锥头弹丸正撞击下金属靶板破坏模式的理论和数值模拟研究
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摘要
本文对刚性锥头弹丸侵彻延性金属靶板的问题进行了较全面的理论研究和数值模拟。分析了不同模式下的破坏现象与破坏机理,建立了适用于不同破坏模式的侵彻模型,成功预测了弹道极限、侵彻耗能和残余速度。研究了不同破坏模式的转化关系,提出了一个适用于不同锥角的刚性弹丸撞击延性金属靶板的靶板破坏模式相图。利用ABAQUS的二次开发模块VUMAT,嵌入了含损伤的JC本构程序,并成功用于不同锥角弹丸正撞击金属靶板的数值模拟。本文的研究和结论可以用于弹丸几何尺寸的优化设计,也可以用来进行防护结构的安全计算(设计)和安全评估。本文的主要内容包括一下几个方面:
系统地研究了锥头弹丸撞击下金属靶板的扩孔破坏。假定会属薄靶板的变形由整体变形和局部变形两部分构成,局部变形分析采用采用准静态的柱形空穴膨胀理论结合构造的考虑靶板背面自由表面效应的柱形空穴膨胀理论的修正函数,给出了靶板对弹丸阻力的表达式,从而计算出局部变形耗能。整体变形的分析采用Wen-Jones模型的近似准静态方法,认为靶板的受力达到靶板的极限载荷后才发生整体变形,靶板的整体变形满足一定的载荷一位移关系,从而计算出整体耗能。通过推导给出了薄靶板的临界穿透耗能公式和弹道极限公式。然后讨论了模型的适用范围,根据靶板是否发生整体变形给出了一个区分薄靶和厚靶的判断条件。对于厚靶的穿透,假定靶板只发生局部变形,改进了的Wen的有关侵彻力的半经验公式,静阻力部分由准静态空穴膨胀结合自由表面修正效应函数给出,动阻力部分与弹丸的瞬时速度有关,结合运动方程给出了弹丸的残余速度和靶板的弹道极限公式。公式的预测结果与实验数据非常吻合。
建立了锥头弹丸撞击下靶板发生冲塞破坏的理论模型。对Wen-Jones模型进行了扩展,考虑了弹头压入阶段消耗的能量,分析了带有总体变形的薄靶的冲塞破坏。对于厚靶的冲塞破坏,只考虑局部变形的影响。首先,研究了平头弹丸正撞击下金属靶板的绝热剪切冲塞破坏,在考虑了一个热粘塑性本构的基础上修正了Bai-Johnson模型,得到了穿透能量、弹丸残余速度和弹道极限的计算公式,并与文献中的相关实验结果进行了比较。并结合Wen-Jones模型研究了带有整体变形的局部简单剪切破坏向局部化的绝热剪切冲塞破坏的临界转化条件。然后将建立的平头弹丸的绝热剪切冲塞破坏模型推广到锥头弹丸的绝热剪切冲塞破坏。
对于锥头弹丸撞击下厚靶的冲塞破坏分为两种情况:两阶段模型和三阶段模型。两阶段模型包括压入阶段和绝热冲塞阶段:三阶段模型包括压入阶段、侵彻阶段和绝热冲塞阶段,压入阶段和侵彻阶段与厚靶的扩孔过程类似,靶体材料对弹丸的阻力通过空穴膨胀理论给出,绝热冲塞阶段计算了绝热剪切耗能,经过推导给出了求解靶板的弹道极限公式,并与实验结果进行了对比。
讨论了破坏模式产生影响的几种因素,着重分析了弹丸正撞击下弹头的几何形状、材料的力学性能和靶板的几何参数等对金属靶板破坏模式产生的影响。结合实验现象介绍了不同的破坏模式,研究了不同破坏模式之间发生转化的条件,通过理论分析得出了对应条件下的破坏模式发生转换的临界锥角,最终给出了不同厚度靶板在不同锥角刚性弹丸正撞击下的破坏模式相图。
利用ABAQUS/VUMAT嵌入了含损伤的JC本构,对平头弹丸侵彻金属靶板进行了数值模拟,分析了不同网格密度对计算结果的影响,与实验结果进行了对比,发现数值计算很好的模拟出了靶板弹道极限随厚度变化曲线的弯折现象(kink),而且弹道极限的计算结果与实验结果符合很好,验证了开发的VUMAT的可靠性。然后用开发的VUMAT对不同锥角的弹丸撞击不同厚度金属靶板的破坏过程进行了计算,模拟结果表明:随着弹丸锥角的增加,有限厚度靶板的破坏模式由扩孔转化到冲塞破坏,靶板的抗弹能力随之降低。对弹丸的运动和侵彻过程中受力等进行了分析,发现弹丸侵彻过程中可能与靶板发生多次碰撞,并与理论分析进行了比较和讨论。
A combined numerical and theoretical study is presented in this thesis to examine the penetration and perforation of ductile metal plates subjected to impact by conical-nosed projectiles.Failure modes of metal plates under normal impact by conical-nosed projectiles are discussed,and for different failure modes corresponding theoretical models are established to predict ballistic limits of the plates,residual velocities of the projectiles and perforation energies.Based on the analysis of critical conditions for the transition of different failure modes,a simplified failure (mechanism) diagram for metallic plates under normal impact by conical-nosed projectiles is proposed.Numerical simulations with ABAQUS/VUMAT in which a modified JC constitutive relation with damage is adopted are performed to study the influence of various parameters on the perforation behaviour of metal plates.The findings and conclusions of the investigations conducted in the thesis are helpful for the design of kenietic energy projectiles,protective structures and safety assessment. This paper mainly consists of the following parts:
Analytical equations for the perforation of fully-clamped thin metallic plates are derived based on the assumption that plate deformation consists of local piercing as well as global response.Local piercing is analyzed by using quasi-static cylindrical cavity expansion theory with free surface effects whilst global deformation is evaluated by adopting the method employed in the Wen-Jones model.Simple analytical equations are obtained to predict the perforation energy and the ballistic limits.Furthermore,the range of applicability of the model is discussed and a criterion for differentiating a thin plate from a thick target is proposed by comparing the collapse load with the maximum local piercing load.For thick plates,based on the assumption that the deformation is localized and that the impact energy is dissipated only by penetration,Modified Wen's semi-empirical equation is applied to the perforation of thick metallic plates,It is further assumed that the mean pressure offered by the target materials to resist the projectiles consists of two parts:a quasi-static part due to the elastic-plastic deformation of the target materials and a dynamic part due to penetration velocity.Equations are obtained for the residual velocity and ballistic limit.It transpires that the present model predictions are in good agreement with available experimental data for metallic plates struck normally by conical-nosed projectiles.
The plugging failure of metallic plates struck normally by a rigid conically-nosed projectile is studied in detail.A modified Bai-Johnson model is suggested herein for the adiabatic shear plugging of a ductile metal plate struck transversely by a flat-ended projectile based on the theories of adiabatic shear instability and thermo-viscoplastic constitutive relationship of ductile metals.By assuming that at post-instability the plate continues to deform the total energy absorbed in the adiabatic shear plugging is analyzed and an expression for the ballistic limit is derived. Furthermore,a critical condition is obtained for differentiating localized adiabatic shear plugging from simple shear plugging failure with global deformations by comparing the model suggested in this paper and the Wen-Jones model.It transpires that the present theoretical predictions are in good agreement with available experimental data in terms of the ballistic limits,perforation energies,residual velocities and the critical transition condition for the modes of plugging failure of ductile metal plates subjected to impact by flat-nosed missiles.
For the plugging failure of thick metallic plates struck by rigid conical-nosed projectiles,two theoretical models are suggested depending on the perforation process. There are two cases for the perforaton process,viz.(1) indentation of conical nose, followed by adiabatic plugging formation;(2) indentation of conical nose,penetration (ductile hole enlargement) and then followed by final adiabatic shear plugging. Equations are obtained for residual velocity and ballistic limit for both cases and are compared with available experiments.It is shown tha the present model predictions are in good agreement with the available experimental results
The effects of projectile nose shape,properties of plate material,and ratio of plate thickness to projectile diameter on the failure modes are discussed.Based on the analysis of critical conditions for the transition between ductile hole enlargement (piercing) and plugging failure,a simplified failure(mechanism) diagram for the perforation of metallic plates subjected to impact by conical-nosed projectiles at normal incidence is proposed.
Numerical simulations with ABAQUS/VUMAT into which a modified JC constitutive relation with damage is incorporated are performed to study the perforaion and penetration of metallic plates struck normally by flat-ended and conical-nose projectiles.Transient deformation and perforation process are obtained. It is shown that with increasing target thickness,target deformation becomes more and more localized and that the present numerical model is capable of reproducing the experimental observations including the "kink" effect.It is also shown that projectile cone angle has significant effect on the perforation modes of ductile metal plates and that for smaller cone angles plates fail by piercing or ductile hole growth and for larger cone angles plates fail by shear plugging or ductile hole enlargement plus shear plugging depending upon the ratio of plate thickness to projectile diameter.Numerical results are found to be in good agreement with available test data for the perforation of steel plates struck normally by flat-ended projectiles.
系统地研究了锥头弹丸撞击下金属靶板的扩孔破坏。假定会属薄靶板的变形由整体变形和局部变形两部分构成,局部变形分析采用采用准静态的柱形空穴膨胀理论结合构造的考虑靶板背面自由表面效应的柱形空穴膨胀理论的修正函数,给出了靶板对弹丸阻力的表达式,从而计算出局部变形耗能。整体变形的分析采用Wen-Jones模型的近似准静态方法,认为靶板的受力达到靶板的极限载荷后才发生整体变形,靶板的整体变形满足一定的载荷一位移关系,从而计算出整体耗能。通过推导给出了薄靶板的临界穿透耗能公式和弹道极限公式。然后讨论了模型的适用范围,根据靶板是否发生整体变形给出了一个区分薄靶和厚靶的判断条件。对于厚靶的穿透,假定靶板只发生局部变形,改进了的Wen的有关侵彻力的半经验公式,静阻力部分由准静态空穴膨胀结合自由表面修正效应函数给出,动阻力部分与弹丸的瞬时速度有关,结合运动方程给出了弹丸的残余速度和靶板的弹道极限公式。公式的预测结果与实验数据非常吻合。
建立了锥头弹丸撞击下靶板发生冲塞破坏的理论模型。对Wen-Jones模型进行了扩展,考虑了弹头压入阶段消耗的能量,分析了带有总体变形的薄靶的冲塞破坏。对于厚靶的冲塞破坏,只考虑局部变形的影响。首先,研究了平头弹丸正撞击下金属靶板的绝热剪切冲塞破坏,在考虑了一个热粘塑性本构的基础上修正了Bai-Johnson模型,得到了穿透能量、弹丸残余速度和弹道极限的计算公式,并与文献中的相关实验结果进行了比较。并结合Wen-Jones模型研究了带有整体变形的局部简单剪切破坏向局部化的绝热剪切冲塞破坏的临界转化条件。然后将建立的平头弹丸的绝热剪切冲塞破坏模型推广到锥头弹丸的绝热剪切冲塞破坏。
对于锥头弹丸撞击下厚靶的冲塞破坏分为两种情况:两阶段模型和三阶段模型。两阶段模型包括压入阶段和绝热冲塞阶段:三阶段模型包括压入阶段、侵彻阶段和绝热冲塞阶段,压入阶段和侵彻阶段与厚靶的扩孔过程类似,靶体材料对弹丸的阻力通过空穴膨胀理论给出,绝热冲塞阶段计算了绝热剪切耗能,经过推导给出了求解靶板的弹道极限公式,并与实验结果进行了对比。
讨论了破坏模式产生影响的几种因素,着重分析了弹丸正撞击下弹头的几何形状、材料的力学性能和靶板的几何参数等对金属靶板破坏模式产生的影响。结合实验现象介绍了不同的破坏模式,研究了不同破坏模式之间发生转化的条件,通过理论分析得出了对应条件下的破坏模式发生转换的临界锥角,最终给出了不同厚度靶板在不同锥角刚性弹丸正撞击下的破坏模式相图。
利用ABAQUS/VUMAT嵌入了含损伤的JC本构,对平头弹丸侵彻金属靶板进行了数值模拟,分析了不同网格密度对计算结果的影响,与实验结果进行了对比,发现数值计算很好的模拟出了靶板弹道极限随厚度变化曲线的弯折现象(kink),而且弹道极限的计算结果与实验结果符合很好,验证了开发的VUMAT的可靠性。然后用开发的VUMAT对不同锥角的弹丸撞击不同厚度金属靶板的破坏过程进行了计算,模拟结果表明:随着弹丸锥角的增加,有限厚度靶板的破坏模式由扩孔转化到冲塞破坏,靶板的抗弹能力随之降低。对弹丸的运动和侵彻过程中受力等进行了分析,发现弹丸侵彻过程中可能与靶板发生多次碰撞,并与理论分析进行了比较和讨论。
A combined numerical and theoretical study is presented in this thesis to examine the penetration and perforation of ductile metal plates subjected to impact by conical-nosed projectiles.Failure modes of metal plates under normal impact by conical-nosed projectiles are discussed,and for different failure modes corresponding theoretical models are established to predict ballistic limits of the plates,residual velocities of the projectiles and perforation energies.Based on the analysis of critical conditions for the transition of different failure modes,a simplified failure (mechanism) diagram for metallic plates under normal impact by conical-nosed projectiles is proposed.Numerical simulations with ABAQUS/VUMAT in which a modified JC constitutive relation with damage is adopted are performed to study the influence of various parameters on the perforation behaviour of metal plates.The findings and conclusions of the investigations conducted in the thesis are helpful for the design of kenietic energy projectiles,protective structures and safety assessment. This paper mainly consists of the following parts:
Analytical equations for the perforation of fully-clamped thin metallic plates are derived based on the assumption that plate deformation consists of local piercing as well as global response.Local piercing is analyzed by using quasi-static cylindrical cavity expansion theory with free surface effects whilst global deformation is evaluated by adopting the method employed in the Wen-Jones model.Simple analytical equations are obtained to predict the perforation energy and the ballistic limits.Furthermore,the range of applicability of the model is discussed and a criterion for differentiating a thin plate from a thick target is proposed by comparing the collapse load with the maximum local piercing load.For thick plates,based on the assumption that the deformation is localized and that the impact energy is dissipated only by penetration,Modified Wen's semi-empirical equation is applied to the perforation of thick metallic plates,It is further assumed that the mean pressure offered by the target materials to resist the projectiles consists of two parts:a quasi-static part due to the elastic-plastic deformation of the target materials and a dynamic part due to penetration velocity.Equations are obtained for the residual velocity and ballistic limit.It transpires that the present model predictions are in good agreement with available experimental data for metallic plates struck normally by conical-nosed projectiles.
The plugging failure of metallic plates struck normally by a rigid conically-nosed projectile is studied in detail.A modified Bai-Johnson model is suggested herein for the adiabatic shear plugging of a ductile metal plate struck transversely by a flat-ended projectile based on the theories of adiabatic shear instability and thermo-viscoplastic constitutive relationship of ductile metals.By assuming that at post-instability the plate continues to deform the total energy absorbed in the adiabatic shear plugging is analyzed and an expression for the ballistic limit is derived. Furthermore,a critical condition is obtained for differentiating localized adiabatic shear plugging from simple shear plugging failure with global deformations by comparing the model suggested in this paper and the Wen-Jones model.It transpires that the present theoretical predictions are in good agreement with available experimental data in terms of the ballistic limits,perforation energies,residual velocities and the critical transition condition for the modes of plugging failure of ductile metal plates subjected to impact by flat-nosed missiles.
For the plugging failure of thick metallic plates struck by rigid conical-nosed projectiles,two theoretical models are suggested depending on the perforation process. There are two cases for the perforaton process,viz.(1) indentation of conical nose, followed by adiabatic plugging formation;(2) indentation of conical nose,penetration (ductile hole enlargement) and then followed by final adiabatic shear plugging. Equations are obtained for residual velocity and ballistic limit for both cases and are compared with available experiments.It is shown tha the present model predictions are in good agreement with the available experimental results
The effects of projectile nose shape,properties of plate material,and ratio of plate thickness to projectile diameter on the failure modes are discussed.Based on the analysis of critical conditions for the transition between ductile hole enlargement (piercing) and plugging failure,a simplified failure(mechanism) diagram for the perforation of metallic plates subjected to impact by conical-nosed projectiles at normal incidence is proposed.
Numerical simulations with ABAQUS/VUMAT into which a modified JC constitutive relation with damage is incorporated are performed to study the perforaion and penetration of metallic plates struck normally by flat-ended and conical-nose projectiles.Transient deformation and perforation process are obtained. It is shown that with increasing target thickness,target deformation becomes more and more localized and that the present numerical model is capable of reproducing the experimental observations including the "kink" effect.It is also shown that projectile cone angle has significant effect on the perforation modes of ductile metal plates and that for smaller cone angles plates fail by piercing or ductile hole growth and for larger cone angles plates fail by shear plugging or ductile hole enlargement plus shear plugging depending upon the ratio of plate thickness to projectile diameter.Numerical results are found to be in good agreement with available test data for the perforation of steel plates struck normally by flat-ended projectiles.
引文
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