摘要
相变对材料和结构的力学响应可造成重大影响,是固体力学和材料科学的基本问题和重点研究领域之一。相变材料由于其独特的力学性能已经得到了广泛的应用,其材料性能的研究也相对成熟,然而对于相变材料结构件的力学性能特别是在冲击载荷下的响应的研究却十分匮乏。本文主要选取一种基本的工程结构件—悬臂梁作为对象,从实验和数值模拟两个方面,对具有相变特性的TiNi合金悬臂梁的冲击响应进行了较为系统的研究,发现了一些新现象和新规律,对相变弯曲波在梁中的传播规律、相变铰的形成与发展规律、以及相变悬臂梁的冲击响应和吸能特性获得了较深入的认识,可为其工程应用提供依据。主要结果有:
对两种典型的相变材料FeMnNi合金和TiNi合金的力学特性进行了实验测定,结果表明,高速冲击下FeMnNi合金的α-ε相变可以引起冲击波形的强烈变化,并能够形成多次层裂,Mn、Ni合金元素的同时加入会大大降低相变应力阈值。TiNi合金由于初始相的不同在室温下分别处于伪弹性(PE)和形状记忆(SME)状态,马氏体相变表现出伪弹性行为,而R相变则表现出形状记忆特性。
利用改装的SHPB装置,对处于PE和SME状态的TiNi合金矩形悬臂梁进行了横向冲击实验研究。实验发现,冲击下悬臂梁中的相变铰具有波动性与可回复性,拉压不对称性并不明显。对于PE梁,打击自由端时,相变铰在根部形成,随着冲击速度的提高,相变铰的最大变形增大,并且形成的时间提前,冲击速度较高时,可能在梁中部首先发生少量相变。打击位置距离自由端1/3处时,会在该处首先形成相变弯曲波,梁中能够形成多个相变铰,靠近根部的两个铰呈现出峰谷相对、此消彼长的趋势。SME梁受冲击时首先会形成R相变弯曲波,当发生马氏体相变时也会形成相变铰。相变的发生、相变铰的存在能够较快的衰减梁的振动,R相变则能够使得SME梁振动衰减更快。冲击结束后,PE梁能完全回复原状,SME粱残余变形很小,不随冲击速度的增大而增大,并且加热后可回复。
采用简化的理想伪弹性本构模型,从理论上分析了TiNi梁微元段在纯弯曲条件下截面上变形行为,揭示了梁截面上相变区的发展演化以及相边界的运动规律,给出相应的解析表达式,由此得到矩形截面梁加、卸载过程中的弯矩-曲率曲线,并给出矩形截面梁在完整的加载卸载循环下由于相变滞回所耗散的能量。
借助有限元计算软件LS-DYNA,对理想伪弹性相变悬臂梁中相变弯曲波的传播规律进行了数值模拟研究,讨论了相变弯曲波的产生、传播、反射以及卸载。相变弯曲波总是通过弹性弯曲波的不断发展增大然后产生的,相变峰中心附近可能形成相变铰,当梁截面材料进入二相弹性时,会形成二相弹性弯曲波,并且波形发生严重的扭曲。反射弯曲波与入射波关于固定端近似对称,固定端反射弹性弯曲波可以显著的改变相变弯曲波的波形,而固定端能否发生相变以及发生的时间,取决于到达固定端并发生反射的弹性波峰的强度。卸载弯曲波也具有弥敞和不断发展的特点,卸载波对加载波的作用取决于两者波峰相遇时的位相差,相变弯曲波的卸载使得相边界发生移动。当受到卸载波和固定端反射波同时作用时,整个相变区的时空演化图表现为许多个离散的封闭区域。
对PE悬臂梁在阶跃载荷和矩形脉冲载荷作用下的动力响应进行了数值模拟研究,分析了相变铰的不同形式及其演化过程,以及高载短脉冲作用下悬臂梁的变形行为。阶跃载荷作用下,可能形成根部相变铰区、中部单铰、双铰以及连续的铰区等不同的形式。卸载后相变铰回复并发生移动,相变区在梁内重新分布,形成复杂的演化模式。高载短脉冲的作用下,PE悬臂梁的响应可分为四个相:加载时弯曲波的传播与相变铰的形成、卸载后相变铰的复杂演变、梁摆动至最大挠度过程中的大幅甩动、梁绕根部的往复振动。前三相所占时间不长,但是消耗能量非常高。
对实验的数值模拟结果表明,早期子弹和梁发生了多次撞击,子弹动能的衰减主要发生在这一短时间内,相变对能量的耗散主要发生在梁第一次回摆至平衡位置之前。模型加入硬化模量之后,模拟结果和实验更加吻合。
Phase transformation(PT) can greatly affect the mechanical response of material and structure. It is a basic problem and major research task of solid mechanics and material science. Because of the peculiar mechanical behavior phase transformation material has gained widespread application. The study of mechanical property is relatively mature, but it is very short of the study of the mechanical property of the phase transformation structures, especially the response under impact loading. In this paper, the impact response of pseudoelastic phase transformation cantilever(PPTC) is systematically investigated experimentally and numerically, and found some interesting phenomena and regularity, gained in-depth understanding about regularity of propagation of the phase transformation flexural wave(PTFW), formation and development of phase transformation hinge(PTH), and impact response of PPTC.
Experimental investigation was conducted on two typical phase transformation materials-FeMnNi alloy and TiNi alloy using light gas gun and MTS. It is found that for FeMnNi alloy upon high velocity impacting the a-e PT can greatly change the shock wave profile and spall the sample into pieces, and addition of Mn and Ni may lower the transformation pressure strongly. Because of the different initial phases, TiNi alloy is in pseudoelastic(PE) or shape memory effect(SME) state. Martensite PT PE and R PT exhibits SME.
Experimental investigation was conducted on PE and SME TiNi cantilever with rectangular section under transversal impact using a revised split Hopkinson pressure bar (SHPB) apparatus. It is found that PTH of the PTC is recoverable and its strain increases fluctantly upon impact, but the asymmetry between the tension and compression side is not remarkable. For PE cantilever, when impacting free end, PTH formed at the root, and the deformation of PTH increases and it forms earlier as the impact velocity increases; When the impact velocity is high a little PT maybe appear in the middle of the beam at first. When the impacting location is at the third of the beam length from free end PTFW may appear at first, several PTHs can form and deformation of the two hinges near the root displays such a trend that when one increases the other decreases, and the peak and valley of the two hinges is opposite. For SME beam R PTFW appears at first, and PTH can also form when martensite PT occurs. Occurrence of PT and existence of PTH can attenuate the vibration of beam greatly, and R PT attenuates the vibration faster. After impact, a PE beam will come back to its original shape, SME beam has some residual deformation which does not increase with increasing impact velocity and disappears upon heating.
Using a simplified ideal PE constitutive model, the behavior of the beam section is theoretically analyzed. Regularity of development and evolvement of PT zone and of motion of phase boundaries is disclosed, and corresponding analytic expression is given. Then moment-curvature relationship of rectangular beam during the loading and unloading procedure is obtained, and the energy dissipation due to PT of rectangular beam during a complete loading-unloading cycle is given.
Numerical simulation study is conducted on the propagation problem of PTFW in ideal PPTC using FEA software LS-DYNA, and the problem of initiation, propagation, reflection and unloading of PTFW is discussed. Results show that PTFW is initiated by development and enlargement of elastic flexural wave(EFW), and PTH may form at the center of the peak of PTFW; When beam section material enter the second phase the second phase EFW may occur and waveform will be distorted seriously. The reflected flexural waves and the incident waves at the fixed end of the beam are approximately symmetry, and the reflected elastic flexural waves could distinctively change the waveform of PTFW. Whether PT occurs at the fixed end or not and the time depends on the intensity of the elastic wave peak which arrives the fixed end and reflects. The effect of the unloading flexural wave, which is dispersive and developing, on the loading wave is depended on the phasic difference when they meet. When the unloading wave and reflected wave at the fixed end action at the same time, the spatio-temporal evolution map of the whole phase transformation zone is represented by many discrete and closed zone.
Numerical simulation study is conducted on the dynamic response of PPTC under step or rectangular pulse load. Different pattern and the evolution procedure of PTH and the dynamic behavior of PPTC under high but short pulse load is analysed. Under step load different patterns such as hinge zone at the root, single, double hinge and continuous hinge zone in the middle may form. After unloading PTH recovers and moves, PT zones redistribute along the beam and different evolution patterns form. Under high but short pulse load response of PPTC may be divided into four phases: propagation of flexural waves and formation of PTH during loading procedure, complex evolution of PTH after unloading, intensive whipping of the beam during swinging toward the maximal deflection, and to-and-fro movement around the root of the beam; the first three phases occupy relatively short time but the majority of energy is dissipated.
Simulation result of the experiment shows that several impacts occur between the bullet and the PPTC at the early stage where the bullet kinetic energy decreases greatly; The occurrence of PT near the free end is caused by the reflection of flexural wave at the free end; The energy dispersion due to PT mainly occurs before the cantilever swing back to the equilibrium position for the first time. When the hardening modulus is added into the model simulation result is more approaching to the experimental result.
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