13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- in the distribution of strengths. fP was estimated using the following equation: 1 f i P N = + (2) where N is the total number of tests and i is the current test number [15]. Figure 4a and b shows the Weibull curve fitting to experimental data of both fabric and single yarn samples, respectively. The fabric data clearly indicate that the fabric breaks at lower stress in warp direction than in fill direction, and wider samples (50 mm) have lower tensile strength. For the single yarn data, as the gage length increases, the cumulative probability plot shifts towards lower stress values, which is a clear indicator of dependence of tensile strength on the gage length. The Weibull parameters identified from both fabric and single yarn tests are presented in Table 2. Table 2. Weibull Parameters of Kevlar 49 Fabric and Single Yarn under Quasi-Static Loading Fabric Single Yarn Size (mm) 25 × 200 50 × 200 50 125 200 275 350 425 Material Direction Warp Fill Warp Fill Warp σ0 (MPa) 1857 2064 1759 2001 1933 1829 1795 1724 1726 1652 m 13.3 27.0 27.5 27.4 21.7 11.5 14.3 11.9 7.9 8.8 3.2. Dynamic response Figure 5(a-d) shows the dependence of the dynamic material properties of Kevlar 49 fabric, defined in terms of Young’s modulus, tensile strength, maximum strain and toughness on strain rates, respectively. There is an apparent dependence of the dynamic material properties on the strain rates discussed as follows: For 25 mm gage length specimen, the Young’s modulus increases from 120 ± 14 GPa at initial strain rate of 30 s-1 to 131 ± 23 and 147 ± 10 GPa at strain rates of 100 s-1, and 170 s-1 respectively. The tensile strength increases from 1489 ± 54 MPa at a strain rate of 30 s-1 to 1968 ± 109 and 2340 ± 134 MPa at strain rates of 100 s-1, and 170 s-1 respectively. Maximum strain increases from 2.92 ± 0.17% to 3.27 ± 0.32% and then to 3.66 ± 0.27%, and toughness increases from 24.6 ± 2.6 MPa to 30.6 ± 1.5 MPa and to 41.4 ± 4.8 MPa when the strain rate increases from 30 to 100 and then to 170 s-1. For 50 mm gage length specimen, the Young’s modulus increases from 127 ± 16 GPa to 144 ± 12 GPa and then to 162 ± 11 GPa, the tensile strength increases from 1677 ± 136 MPa to 1954 ± 104 MPa and then to 2108 ± 83 MPa, the maximum strain increases from 2.58 ± 0.34% to 2.82 ± 0.18% and then to 2.83 ± 0.28%, and toughness increases from 21.6 ± 3.8 MPa to 22.2 ± 3.3 MPa and then to 25.8 ± 1.8 MPa when the strain rate increases from 25 to 60 and then to 100 s-1. Figure 6(a-d) shows the dependence of the dynamic material properties of Kevlar 49 single yarn on the strain rate. There is an apparent dependence of the dynamic material properties on the strain rate; however there is no clear dependence between the properties and gage lengths investigated. For the
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