TiNi相变柱壳的轴向静动态屈曲特性研究
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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基本问题和重点研究领域之一。形状记忆合金(SMA)是典型的相变材料,因此,SMA柱壳的冲击力学行为的研究必须涉及相变对其影响的研究。
本文针对工程中广泛使用的基本构件一圆柱薄壳结构作为研究对象,从实验和数值模拟两个方面,对处于伪弹性状态(PE)的具有相变特性的TiNi合金柱壳的准静态及轴向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,对不同尺寸,不同边界条件下相变柱壳静压屈曲特性以及相变铰的形成与发展规律、以及单脉冲加载下相变柱壳的动屈曲响应响应和吸能特性获得了较深入的认识,得到一些有意义的结果,可为其工程应用提供依据。
PE态相变柱壳的静压屈曲特性明显不同于弹塑性柱壳,与马氏体相变和相变铰的行为相关,卸载后可恢复原状。相变柱壳的径厚比D/t和长径比L/D两大尺寸要素与相变屈曲模式之间关系密切。在相同的长径比下,随着径厚比增大,相变柱壳的周向折屈边数增多,即周向折屈辦数增加。
相变柱壳的静压比能S_e与相变柱壳的几何尺寸,屈曲模态关系密切,长径比较小时相变柱壳的比能随着径厚比增大而减小。三辦的相变屈曲模式静压比能S_e最大,二辦与混合模式次之,四辦屈曲模式最小。其中长径比为2.5,径厚比为30时的三辦屈曲模式,其静压比能S_e最大,达到2257.62J·Kg~(-1)。
采用简化的理想伪弹性本构模型,从理论上分析了TiNi相变柱壳周向相变铰处微元段在轴压失稳条件下截面变形行为,揭示了壳体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,并给出轴压失稳下整个壳截面在完整的加载卸载循环下由于相变滞回所耗散的能量。
我们改进了原有的分离式Hopkinson压杆装置,使得只产生单脉冲加载,对不同长径比和边界条件下的PE相变柱壳进行了较为系统的单脉冲轴向加载冲击实验。实验中发现:不同边界条件和不同长径比呈现出不同的屈曲模态。相变柱壳中的相变铰具有以下特点:①可回复性;②出现相变铰的时间尺度为微秒量级,与波动效应耦合在一起,变形呈现波动性:③多相变铰形成。动态载荷下名义应力应变曲线滞回面积远大于准静态压缩下的滞回面积,吸能效率更高。
对半无限长相变柱壳受阶跃载荷冲击的数值模拟表明,当载荷幅值低于相变起始应力σ_(MS)时,壳体中末发生相变,仅有弹性纵波传播,未出现屈曲。当载荷幅值高于σ_(MS)时,理论上应出现弹性波和相变沖击波的双波结构,计算表明在弹性波后方对应于相变冲击波的范围出现了轴对称的屈曲波纹,屈曲边界的传播速度在460-500m/s之间.计算分析还表明,由于突加冲击下横向惯性效应产生的弯曲扰动,相变区材料模量的突然软化以及较高的轴向应力载荷是引起相变柱壳冲击屈曲的物理机制。
对具体冲击实验的数值模拟结果表明:相变柱壳的卸载恢复过程在柱壳结构中是不均匀的,伴随着壳体局部应力释放和局部应力集中,可以分为以下四个阶段:1、柱壳中部发生弯曲变形的壳体应力首先释放,2、靠近入射杆端的壳体应力继续释放,3、靠近透射杆端的壳体应力释放,第一层与第二层相变屈曲皱褶消失,4、柱壳整体弹性振动。计算表明,铰点处相变含量沿壁厚方向的分布以周向相变铰分布最不均匀,轴向相变铰次之,斜向相变铰较为均匀。
Phase transformation(PT) can greatly affect the mechanical responses of materials and structures.It is one of the basic problems and major research fields of solid mechanics and material science.Study of the mechanical behavior of shape memory alloy(SMA) cylindrical shells under impact inevitably involves the study of the effect of phase transformation on the structures because SMA is a typical phase transformation material.
In this paper,the quasi-static axial compression and impact response of the pseudo-elastic phase transformation cylindrical shells(PTCS) are systematically investigated experimentally and numerically.Some interesting phenomena and regularities are found and in-depth understanding is gained:(ⅰ).static buckling instability properties of the PTCS with different sizes under different boundary conditions;(ⅱ).the formation and development regularities of the phase transformation hinges(PTHs);(ⅲ).dynamic buckling response and energy absorbing ability of the PTCS under single loading.The conclusions can provide the basis for its engineering applications.
Static buckling instability characteristics of PTCS are related to martensitic transformation,the behavior of phase transformation hinges,and recovery upon unloading which is significantly different from elastic-plastic cylindrical shells (EPCS).The diameter-thickness ratio(DTR) and length-diameter ratio(LDR) of the PTCS is closely related to its buckling mode.With the same length-diameter ratio,the number of its circumferential folds increases with the increasing diameter-thickness ratio.
The static specific energy S_c of the PTCS has a relationship with its geometry and buckling mode,and decreases with the increasing DTR as the LDR is smaller.The static specific energy S_e is the largest with the buckling mode of three hinges,the next is that with the buckling mode of two hinges or mixed-mode,and the smallest is that with the buckling mode of four hinges at the same axial height.As the LDR of the PTCS is 2.5,the DTR is 30,and the buckling mode is three hinges at the same axial height,the static specific energy is the largest and reaches 2257.62J.Kg~(-1).
Using a simplified ideal PE constitutive model,the behavior of circumferential phase transformation hinges(CPTH) of the PTCS section is theoretically analyzed. Regularity of PT zone development and evolvement as well as of phase boundaries motion is disclosed,and corresponding analytic expression is given.The energy dissipation due to PT of the shell section during a complete loading-unloading cycle is given.
Experimental investigation was conducted on PTCSs with different LDR and boundary conditions under single pulse loading using a modified split Hopkinson pressure bar(SHPB) apparatus.It is found that PTCSs with different LDR and boundary conditions have different buckling modes.The PTH of the PTCS is characterized by the following:1.Recoverability;2.the phase-change hinge appears on the microsecond time scale that is coupled with the fluctuation effect and its deformation increase is fluctuant;3.there are a number of PTHs in the PTCS under impact loading.The area of the dynamic hysteresis curve is much larger than that of the static compression,so energy absorption efficiency can be much higher.
Numerical simulation on the semi-infinite PTCSs subject to step loading is studied.When the step loading amplitude is lower than the initial stress inducing martensite transformation(σ_(MS)),there is only transmission of an elastic P-wave and no phase transition buckling in the shell.When the step loading is aboveσ_(MS), two-wave structure of elastic P-wave and PT shock wave occur according to theoretical analysis and numerical simulation indicates axial symmetry bucking ripples occur at the zone corresponding to the PT shock wave after the elastic wave. Propagating speed of buckling boundary is about 460-500m/s.Bending disturbances produced by the influence of lateral inertia,sudden softening of material module in the PT zone and higher axial load under rapid impact loading are the physical mechanisms that induce phase transformation buckling of PTCS.
Simulation result of the experiment shows that unloading and recovery process of PTCS is not consistent with the local stress redistribution and concentration.It can be divided into four phases:1.local stress unloads first in the middle of PTCS;2. stress continues to unload near the incident bar.3.Stress continues to unload near the transmission bar,the first and second layer PT buckling rumple disappear;4.the whole PTCS vibrates elastically.Martensite fraction distribution along the wall thickness of CPTH is the most non-uniformly,that of axial phase transformation hinge takes second place,and that of the phase transformation diagonal hinge is the most uniform.
本文针对工程中广泛使用的基本构件一圆柱薄壳结构作为研究对象,从实验和数值模拟两个方面,对处于伪弹性状态(PE)的具有相变特性的TiNi合金柱壳的准静态及轴向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,对不同尺寸,不同边界条件下相变柱壳静压屈曲特性以及相变铰的形成与发展规律、以及单脉冲加载下相变柱壳的动屈曲响应响应和吸能特性获得了较深入的认识,得到一些有意义的结果,可为其工程应用提供依据。
PE态相变柱壳的静压屈曲特性明显不同于弹塑性柱壳,与马氏体相变和相变铰的行为相关,卸载后可恢复原状。相变柱壳的径厚比D/t和长径比L/D两大尺寸要素与相变屈曲模式之间关系密切。在相同的长径比下,随着径厚比增大,相变柱壳的周向折屈边数增多,即周向折屈辦数增加。
相变柱壳的静压比能S_e与相变柱壳的几何尺寸,屈曲模态关系密切,长径比较小时相变柱壳的比能随着径厚比增大而减小。三辦的相变屈曲模式静压比能S_e最大,二辦与混合模式次之,四辦屈曲模式最小。其中长径比为2.5,径厚比为30时的三辦屈曲模式,其静压比能S_e最大,达到2257.62J·Kg~(-1)。
采用简化的理想伪弹性本构模型,从理论上分析了TiNi相变柱壳周向相变铰处微元段在轴压失稳条件下截面变形行为,揭示了壳体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,并给出轴压失稳下整个壳截面在完整的加载卸载循环下由于相变滞回所耗散的能量。
我们改进了原有的分离式Hopkinson压杆装置,使得只产生单脉冲加载,对不同长径比和边界条件下的PE相变柱壳进行了较为系统的单脉冲轴向加载冲击实验。实验中发现:不同边界条件和不同长径比呈现出不同的屈曲模态。相变柱壳中的相变铰具有以下特点:①可回复性;②出现相变铰的时间尺度为微秒量级,与波动效应耦合在一起,变形呈现波动性:③多相变铰形成。动态载荷下名义应力应变曲线滞回面积远大于准静态压缩下的滞回面积,吸能效率更高。
对半无限长相变柱壳受阶跃载荷冲击的数值模拟表明,当载荷幅值低于相变起始应力σ_(MS)时,壳体中末发生相变,仅有弹性纵波传播,未出现屈曲。当载荷幅值高于σ_(MS)时,理论上应出现弹性波和相变沖击波的双波结构,计算表明在弹性波后方对应于相变冲击波的范围出现了轴对称的屈曲波纹,屈曲边界的传播速度在460-500m/s之间.计算分析还表明,由于突加冲击下横向惯性效应产生的弯曲扰动,相变区材料模量的突然软化以及较高的轴向应力载荷是引起相变柱壳冲击屈曲的物理机制。
对具体冲击实验的数值模拟结果表明:相变柱壳的卸载恢复过程在柱壳结构中是不均匀的,伴随着壳体局部应力释放和局部应力集中,可以分为以下四个阶段:1、柱壳中部发生弯曲变形的壳体应力首先释放,2、靠近入射杆端的壳体应力继续释放,3、靠近透射杆端的壳体应力释放,第一层与第二层相变屈曲皱褶消失,4、柱壳整体弹性振动。计算表明,铰点处相变含量沿壁厚方向的分布以周向相变铰分布最不均匀,轴向相变铰次之,斜向相变铰较为均匀。
Phase transformation(PT) can greatly affect the mechanical responses of materials and structures.It is one of the basic problems and major research fields of solid mechanics and material science.Study of the mechanical behavior of shape memory alloy(SMA) cylindrical shells under impact inevitably involves the study of the effect of phase transformation on the structures because SMA is a typical phase transformation material.
In this paper,the quasi-static axial compression and impact response of the pseudo-elastic phase transformation cylindrical shells(PTCS) are systematically investigated experimentally and numerically.Some interesting phenomena and regularities are found and in-depth understanding is gained:(ⅰ).static buckling instability properties of the PTCS with different sizes under different boundary conditions;(ⅱ).the formation and development regularities of the phase transformation hinges(PTHs);(ⅲ).dynamic buckling response and energy absorbing ability of the PTCS under single loading.The conclusions can provide the basis for its engineering applications.
Static buckling instability characteristics of PTCS are related to martensitic transformation,the behavior of phase transformation hinges,and recovery upon unloading which is significantly different from elastic-plastic cylindrical shells (EPCS).The diameter-thickness ratio(DTR) and length-diameter ratio(LDR) of the PTCS is closely related to its buckling mode.With the same length-diameter ratio,the number of its circumferential folds increases with the increasing diameter-thickness ratio.
The static specific energy S_c of the PTCS has a relationship with its geometry and buckling mode,and decreases with the increasing DTR as the LDR is smaller.The static specific energy S_e is the largest with the buckling mode of three hinges,the next is that with the buckling mode of two hinges or mixed-mode,and the smallest is that with the buckling mode of four hinges at the same axial height.As the LDR of the PTCS is 2.5,the DTR is 30,and the buckling mode is three hinges at the same axial height,the static specific energy is the largest and reaches 2257.62J.Kg~(-1).
Using a simplified ideal PE constitutive model,the behavior of circumferential phase transformation hinges(CPTH) of the PTCS section is theoretically analyzed. Regularity of PT zone development and evolvement as well as of phase boundaries motion is disclosed,and corresponding analytic expression is given.The energy dissipation due to PT of the shell section during a complete loading-unloading cycle is given.
Experimental investigation was conducted on PTCSs with different LDR and boundary conditions under single pulse loading using a modified split Hopkinson pressure bar(SHPB) apparatus.It is found that PTCSs with different LDR and boundary conditions have different buckling modes.The PTH of the PTCS is characterized by the following:1.Recoverability;2.the phase-change hinge appears on the microsecond time scale that is coupled with the fluctuation effect and its deformation increase is fluctuant;3.there are a number of PTHs in the PTCS under impact loading.The area of the dynamic hysteresis curve is much larger than that of the static compression,so energy absorption efficiency can be much higher.
Numerical simulation on the semi-infinite PTCSs subject to step loading is studied.When the step loading amplitude is lower than the initial stress inducing martensite transformation(σ_(MS)),there is only transmission of an elastic P-wave and no phase transition buckling in the shell.When the step loading is aboveσ_(MS), two-wave structure of elastic P-wave and PT shock wave occur according to theoretical analysis and numerical simulation indicates axial symmetry bucking ripples occur at the zone corresponding to the PT shock wave after the elastic wave. Propagating speed of buckling boundary is about 460-500m/s.Bending disturbances produced by the influence of lateral inertia,sudden softening of material module in the PT zone and higher axial load under rapid impact loading are the physical mechanisms that induce phase transformation buckling of PTCS.
Simulation result of the experiment shows that unloading and recovery process of PTCS is not consistent with the local stress redistribution and concentration.It can be divided into four phases:1.local stress unloads first in the middle of PTCS;2. stress continues to unload near the incident bar.3.Stress continues to unload near the transmission bar,the first and second layer PT buckling rumple disappear;4.the whole PTCS vibrates elastically.Martensite fraction distribution along the wall thickness of CPTH is the most non-uniformly,that of axial phase transformation hinge takes second place,and that of the phase transformation diagonal hinge is the most uniform.
引文
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