陶瓷/金属复合靶板受变形弹体撞击问题的研究
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摘要
复合装甲板是将各种特性的材料进行优化配置，通过粘接或压力加工的方式结合而成。陶瓷和铝合金(或钢板)构成的陶瓷／金属复合装甲，是将韧性材料和高硬度的脆性材料结合到一起，具有良好的抗弹效果。在轻型装甲车辆、舰船、坦克和直升飞机中有很好的应用。因此研究弹体对陶瓷／金属复合靶板的撞击具有重要意义。
本文主要研究弹体撞击陶瓷／金属复合靶板中有关现象和规律，具体内容包括：陶瓷材料动态力学性能的实验研究，弹体撞击靶板时的变形分析，弹体撞击陶瓷／金属复合靶板的理论分析模型和数值模拟，得到了一些有意义的结果。
1．SHPB实验方法的改进和Al_2O_3陶瓷动态力学性能的实验研究
为了了解材料特性，首先对陶瓷材料的动态力学特性进行了实验研究。所选材料为四川宜宾金洋电子陶瓷厂制备的95％Al_2O_3陶瓷。由于陶瓷为脆性材料，而且抗压强度非常高，其破坏应变极其微小，在SHPB装置上对其进行冲击压缩实验难度较大，且有很多不足之处。本文首先采用常规SHPB实验方法进行了实验，得到了陶瓷材料在低应变率范围的动态应力应变关系；然后对常规SHPB实验方法作了改进，并应用一维应力波理论对数据处理方法进行了修正，有效地改善了采用SHPB装置研究脆性高抗压强度材料力学性能的方法；采用新的改进的实验方法对Al_2O_3陶瓷的动态力学性能进行研究，得到了陶瓷材料较高应变率范围的应力应变曲线；结果表明，Al_2O_3陶瓷材料具有以下特性：①Al_2O_3陶瓷的变形主要为弹性变形，在弹性范围就会发生脆性断裂破坏，我们认为Al_2O_3陶瓷为弹脆性材料；②Al_2O_3陶瓷动态应力应变呈非线性关系；③在低应变率范围陶瓷材料的动态应力应变关系是应变率无关的；④在较高的应变率范围内，陶瓷材料的动态应力应变关系是应变率相关的；⑤材料的初始弹性模量、破坏应力、破坏应变值随应变率的增大而增大。最后，应用损伤力学基本理论，对95％Al_2O_3陶瓷建立了新的实用的损伤型动态本构模型。
2．弹体墩粗变形的分析
对于弹靶撞击过程中弹体的变形，多数的分析理论均不考虑靶板的变形，本文在Taylor模型和Hawkyard模型的基础上，考虑了刚塑性弹体对变形靶板的侵入，构造了新的弹体墩粗变形的分析模型。模型考虑了弹体刚性区长度和运动速度的变化，塑性变形区长度、横截面积以及其运动速度的变化以及弹体对靶板的侵入速度和深度。
最后给出了其分析解，得到了各个变量随时间的变化，给出了不同撞击速度下弹体撞
击结束后的整体形状尺寸，得到了各形状参数和变形延续时间与撞击速度的关系曲
线，并与实验结果进行对比，吻合较好。
3.变形弹体对陶瓷/金属复合靶板撞击问题的理论分析
针对弹体撞击陶瓷/金属复合靶板的实验现象，将弹体的变形、陶瓷面板的碎裂
和金属背板的变形结合起来，建立了新的变形弹体垂直撞击陶瓷/金属靶板的理论分
析模型。模型中计入了弹体刚性区长度和运动速度、塑性变形区长度、横截面积和运
动速度的变化以及弹体对靶板的侵入速度和深度，对陶瓷面板考虑了陶瓷锥体积和抗
压强度的变化;对金属背板的变形，根据其塑性变形功、外力功及其动能守恒原理，
得到金属背板的运动方程。最后对具体算例进行了分析，得到了弹体刚性区长度和运
动速度的变化，弹体塑性变形区长度、横截面积以及其运动速度的变化;弹体侵入靶
板深度和侵入速度的变化;背板中心位置的位移及运动速度的变化;陶瓷锥体积和抗
压强度的变化，给出了一些有价值的规律，计算结果表明，模型能较好的描述撞击过
程中的有关规律，而且与实验结果吻合较好，说明了模型的有效性。
4.变形弹体对陶瓷/金属复合靶板撞击问题的数值模拟
利用大型非线性有限元程序LS一DYNA3D，对平头弹侵彻金属、陶瓷、陶瓷/金属
复合靶板的问题分别进行数值模拟。结果发现，金属冲塞现象和陶瓷锥现象均是靶板
受冲击时的特殊破坏形式，通常出现在较薄的靶板中，并且子弹的速度、长度、形状
均有直接的影响。在对陶瓷/金属复合靶板的数值模拟中，给出了弹体墩粗变形的过
程，陶瓷面板的碎裂和陶瓷锥的形成过程，以及金属背板的弯曲变形。而且分别给出
了背板中心位置、弹靶接触面和弹体尾部三个位置的坐标随时间的变化曲线，与本文
的理论分析结果和前人的实验结果进行了比较。结果发现，数值模拟结果和理论分析
结果与实验结果基本吻合，表明本文进行的数值模拟和建立的理论分析模型能较准确
地反映弹体对陶瓷/金属复合靶板的撞击过程，对陶瓷/金属复合靶板抗侵彻能力的研
究具有一定的指导意义。
The main requirements of materials involved in armour design are: low density and high dynamic strength. Metals, in general, fulfil all the requirements except that of density. Ceramics satisfy the both demands but are brittle, which makes for extensive fragmentation due to the tensile waves generated by the compressive waves reflected from the free surfaces. Mixed armours, however, made of ceramic tiles and a metallic backup plate, form a very efficient shield against projectiles since they combine the lightweight and high resistance of ceramic with the ductility of metallic materials.
This paper aims at the problem of ceramic/metal armours impacted by deformable projectile. The researches are outlined as following: 1. A new experimental method for brittle high-compressive-strength materials
Al2O3 ceramics is a brittle material with high compressive strength so that only small strain is produced when breaking. It is very difficult to study the dynamic behavior of ceramics by classical SHPB technology. Firstly, the stress-strain curves in the rigid of low strain rate of Al2O3 ceramics are measured adopting the classical SHPB apparatus. At the same time, we have a sight of several disadvantages of classical SHPB technology. In order to obtain more desirable results, several modifications on classical SHPB technology were implemented. A new experimental method is presented for brittle materials with high compressive strength. By the use of the improved SHPB apparatus, the uniaxial compression tests for Al2O3 ceramics in the strain-rate range of 560-750 s-1 were carried out and the stress-strain curves of Al2O3 ceramics were obtained. It is shown that ceramics is a nonlinear elastic-brittle material. It is sensitive to strain-rate at higher strain-rate. The modulus of elasticity and dynamic compress
ive strength of ceramics increases with increasing the strain rate. Based on the theory of damage mechanics, an elastic-brittle damage-modified constitutive model is given. The parameters are obtained by fitting the SHPB test data. A strain-rate dependent damage-modified constitutive equation of Al2O3 ceramics is obtained.
2. A new simple model for the deformation of projectile impacting a deformable target
Up to now several analytical models aiming at the mushrooming deformation of projectile impacting a target have been developed, but in which the deformation of target was not been taken into consideration. Based on Taylor's model and Hawkyard's, A new simple model for the deformation of projectile impacting a deformable target is installed considering the penetration of the projectile to the deformable target. In the model, the following time-dependent variables are involved in: the extent and the particle velocity in the rigid zone; the extent, the cross-section area and the particle velocity in plastic zone; the velocity and depth of the penetrating of projectile to the target. Solving the set of equations, analytic solution is given. The profiles of projectile and shape parameters for different initial impact velocities are shown. The duration time of deformation increases with increasing the impact velocity. The analytical results by using this model are coincident with experimental result.
3. A new analytical model of ceramic/metal armours impacted by deformable projectile
A new analytical model is established to describe the complex behavior of ceramic/metal armours under impact of deformable projectile by assuming some hypotheses. Three aspects are taken into account: the mushrooming deformation of the projectile, the fragment of ceramic tile and the formation and changement of ceramic conoid and the deformation of the metal backup plate. Solving the set of equations, all the variables are obtained. For the different impact velocities, we get: the extent and the particle velocity in the rigid zone; the extent, the cross-section area and the particle velocity in plastic zone; the velocity and depth of the penetrating of projectile to the target; the reduction in volume and compressive strength of the f
本文主要研究弹体撞击陶瓷／金属复合靶板中有关现象和规律，具体内容包括：陶瓷材料动态力学性能的实验研究，弹体撞击靶板时的变形分析，弹体撞击陶瓷／金属复合靶板的理论分析模型和数值模拟，得到了一些有意义的结果。
1．SHPB实验方法的改进和Al_2O_3陶瓷动态力学性能的实验研究
为了了解材料特性，首先对陶瓷材料的动态力学特性进行了实验研究。所选材料为四川宜宾金洋电子陶瓷厂制备的95％Al_2O_3陶瓷。由于陶瓷为脆性材料，而且抗压强度非常高，其破坏应变极其微小，在SHPB装置上对其进行冲击压缩实验难度较大，且有很多不足之处。本文首先采用常规SHPB实验方法进行了实验，得到了陶瓷材料在低应变率范围的动态应力应变关系；然后对常规SHPB实验方法作了改进，并应用一维应力波理论对数据处理方法进行了修正，有效地改善了采用SHPB装置研究脆性高抗压强度材料力学性能的方法；采用新的改进的实验方法对Al_2O_3陶瓷的动态力学性能进行研究，得到了陶瓷材料较高应变率范围的应力应变曲线；结果表明，Al_2O_3陶瓷材料具有以下特性：①Al_2O_3陶瓷的变形主要为弹性变形，在弹性范围就会发生脆性断裂破坏，我们认为Al_2O_3陶瓷为弹脆性材料；②Al_2O_3陶瓷动态应力应变呈非线性关系；③在低应变率范围陶瓷材料的动态应力应变关系是应变率无关的；④在较高的应变率范围内，陶瓷材料的动态应力应变关系是应变率相关的；⑤材料的初始弹性模量、破坏应力、破坏应变值随应变率的增大而增大。最后，应用损伤力学基本理论，对95％Al_2O_3陶瓷建立了新的实用的损伤型动态本构模型。
2．弹体墩粗变形的分析
对于弹靶撞击过程中弹体的变形，多数的分析理论均不考虑靶板的变形，本文在Taylor模型和Hawkyard模型的基础上，考虑了刚塑性弹体对变形靶板的侵入，构造了新的弹体墩粗变形的分析模型。模型考虑了弹体刚性区长度和运动速度的变化，塑性变形区长度、横截面积以及其运动速度的变化以及弹体对靶板的侵入速度和深度。
最后给出了其分析解，得到了各个变量随时间的变化，给出了不同撞击速度下弹体撞
击结束后的整体形状尺寸，得到了各形状参数和变形延续时间与撞击速度的关系曲
线，并与实验结果进行对比，吻合较好。
3.变形弹体对陶瓷/金属复合靶板撞击问题的理论分析
针对弹体撞击陶瓷/金属复合靶板的实验现象，将弹体的变形、陶瓷面板的碎裂
和金属背板的变形结合起来，建立了新的变形弹体垂直撞击陶瓷/金属靶板的理论分
析模型。模型中计入了弹体刚性区长度和运动速度、塑性变形区长度、横截面积和运
动速度的变化以及弹体对靶板的侵入速度和深度，对陶瓷面板考虑了陶瓷锥体积和抗
压强度的变化;对金属背板的变形，根据其塑性变形功、外力功及其动能守恒原理，
得到金属背板的运动方程。最后对具体算例进行了分析，得到了弹体刚性区长度和运
动速度的变化，弹体塑性变形区长度、横截面积以及其运动速度的变化;弹体侵入靶
板深度和侵入速度的变化;背板中心位置的位移及运动速度的变化;陶瓷锥体积和抗
压强度的变化，给出了一些有价值的规律，计算结果表明，模型能较好的描述撞击过
程中的有关规律，而且与实验结果吻合较好，说明了模型的有效性。
4.变形弹体对陶瓷/金属复合靶板撞击问题的数值模拟
利用大型非线性有限元程序LS一DYNA3D，对平头弹侵彻金属、陶瓷、陶瓷/金属
复合靶板的问题分别进行数值模拟。结果发现，金属冲塞现象和陶瓷锥现象均是靶板
受冲击时的特殊破坏形式，通常出现在较薄的靶板中，并且子弹的速度、长度、形状
均有直接的影响。在对陶瓷/金属复合靶板的数值模拟中，给出了弹体墩粗变形的过
程，陶瓷面板的碎裂和陶瓷锥的形成过程，以及金属背板的弯曲变形。而且分别给出
了背板中心位置、弹靶接触面和弹体尾部三个位置的坐标随时间的变化曲线，与本文
的理论分析结果和前人的实验结果进行了比较。结果发现，数值模拟结果和理论分析
结果与实验结果基本吻合，表明本文进行的数值模拟和建立的理论分析模型能较准确
地反映弹体对陶瓷/金属复合靶板的撞击过程，对陶瓷/金属复合靶板抗侵彻能力的研
究具有一定的指导意义。
The main requirements of materials involved in armour design are: low density and high dynamic strength. Metals, in general, fulfil all the requirements except that of density. Ceramics satisfy the both demands but are brittle, which makes for extensive fragmentation due to the tensile waves generated by the compressive waves reflected from the free surfaces. Mixed armours, however, made of ceramic tiles and a metallic backup plate, form a very efficient shield against projectiles since they combine the lightweight and high resistance of ceramic with the ductility of metallic materials.
This paper aims at the problem of ceramic/metal armours impacted by deformable projectile. The researches are outlined as following: 1. A new experimental method for brittle high-compressive-strength materials
Al2O3 ceramics is a brittle material with high compressive strength so that only small strain is produced when breaking. It is very difficult to study the dynamic behavior of ceramics by classical SHPB technology. Firstly, the stress-strain curves in the rigid of low strain rate of Al2O3 ceramics are measured adopting the classical SHPB apparatus. At the same time, we have a sight of several disadvantages of classical SHPB technology. In order to obtain more desirable results, several modifications on classical SHPB technology were implemented. A new experimental method is presented for brittle materials with high compressive strength. By the use of the improved SHPB apparatus, the uniaxial compression tests for Al2O3 ceramics in the strain-rate range of 560-750 s-1 were carried out and the stress-strain curves of Al2O3 ceramics were obtained. It is shown that ceramics is a nonlinear elastic-brittle material. It is sensitive to strain-rate at higher strain-rate. The modulus of elasticity and dynamic compress
ive strength of ceramics increases with increasing the strain rate. Based on the theory of damage mechanics, an elastic-brittle damage-modified constitutive model is given. The parameters are obtained by fitting the SHPB test data. A strain-rate dependent damage-modified constitutive equation of Al2O3 ceramics is obtained.
2. A new simple model for the deformation of projectile impacting a deformable target
Up to now several analytical models aiming at the mushrooming deformation of projectile impacting a target have been developed, but in which the deformation of target was not been taken into consideration. Based on Taylor's model and Hawkyard's, A new simple model for the deformation of projectile impacting a deformable target is installed considering the penetration of the projectile to the deformable target. In the model, the following time-dependent variables are involved in: the extent and the particle velocity in the rigid zone; the extent, the cross-section area and the particle velocity in plastic zone; the velocity and depth of the penetrating of projectile to the target. Solving the set of equations, analytic solution is given. The profiles of projectile and shape parameters for different initial impact velocities are shown. The duration time of deformation increases with increasing the impact velocity. The analytical results by using this model are coincident with experimental result.
3. A new analytical model of ceramic/metal armours impacted by deformable projectile
A new analytical model is established to describe the complex behavior of ceramic/metal armours under impact of deformable projectile by assuming some hypotheses. Three aspects are taken into account: the mushrooming deformation of the projectile, the fragment of ceramic tile and the formation and changement of ceramic conoid and the deformation of the metal backup plate. Solving the set of equations, all the variables are obtained. For the different impact velocities, we get: the extent and the particle velocity in the rigid zone; the extent, the cross-section area and the particle velocity in plastic zone; the velocity and depth of the penetrating of projectile to the target; the reduction in volume and compressive strength of the f
引文
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