Dynamic split tests of UHPFRC discs and failure mechanism analysis based on μXCT images
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摘要: 采用分离式霍普金森压杆对钢纤维体积分数为0～3%的超高性能纤维增强混凝土（ultra high performance fibre reinforced concrete, UHPFRC）圆盘试件进行应变率为1.72～7.42 s−1的动态劈裂试验，使用高速摄像机结合数字图像相关（digital image correlation, DIC）法获得试件表面裂缝扩展全过程图像和应变演化过程，并对冲击前后试件进行微观X射线计算断层扫描（micro X-ray computed tomography, μXCT），获得分辨率为56.7 μm的三维内部图像，并进行统计和破坏机理分析。结果表明：(1)相比无纤维试件，掺入1%～3%的钢纤维，静、动劈裂强度分别提高84%～131%和47%～87%，动劈裂强度增强因子（即动静强度比值）为1.07～1.72；(2) DIC应变图像分析表明，无纤维试件裂缝集中、破坏快、能耗低；含纤维试件裂缝弥散程度大、能耗高、延性好，且随着纤维含量的提高而提升；(3) μXCT图像分析表明，试件中钢纤维体积分数为1.04%～2.47%，与设计基本一致，孔洞体积分数为0.98%～1.71%，纤维掺量的提高，降低了孔洞数量和总体积分数，但孔洞的平均体积和平均等效直径增大；裂缝桥连纤维数量的增加，减小了主裂缝的体积和平均宽度，提高了裂缝面的粗糙度和相对表面积，从而提高了试件的强度、能耗、韧性和延性。
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关键词:
- 动态劈裂 /
- 超高性能纤维增强混凝土 /
- 微观X射线计算断层扫描 /
- 断裂机理 /
- 数字图像相关
Abstract: In order to better investigate the dynamic tensile properties and damage mechanism of ultra-high performance fibre reinforced concrete (UHPFRC), dynamic split tests with the strain rates of 1.72－7.42 s-1 were carried out by a split Hopkinson pressure bar for UHPFRC discs with the fibre volume fractions of 0－3%. The surface crack propagation processes of the UHPFRC discs were captured by a high-speed camera and the images were analyzed by the digital image correlation (DIC) technique for strain evolution. Micro X-ray computed tomography (μXCT) scanning of the UHPFRC disc specimens before and after the dynamic tests was also conducted. The 3D images of the internal micro structures of the specimens with a voxel resolution of 56.7 μm were reconstructed, and they were then processed to statistically quantify the distribution, volume fractions and sizes of pores, fibres and cracks. Moreover, the dynamic failure mechanisms, such as pullout from the matrix, bending and breakage of steel fibres, crack propagation and merging in the mortar, etc., were visualized and analyzed. The main results obtained are as follows. (1) The addition of 1%－3% steel fibres raises the static and dynamic splitting strength by 84%－131% and 47%－87%, respectively. The dynamic increase factor (ratio of dynamic to static strength) is 1.07－1.72. (2) DIC images demonstrate that the fibres lead to more dispersed cracks, slower crack propagation, higher energy consumption and higher ductility. (3) The μXCT image analysis shows that the fibre volume fraction is 1.04%－2.47%, consistent with the designed proportion, while the porosity is 0.98%－1.71%. Fibres reduce the porosity and the number of pores, but increase their average volume and equivalent diameter. The increase of crack-bridging fibres reduces the volume and width of main cracks and raises the surface roughness and the relative surface area of cracks, resulting in the increase of strength, energy dissipation, toughness and ductility of specimens. The research data are useful for improvement of dynamic design guidelines and optimization for UHPFRC materials and structures. -
在现代海战中，大型舰船遭受鱼雷、水雷等武器的近场或接触爆炸破坏后，其生命力将受到严重威胁，因此往往在大型舰船水下舷侧部位设计防雷舱结构。在水下武器的近场或接触爆炸下，船体结构在前期爆炸冲击波的作用下产生破口，形成不完整边界，致使水下爆炸气泡处于复杂的流场环境——既有自由液面，又有产生初始破口的船体结构，此外气泡还受反射冲击波的作用[1]。气泡在自由液面、不完整边界以及反射冲击波的作用下将产生“腔吸现象”、反射流、对射流等强非线性力学特征，因此水下爆炸气泡与船体结构的相互作用问题成为近年来的研究热点和难点。目前，国内外的相关研究主要集中在水下近场爆炸作用下简单规则结构的破坏形式上[2-6]，而对于水下爆炸气泡与具有初始破口船体结构的相互作用问题，相关报道则十分少见。由于水下接触爆炸载荷与防雷舱结构的相互作用问题非常复杂，尽管国内学者在防雷舱结构研究中取得了一些成果[7-11]，为防雷舱结构设计提供了参考，但是对水下接触爆炸下防雷舱舷侧空舱内的压力载荷特性仍未获得清晰的认识。鉴于采用数值和理论方法研究此问题十分困难，本文中采用实验方法开展研究，旨在进一步揭示水下接触爆炸下防雷舱舷侧空舱内的压力载荷特性。
1. 实验模型
参考文献[9]，结合实验场地(爆炸筒)条件，按照12.5:1的缩比，设计如图 1所示的实验模型，其组成构件从左至右依次为：固定压条、外板、密封圈、舷侧空舱框架、密封圈、液舱前板、密封圈、液舱框架、密封圈、液舱后板、密封圈、水密舱框架、密封圈、封闭盖板。
实验模型采用Q235钢制作。固定压条、空舱框架(包括舷侧空舱框架和水密舱框架)、液舱框架和封闭盖板的尺寸如图 2所示。外板、液舱前板和液舱后板长1 360 mm，宽960 mm，厚度分别为1.40、0.94和2.68 mm。密封圈厚4 mm，其正视图同图 2(a)，采用橡胶制作。在空舱框架顶部开3个螺孔(见图 2(b))，用以安装PCB压电传感器，传感器型号为102B03，量程为69 MPa。安装传感器时，其测压端面与空舱框架侧板内表面平齐。液舱内注入80%的水(见图 2(c))。
图 2 实验模型工装件设计图(单位：mm)Figure 2. Design drawings of experimental model components (unit: mm)为保证空舱和液舱的水密性，必须拧紧螺栓，从而使密封圈被压薄，因此空舱和液舱的实际内部空间尺寸约为1 200 mm×800 mm×126 mm。
2. 实验实施
由于此项实验需要耗费较多的人力和物力，故仅进行了两次实验，即55和110 g装药(TNT)在水下0.32 m深处的外板正中心接触爆炸。
实验在直径为5 m的爆炸筒内进行。预先在外板、液舱前板和液舱后板上绘制间距为5 cm的白色正交网格线，按图 1装配实验模型，并安装压力传感器；然后，吊起实验模型，将其8角用钢索固定，使外板中心距爆炸筒底约1.68 m、距爆炸筒壁约2.50 m，同时将模型顶部调至水平；接着，通过液舱框架顶部的注水管向液舱内注水，当水从液舱框架侧壁小螺孔(见图 2(c)中的侧视图)流出时，停止注水，并用螺丝将该螺孔堵住，此时液舱刚好注入80%的水；将圆柱形TNT装药套上气球(避免药柱被水浸湿)并固定在外板中心处；随后，向爆炸筒内注水，使水面在外板中心上方约0.32 m处，此时实验准备完毕，如图 3所示；最后，所有实验人员撤出爆炸筒，紧闭爆炸筒门，起爆炸药，并采集压力测试数据。
3. 实验结果
在仅改变药量的条件下，先后进行了两次实验。第1次实验采用55 g药量，第2次实验采用110 g药量。
3.1 模型破坏结果
在55和110 g药量近水面接触爆炸下，实验模型的破坏情况分别如图 4、图 5所示，外板、液舱前板和液舱后板的破坏情况分别如图 6、图 7所示，在爆炸筒底、舷侧空舱内和液舱内搜集到的破片如图 8、图 9所示。
图 4 55 g装药近水面接触爆炸下模型的破坏Figure 4. Experimental model damaged by underwater contact explosion of 55 g charge
图 5 110 g装药近水面接触爆炸下模型的破坏Figure 5. Experimental model damaged by underwater contact explosion of 110 g charge
图 6 55 g装药近水面接触爆炸下钢板的破坏Figure 6. Steel plates damaged by underwater contact explosion of 55 g charge
图 7 110 g装药近水面接触爆炸下钢板的破坏Figure 7. Steel plates damaged by underwater contact explosion of 110 g charge
图 8 55 g装药近水面接触爆炸下形成的破片Figure 8. Fragments formed in underwater contact explosion of 55 g charge
图 9 110 g装药近水面接触爆炸下形成的破片Figure 9. Fragments formed in underwater contact explosion of 110 g charge由图 4和图 5可见，在55和110 g装药近水面接触爆炸下，实验模型的外板和液舱前板均产生了花瓣形大破口，在爆炸筒底均有一个内径约等于药柱直径、外径约16 cm、厚度约0.94 mm的圆环状大破片，推断其来源于液舱前板。
观察图 6和图 7，从整体上看，实验模型的外板和液舱前板在破口以外的区域向外凸起，花瓣向里翻转，且花瓣尖端出现反向折弯现象。液舱后板没有破口，而是发生向里的凹陷大变形。液舱后板的中心挠度最大，且其下部的挠度比上部大。在55和110 g药量下液舱后板的最大挠度分别约为26和54 mm。
陈海龙等[12]提出了破口半径Rb与破损半径Rd的概念(如图 10所示)，用以区分破口尺寸和破损范围，本文中沿用这两个概念。由图 6可知，在55 g药量下：外板的破口半径和破损半径分别约为18.5和29.0 cm；液舱前板的破口半径与破损半径近似相同，约为28.0 cm。由图 7可知，在110 g药量下：外板的破口半径和破损半径分别约为22.5和33.5 cm；液舱前板的破口半径和破损半径也近似相同，约为42.0 cm。
对爆炸筒底、舷侧空舱内和液舱内搜集的破片质量进行统计，结果列于表 1，其中w为装药质量。
表 1 破片质量Table 1. Mass of fragmentsw/g 不同位置搜集的破片质量/g 破片总质量/g 爆炸筒底 舷侧空舱内 液舱内 圆环状大破片 其余小破片 55 150.7 41.2 44.9 50.0 286.8 110 117.6 23.4 169.8 135.2 446.0 3.2 压力测试结果
采用DHDAS动态信号采集分析系统采集压力信号，采样率为1 MHz。实验后3#传感器被破片击中而损坏，只有1#和2#传感器测得压力数据。图 11和图 12分别显示了55和110 g药量下1#和2#传感器所测压力曲线。
图 11 55 g装药近水面接触爆炸下两个传感器测得的压力曲线Figure 11. Pressure curves measured by two sensors in underwater contact explosion of 55 g charge
图 12 110 g装药近水面接触爆炸下两个传感器测得的压力曲线Figure 12. Pressure curves measured by two sensors in underwater contact explosion of 110 g charge4. 舷侧空舱的载荷特性
张婧等[7]从仿真和实验两方面对水下接触爆炸下防雷舱结构的破坏进行了研究。与张婧等[7]的研究相比，本文中的实验对象也是三舱防护模型，与张婧等实验的最大区别在于：他们将实验模型沉入较深的水中，以确保炸药爆炸后在水中产生的超压不发生泄漏；而本课题组将实验模型的小部分露出水面，炸药爆炸后在水中产生的超压将在自由水面发生泄漏，从而考虑了自由水面对水下爆炸气泡与实验模型的影响。从工程角度上看，本实验工况更符合水面舰船遭受鱼雷攻击的实际情况。
在本实验中，当55或110 g装药在水下0.32 m处爆炸时，其装药比例沉深h/w1/3(h为装药在水下的深度，单位m；w为装药质量，单位kg)均小于1，由装药比例沉深与气泡脉动次数的关系[13]可知，55或110 g装药在水下0.32 m处爆炸所产生的气泡脉动次数均不足1次。换言之，55或110 g装药在水下0.32 m处爆炸时，爆炸产物气体会喷出水面而不会形成完整的气泡脉动。然而，在张婧等[7]的实验中，当200或400 g装药在大于2.50 m的水深处爆炸时，其装药比例沉深均大于4，炸药爆炸产生的气泡脉动次数在3次以上，从而导致其实验结果与本研究存在差别。
在张婧等[7]的研究中，200 g装药下实验模型的外板和液舱前板的破口如图 13所示。可见，在液舱前板破口范围内有一块尚未完全脱落的圆环形大破片。据此可知：本实验中在爆炸筒底发现的圆环形大破片(见图 8(a)和图 9(a))确实来自液舱前板，其中间圆孔是由产生于外板的圆形冲塞破片高速撞击而形成，其四周边缘则是由外板开裂形成花瓣的尖端高速撞击而“剪切”形成；图 6(b)和图 7(b)所示的液舱前板破口主要是由外板开裂形成的花瓣“刨挖”而形成。
综合分析本文中实验模型的破坏结果和压力测试结果可知，当55或110 g装药在水下0.32 m处与实验模型接触爆炸时，在水下爆炸气泡与实验模型的相互作用过程中，水下爆炸气泡的运动和舷侧空舱内的压力变化可分为3个阶段：冲击波载荷阶段、准静态压力载荷阶段、负压载荷阶段，如表 2所示。
表 2 压力曲线的3个阶段Table 2. Three phases of pressure curvew/g 传感器编号 冲击波载荷阶段 准静态压力载荷阶段 负压载荷阶段起始时刻/ms 起止时刻/ms 超压峰值/MPa 比冲量/(Pa·s) 起止时刻/ms 超压峰值/MPa 比冲量/(Pa·s) 55 1#
2#5.2-5.8
5.1-5.60.647
1.39985.2
136.75.8-14.2
5.6-12.40.345
0.213624.2
460.314.2
12.4110 1#
2#4.2-4.6
4.0-4.30.788
1.61195.6
113.74.6-12.2
4.3-9.80.527
0.4321 125.1
505.412.2
9.8第1阶段：外板在水下接触爆炸瞬间发生冲塞破坏，冲塞破片向舷侧空舱内高速运动，爆炸产物气体一边向舷侧空舱涌入，一边在水中形成半球状气泡；舷侧空舱内原有的空气受到压缩，舷侧空舱各壁面先后受到冲击波载荷作用。由图 11和图 12可见，此阶段舷侧空舱内的压力呈现出峰值很大、时间很短的冲击波特性，故称此阶段为冲击波载荷阶段。
第2阶段：在图 11和图 12的局部放大图中可见若干个反射波，并且在此阶段舷侧空舱内的压力呈现出峰值较小、时间较长的准静态压力特性，表明冲击波在舷侧空舱内不断地反射而使舷侧空舱内的压力逐渐趋于均匀；与此同时，水中的气泡逐渐膨胀，气泡内部压力逐渐减小，当舷侧空舱内部压力比外部气体压力高时，气体就会向舷侧空舱外侧逸出，从而使舷侧空舱内、外的气压差减小，并导致外板逐渐向外鼓起(见图 6(a)和图 7(a))；当水中气泡膨胀到某一时刻时，舷侧空舱内的气体超压减小至零，之后进入第3阶段。由于在此阶段舷侧空舱内的气体压力呈现出准静态压力特性，故将此阶段称为准静态压力载荷阶段。
第3阶段：当舷侧空舱内的气体超压减小至零之后，由于惯性水会继续向外运动，水中气泡将“过度”膨胀，使气泡内部压力小于周围水的静压力；舷侧空舱内的气体继续向外逸出，使舷侧空舱内的超压峰值变为负值，故将此阶段称为负压载荷阶段。由外板的冲塞破片和开裂花瓣撞击形成的大质量圆环形大破片和少量小破片正是在这一阶段随着逸出的气流运动到舷侧空舱外侧，并最终掉落在爆炸筒底。尽管舷侧空舱内的超压为负值，但是舷侧空舱内的气体向外逸出，表明外板内侧压力比外侧压力大，此压差推动外板向外凸起。舷侧空舱内的超压为负值之后，液舱前板内侧的水压力明显比外侧的气体压力大，此压差推动液舱前板向外凸起。气泡膨胀到某一时刻，其顶部将与水面上的空气相连通，若此时气泡内部压力低于大气压力，则水面上的空气将流向气泡内部。随后，与水面上空气相连通的气泡逐渐坍塌，被推开的水逐渐回流并填充空穴。由于外板在爆炸冲击波作用下产生破口，爆炸产物气体向舷侧空舱涌入，导致水中气泡的膨胀速度与自由场水下爆炸相比减小，因而水向外流动的惯性将减小，从而推断气泡膨胀的最大半径也会减小。舷侧空舱内形成负压载荷的根本原因是水中气泡的“过度”膨胀，由于气泡膨胀历时较长，因此负压载荷阶段相比准静态压力载荷阶段持续的时间要长得多。
由以上分析可知，防雷舱舷侧空舱的破坏主要是由冲击波载荷和准静态压力载荷造成，并且由表 2可见准静态压力载荷的比冲量是冲击波载荷的数倍，而负压载荷对防雷舱舷侧空舱的影响可以忽略。
5. 结论
采用模型实验的方法，研究了近自由面水下接触爆炸下防雷舱舷侧空舱的内压载荷特性。根据实验模型的破坏结果和压力测试结果，分析了水下爆炸产物与防雷舱舷侧空舱的相互作用过程以及水下爆炸产物的压力变化规律。研究表明：在近自由面水下接触爆炸下，防雷舱舷侧空舱的内压载荷可分为冲击波载荷、准静态压力载荷和负压载荷3种，防雷舱舷侧空舱的破坏主要由冲击波载荷和准静态压力载荷造成，并且准静态压力载荷的比冲量是冲击波载荷的数倍，而负压载荷对防雷舱舷侧空舱的影响可忽略不计。
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图 8 动态劈裂后的试件（冲击应变率为1.72～7.42 s−1）
Figure 8. Specimens after dynamic splitting at the strain rates of 1.72－7.42 s−1
图 9 由高速摄影和数字图像相关技术结合获得的试件DT0-3开裂过程和竖向拉应变场演化
Figure 9. Crack and vertical tensile strain field evolutionsin specimen DT0-3 by combining the high-speed videoand digital image correlation techniques
图 10 由高速摄影和数字图像相关技术结合获得的试件DT1-3开裂过程和竖向拉应变场演化
Figure 10. Crack and vertical tensile strain field evolutionsin specimen DT1-3 by combining the high-speed videoand digital image correlation techniques
图 11 DT0～DT3组试件劈裂应力-时间曲线
Figure 11. Splitting stress-time curves of specimen groups DT0－DT3
图 12 试件劈裂强度与钢纤维掺量的关系
Figure 12. Splitting strength of specimens varied with steel fibre content
图 13 钢纤维对试件劈裂强度的增强效应
Figure 13. Enhancement effect of steel fiber on splitting strength of specimens
图 14 UHPFRC的动态劈裂平均能耗
Figure 14. Average energy consumption of UHPFRC in dynamic splitting
图 15 经裁剪、降噪和过滤处理后的μXCT图像
Figure 15. The μXCT images after cropping, filtering, and segmentation
图 16 纤维和孔洞灰度阈值的初步确定
Figure 16. Initial determination of grey thresholds for pores and fibres
图 17 孔洞体积分数对灰度阈值的灵敏度分析
Figure 17. Sensitivity analysis of pore volume fraction to the grey threshold
图 19 试件DT0-3～DT3-3分割后孔洞3D图像
Figure 19. Segmented 3D images of pores for specimens DT0-3－DT3-3
图 20 试件DT1-3～DT3-3分割后的纤维
Figure 20. Segmented 3D images and skeleton of fibres for specimens DT1-3－DT3-3
图 21 试件DT1-3在xy平面裂缝宽度（切片 400）
Figure 21. Crack width on the xy plane of the specimen DT1-3 (slice 400)
图 25 试件DT1-3主裂缝及跨过裂缝的纤维
Figure 25. The main crack and crack-crossing fibres of specimen DT1-3
图 26 试件DT2-3主裂缝及跨过裂缝的纤维
Figure 26. The main crack and crack-crossing fibres of specimen DT2-3
图 27 试件DT3-3主裂缝及跨过裂缝的纤维
Figure 27. The main crack and crack-crossing fibres of specimen DT3-3
表 1 各组UHPFRC试件的配合比
Table 1. Mixing proportions of UHPFRC specimens for each test group
试件 钢纤维体积分数/% 配合比/(kg·m−3) 静力压缩 准静态劈裂 动态劈裂 水泥 硅灰 水 细砂 石英粉 减水剂 钢纤维 C0 ST0 DT0 0 1054 263 263 580 316 24 0 C1 ST1 DT1 1 1054 263 263 580 316 24 78 C2 ST2 DT2 2 1054 263 263 580 316 24 156 C3 ST3 DT3 3 1054 263 263 580 316 24 234 
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表 2 静力压缩试验结果
Table 2. Results of static compression tests
试件 钢纤维体积分数/% 峰值应变/% 峰值应力/MPa 弹性模量/GPa SC0 0 0.325±0.039 106.82±5.03 39.68±1.88 SC1 1 0.327±0.030 118.82±4.18 40.31±1.34 SC2 2 0.351±0.064 138.43±6.51 44.12±1.19 SC3 3 0.359±0.016 155.12±0.40 45.14±1.26
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表 3 静力劈裂试验结果
Table 3. Results of static split tests
试件 钢纤维体积分数/% 劈裂强度/MPa 试件 钢纤维体积分数/% 劈裂强度/MPa ST0 0 11.41±0.46 ST2 2 23.47±1.04 ST1 1 20.98±1.23 ST3 3 26.37±0.22
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表 4 动态劈裂试验结果
Table 4. Results of dynamic split tests
试件 ˙σ/(GPa·s−1) ˙ε/s−1 T/μs σT/MPa σT,a/MPa δt DT0-1 66.80 1.72 228 15.23 16.62 ± 2.12 1.33 DT0-2 89.40 2.30 168 15.02 1.32 DT0-3 118.13 3.04 166 19.61 1.72 DT1-1 258.37 6.41 94 24.29 24.41± 0.11 1.16 DT1-2 191.70 4.76 128 24.54 1.17 DT1-3 217.20 5.39 112 24.33 1.16 DT2-1 186.67 4.23 134 25.01 25.65± 0.79 1.07 DT2-2 233.08 5.28 108 25.17 1.07 DT2-3 196.76 4.46 136 26.76 1.14 DT3-1 177.31 3.93 170 30.14 31.06 ±0.83 1.14 DT3-2 334.93 7.42 96 32.15 1.22 DT3-3 166.04 3.68 186 30.88 1.17
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表 5 试件DT0-3～DT3-3孔洞分布统计
Table 5. Statistics of pore distribution of specimens DT0-3－DT3-3
试件 孔洞体积
分数/%孔洞数目 孔洞平均
体积/mm3平均等效
直径/mm孔洞数目（占比） de=56.7～400 μm de=>400～800 μm de=>800～1600 μm de>1600 μm DT0-3 1.71 38671 0.053 0.466 27089
(70.05%)10012
(25.89%)1439
(3.72%)131
(0.34%)DT1-3 1.58 21384 0.089 0.554 12859
(60.13%)7389
(34.55%)983
(4.60%)153
(0.72%)DT2-3 1.20 15508 0.093 0.563 8847
(57.05%)5736
(36.99%)810
(5.22%)115
(0.74%)DT3-3 0.98 10158 0.101 0.579 6404
(63.04%)3134
(30.85%)548
(5.39%)72
(0.71%)
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表 6 裂缝及桥连纤维的统计分析
Table 6. Statistical analysis of cracks and bridged fibers
试件 桥连纤维
根数裂缝体积/
mm3裂缝表面积/
mm2相对表面积/
mm−1DT1-3 328 7118.97 10963.40 1.54 DT2-3 747 3234.73 6319.61 1.95 DT3-3 1 468 3081.81 6545.25 2.12
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