Failure of Square Plate under the Influence of Boundary Conditions Subjected to Shock Loading
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摘要: 冲击载荷作用下边界条件对方板的毁伤破坏具有很大影响。利用落锤试验机开展了不同边界支撑下固支方板的冲击试验，为获取固支方板边界撕裂的典型破坏模式，专门设计加工了与固支方板尺寸相当的冲击锤头和可改变倒角的方板支撑框架。研究结果表明：（1）冲击载荷作用下，固支方板呈现出塑性大变形、单边撕裂、双边撕裂等典型破坏模式，倒角越小，方板越容易撕裂；（2）边界支撑对固支方板中心位移、整体变形轮廓影响较小，但对方板的撕裂长度、临界撕裂阈值存在较大影响；（3）不同边界支撑主要改变方板边界处的剪切应变，边界支撑倒角越小，剪切效果越明显，方板边界临界撕裂应变位于[0.191，0.241]区间。Abstract: Boundary condition exerts great influence on the failure mode of square plate under intensive loading. In this paper, a series of experiments of clamped square plates with different boundary chamfer radius were performed in the drop hammer impacting machine, in which the drop hammer was specially designed nearly same as the square plate in dimension and the supporting framework could offer various boundary conditions. The results show that: (1) the failure mode of large plastic deformation, one-side tearing and double-side tearing can be observed, and the square plates are more easily damaged under smaller boundary chamfer radius. (2) The boundary chamfer radius has a minor effect on the plate center displacement and deformation profile, but a major influence on the boundary tearing length and crack forming process. (3) The shear effect on the boundary region of clamped square plate would decrease with increasing boundary chamfer radius, and it is more easier for the plate with smaller boundary chamfer radius to get torn under the same intense impulsive loading. The critical failure strain of square plate is among [0.191, 0.241].
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Key words:
- boundary chamfer /
- deformation/failure mode /
- square plate /
- drop hammer /
- stress state
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图 5 落锤高度为400 mm时边界倒角对固支方板毁伤的影响
Figure 5. Dynamic behavior of square plates under boundary conditions with 400 mm hammer height
图 6 落锤高度为500 mm时边界倒角对固支方板毁伤的影响
Figure 6. Dynamic behavior of square plates under boundary conditions with 500 mm hammer height
图 7 落锤高度为700 mm时边界倒角对固支方板毁伤的影响
Figure 7. Dynamic behavior of square plates under boundary conditions with 700 mm hammer height
图 8 不同边界倒角半径和落锤高度对固支方板中心位移的影响
Figure 8. Center displacement of square plates under different boundary chamfer radius and hammer height
图 9 落锤高度为500 mm时边界倒角半径对固支方板中心位移的影响曲线
Figure 9. Center displacement curves of plates under different boundary chamfer radius with 500 mm hammer height
图 10 落锤高度为700 mm时边界倒角半径对固支方板中心位移的影响曲线
Figure 10. Center displacement curves of plates under different boundary chamfer radius with 700 mm hammer height
图 11 边界倒角半径对固支方板裂缝总长度的影响
Figure 11. Total crack length of square plates underdifferent boundary chamfer radius
图 12 边界倒角半径对固支方板长裂缝长度的影响
Figure 12. Longest crack length of square plates underdifferent boundary chamfer radius
图 13 落锤高度为400 mm时不同倒角半径固支方板的仿真计算结果
Figure 13. Simulation results of square plates under different boundary chamfer radius with 400 mm hammer height
图 14 不同倒角下固支方板最大塑性应变点的应力状态
Figure 14. Stress triaxility of the max PEEQ element of square plates under different boundary chamfer radius
表 1 试验工况及试验结果
Table 1. Experiment cases and experiment results
Experiment
caseSpecimen No. R/mm h/mm v/(m·s−1) M/kg E/kJ Experiment results D/mm Failure mode 1 S6-1 6 400 2.80 2 024 7.934 41.2 One-side tearing 2 S6-2 6 500 3.13 2 024 9.917 45.7 Double-side tearing 3 S6-3 6 600 3.42 2 024 11.901 52.0 One-side tearing 4 S6-4 6 700 3.70 2 024 13.884 56.4 Double-side tearing 5 S9-1 9 400 2.80 2 024 7.934 39.3 Plastic deformation 6 S9-2 9 500 3.13 2 024 9.917 45.9 One-side tearing 7 S9-3 9 600 3.42 2 024 11.901 48.6 Double-side tearing 8 S9-4 9 700 3.70 2 024 13.884 55.8 Double-side tearing 9 S12-1 12 400 2.80 2 024 7.934 39.8 Plastic deformation 10 S12-2 12 500 3.13 2 024 9.917 44.6 One-side tearing 11 S12-3 12 600 3.42 2 024 11.901 51.1 One-side tearing 12 S12-4 12 700 3.70 2 024 13.884 56.9 One-side tearing 
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表 2 不同工况下固支方板的裂缝长度
Table 2. Crack length of square plates under different experiment cases
Experiment
caseSpecimen
No.R/mm h/mm Failure mode Crack length/mm Crack 1 Crack 2 1 S6-1 6 400 One-side tearing 207 2 S6-2 6 500 Double-side tearing 216 125 3 S6-3 6 600 One-side tearing 290 4 S6-4 6 700 Double-side tearing 294 184 5 S9-1 9 400 Plastic deformation 6 S9-2 9 500 One-side tearing 195 7 S9-3 9 600 Double-side tearing 250 213 8 S9-4 9 700 Double-side tearing 184 132 9 S12-1 12 400 Plastic deformation 10 S12-2 12 500 One-side tearing 170 11 S12-3 12 600 One-side tearing 230 12 S12-4 12 700 One-side tearing 280
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表 3 最大塑性应变单元结果对比
Table 3. Comparison of the max PEEQ results
Experiment
caseR/mm h/mm Plastic deformation Stress triaxility PEEQ $\varepsilon_{11} $ $\varepsilon_{33} $ $\varepsilon_{13} $ 1 6 400 0.241 –0.137 0.139 0.268 [0.5, 0.6] 5 9 400 0.191 –0.133 0.130 0.219 [0.5, 0.6] 9 12 400 0.185 –0.141 0.133 0.210 [0.5, 0.6]
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