Determination of dynamic initiation toughness and propagation toughness of sandstone using CSTBD specimens
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摘要: 利用大直径霍普金森压杆径向冲击中心直裂纹巴西圆盘(CSTBD)砂岩试样，完成Ⅰ型动态断裂实验。利用实验-数值方法确定了不同动态加载率下砂岩的动态起裂韧度；结合实验-数值法以及普适函数确定了不同裂纹扩展速度下砂岩的动态扩展韧度。为验证普适函数法和实验-数值法的有效性，将实验所得结果与其他学者的研究成果进行了对比分析，得到了相同的规律。所确定的岩石动态起裂韧度和动态扩展韧度分别随动态加载率的提高和裂纹扩展速度的提高而增加。Abstract: The CSTBD (cracked straight-through Brazilian disc) specimens of sandstone were diametrically impacted by the split Hopkinson pressure bar of large diameter in the mode-Ⅰ (opening mode) rock dynamic fracture test.The experimental-numerical method was employed to obtain the dynamic initiation toughness under different dynamic loading rates; and based on some theoretical analysis and reasonable simplification, the experimental-numerical method and universal function were employed to obtain the dynamic propagation toughness with different crack velocities.In order to verify the validity of the universal function and the experimental-numerical method, comparisons with well-established references of concern were made, and our results present the same law of phenomena as those derived from other researchers.Increases in the dynamic initiation toughness and the dynamic propagation toughness were observed with increasing dynamic loading rate and crack tip speed, respectively.
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1. 实验过程
1.1 试样制备
1.2 实验装置
1.3 实验数据的处理
2. 普适函数和动态断裂准则
3. 结果与讨论
3.1 动态断裂韧度的确定
3.2 起裂韧度与动态加载率的关系
3.3 扩展断裂韧度与裂纹扩展速度的关系
4. 结论
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图 6 裂尖坐标和1/4节点奇异单元
Figure 6. Crack tip coordinate system and singular element with quarter points
图 7 实验-数值法所得CSTBD-1-3的计算结果
Figure 7. Results of CSTBD-1-3 by experimental-numerical method
图 8 实验-数值法所得动态起裂韧度与动态加载率
Figure 8. Dynamic initiation toughness and dynamic loading rate obtained by experimental-numerical method
图 9 实验-数值法所得扩展断裂韧度和扩展速度
Figure 9. Crack growth toughness and crack speed obtained by experimental-numerical method
表 1 CSTBD试样的实验数据
Table 1. Experimental data of the CSTBD specimens
试样 tf/μs tp/μs t′f/μs tf-p/μs va/(m·s-1) k(va) CSTBD-1-3 143.7 170.9 171.5 27.2 367.6 0.799 CSTBD-1-4 134.0 158.5 168.2 24.5 408.1 0.775 CSTBD-2-1 129.4 154.1 149.1 24.7 404.9 0.777 CSTBD-2-2 127.6 152.1 153.4 24.5 408.1 0.775 CSTBD-2-3 132.2 160.8 162.4 28.6 349.7 0.810 CSTBD-3-1 131.3 160.6 169.1 29.3 341.3 0.815 CSTBD-3-2 125.1 150.0 164.5 24.9 401.6 0.779 CSTBD-3-3 122.7 148.8 166.1 26.1 383.1 0.790 
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表 2 CSTBD试样的计算结果
Table 2. Results of the CSTBD specimens
试样 KⅠ0/
(MPa·m1/2)KⅠCd/
(MPa·m1/2)KⅠCD/
(MPa·m1/2)KⅠCD[9]/
(MPa·m1/2)e/
%˙KI/
(GPa·m1/2·s-1)CSTBD-1-3 17.192 13.736 12.766 12.763 0.02 88.84 CSTBD-1-4 16.094 12.473 10.318 10.117 1.99 77.00 CSTBD-2-1 21.619 16.798 16.301 16.745 -2.65 125.97 CSTBD-2-2 23.250 18.019 17.812 17.326 2.81 139.59 CSTBD-2-3 17.926 14.520 14.244 14.391 -1.02 107.75 CSTBD-3-1 19.005 15.489 17.060 17.098 -0.22 129.93 CSTBD-3-2 19.175 14.937 14.372 14.345 0.19 114.88 CSTBD-3-3 18.553 14.657 13.151 12.958 1.49 107.18 e=(KⅠCD－KⅠCD[9])/KⅠCD[9]。
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