Line Method Area Method FIGURE 3.14 Illustration of area and line methods. where Ar and A are the total fiber area and the area of the selected region of the micrograph,respectively. An alternative way,the line method (Figure 3.14),can also be used to determine the fiber volume fraction from the micrograph.In this method,a number of lines are randomly drawn on the micrograph.The fiber volume fraction is evaluated as the ratio of the cumulative length of fiber cross sections along the line to the length of the line.For a representative result,an average value should be determined from measurements along several lines. For a cross section of the carbon/epoxy composite discussed in the previ- ous section,the results shown in Table 3.2 were obtained.From these data an average fiber volume fraction was determined,V=0.62,which can be compared with Vi=0.65,determined with the acid digestion method.Dif- ferences between the two methods are likely due to the smaller region of the composite which is studied in the micrograph and to uncertainty in determining the length of the fiber cross sections. TABLE 3.2 Determination of Fiber Volume Fraction with the Line Method Line Lf(mm) Vi 44.5 0.58 2 40.8 0.54 3 54.9 0.72 ￥ 453 0.60 48.3 0.63 6 48.1 0.63 L=cumulative length of fiber cross sections. Total length of each line was 76.2 mm. ©2003 by CRC Press LLCwhere Af and A are the total fiber area and the area of the selected region of the micrograph, respectively. An alternative way, the line method (Figure 3.14), can also be used to determine the fiber volume fraction from the micrograph. In this method, a number of lines are randomly drawn on the micrograph. The fiber volume fraction is evaluated as the ratio of the cumulative length of fiber cross sections along the line to the length of the line. For a representative result, an average value should be determined from measurements along several lines. For a cross section of the carbon/epoxy composite discussed in the previ￾ous section, the results shown in Table 3.2 were obtained. From these data an average fiber volume fraction was determined, Vf = 0.62, which can be compared with Vf = 0.65, determined with the acid digestion method. Dif￾ferences between the two methods are likely due to the smaller region of the composite which is studied in the micrograph and to uncertainty in determining the length of the fiber cross sections. FIGURE 3.14 Illustration of area and line methods. TABLE 3.2 Determination of Fiber Volume Fraction with the Line Method Line Lf (mm)a Vf 1 44.5 0.58 2 40.8 0.54 3 54.9 0.72 4 45.3 0.60 5 48.3 0.63 6 48.1 0.63 a Lf = cumulative length of fiber cross sections. Total length of each line was 76.2 mm. TX001_ch03_Frame Page 54 Saturday, September 21, 2002 4:51 AM © 2003 by CRC Press LLC