the is frequently observed in the distribution of strength from sized data for the water sized fibres. It can be observed that there is con- and carbon fibres and analysis using different forms of bimo- siderable separation between the unsized fibres conditioned above dal Weibull strength distribution has been attempted. Thomason 300C and the as-received fibres. The region between these two et al. recently presented data on the aps sized fibres used in this groups appears to be spanned by the distribution for the fibres con- investigation indicating that the partially concurrent bimodal Wei- ditioned at 250C. It can also be observed that all the heat condi bull distribution gave the most realistic model for these results tioned fibres have a similar low strength distribution for the first 12 25-30% of the distribution. One possible explanation for these Typical examples are presented in Fig. 6 which shows Weibull observations is that the low strength region of fibre strength of plots of the strength data for the APS fibres before heat condition- the heat conditioned fibres is a result of further mechanical dam g and for the water-sized fibres after heat conditioning at 600C. age to the unsized fibres caused by the handling of the fibres in This covers the full range of behaviour observed in Weibull analy- the process of heat conditioning. The strength of any strongerthan that of the silane coated fibres after elevated temperature conditioning. Hence it appears that the silane coating impedes the mechanism that leads to an increase in modulus of the fibres during the hot conditioning. Results for the unconditioned fibre modulus for both samples from a previous investigation measured approximately 20 months prior to the current measurements are also presented in Fig. 5. It is noted that the modulus values for both fibre samples are significantly lower in this investigation. 3.3. Discussion of fibre strength results Data from single fibre strength measurement are commonly subjected to further detailed analysis using Weibull methods [20]. These details of the Weibull method are well documented and will not be reproduced here [17,20]. In some cases, experimen￾tal single fibre tensile strength data can be well described using a two parameter unimodal Weibull analysis. However, curvature in the Weibull plot of experimental single fibre data is frequently ob￾served at low strength values [17]. A recent study has demon￾strated that this deviation can be well explained by the existence of an experimental lower strength limit (rT) below which the fibre is not strong enough to survive the pretest sample preparation and handling [17]. Consequently, the lowest strength values of the esti￾mated Weibull distribution do not appear in the experimental data. In such cases it is necessary to revert to the original three parameter form of Weibull distribution [17]. Unfortunately this phenomenon seriously complicates attempts to use Weibull anal￾ysis of single fibre strength data to distil useful information about the materials science of the tested single fibres. The experimentally reflected lower strength limit is operator sensitive, sample prepa￾ration dependent, and test procedure dependent as well as being related to the material properties. Consequently, although average values for rT can be obtained, the value of rT is not a constant parameter but can be different for each individual fibre test. This situation can become even more complex when further structure is observed in a Weibull plot, often interpreted as evidence for multiple flaw populations in the fibres under test [12,16,17]. This is frequently observed in the distribution of strength from sized glass and carbon fibres and analysis using different forms of bimo￾dal Weibull strength distribution has been attempted. Thomason et al. recently presented data on the APS sized fibres used in this investigation indicating that the partially concurrent bimodal Wei￾bull distribution gave the most realistic model for these results [12]. Typical examples are presented in Fig. 6 which shows Weibull plots of the strength data for the APS fibres before heat condition￾ing and for the water-sized fibres after heat conditioning at 600 C. This covers the full range of behaviour observed in Weibull analy￾sis of the data from all fibres and conditions as all sample strength data produced Weibull plots similar in form to one of these two examples. At higher strength values the data for the 600 C condi￾tioned fibres mainly follow a linear relationship typical of a uni￾modal flaw distribution. However, at lower strengths the data exhibit a downward deviation in curvature that is a symptom of the experimental inability to access very low strength values as discussed above. Consequently the data are poorly fitted by a straight line (indicative of the simplest two parameter Weibull dis￾tribution) but can be well fitted, as shown, by a more general three parameter Weibull distribution. Nevertheless, it has been shown that it is actually more accurate to fit the data with a two-param￾eter model where the calculated values below the lower experi￾mental limit rL have been removed [17]. The data for the APS sized fibres without any heat conditioning exhibited a more com￾plex fibre strength distribution and appear to exhibit three distinct regions in Fig. 6. This could be interpreted as indicating that the failure of silane coated glass fibres is controlled by two, or more, distinct types of flaw population. The overall failure distribution is then the result of the interaction of these flaw populations, which may be described by the multimodal Weibull distribution and precludes the use of the simple linear fitting to obtain the Wei￾bull parameters. It is possible to fit the results for the APS sized fi- bres using a partially concurrent bimodal Weibull distribution [12] where the lower strength part of the distribution also includes a non-zero value of rT. However, it bears commenting that this re￾quires the reliable estimation of six adjustable parameters. Although further discussion and analysis of all fibre strength data is certainly possible, one has to question whether all of the exper￾imental and theoretical uncertainties discussed above warrant any attempts at interpretation of this type of Weibull analysis in terms of real material parameters. A more robust analysis method that requires a less complex theoretical background is simply to plot the cumulative probability of fibre failure (PF) as a function of fibre strength as shown in Figs. 7 and 8 for the two fibre types in this investigation. Fig. 7 shows the data for the water sized fibres. It can be observed that there is con￾siderable separation between the unsized fibres conditioned above 300 C and the as-received fibres. The region between these two groups appears to be spanned by the distribution for the fibres con￾ditioned at 250 C. It can also be observed that all the heat condi￾tioned fibres have a similar low strength distribution for the first 25–30% of the distribution. One possible explanation for these observations is that the low strength region of fibre strength of the heat conditioned fibres is a result of further mechanical dam￾age to the unsized fibres caused by the handling of the fibres in the process of heat conditioning. The strength of any stronger 68 70 72 74 76 78 80 0 100 200 300 400 500 600 Fibre Modulus (GPa) Treatment Temperature (°C) Measured 20 months earlier (Ref xx) Fig. 5. Influence of heat treatment temperature on room temperature glass fibre average modulus (N water sized, d APS sized). -6 -5 -4 -3 -2 -1 0 1 2 3 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 ln (-ln(1-P)) ln(σ) [GPa] Silane Sized 23 oC Water Sized 600 oC Fig. 6. Weibull plot of single fibre strength (+ water sized fibres after 600 C conditioning, unconditioned APS sized fibres. 204 J.L. Thomason et al. / Composites: Part A 61 (2014) 201–208