Dynamic failure mechanism of HDPE pipelines with a gasketed bell and spigot joint subjected to blasting seismic load
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摘要: 承插式管道接口更易受到外界荷载破坏导致管道失效，为保证爆破开挖过程中邻近承插式高密度聚乙烯（high-density polyethylene，HDPE）波纹管道的安全运营，控制爆破振动荷载对管道的影响是重点关注内容。通过全尺度预埋单段HDPE波纹管道现场试验，得到管道的振动速度和动应变响应数据，结合LS-DYNA数值模拟软件分别建立了无承插接口管道与含弹性密封圈的承插式HDPE波纹管道；利用现场试验数据验证了无承插口管道模型参数的可靠性，并对比分析了承插式管道的结构位移、振动速度、有效应力的响应规律与失效机制；结合现行规范，根据管道响应规律与接口允许旋转角度计算得到了承插式管道的安全振动速度。研究结果表明：有承插口管道的合振速、合位移和有效应力大于无承插口管道；在同一截面上，有承插口管道迎爆侧的合振速和有效应力更大，而最大合位移出现在截面的背爆侧；管道合位移与合振速在轴线中心处截面最大，并向两端不断减小，有承插口管道中心合位移更大；通过接口允许旋转角度得到此类工况条件下的承插式管道的安全振速为24.77 cm/s。Abstract: Pipelines with a gasketed bell and spigot joint are more vulnerable to external load damage, leading to pipeline failure. To ensure the safe operation of adjacent high-density polyethylene (HDPE) bellows during blasting excavation, control of the influence of blasting vibration load on the pipeline is the main focus. The vibration velocity and dynamic strain response data of the pipeline were collected from the field test of a full-scale embedded single-segment HDPE bellow. The HDPE bellow models without socket contact and with an elastic sealing ring were established using the LS-DYNA numerical simulation software. The reliability of the model parameters of the HDPE bellows without a joint was verified by the field test data, and the response laws and failure mechanisms of the structural displacement, vibration velocity, and effective stress of the HDPE bellows with a gasketed bell and spigot joint were compared and analyzed. The safe vibration velocity of the pipe was determined using the pipeline response law and the allowable rotation angle of the interface in conjunction with the current specification. The research results show that the resultant vibration velocity, resultant displacement, and effective stress of the bellow with a gasketed bell and spigot joint are greater than those of the bellow without a joint. At the same cross-section, the resultant vibration velocity and effective stress on the explosion side of the bellow with a gasketed bell and spigot joint are higher, and the maximum resultant displacement occurs on the back of the explosion side of the cross-section. Along the axis direction of the pipeline, the resultant displacement and the resultant vibration velocity of the pipeline decrease continuously from the center to both ends of the pipeline, and the resultant displacement of the pipeline with a gasketed bell and spigot joint is larger. The safe vibration velocity of the pipeline with a gasketed bell and spigot joint under such working conditions is 24.77 cm/s, according to the allowable rotation angle of the interface.
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利用压痕法测试材料的力学性能已有悠久的历史, 与其它的材料性能测试方法相比, 压痕法具有无损(微损)、便捷等优点[1-3]。传统的硬度检测就是压痕法的一种应用——通过分析压痕的最终几何量及荷载, 给出材料的硬度指标。硬度按照不同的测试方法又可分为布氏、维氏、洛氏、里氏、肖氏等硬度[4]。随着实验技术的进步, 已容易通过仪器化的压痕实验获取实验的压入荷载与位移(p-d)曲线, 如何从p-d曲线中获得更多的材料力学参数成为研究者们关注的问题。W.C.Oliver等[5]提出了由静态球形压痕力与位移的关系确定金属材料弹性模量的方法。此后, Y.P.Cao等[6]也进行了该方面的工作; Y.T.Cheng等[7-8]利用量纲分析方法对压痕实验进行了归纳, 并结合有限元数值模拟进行分析, 总结出压痕测试的基本原则。Y.P.Cao等[9]提出了一个分析框架, 从球形静压痕实验的p-d曲线进行反演, 获得幂强化材料的弹性模量、屈服应力及硬化指数等参数。
随着压痕法测试技术的发展, 研究者开始将其用于材料动态力学性能的研究。20世纪90年代霍普金森压杆(SHPB)被用于动态压痕测试。G.Subhash等[10]将SHPB入射杆作为加载部件, 杆与试件接触端套上锥形压头, 分别采用力、位移传感器测试压入力和位移, 获得相应的p-d曲线。M.Nilsson[11]采用一维应力波理论通过入射杆与透射杆上的信号来计算压头的压入位移。张新等[12]在上述装置上进行了铜、钛、铝合金动压痕实验研究。G.Subhash的方法[10]中采用悬臂梁测量位移时程曲线, 由于悬臂梁的振动模态比较复杂, 各个模态被激发的程度与加载速率有关, 应变测量值和端点的位移关系是不确定的, 所以无法的到准确的测量结果。M.Nilsson[11]采用了传统的实验方法[10], 利用入射、反射波信号来计算压头的位移, 但是锥形段的存在以及压头的安装导致其有效性存在疑问。
本文中提出一种采用双试件的球形压痕测试方法; 采用有限元软件ABAQUS/Explicit对该实验方法进行数值模拟, 以评估方法的有效性与准确性; 采用新测试方法对7075铝合金进行动态压痕实验, 研究7075铝合金的动态力学性能。
1. 动态压痕实验
1.1 实验装置
图 1为双试件动压痕实验装置示意图。将硬质合金小球放在2个试件中间(如图 1(b)所示), 以此取代传统霍普金森压杆实验装置中的试件。在入射应力脉冲作用下, 硬质合金小球同时压入2个试件, 小球对其两侧试件有相同的压入力, 因此能够方便地利用传统霍普金森压杆实验方法测出硬质合金小球压入试件过程中的压入位移和压入力。通过入射杆和透射杆的输出信号可得到材料的p-d曲线。
1.2 实验数据处理
将测量得到的入射波信号εi(t)、反射波信号εr(t)和透射波信号εt(t), 代入式(1), 即可获得小球对2个试件的压入速度、加速度和压力与时间的关系:
{˙u(t)=12c0[εi(t)−εr(t)−εt(t)]u(t)=12c0∫t0[εi(t)−εr(t)−εt(t)]dtp(t)=A0E0εt(t) (1) 式中:c0为应力波在杆件中的传播速度, E0为压杆的杨氏模量, A0为杆件的横截面面积, u(t)和
(t)为每一时刻硬质合金小球压入试件的深度与速度, p(t)为试件受到的压入力。
2. 动态压痕实验的数值模拟
2.1 计算模型
利用有限元软件ABAQUS/Explicit中的轴对称模型, 对M.Nilsson的方法[11]和本文中提出的新方法进行数值模拟, 并将模拟结果与实验结果进行了比对。计算中, 试件与杆件之间保持波阻抗匹配:ρscsAs=ρ0c0A0, 其中ρs、cs、和As分别为试件的密度、弹性波速和横截面积。子弹为尺寸为Ø14.5 mm×400 mm, 入射杆与透射杆尺寸均为Ø14.5 mm×1 000 mm。钢试件匹配的杆件材料为60Si2Mn, 铝合金试件匹配的杆件材料为铝合金。试件尺寸为Ø14.5 mm×6 mm, 试件材料模型选用Johnson-Cook(J-C)本构模型。硬质合金小球的材料为碳化钨, 直径为1.6 mm。材料具体参数见表 1~2, 其中:E为弹性模量, μ为泊松比, ρ为密度, A、B、C、n和m为试件的J-C本构常数。
表 1 杆件及试件的弹性参数Table 1. Elastic constants of the bars and the specimens材料 E/GPa μ ρ/(g·m-3) 60Si2Mn 206 0.29 7.80 45钢 210 0.29 7.80 铝合金 71 0.28 2.70 碳化钨 450 0.28 18.00 表 2 试件的J-C本构参数Table 2. J-C constants of specimens材料 A/MPa B/MPa C n m 45钢 1 150 739 0.014 0.26 1.03 铝合金 369 684 0.008 3 0.73 1.70 图 2为2种试件的加载方式示意图。在入射杆和透射杆中布置波形测量点, 在试件两端设置位移测量点。对于M.Nilsson的方法[11], 采取2个不同角度的压头:锥头(45°半锥角如图 2(a)所示)和平头(90°半锥角)。
图 2 试件加载方式和位移测量基准点Figure 2. Specimen loading patterns and reference points for displacement measurement2.2 实验的模拟分析
图 3为根据M.Nilsson的实验方法[11]模拟得到的压入深度时程曲线, 从图中可以看出, 压入深度的计算值与测量值存在较大差异。造成误差的原因主要是应力波在锥形段中的反射透射, 会影响最终计算结果。在实验中, 小球需要焊接在锥头上, 锥头与杆连接通常采用粘接的方式[12], 这使得局部的变形状况变得复杂, 也会导致计算结果与实验结果有差异。图 4为根据本文中实验方法模拟得到的压入深度时程曲线。由于排除了锥头与杆之间的波阻抗不匹配带来的影响, 提高了实验的准确性, 因此能够得到与位移测量点输出结果较一致的压头压入位移时程曲线。图 4(a)为铝合金计算结果, 与测量点测到的结果比较一致; 图 4(b)为45钢计算结果, 虽然与测量点的测试结果存在一定的误差, 但与真实压入过程吻合很好。
图 3 计算压痕深度与基准点测量压痕深度比较(Nilsson方法)Figure 3. Calculated indentation depths compared with the ones measured from the refence points (in Nillson's method)
图 4 计算压痕深度与基准点测量压痕深度比较(本文方法)Figure 4. Calculated indentation depths compared with the ones measured from the refence points (in this paper)图 5为铝合金试件的Misses应力云图。由图 5可以看出, 在加载过程中, 入射杆端试件在应力脉冲作用下首先与硬质合金小球发生碰撞, 获得压痕, 然后压力脉冲再通过小球, 与透射杆端试件发生作用, 最终透射杆端试件得到压痕。图 5显示在撞击开始阶段, 前后试件的压痕存在较小的差异, 碰撞发生10 μs之后, Misses应力基本上达到对称, 两试件得到相同的压痕深度。
图 5 采用本文方法得到接触过程中的Misses应力云图Figure 5. Misses stress contours in the contact process using the method in this paper3. 铝合金动态力学性能的实验测量
采用双试件方法对7075铝合金试件进行动态压痕实验, 实验在Ø14.5 mm霍普金森压杆装置上进行, 选用规格为Ø14.5 mm×400 mm的子弹进行打击, 得到3.5、8和12 m/s等3种打击速度下的实验结果。图 6为实验测得的典型波形(电压信号), 由于透射波信号非常微弱, 透射杆上采用了半导体应变片。
图 7为波形处理得到的相关曲线, 其中应变率强化作用明显。由图 5也可观察到, 压痕范围内应变分布非常复杂, 在凹痕顶部应变由内向外依次变小(但未到零), 应变率难以给出。G.Subhash等[10]将压痕的压入速度与压痕几何尺寸的比值定义为平均应变率, 其中压痕几何尺寸为压痕深度或对角线的长度, 则上述实验的平均应变率分别约为3.5×104、4.0×104和4.2×104 s-1, 一般SHPB实验很难达到。
图 7 双试件新方法的波形处理结果Figure 7. Waveforms aquired by using the new method with double specimens4. 结论
提出了双试件动态压痕实验方法, 通过数值模拟对其与现有实验方法进行比较, 结果表明采用双试件法能够得到较现有方法更准确的压头压入位移-时间曲线, 且双试件法的理想实验条件更易满足, 实验可靠性更高。在对铝合金材料进行实际实验后, 得到4×104 s-1左右的平均应变率估计值。该方法可在传统SHPB上轻易实现, 同时数据处理简单, 能够用于104~105 s-1应变率范围内材料动态性能的研究。
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图 5 数值模拟与现场试验峰值合振速的对比
Figure 5. Comparison of peak resultant vibration velocities between numerical simulation and field test
图 7 同一截面管道峰值合振速
Figure 7. Comparison of peak resultant vibration velocities at the same section of different pipelines
图 8 同一截面管道峰值有效应力
Figure 8. Comparison of peak effective stresses at the same section of different pipelines
图 9 同一截面管道峰值合位移
Figure 9. Comparison of peak resultant displacements at the same section of different pipelines
表 1 预埋管道力学参数
Table 1. Mechanical parameters of buried pipeline
材料 弹性模量/MPa 密度/(g·cm−3) 环刚度/(kN·m−2) 极限强度/MPa 泊松比 HDPE 834.9 0.936 8 31.6 0.46 
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表 2 管道、橡胶、粉质黏土与砂岩材料模型参数
Table 2. Parameters of pipeline, rubber, silty clay and sandstone material models
材料 密度/(g·cm−3) 弹性模量/GPa 剪切模量/GPa 泊松比 黏聚力/MPa 内摩擦角/(°) 抗拉强度/MPa 管道 0.936 0.834 9 0.46 31.6 粉质黏土 1.980 0.039 4.3 0.35 0.035 15 0.028 砂岩 2.680 52 11.2 0.25 5.5 43 2.58 橡胶 1.200 0.49
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表 3 炸药参数
Table 3. Parameters of the explosive
材料 ρ/(g·cm−3) A/GPa B/GPa R1 R2 ω E0/GPa V 炸药 1.25 214 18.2 4.2 0.9 0.15 4.19 1
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