# A Simple Estimation Method of Weibull Modulus and Verification with Strength Data
## 4 Material Strength Data
### Composites  
Table 6 lists the strength and Weibull modulus data of composite materials. For these datasets, the average of m\({}_{\text{obs}}\)/m\({}_{\text{est}}\) is 0.992, and the standard deviation is 0.088. The average m\({}_{\text{obs}}\)/m\({}_{\text{est}}\) value is 2% lower than that of the entire data, while the general trends seen in Figure 8 appear to skew slightly to lower m\({}_{\text{obs}}\) as the m values increase. However, high m\({}_{\text{obs}}\)/m\({}_{\text{est}}\) values are mostly populated at low m values in Figure 8b. The m value of composites reached 44, exceeded only by ductile metals. Many Weibull studies were conducted earlier, but typically no values of \(<\)\(\alpha\)\(>\) and S were included. Two articles are useful in finding Weibull modulus values for many composites not included here [27; 90]. Another article to be noted is [91], as it included many lay-ups and tested at different loading rates. However, the sample counts were three for each condition, so it is hardly worth calling it a \"statistical\" study. However, no similar tests appear to exist, and it may serve as a preliminary guide. In regard to small sample counts, four datasets with N = 5 are included in Table 6 for glass fiber composites. They used samples of large diameter (12 to 18 mm), and the tests followed an industrial guideline [17] for concrete-reinforcing bars. Since the m values were from 20 to 40, the sample count of five or more was deemed adequate for quality control purposes. Figure 8: (**a**) Plots of m\({}_{\rm obs}\) (red + symbol) and m\({}_{\rm est}\) (blue dot) vs. \(<\)\(\sigma\)\(>\)/S for composite data. (**b**) Plot of m\({}_{\rm obs}\)/m\({}_{\rm est}\) (blue dot) vs. \(<\)\(\sigma\)\(>\)/S for the same. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Composites** & **c0\textgreater{}** & **S** & **c0\textgreater{}/SD** & **m\textgreater{}obs** & **m\textgreater{}set** & **N** & **m\textgreater{}obs/m\textgreater{}set** & **Note** & **D/V** & **Ref** \\ \hline CFRP unidirectional & 2504.0 & 82.9 & 30.22 & 33.41 & 33.25 & 35 & 1.005 & Fiber fraction 0.68 & V & [92] \\ CFRP unidirectional & 2751.0 & 62.1 & 44.30 & 44.10 & 48.73 & 35 & 0.905 & Fiber fraction unknown & V & [92] \\ CFRP unidirectional & 2237.4 & 83.1 & 26.92 & 29.58 & 29.62 & 35 & 0.999 & Fiber fraction 0.62 & V & [92] \\ CFRP unidirectional & 2497.6 & 223.9 & 11.15 & 12.98 & 12.27 & 105 & 1.058 & Combined & V & [92] \\ CFRP unidirectional & 2718.0 & 127.0 & 21.40 & 22.90 & 23.54 & 20 & 0.973 & IM60 fiber & V & [93] \\ CFRP unidirectional & 1638.0 & 119.0 & 13.76 & 14.40 & 15.14 & 20 & 0.951 & K310 fiber & V & [93] \\ CFRP unidirectional & 1337.0 & 68.0 & 19.66 & 20.60 & 21.63 & 20 & 0.952 & Combined & V & [93] \\ Cy/glass hybrid rod & 1423.0 & 54.6 & 26.06 & 23.77 & 28.67 & 10 & 0.829 & TW005/CE-glass K241P & D & [94] \\ Cy/glass hybrid rod & 1803.0 & 66.1 & 27.28 & 27.29 & 30.00 & 10 & 0.910 & TW005/CE-glass K242P & D & [94] \\ Cy/glass hybrid rod & 1837.0 & 58.4 & 31.46 & 32.50 & 34.60 & 10 & 0.939 & TW005/CE-glass K243P & D & [94] \\ CFRP unidirectional & 1815.0 & 117.0 & 15.51 & 17.44 & 17.06 & 13 & 1.022 & TW00 fiber & D & [95] \\ CFRP unidirectional & 2209.0 & 157.4 & 14.03 & 14.83 & 15.44 & 13 & 0.961 & TC35 fiber & D & [96] \\ CFRP unidirectional & 3156.0 & 270.0 & 11.69 & 11.11 & 28.6 & 12 & 0.864 & TW00-T600 fiber & D & [96] \\ CFRP unidirectional & 1695.0 & 107.8 & 15.72 & 16.11 & 17.29 & 23 & 0.932 & Ring-Nolt.