分离式霍普金森压剪杆实验技术及其应用研究
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摘要
在各类涉及爆炸、冲击加载的工程技术和科学研究领域中,材料的动态本构关系研究始终是重要的研究课题。传统的一维波加载实验只能确定部分本构参数,动态压-剪复合加载实验则可以提供材料的动态压缩和剪切特性,为本构关系提供更加完整的实验参数。除此之外,材料的屈服、损伤演化、失效、相变等均与剪切密切相关。材料动态压-剪加载的研究不仅丰富了材料的动态力学现象,拓展了研究范围,而且对于认识材料动态响应的演化规律和机理有重要的意义。在武器系统应用中,炸药在压-剪复合加载响应研究,更是关系到武器系统安全性问题的一个关键环节。因此研究和发展压-剪复合加载实验技术不仅具有重要的学术价值而且也是实际应用的迫切需要。本文旨在研究和发展高应变率下的压-剪复合加载实验技术,论证和发展能够有效用于研究材料高应变率压-剪动态力学行为的SHPSB(分离式霍普金森压剪杆,Split Hopkinson Pressure Shear Bar)实验技术,并拓展其应用领域,最终为研究材料特别是含能材料在压-剪复合加载下的动态力学响应提供实验支撑。本文是在国家自然科学基金项目(10672177,10872215)的资助下开展的实验技术和应用研究。
本文的主要内容分为以下三部分:
第一部分内容是对分离式霍普金森压剪杆实验技术的基本加载原理及装置中传播的应力波的类型和规律进行研究。讨论了弹性弯曲波与弹性纵波复合传播的问题,建立了弯曲波和纵波复合传播的动力学方程。分析结果表明,一般情况下杆中弯曲波和纵波同时传播时,两者在一定程度上是耦合的。然而在弹性小变形情况下,两者可以进行解耦处理,利用数值模拟验证了分析结果。对SHPSB实验过程进行了数值模拟。结果表明:入射杆中反射波为平面纵波,不存在弯曲波扰动;试样在横截面内平均轴向压缩应力与平均剪切应力沿试样轴向是一致的。
第二部分内容是对分离式霍普金森压剪杆实验测试技术的研究,并对实验误差进行了分析,进一步对试样构型进行了优化探索。
压缩应力、压缩应变测试技术是基于电阻应变片测试方法,利用实验杆上所贴的应变片组,通过半桥接法,消除弯曲波的影响,间接地测量得到了试样的压缩应力、压缩应变。从数值模拟和验证实验两方面证明了压缩应力测试技术、压缩应变测试技术的有效性。提出了基于压电效应的剪切应力测试技术。剪切应力计为Y切旋转17.705°(yzw/17.705°)石英晶体片,利用数值模拟和实验研究了剪切应力在透射杆中的衰减规律,结果表明本文采用的剪切应力测试技术有效。通过理论分析表明,建立起简单可用的剪切应变与实验所测得的剪切应力之间的关系是非常困难的,因此本研究采用了光通量法对剪切应变进行间接测量,由基于数字图像处理的验证实验的结果证明剪切应变测试技术是合理的。
分析了实验测试的主要误差源。结果表明:压缩应力测试的主要误差是在加载初始阶段,试样与实验杆没有达到应力平衡造成的。压缩应变测试的主要误差是透射杆-试样界面与入射杆-试样界面的压缩速度时间不同步,而这一误差的引入具有明显的主观性。剪切应力测试的主要误差有:由于剪切应力计距试样有一定距离,由此引起的系统误差;动态压电系数的标定结果引入的随机误差;电荷放大器的系统噪声误差。剪切应变测试的主要误差是:电压-距离转换系数标定结果引入的随机误差;光电接收器的系统噪声误差。对于本文给出的算例,分别计算出剪切应力的极限误差为0.24 MPa,剪切应变测量极限误差为0.00038。
提出了两种优化的试样构型(试样构型I、试样构型II)以简化试样的应力状态。分别通过数值模拟以及SHPB实验对优化的试样构型的合理性进行了验证。结果表明:试样构型I的计算结果与真实应力-应变曲线吻合较差,而在应变不超过5%情况下,试样构型II与数值模拟以及真实应力-应变曲线吻合较好。第三部分是对分离式霍普金森压剪杆实验技术的应用研究。对某含铝PBX炸药试样进行了SHPSB实验和动态摩擦研究。
建立了一个率相关的损伤本构模型来描述PBX炸药试样不同动态加载下的力学响应。采用试样构型II对PBX炸药进行了分离式霍普金森压剪杆实验。实验结果表明PBX试样在破坏前达到了压力和剪力平衡,符合SHPSB的基本假定;随着加载应变率的增大,试样压缩破坏强度增大而剪切破坏强度减小;随着应变率的增加,试样由“剪切破坏-压缩破坏”的顺序向“压缩破坏-剪切破坏”的顺序转变。分析表明这些现象均与实验的加载路径有关。基于损伤力学,建立了一个包含应变率效应的损伤本构模型,模型参数由SHPSB实验、被动围压实验、动态巴西实验结果标定获得。进一步利用LS-DYNA提供的二次开发接口将本文建立的损伤本构模型添加到材料模型库中。对SHPB实验、动态巴西实验、SHPSB实验进行了模拟,结果表明本文建立的本构模型较为准确地预测了所研究PBX炸药试样不同加载下试样力学性能的劣化以及试样的破坏,具有较强的普适性。
利用SHPSB实验技术对一种PBX炸药试样和钢摩擦副进行了动态摩擦实验。实验结果表明:本文研究的两种摩擦副在稳定摩擦阶段的摩擦系数并非恒定值,摩擦系数在0.09-0.19范围内变化,表面粗糙度越大的摩擦副的摩擦系数越大。由实验结果表明,分离式霍普金森压剪杆可以方便地应用于动态摩擦研究。基于SHPSB实验技术,实现了对试样的压剪破坏-动态摩擦过程的实验研究。实验结果表明:在试样压剪破坏过程中,试样出现了微观裂纹萌生-发展、宏观裂纹形成、宏观裂纹发展—宏观裂纹界面滑动三个过程。在试样动态摩擦过程可分为稳定摩擦阶段与摩擦系数增大阶段。在稳定摩擦阶段,相互滑动摩擦的界面基本是原有的破坏界面,摩擦系数比较稳定;在摩擦系数增大阶段,相互接触的摩擦面不再是裂纹开裂界面,摩擦界面不再平滑,粗糙度增大,随之摩擦系数也增大。而裂纹摩擦系数增大必然导致裂纹的温升增大,对于炸药的安全性将构成严重的威胁。
In the engineering and scientific fields relating with blast and dynamic loading, the dynamic constitutive research is one of major issues. However, traditional one dimension wave experiments is not compatible for furnishing all the constitutive parameters. The combined pressure and shear waves can disclose both the dynamic compression and shear properties of materials directly, which offers more integrated parameters. Besides, materials’yield, damage evolution, failure, phase transition etc, have great correlation to shear process. Study on the dynamic compression and shear load on materials not only enriches materials’dynamic phenomenon and extends the research field, but also makes a great sense to understand the dynamic response evolution and its mechanism of materials. In weapon system application, the study on the compression and shear response of explosives is the key part correlated to the security of the weapon system. So, to investigate and develop the experiment technique of compression and shear load is not only important for academic research, but also the imperious requirement of practical application.
This dissertation focuses on developing a SHPSB (Split Hopkinson Pressure Shear Bar) technique, validating the experimental results, extending the application of the SHPSB and finally makes the technique well serving researches of materials constitutive, especially energetic materials. This work was supported by the Natural Science Foundation of China (NSFC) through Grant No. 10672177 and 10872215.
The main contents are divided into three parts:
The first partial work includes basic theory and the propagation of stress waves in the SHPSB bars. The combined propagation of the bending wave and longitudinal wave are discussed. The analysis indicates that two kinds of waves are coupled in general; but in the case of small elastic deformation, they can be uncoupled approximately, which is validated by the numerical results. Detailed simulation of the SHPSB experimental process has been taken. The numerical results indicate that the reflected wave in the incident bar is the longitudinal wave without bending motion; the compression and shear forces are balanced in the specimen.
The second partial work is measuring techniques of the SHPSB, the corresponding error analysis and the optimization of specimen outline. The measurements of the compression stress and strain are based on the strain gauges on the bars. The shear stress is measured by two piezoelectric transducers of quartz (Y-cut with rotation angle-17.7°, yzw/17.705°) embedded at the close-to-specimen end of transmission bars; the shear strain is measured with a novel optical technique which is based on the luminous flux method. The numerical and experimental results validate the measuring techniques of the SHPSB.
It indicates that the error of the compression stress measuring is mainly introduced at early stage of testing, due to the force un-equilibrium in the sample. The error of the compression strain is mainly introduced during data processing. The measuring error of shear stress is aroused by the difference of the shear stress in the specimen and that in the transmission bar, the scatter of the calibration and the system noise of the charge amplifier. The error of shear strain measuring is resulted by the scatter of the calibration and the system noise of the photodiode light detector. The errors of the shear stress and strain measurement are respectively 0.24 MPa and 0.00038 in the examples provided in this paper.
Two kinds of specimen outline (plane stress and plane strain specimen) are proposed, and validated by the numerical simulations and experimental results. The results indicate that the plane stress specimen is better than the plane strain model. When the strain is less than 5%, the simulation and the validated experiment yield good agreement with the analytic results of the plane stress specimen.
The third partial work is application of the split Hopkinson pressure and shear bar technique.
We performed SHPSB experimental method on a PBX. The plane stress specimens are used. The results indicate that the dynamic compression and shear forces equilibrium are reached in specimens; the compression failure stress enhances, but the shear failure stress decreases with the strain rate increasing; the compression and shear failure time run earlier with the strain rate increasing; the shift of compression failure time is larger than that of shear failure time. Based on the maximum shear failure criterion, we analyze the experimental results. The analysis results show that the above mentioned experimental phenomena are related with experimental loading path. A damage constitutive model including rate-effect is built up. The parameters of the model are calibrated by confinement-SHPB tests, flattened Brazilian disc tests and SHPSB experiments. The proposed damage model is implemented in LS-DYNA as a user defined subroutine. SHPB tests, flattened Brazilian disc tests and SHPSB tests are simulated. The numerical results yield good agreement with experimental results. It indicates that the proposed damage model can rationally predict the PBX mechanical behaviors at different dynamic loadings.
The SHPSB technique is extended to investigate dynamic friction of a steel-PBX friction pair. The results indicate that rough steel-PBX pair takes on a larger friction coefficient (0.09-0.14) than that of the flat one (0.09-0.19). Based on the SHPSB, the response of the PBX at the process of the compression and shear failure-friction loading is investigated. The results indicate that process of the compression and shear failure includes three stages; micro cracks developing, macro cracks appearing and macro cracks developing-macro cracks sliding. In the early process of dynamic friction, the friction coefficient is less than the ratio of the shear stress to the compression stress in the failure process. The friction coefficient increases finally. It may be related with the roughness change in the cracks.
本文的主要内容分为以下三部分:
第一部分内容是对分离式霍普金森压剪杆实验技术的基本加载原理及装置中传播的应力波的类型和规律进行研究。讨论了弹性弯曲波与弹性纵波复合传播的问题,建立了弯曲波和纵波复合传播的动力学方程。分析结果表明,一般情况下杆中弯曲波和纵波同时传播时,两者在一定程度上是耦合的。然而在弹性小变形情况下,两者可以进行解耦处理,利用数值模拟验证了分析结果。对SHPSB实验过程进行了数值模拟。结果表明:入射杆中反射波为平面纵波,不存在弯曲波扰动;试样在横截面内平均轴向压缩应力与平均剪切应力沿试样轴向是一致的。
第二部分内容是对分离式霍普金森压剪杆实验测试技术的研究,并对实验误差进行了分析,进一步对试样构型进行了优化探索。
压缩应力、压缩应变测试技术是基于电阻应变片测试方法,利用实验杆上所贴的应变片组,通过半桥接法,消除弯曲波的影响,间接地测量得到了试样的压缩应力、压缩应变。从数值模拟和验证实验两方面证明了压缩应力测试技术、压缩应变测试技术的有效性。提出了基于压电效应的剪切应力测试技术。剪切应力计为Y切旋转17.705°(yzw/17.705°)石英晶体片,利用数值模拟和实验研究了剪切应力在透射杆中的衰减规律,结果表明本文采用的剪切应力测试技术有效。通过理论分析表明,建立起简单可用的剪切应变与实验所测得的剪切应力之间的关系是非常困难的,因此本研究采用了光通量法对剪切应变进行间接测量,由基于数字图像处理的验证实验的结果证明剪切应变测试技术是合理的。
分析了实验测试的主要误差源。结果表明:压缩应力测试的主要误差是在加载初始阶段,试样与实验杆没有达到应力平衡造成的。压缩应变测试的主要误差是透射杆-试样界面与入射杆-试样界面的压缩速度时间不同步,而这一误差的引入具有明显的主观性。剪切应力测试的主要误差有:由于剪切应力计距试样有一定距离,由此引起的系统误差;动态压电系数的标定结果引入的随机误差;电荷放大器的系统噪声误差。剪切应变测试的主要误差是:电压-距离转换系数标定结果引入的随机误差;光电接收器的系统噪声误差。对于本文给出的算例,分别计算出剪切应力的极限误差为0.24 MPa,剪切应变测量极限误差为0.00038。
提出了两种优化的试样构型(试样构型I、试样构型II)以简化试样的应力状态。分别通过数值模拟以及SHPB实验对优化的试样构型的合理性进行了验证。结果表明:试样构型I的计算结果与真实应力-应变曲线吻合较差,而在应变不超过5%情况下,试样构型II与数值模拟以及真实应力-应变曲线吻合较好。第三部分是对分离式霍普金森压剪杆实验技术的应用研究。对某含铝PBX炸药试样进行了SHPSB实验和动态摩擦研究。
建立了一个率相关的损伤本构模型来描述PBX炸药试样不同动态加载下的力学响应。采用试样构型II对PBX炸药进行了分离式霍普金森压剪杆实验。实验结果表明PBX试样在破坏前达到了压力和剪力平衡,符合SHPSB的基本假定;随着加载应变率的增大,试样压缩破坏强度增大而剪切破坏强度减小;随着应变率的增加,试样由“剪切破坏-压缩破坏”的顺序向“压缩破坏-剪切破坏”的顺序转变。分析表明这些现象均与实验的加载路径有关。基于损伤力学,建立了一个包含应变率效应的损伤本构模型,模型参数由SHPSB实验、被动围压实验、动态巴西实验结果标定获得。进一步利用LS-DYNA提供的二次开发接口将本文建立的损伤本构模型添加到材料模型库中。对SHPB实验、动态巴西实验、SHPSB实验进行了模拟,结果表明本文建立的本构模型较为准确地预测了所研究PBX炸药试样不同加载下试样力学性能的劣化以及试样的破坏,具有较强的普适性。
利用SHPSB实验技术对一种PBX炸药试样和钢摩擦副进行了动态摩擦实验。实验结果表明:本文研究的两种摩擦副在稳定摩擦阶段的摩擦系数并非恒定值,摩擦系数在0.09-0.19范围内变化,表面粗糙度越大的摩擦副的摩擦系数越大。由实验结果表明,分离式霍普金森压剪杆可以方便地应用于动态摩擦研究。基于SHPSB实验技术,实现了对试样的压剪破坏-动态摩擦过程的实验研究。实验结果表明:在试样压剪破坏过程中,试样出现了微观裂纹萌生-发展、宏观裂纹形成、宏观裂纹发展—宏观裂纹界面滑动三个过程。在试样动态摩擦过程可分为稳定摩擦阶段与摩擦系数增大阶段。在稳定摩擦阶段,相互滑动摩擦的界面基本是原有的破坏界面,摩擦系数比较稳定;在摩擦系数增大阶段,相互接触的摩擦面不再是裂纹开裂界面,摩擦界面不再平滑,粗糙度增大,随之摩擦系数也增大。而裂纹摩擦系数增大必然导致裂纹的温升增大,对于炸药的安全性将构成严重的威胁。
In the engineering and scientific fields relating with blast and dynamic loading, the dynamic constitutive research is one of major issues. However, traditional one dimension wave experiments is not compatible for furnishing all the constitutive parameters. The combined pressure and shear waves can disclose both the dynamic compression and shear properties of materials directly, which offers more integrated parameters. Besides, materials’yield, damage evolution, failure, phase transition etc, have great correlation to shear process. Study on the dynamic compression and shear load on materials not only enriches materials’dynamic phenomenon and extends the research field, but also makes a great sense to understand the dynamic response evolution and its mechanism of materials. In weapon system application, the study on the compression and shear response of explosives is the key part correlated to the security of the weapon system. So, to investigate and develop the experiment technique of compression and shear load is not only important for academic research, but also the imperious requirement of practical application.
This dissertation focuses on developing a SHPSB (Split Hopkinson Pressure Shear Bar) technique, validating the experimental results, extending the application of the SHPSB and finally makes the technique well serving researches of materials constitutive, especially energetic materials. This work was supported by the Natural Science Foundation of China (NSFC) through Grant No. 10672177 and 10872215.
The main contents are divided into three parts:
The first partial work includes basic theory and the propagation of stress waves in the SHPSB bars. The combined propagation of the bending wave and longitudinal wave are discussed. The analysis indicates that two kinds of waves are coupled in general; but in the case of small elastic deformation, they can be uncoupled approximately, which is validated by the numerical results. Detailed simulation of the SHPSB experimental process has been taken. The numerical results indicate that the reflected wave in the incident bar is the longitudinal wave without bending motion; the compression and shear forces are balanced in the specimen.
The second partial work is measuring techniques of the SHPSB, the corresponding error analysis and the optimization of specimen outline. The measurements of the compression stress and strain are based on the strain gauges on the bars. The shear stress is measured by two piezoelectric transducers of quartz (Y-cut with rotation angle-17.7°, yzw/17.705°) embedded at the close-to-specimen end of transmission bars; the shear strain is measured with a novel optical technique which is based on the luminous flux method. The numerical and experimental results validate the measuring techniques of the SHPSB.
It indicates that the error of the compression stress measuring is mainly introduced at early stage of testing, due to the force un-equilibrium in the sample. The error of the compression strain is mainly introduced during data processing. The measuring error of shear stress is aroused by the difference of the shear stress in the specimen and that in the transmission bar, the scatter of the calibration and the system noise of the charge amplifier. The error of shear strain measuring is resulted by the scatter of the calibration and the system noise of the photodiode light detector. The errors of the shear stress and strain measurement are respectively 0.24 MPa and 0.00038 in the examples provided in this paper.
Two kinds of specimen outline (plane stress and plane strain specimen) are proposed, and validated by the numerical simulations and experimental results. The results indicate that the plane stress specimen is better than the plane strain model. When the strain is less than 5%, the simulation and the validated experiment yield good agreement with the analytic results of the plane stress specimen.
The third partial work is application of the split Hopkinson pressure and shear bar technique.
We performed SHPSB experimental method on a PBX. The plane stress specimens are used. The results indicate that the dynamic compression and shear forces equilibrium are reached in specimens; the compression failure stress enhances, but the shear failure stress decreases with the strain rate increasing; the compression and shear failure time run earlier with the strain rate increasing; the shift of compression failure time is larger than that of shear failure time. Based on the maximum shear failure criterion, we analyze the experimental results. The analysis results show that the above mentioned experimental phenomena are related with experimental loading path. A damage constitutive model including rate-effect is built up. The parameters of the model are calibrated by confinement-SHPB tests, flattened Brazilian disc tests and SHPSB experiments. The proposed damage model is implemented in LS-DYNA as a user defined subroutine. SHPB tests, flattened Brazilian disc tests and SHPSB tests are simulated. The numerical results yield good agreement with experimental results. It indicates that the proposed damage model can rationally predict the PBX mechanical behaviors at different dynamic loadings.
The SHPSB technique is extended to investigate dynamic friction of a steel-PBX friction pair. The results indicate that rough steel-PBX pair takes on a larger friction coefficient (0.09-0.14) than that of the flat one (0.09-0.19). Based on the SHPSB, the response of the PBX at the process of the compression and shear failure-friction loading is investigated. The results indicate that process of the compression and shear failure includes three stages; micro cracks developing, macro cracks appearing and macro cracks developing-macro cracks sliding. In the early process of dynamic friction, the friction coefficient is less than the ratio of the shear stress to the compression stress in the failure process. The friction coefficient increases finally. It may be related with the roughness change in the cracks.
引文
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