几种基本构件的冲击相变响应的数值模拟研究
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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綦本问题和重点研究领域之一。相变材料的材料性能的研究已相对成熟,然而对于结构件在动载下的力学响应的研究却十分缺乏。本文主要选取一些基本的工程结构件一杆、板和壳作为对象,从理论和数值模拟两个方面,对具有相变特性的上述结构在冲击载荷下的早期波传播过程及动力响应进行了较为系统的研究,发现了一些新现象和新规律。
运用特征线法和有限差分数值方法,对矩形脉冲载荷下一维有限长杆中宏观相边界的传播规律进行了研究。结果表明,自由面总是对入射波起应力卸载作用,固定端的作用则与入射波的条件有关。对于可逆相变材料,载荷幅值、脉宽和端部边界条件均可能影响杆中加载相边界的传播和卸载模式,相应的影响到杆中应力拉伸区出现的位置。对于另一端为自由面的杆,脉宽较短时,应力拉伸区将首先出现在相边界消失的位置附近,当脉宽较长时,加载端附近将首先出现应力拉伸区。加载端卸载后,杆处于两端自由面共同应力卸载作用下,可能出现多重层裂的现象。对于另一端为固定端的杆,杆中应力拉伸区出现的相对较晚,靠近固定端处将可能首先达到拉伸极限发生层裂。对于不可逆相变材料杆,着重分析了端部边界条件对杆中相转变的影响,提出了通过控制应力加载脉冲的形状、幅值、长度和边界条件,制备对称型梯度材料的可能性。并应用该理论,较成功的解释了郭扬波等最近在相变Taylor杆中发现的实验新现象。
针对最近发现的工业纯铁平板等厚对称碰撞实验和FeMnNi合金的非等厚碰撞实验中的异常层裂现象,本文运用特征线方法,通过对弹塑性波和宏观相边界传播的定量分析,对该异常层裂现象产生的机理给出了理论解释。分析表明,相变和逆相变过程会强烈地改变靶板中的冲击波波结构,各波系间复杂的相互作用将导致异常层裂。并在较大速度范围内得到了FeMnNi合金平板等厚对称碰撞层裂位置随碰撞速度的变化规律。研究表明,弹塑性材料并不会发生异常层裂现象,上述异常层裂现象的发生是相变材料特有的。
将一种可描写冲击下各向同性材料中的“应力诱发”相变的三维动态相变本构成功地嵌入有限元软件ABAQUS中,使之可用于对SMA合金结构的数值模拟。
对顶端受到径向冲击载荷的伪弹性相变圆柱壳中相变弯曲波的产生、传播规律进行了数值模拟研究,对壳曲率对弯曲波的影响进行了讨论。结果表明,相变弯曲波的形成总是通过弹性弯曲波的不断发展增大后产生;相变峰首先出现的位置在加载处,并稳定在该处形成一相变主峰。随着加载载荷的增大,除加载端外,壳中将形成向壳底部方向移动的移行相变峰,不同的加载强度下,相变峰移动的速度基本相同。弯曲波传播速度对曲率不敏感;曲率的变化对加载端附近幅值较大的弯矩峰有明显影响,对传播速度较快、波长较短、幅值较小的弹性弯曲波影响可忽略。对底端自由的相变壳,反射弹性弯曲波与入射弹性弯曲波早期关于反射面近似对称;对底端受到约束的壳,由于约束反力导致的附加弯矩的影响,壳中的弯曲波形更加复杂。卸载弯曲波也具有弥散和不断发展的特点,其对加载波的作用取决于两种波峰相遇时的位相差。当受到卸载波和反射波同时作用时,壳中相变区的时空演化图表现为一些互不联通的的区域。
对PE圆柱壳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研究,分析了相变铰的不同形式及演化过程。阶跃载荷作用下,壳中可能形成加载端相变铰区、中部单铰、双铰等不同的形式。高载短脉冲作用下PE圆柱壳的响应可分为四个阶段: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、壳中部在加载端运动至最大行程过程中的大幅摆动、相变铰卸载回复后壳沿加载方向的往复振动。前三阶段所占时间不长,但耗能很高。
对置于刚性边界上的PE圆柱壳在具有一定初速度的刚板冲击下的动力响应进行了研究,结果表明,响应过程可分为壳中相变铰的形成和移动、各驻定相变铰的发展以及各相变铰的卸载回复三个阶段。在大质量、低速度刚板冲击下,壳呈现与准静态加载相似的四相变铰模式,在小质量、高速度刚板冲击下,形成四驻定相变铰前,壳中有明显的相变铰移动过程,其间有多次板、壳及底部边界的分离和再碰撞过程。对处于三向、四向和六向约束条件下的相变壳的动力响应进行的研究表明,增加边界约束后,壳的动力响应过程与两向约束类似,但壳中将产生更多的相变铰,壳的变形和相变更呈现局部化,集中在加载面附近,加载面易发生屈曲。随着约束数量的增加,壳刚度增大,缓冲能力下降,吸能效果变化不大。
Phase transition(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.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 phase transformation rod,bar and shell are systematically investigated by analytical and numerical methods, and some interesting phenomena and regularity are found.
By characteristic method and finite difference numerical method,the rules for the propagation of macroscopic phase boundary under rectangular pulse load in a finite rod are investigated.It is found that the free surface always plays the role of stress unloading for the incident stress wave,while the fixed surface will affect the stress amplitude according the incident wave conditions.For the reversible PT materials rod,the impact amplitude,pulse width and the boundary conditions will all affect the propagation of macroscopic phase boundary and the unloading process,and the position where the tensile stress zone may appear will change correspondly.For the rod with free surface, under short pulse load,the tensile stress zone will first appear near the location where the phase boundary disappear,and when the pulse duration is longer,the tensile stress zone may first appear near the load surface.After unloading,both ends of the rod become free surface,which both play the role of stress unloading for the incident stress wave,and multiple spalls may occur.For the rod with fixed surface,the tensile stress zone will appear relatively late,and the spall may first occur near the fixed end.For the inversible PT materials rod,the effects of the boundary conditions to the phase transition are investigated.The possibility of producing symmetric distributed Functionally Graded Materials(FGMs) by controlling the shape,stress amplitude and duration of the loading pulse under different boundary conditions is proposed.By this theory,some new phenomenon,recently found in the phase transtion Taylor bar experiment can be explained successfully
For the abnormal spall phenomena recently observed in impact experiments for symmetrical and the same thickness of pure iron plates and for the different thickness of FeMnNi alloy plates,in this article,the propagation of the elastic and plastic waves as well as the macroscopic phase boundary is studied quantitatively by characteristic line method,and the mechanism of the abnormal spall phenomena mentioned above is explained theoretically.The investigation shows that PT and reverse PT can strongly affect the profiles of the shock waves in the target,and the more complex interactions of the waves may cause abnormal spall.And for the impact of symmetrical and the same thickness of FeMnNi alloy plates,the rules of the position where the abnormal spall may occur with change of impact speed is found.Reserch shows that the abnormal phenomena will not occur for elastic-plastic materials,and it is unique for PT materials.
A dynamic constitutive model for phase transformation which can describe the "stress-induced" phase transformation in isotropic material is succsessfully implemented in ABAQUS finite element software,thus numerical simulation study can be conduncted for Shape Memory Alloy(SMA) structures.
The formation and propagation of phase transition flexurai wave(PTFW) in a pseudoelastic phase transition circular shell(PPTCS) which under radial impact at the top is numerically studied,and the effects of curvature on the PTFW are examined.Results show that PTFW is initiated by development and enlargement of elastic flexurai wave (EFW).PTFW always appers first at the impact point and remain there,forming a main PTFW peak.If the impact amplitude is large enough,several removing PTFW peaks may apper in the shell,which will move in the direction of the shell bottom at the same speed under different impact amplitude.Study shows that the flexural wave velocity is not sensitive to the shell curvature.For the PTFW peaks near the load point,the amplitude of bending moment is significantly affected by curvature,while for the elastic flexural wave of faster speed,shorter wavelength and small amplitude,the curvature effect can be ignored.For the shell with free bottom,the reflected flexural waves and the incident waves at the bottom of the shell are approximately symmetry,while for the shell with fixed bottom,additional PTFW will be caused by the bottom constraint,and the wave propagetion is more complex.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 from the bottom action at the same time,the spatio-temporal evolution map of the whole phase transformation zone is represented by some discrete zones.
Numerical simulation study is conducted on the dynamic response of PPTCS under step or rectangular pulse load.Different pattern and the evolution procedure of phase transition hinge(PTH) is analysed.Under step load,different patterns such as hinge zone at the load point,single,double hinges in the shell may form.Under high but short pulse load,response of PPTCS may be divided into four stages:propagation of flexural waves and formation of PTH during loading,complex evolution of PTH after unloading, intensive whipping of the shell during the load point swinging toward the maximal displacement,and to-and-fro movement around the bottom of the shell;the first three phases occupy relatively short time but the majority of energy is dissipated.
When the PPTCS,which is placed on a rigid boundary,is impacted by a rigid plate with an initial velocity,the dynamic response of PPTCS is investigated numerically. Results show that the dynamic response may be divided into three stages:formation and movement of PTHs,the evolution of PTHs,and the unloading of PTHs.When impacted by a rigid plate with large mass and slow velocity,the shell present a four PTHs formation and unloading process similar to quasi-static resoponse.When impacted by a plate with little mass but high velocity,there will be a siginificant PTHs removement process before the four PTHs form,during which there will been several separation and re-collision processes among the impact plate,shell and the rigid boundary.Besides,the study for response of PPTCS under three,four and six constraints condition show that when the number of constraints increases,though the dynamic response process is similar, more PTHs will apper in the shell,and the deformation and PT will occur more locally near the impact suface,as a result,buckling may occur more easily near the impact suface.With the increase in the number of constraints,shell stiffness will increase,while the energy absorption changs little.
运用特征线法和有限差分数值方法,对矩形脉冲载荷下一维有限长杆中宏观相边界的传播规律进行了研究。结果表明,自由面总是对入射波起应力卸载作用,固定端的作用则与入射波的条件有关。对于可逆相变材料,载荷幅值、脉宽和端部边界条件均可能影响杆中加载相边界的传播和卸载模式,相应的影响到杆中应力拉伸区出现的位置。对于另一端为自由面的杆,脉宽较短时,应力拉伸区将首先出现在相边界消失的位置附近,当脉宽较长时,加载端附近将首先出现应力拉伸区。加载端卸载后,杆处于两端自由面共同应力卸载作用下,可能出现多重层裂的现象。对于另一端为固定端的杆,杆中应力拉伸区出现的相对较晚,靠近固定端处将可能首先达到拉伸极限发生层裂。对于不可逆相变材料杆,着重分析了端部边界条件对杆中相转变的影响,提出了通过控制应力加载脉冲的形状、幅值、长度和边界条件,制备对称型梯度材料的可能性。并应用该理论,较成功的解释了郭扬波等最近在相变Taylor杆中发现的实验新现象。
针对最近发现的工业纯铁平板等厚对称碰撞实验和FeMnNi合金的非等厚碰撞实验中的异常层裂现象,本文运用特征线方法,通过对弹塑性波和宏观相边界传播的定量分析,对该异常层裂现象产生的机理给出了理论解释。分析表明,相变和逆相变过程会强烈地改变靶板中的冲击波波结构,各波系间复杂的相互作用将导致异常层裂。并在较大速度范围内得到了FeMnNi合金平板等厚对称碰撞层裂位置随碰撞速度的变化规律。研究表明,弹塑性材料并不会发生异常层裂现象,上述异常层裂现象的发生是相变材料特有的。
将一种可描写冲击下各向同性材料中的“应力诱发”相变的三维动态相变本构成功地嵌入有限元软件ABAQUS中,使之可用于对SMA合金结构的数值模拟。
对顶端受到径向冲击载荷的伪弹性相变圆柱壳中相变弯曲波的产生、传播规律进行了数值模拟研究,对壳曲率对弯曲波的影响进行了讨论。结果表明,相变弯曲波的形成总是通过弹性弯曲波的不断发展增大后产生;相变峰首先出现的位置在加载处,并稳定在该处形成一相变主峰。随着加载载荷的增大,除加载端外,壳中将形成向壳底部方向移动的移行相变峰,不同的加载强度下,相变峰移动的速度基本相同。弯曲波传播速度对曲率不敏感;曲率的变化对加载端附近幅值较大的弯矩峰有明显影响,对传播速度较快、波长较短、幅值较小的弹性弯曲波影响可忽略。对底端自由的相变壳,反射弹性弯曲波与入射弹性弯曲波早期关于反射面近似对称;对底端受到约束的壳,由于约束反力导致的附加弯矩的影响,壳中的弯曲波形更加复杂。卸载弯曲波也具有弥散和不断发展的特点,其对加载波的作用取决于两种波峰相遇时的位相差。当受到卸载波和反射波同时作用时,壳中相变区的时空演化图表现为一些互不联通的的区域。
对PE圆柱壳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研究,分析了相变铰的不同形式及演化过程。阶跃载荷作用下,壳中可能形成加载端相变铰区、中部单铰、双铰等不同的形式。高载短脉冲作用下PE圆柱壳的响应可分为四个阶段: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、壳中部在加载端运动至最大行程过程中的大幅摆动、相变铰卸载回复后壳沿加载方向的往复振动。前三阶段所占时间不长,但耗能很高。
对置于刚性边界上的PE圆柱壳在具有一定初速度的刚板冲击下的动力响应进行了研究,结果表明,响应过程可分为壳中相变铰的形成和移动、各驻定相变铰的发展以及各相变铰的卸载回复三个阶段。在大质量、低速度刚板冲击下,壳呈现与准静态加载相似的四相变铰模式,在小质量、高速度刚板冲击下,形成四驻定相变铰前,壳中有明显的相变铰移动过程,其间有多次板、壳及底部边界的分离和再碰撞过程。对处于三向、四向和六向约束条件下的相变壳的动力响应进行的研究表明,增加边界约束后,壳的动力响应过程与两向约束类似,但壳中将产生更多的相变铰,壳的变形和相变更呈现局部化,集中在加载面附近,加载面易发生屈曲。随着约束数量的增加,壳刚度增大,缓冲能力下降,吸能效果变化不大。
Phase transition(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.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 phase transformation rod,bar and shell are systematically investigated by analytical and numerical methods, and some interesting phenomena and regularity are found.
By characteristic method and finite difference numerical method,the rules for the propagation of macroscopic phase boundary under rectangular pulse load in a finite rod are investigated.It is found that the free surface always plays the role of stress unloading for the incident stress wave,while the fixed surface will affect the stress amplitude according the incident wave conditions.For the reversible PT materials rod,the impact amplitude,pulse width and the boundary conditions will all affect the propagation of macroscopic phase boundary and the unloading process,and the position where the tensile stress zone may appear will change correspondly.For the rod with free surface, under short pulse load,the tensile stress zone will first appear near the location where the phase boundary disappear,and when the pulse duration is longer,the tensile stress zone may first appear near the load surface.After unloading,both ends of the rod become free surface,which both play the role of stress unloading for the incident stress wave,and multiple spalls may occur.For the rod with fixed surface,the tensile stress zone will appear relatively late,and the spall may first occur near the fixed end.For the inversible PT materials rod,the effects of the boundary conditions to the phase transition are investigated.The possibility of producing symmetric distributed Functionally Graded Materials(FGMs) by controlling the shape,stress amplitude and duration of the loading pulse under different boundary conditions is proposed.By this theory,some new phenomenon,recently found in the phase transtion Taylor bar experiment can be explained successfully
For the abnormal spall phenomena recently observed in impact experiments for symmetrical and the same thickness of pure iron plates and for the different thickness of FeMnNi alloy plates,in this article,the propagation of the elastic and plastic waves as well as the macroscopic phase boundary is studied quantitatively by characteristic line method,and the mechanism of the abnormal spall phenomena mentioned above is explained theoretically.The investigation shows that PT and reverse PT can strongly affect the profiles of the shock waves in the target,and the more complex interactions of the waves may cause abnormal spall.And for the impact of symmetrical and the same thickness of FeMnNi alloy plates,the rules of the position where the abnormal spall may occur with change of impact speed is found.Reserch shows that the abnormal phenomena will not occur for elastic-plastic materials,and it is unique for PT materials.
A dynamic constitutive model for phase transformation which can describe the "stress-induced" phase transformation in isotropic material is succsessfully implemented in ABAQUS finite element software,thus numerical simulation study can be conduncted for Shape Memory Alloy(SMA) structures.
The formation and propagation of phase transition flexurai wave(PTFW) in a pseudoelastic phase transition circular shell(PPTCS) which under radial impact at the top is numerically studied,and the effects of curvature on the PTFW are examined.Results show that PTFW is initiated by development and enlargement of elastic flexurai wave (EFW).PTFW always appers first at the impact point and remain there,forming a main PTFW peak.If the impact amplitude is large enough,several removing PTFW peaks may apper in the shell,which will move in the direction of the shell bottom at the same speed under different impact amplitude.Study shows that the flexural wave velocity is not sensitive to the shell curvature.For the PTFW peaks near the load point,the amplitude of bending moment is significantly affected by curvature,while for the elastic flexural wave of faster speed,shorter wavelength and small amplitude,the curvature effect can be ignored.For the shell with free bottom,the reflected flexural waves and the incident waves at the bottom of the shell are approximately symmetry,while for the shell with fixed bottom,additional PTFW will be caused by the bottom constraint,and the wave propagetion is more complex.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 from the bottom action at the same time,the spatio-temporal evolution map of the whole phase transformation zone is represented by some discrete zones.
Numerical simulation study is conducted on the dynamic response of PPTCS under step or rectangular pulse load.Different pattern and the evolution procedure of phase transition hinge(PTH) is analysed.Under step load,different patterns such as hinge zone at the load point,single,double hinges in the shell may form.Under high but short pulse load,response of PPTCS may be divided into four stages:propagation of flexural waves and formation of PTH during loading,complex evolution of PTH after unloading, intensive whipping of the shell during the load point swinging toward the maximal displacement,and to-and-fro movement around the bottom of the shell;the first three phases occupy relatively short time but the majority of energy is dissipated.
When the PPTCS,which is placed on a rigid boundary,is impacted by a rigid plate with an initial velocity,the dynamic response of PPTCS is investigated numerically. Results show that the dynamic response may be divided into three stages:formation and movement of PTHs,the evolution of PTHs,and the unloading of PTHs.When impacted by a rigid plate with large mass and slow velocity,the shell present a four PTHs formation and unloading process similar to quasi-static resoponse.When impacted by a plate with little mass but high velocity,there will be a siginificant PTHs removement process before the four PTHs form,during which there will been several separation and re-collision processes among the impact plate,shell and the rigid boundary.Besides,the study for response of PPTCS under three,four and six constraints condition show that when the number of constraints increases,though the dynamic response process is similar, more PTHs will apper in the shell,and the deformation and PT will occur more locally near the impact suface,as a result,buckling may occur more easily near the impact suface.With the increase in the number of constraints,shell stiffness will increase,while the energy absorption changs little.
引文
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