Figure 12
The six panels, labeled “(a)” to “(f)”, are arranged in three rows and two columns. The top row shows “S C, m: 0.0316” and “S C, m: 0.1633”; the middle row shows “B C C, m: 0.0316” and “B C C, m: 0.1633”; and the bottom row shows “F C C, m: 0.0316” and “F C C, m: 0.1633”. In each panel, the horizontal axis is labeled “Strain rate: epsilon dot [per second]” and ranges from 1.0 E minus 04 to 1.0 E minus 01 on a logarithmic scale, while the vertical axis is labeled “Yield ratio: lowercase sigma over lowercase sigma subscript 0”. In m: 0.0316 column, the vertical axis ranges from 0.8 to 1.5 in increments of 0.1 units for S C and from 0.8 to 1.5 in increments of 0.1 units for B C C and F C C. In m: 0.1633 column, it ranges from 1.1 to 2.9 in increments of 0.2 units for S C and from 1 to 3 in increments of 0.5 units for B C C and F C C. Each panel shows five curves labeled “V f: 0 percent”, “V f: 5 percent”, “V f: 10 percent”, “V f: 15 percent”, and “V f: 20 percent”. All curves increase with increasing strain rate. Panels m: 0.0316: For S C, values increase from 1.14 at 1.0 E minus 04 to about 1.36 at 1.0 E minus 01 for 0 percent porosity, with lower curves for higher porosity increasing from 0.82 to 0.97 for 20 percent porosity. For B C C, values increase from about 1.15 at 1.0 E minus 04 to about 1.37 at 1.0 E minus 01 for 0 percent porosity, while the 20 percent porosity curve increases from about 0.75 to about 0.9. For F C C, values increase from about 1.15 at 1.0 E minus 04 to about 1.36 at 1.0 E minus 01 for 0 percent porosity, while the 20 percent porosity curve increases from about 0.8 to about 0.93. Panels m: 0.1633: For S C, values increase from about 1.75 at 1.0 E minus 04 to about 2.85 at 1.0 E minus 01 for 0 percent porosity, while the 20 percent porosity curve increases from about 1.2 to about 1.85. For B C C, values increase from about 1.7 to about 2.85 for 0 percent porosity, while the 20 percent porosity curve increases from about 1.2 to about 1.85. For F C C, values increase from about 1.7 to about 2.85 for 0 percent porosity, while the 20 percent porosity curve increases from about 1.2 to about 2.0. Arrows and labels indicate the porosity values for each curve. Note: All numerical data values are approximated.Numerical results of effective yield ratio as a function of applied strain rate, for the closed-cell porous structures with different porosities and values: (a) SC, = 0.0316, (b) SC, = 0.1633, (c) BCC, = 0.0316, (d) BCC, = 0.1633, (e) FCC, = 0.0316, (f) FCC, = 0.1633. The effective yield ratio is the effective plastic flow stress of the perfectly plastic porous structure, , normalized by the static yield strength of the solid matrix,