弹靶侵彻动态响应的理论与数值分析

【作者】 王政；

【导师】 张文；

【作者基本信息】 复旦大学 ， 流体力学， 2005， 博士

【摘要】 本文讨论国防工程中钻地弹等武器研制以及防护设施建设相关的弹靶动态响应问题。弹体碰撞靶体并进入靶体内部的动力学过程称为侵彻，它涉及到弹体和靶体的大变形等几何非线性、塑性和损伤断裂等材料非线性和接触作用的边界非线性问题，因此是力学、材料学和计算数学学科中的挑战性课题，目前还有许多与实际工程密切相关的问题得不到很好的解答。本文的主要工作如下：1长杆弹体侵彻问题理论分析及应用研究。长杆弹体是侵彻较厚靶体的常见弹体。分析长杆弹体侵彻厚靶问题的理论方法主要有空腔膨胀模型和Tate模型，其缺点是在实际应用中都需要人为调整材料参数。本文基于速度势分析的方法研究刚性长杆弹体对有限厚靶的侵彻与穿透问题。推导了靶体中速度场与应力场的计算方法，据此研制了分析侵彻过程的计算程序。利用该程序计算了卵形、锥形和球形等不同头部形状的长杆弹侵彻问题，同实验和有限元程序的比较表明该理论分析方法能够反映弹靶侵彻过程的力学机制，其计算结果切实可信。同其它侵彻问题分析方法相比，该分析方法无需人为调整材料参数即可得到同实验一致的结果。同基于大型程序软件的数值模拟相比，其材料参数易于确定，计算时间大大减小。计算分析铝靶侵彻和穿透的缩比模型问题，得到了无量纲侵彻深度和剩余速度相等以及弹体减加速度与几何尺寸成反比的重要结果。研究混凝土靶板侵彻问题，适当选取混凝土强度参数后可得到同实验基本一致的计算结果。该分析方法可以在相关的工程问题研究中广泛应用。2 LTZ-2D程序数值模拟弹体侵彻混凝土靶板时的动态响应问题。LTZ-2D程序是二维有限元弹塑性流体力学程序，适用于高速碰撞等问题的动力学分析。LTZ-2D程序在数值模拟厚靶侵彻问题时，侵彻深度等计算结果的误差较大。为解决这一问题，本文对LTZ-2D程序进行了二次开发。LTZ-2D程序中的混凝土本构模型主要采用JH-1模型，其缺点是损伤度对强度影响较小，本文对JH-1本构模型进行了修正。另外，分析计算模型中靶体网格划分和侵蚀因子等因素对计算结果的影响，确定了建立计算模型的基本方法。减小了LTZ-2D程序侵彻深度等计算结果的人为性影响。给出同实验相符的侵彻深度、弹体速度和减加速度随时间的变化等计算结果，以及定性合理的弹体压力、等效应力和等效应变的分布等结果。据此对装药弹体模型优化设计等问题进行数值模拟的论证分析。3冲击载荷下混凝土本构模型的分析与构建研究。防护工程以及多级弹体对混凝土介质的冲击等问题中需要密切关注混凝土介质的损伤和破裂情形，为对此问题进行更有效的数值模拟分析，迫切需要构建能够更好地描述冲击载荷下混凝土动态力学性能的本构模型。本文系统总结了混凝土的动态力学性能实验结果和有代表性的混凝土本构模型，分析适用于冲击问题的混凝土本构模型的构建要素。在此基础上，构建了一个适用于数值模拟冲击问题的新的混凝土本构模型，该本构模型全面考虑了应力的第二和第三不变量、应变率以及拉伸和剪切损伤等诸多影响因素，可以描述混凝土力学响应中线弹性、塑性硬化和损伤软化的力学过程。构建本构模型时，在拉压子午线之比同应力球量的关系、各个屈服面之间硬化与软化的描述以及拉伸损伤等几个方面提出了新的方法。将所构建的本构模型加入到LTZ-2D程序，研究确定了混凝土本构模型参数，对混凝土靶板的穿透问题进行了数值验证分析。结果表明计算得到的弹体剩余速度同实验结果基本一致，并成功得到混凝土靶板破裂的计算图像。本文所构建的本构模型能够较好地反映冲击载荷作用下混凝土动态响应的主要特性，比冲击问题分析中常用的JH-1混凝土本构模型优越。4混凝土靶斜侵彻问题三维数值计算与分析。武器与目标的相互作用的过程通常都属于斜侵彻问题，此时弹体碰撞靶体有一定的倾角(弹体轴向与目标面法向夹角大小)，或有一定的攻角(速度方向与弹体轴向夹角大小)。斜侵彻相关问题的数值模拟需要三维程序计算，LS-DYNA是使用较多的软件之一。本文对LS-DYNA软件的计算结果进行了详尽的定量检验和定性分析。利用LS-DYNA数值计算装药弹体斜侵彻混凝土靶问题，主要关注弹壳内部装药的压实效应以及倾角和攻角对弹体动态响应的影响。计算结果及其分析表明，在侵彻的早期阶段，装药已经压实，装药和弹体尾部留出空隙。倾角和攻角都会引起弹体的偏转和弹壳应力的升高，降低弹体的侵彻能力。攻角(如5°)可能严重地影响侵彻过程。更多还原

【Abstract】 In this dissertation, we discuss dynamic response of the projectile and target involved in developing earth penetrator and building safeguard in national defense engineering research. Penetration is dynamic process of a projectile impacting and getting into a target. And it is usually come down to three kinds of non-linear problems of large strain geometry, material constitutive model and contacting boundary. It is a great challenge in mechanics, material science, and computational mathematics. And many problems in touch with practice engineering can not be entirely solved.The following is the main contents of the dissertation.1 Theoretical and applied analysis on penetration of long rod projectile.Long rod projectiles are usually used to penetrate thick targets. The mostly used theoretical models of analyzing the long rod projectile penetrating into thick targets are cavity-expansion model and Tate model. Both of these two models need to adjust the material parameters in engineering research.Based on a theoretical model of determination of the velocity potential and the velocity field in the targets, the problems of rigid long rod projectile penetrating or perforating thick targets are studied. The method of calculation is presented, and a code according to it has been written to calculate varied penetration problems of long rod projectile with different nose shape, such as ogive, cone and sphere. Compared with the results of the tests and FEM code, the creditability and applicability of the theory model are studied. The theoretical model has stable analytical foundation and well describes kinetic mechanics of penetrating process. It may get consistent results without modifying material parameters not as other models. And it use less time than other numerical code.The comparability problems on penetrating into aluminum targets are also analyzed. The results showed that the dimensionless residual velocity and penetration depth is equal and the deceleration is in reverse to dimension. At last, the code is tried to calculate penetration problems on concrete targets. And numerical results agreed with the tests are obtained with adjust value of concrete strength. The theoretical model may be abroad used in research of correlative engineering problems.2 Computation and analysis on dynamical responses of the projectile whennormal penetrating into concrete targets with LTZ-2D code.LTZ-2D code is a two dimensional FEM programme to study elastic-plastic hydrodynamics problems. It may be used to analyze dynamic response of projectiles and targets under high velocity impacting. There is error in the computated penetration depth of the code while simulating the problem of penetrating into a thick target. We revise the code to resolve this problem in this dissertation.A shorcoming in the JH-1 constitutive model of concrete in the code that damage has little influence on strength is mended. Then the study presents a careful analysis of the factors such as element dimension and erosion threshold which have influence on the computational results when using LTZ-2D code and confirms some principles of making a computational model. Some reasonable results such as penetration depth, the change of velocity and deceleration of the projectile with change of time are obtained and analyzed in detail, as well as the distribution of pressure, equivalent stress and equivalent strain of the projectile. On the base of those results, the optimized problems of the explosive projectile models are studied by numrical simulation.3 Analysis and construction of constitutive model of concrete under impact loading.The simulation of problems of safety engineering research or tandem projectile penetration into concrete targets require exact describing the damage and fracture of concrete. So we develop a constitutive model that may be used to describe dynamic behavior of concrete under impact loading.Making conclusion on dynamical tests and varied dynamical constitutive models of concrete, a constitutive model is made up for numerical simulation of kinetic energy projectile penetrating into a concrete target. Several factors such as the second and third invariant of stress, strain rate, tension or shear damage are taken into account in this model and it can be used to describe the full mechanical process of linear elastic, hardening plastic and damage softening of geological material. This study gave new model of describing the relation between eccentricity and pressure, the variation between three strength surfaces and tension damage of concrete. The constitutive model is put into LTZ-2D code. The computed results of residual velocity are well consistent with the tests data. And the reasonable figure of fractured concrete target is also obtained. The results show that the constitutive model can well describe the main characters of concrete under impact loading and be better thanJH-1 concrete model mostly used in analysis of impact problems.4 Numerical simulations and analysis on problems of oblique penetrating into concrete targets with 3D code.The process of warheads moving into targets usually be taken as oblique penetration problems. In such situation the projectile impact the target at a oblique angle, the angle between projectile axis and normal surface of the target, as well as a attack angle that between axis and velocity of projectile. Simulation of the problem need three dimesional code. The LS-DYNA software is one of them.The calculated results of LS-DYNA is verified and analysized with tests data. Presenting a numrical computation and analysis on explosive peojectile penetrating into concrete targets, it shows that the explosive is crushed at the begaining of the penetration process and there is interspace between explosive and the tail case of the projectile. The oblique angle and attack angle will decreased the penetrating capability of the projectile as the deflected projectile and incresing stress of the case. Attack angle such as 5° will have a great influence on penetration process.更多还原