高密度PZT95/5陶瓷的冲击相变及放电性能研究
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摘要
利用PZT 95/5陶瓷在冲击波作用下发生铁电三角相(F_R)→反铁电正交相(A_O)的相变、瞬间去极化、释放陶瓷电极表面束缚的电荷,在微秒量级输出大电流的性能研制的新型脉冲能源,在美国、英国及俄罗斯等国家的高新技术上已得到了应用。研究PZT 95/5铁电陶瓷冲击相变及相变导致的放电性能,对拓展该材料在冲击波条件下的使用有重要价值。同时,由于该冲击相变发生在弹性区内,相变过程受材料本构关系影响较大,有关实验方法和诊断技术的研究报道较少、难度较大,因此PZT 95/5陶瓷的冲击相变研究对发展材料弹性区内冲击相变的实验研究方法、建立包含相变的本构模型有积极意义。
本文以国产高密度(7.76 g/cm~3)PZT 95/5陶瓷作为研究对象,在一级气体炮上开展了一维应变平面冲击波加载实验。
通过研究冲击波传播过程中陶瓷的Hugoniot性能、高压声速及冲击去极化释放的电性能,提出了一种弹性区不可逆相变本构模型,深入分析了相变与冲击轴向应力、冲击释电的关系。本文的主要工作及创新点归纳如下:
1.在逆向碰撞实验中,使用含熔石英窗口的激光速度干涉测量技术(VISAR),精确测试了0.48-3.78 GPa压力范围内PZT 95/5陶瓷的轴向应力-粒子速度Hugoniot关系。与未极化陶瓷在弹性区的线性冲击轴向应力-粒子速度Hugoniot关系明显不同的是,弹性区内极化陶瓷的冲击轴向应力-粒子速度Hugoniot关系可以用三段式折线表示。综合Setchell(J Appl Phys,2003,94(1)573)对PZT 95/5陶瓷屈服起始应力和Avdeev(Phys Rev B,2006,73:064105)对PZT 95/5陶瓷F_R→A_O相变前后晶格参数变化的研究结果,得到了国产高密度PZT 95/5陶瓷在大约0.5-2.0 GPa应力范围发生了弹性区一级结构相变的结论。研究结果为建立弹性应力区内包含相变的材料的本构关系奠定了基础。
2.利用上述逆向碰撞实验中得到的PZT 95/5陶瓷粒子速度剖面,计算了在弹性区内的纵波声速。结果表明,PZT 95/5陶瓷在弹性区内的纵波声速随冲击加载应力的增加而增大。纵波声速随冲击加载应力的变化的斜率因相变而发生拐折,也可以用三段折线描写。
3.对国产高密度PZT 95/5陶瓷的相变引起的去极化过程和电流释放性能进行了研究。首先,通过比较冲击释放剩余极化强度P_(rs)与陶瓷的初始剩余极化强度P_r,确定了该陶瓷材料相变起始应力为(0.30±0.15)GPa,相变完成应力为(1.90±0.15)GPa。实验结果表明:在陶瓷相变区内,冲击轴向应力幅值越大,电流幅值越大。其次,对于完全相变后的PZT 95/5陶瓷,研究了外电路负载对陶瓷电流输出性能的影响。通过等效电路的计算分析,并经实验验证表明:完全相变后的PZT 95/5陶瓷可等效为脉冲恒流源,释放的电流为恒定值;释放的电流受外电路的RLC负载参数影响:电感负载导致电流幅值增加,波形振荡;纯电阻负载的电流幅值稳定,电流响应时间随负载电阻的增加而增加。
4.在高密度PZT 95/5陶瓷Hugoniot性能、声速、弹性模量的实验研究基础上,将唐志平等人提出的描写一维应力加载下弹性区不可逆相变本构模型拓展到本文研究的一维应变加载条件下,建立了PZT 95/5陶瓷F_R→A_O相变本构模型:
式中,σ_A、ε_A分别表示相变起始点的冲击轴向应力和应变,σ_B、ε_B分别表示相变完成点的冲击轴向应力和应变。根据本文对国产高密度PZT 95/5陶瓷实验的研究结果,σ_A=0.23 GPa,ε_A=1.48×10~(-3),σ_B=1.94 GPa,ε_B=1.34×10~(-2)。
5.根据实验测量的PZT 95/5陶瓷在相变过程中释放的电荷,提出了用冲击相变过程中陶瓷的A_O相的体积分数ξ来描述陶瓷的动态相变特性,A_O相的体积分数ξ定义为陶瓷冲击释放的剩余极化强度P_(rs)和陶瓷初始剩余极化强度P_r的比值。由于F_R相和A_O相的密度已知,相变过程中A_O相的质量分数可以通过体积分数ξ确定。结合实验测得的PZT 95/5陶瓷的σ-u Hugoniot性能和电释放性能,描写国产高密度PZT 95/5陶瓷的A_O相体积含量ξ随冲击轴向应力σ的变化的关系式如下:
根据相变体积含量关系式,极化高密度PZT 95/5陶瓷的相变起始应力为0.23 GPa,相变结束应力为1.94 GPa。
综上所述,本文发展了一种一维应变条件下研究弹性区相变材料的本构关系的实验研究方法,并确定了国产高密度PZT 95/5陶瓷的冲击相变动力学模型。本实验研究方法采用逆向碰撞实验技术和带窗VISAR测试技术,用于获取“样品/透明窗口界面”的粒子速度和冲击加载下的声速。本方法可用于其它材料的本构关系及低压相变研究。本研究获得的国产高密度PZT 95/5陶瓷的冲击动力学参数、冲击相变动力学特性,对于拓展该材料的应用,具有重要价值。
The polarized PZT 95/5 ferroelectric ceramics with a rhombohedral structure (F_R) will transform into the antiferroelectric phase with an orthorhombic structure(A_O) when subjecting to proper shock loadings. This Phase transition will result in a rapidly depolarizing process, in which the dramatic releasing of the surface charges bounded in the ceramics happens. This kind of ceramics has been successfully used in the United States, United Kingdoms and Russia as the promising pulsed power supplies to provide large amplitude current. Studies of the phase transition mechanism and electric current generation behavior are of essential importance for exploiting and developing applications of the materials. Furthermore, the accurate identify of the F_R to A_O phase transition is also a challenge to the experimental researchers, both in method and diagnosis techniques, for it occurs below the Hugoniot elastic limits of the ceramics and the phase transition process would be seriously affected by its constitutive behavior, and the construction of the constitutive relations in the elastic stress region involving phase transition is not yet an easy job.
In this paper, the domestic PZT 95/5 ceramic with a density of 7.76g/cm~3 was chosen as our test sample and the one-stage gas gun at LSD was used as the planar shock-loading tools to create the one-dimensional strain states in the ceramics. Based on the measured Hugoniot data, the sound velocities at the Hugoniot states and the depoling current profiles determined from the experiments, a constitutive model involving the irreversible phase transition in the elastic stress region was proposed; behavior of the phase transition related with the shock loading stresses and the shock-depoling properties was carefully analyzed. Main results are as follows:
1. The axial stress(σ) to particle velocity(u) relation, i.e. the Hugoniot of the polarized high density PZT 95/5 ceramics at stresses ranging from 0.48 GPa to 3.78 GPa, were measured via reverse-impact experiments, by using the VISAR instrumentation techniques coupled with a fused quartz window. The elasticσ-u Hugoniot of the polarized ceramics behaves totally different from that of the un-polarized ones in that the former can be characterized by a three-sections broken-line while the latter is linear. These results provided a basis for establishing a constitutive relation involving the phase transition in the elastic stress regions. In reference to the dynamic yielding threshold stress data for low density PZT 95/5 ceramics by Setchell et al and to the crystal lattice parameter changes before and after the phase transition by Avdeev et al, it is concluded that the phase transformation of domestic high density PZT 95/5 is a first order phase transition occurring in the stress region, roughly from about 0.5 GPa to about 2.0 GPa.
2. Sound velocities were calculated from the particle velocity profile of PZT 95/5 ceramic, which is obtained from the reverse-impact experiments. Result shows that the longitudinal sound velocity increase with shock stress, it can also be expressed by a three-sections broken line. It is the phase transition that results in the inflections in the slopes of the sound velocity versus stress curve.
3. Shock-induced depoling process and electric current releasing of the high density PZT 95/5 ceramics were studied. Firstly, the current-releasing behavior in the phase transition stress region was studied by comparing the released polarization (P_(rs)) under shock compression and the initial remanent polarization (P_r). Results show that the magnitude of the current released increases with the shock stress. Analysis of the current data further confirms that the phase transition should start at stress about 0.30±0.15 GPa and almost complete at 1.90±0.15 GPa. Secondly, the influence of the circuit loads on the output currents at stresses where phase transition completes was discussed. Analyses of the equivalent circuit and the experiment results show that the current magnitude will keep constant when phase transition has completed. The current in circuit will only be influenced by RLC loads such that: the inductance loads will induce a rising current magnitude and a oscillatory profile, the pure resistance loads will induce a stable current output and the response time will increase with the resistance magnitude.
4. By using the experiment data of the Hugoniot, the sound velocity ,and the elastic modulus at ambient conditions for the high density PZT 95/5 ceramics, and by expanding Tang Zhiping's irreversible phase transition model for 1-D stress loading conditions to 1 -D strain conditions of this study, a new constitutive model for F_R→A_O phase transition of the high density PZT 95/5 ceramics was proposed: whereσ_A andε_A are threshold stress and strain, andσ_B andε_B are ending stress and strain of the phase transition, respectively. All of them were determined from F_R→A_O phase transition experiment:σ_A=0.23 GPa,ε_A=1.48×10~(-3),σ_B=1.94 GPa,ε_B=1.34×10~(-2).
5. Based on the experimentally measured electric charges released during the phase transition, a volume fraction function,ξof the A_O phase due to the phase transition is introduced to describe the dynamic phase transition behavior by definition, the volume fraction fuctionξcan be expressed as the ratio of the released polarization P_(rs) to the remanent polarization P_r Since the density of the F_r phase and A_O phase have been precisely determined, the mass fraction change of the A_O phase due to the phase transition can easily be calculated from the volume fractionξ. By combination of theσ-u Hugoniot and the measured electric charges released, the volume fraction parameterξcan further be expressed as the function of the shock stress (σ) such that:This also implies that the phase transition of the polarized high density PZT 95/5 ceramics initiates at stress of 0.23 GPa and completes at 1.94 GPa.
In conclusion, a method for studying experimentally the constitutive relations under 1-D strain condition and a model for describing the dynamic phase transition behavior of the domestic high density PZT 95/5 ceramics have been developed. The method mainly includes two basic experimental techniques-the reverse impact techniques and the VISAR instrumentation techniques coupled with a transparent window, to obtain the particle velocity profile at the sample-window interface and the sound velocity profile of the sample under shock loadings. These methods should be applicable to other materials for constitutive measurement and phase transition study. The authors believe that the shock dynamic parameters and the characteristics of the shock-induced phase transition of the domestic high density PZT 95/5 ceramics obtained in this study would be of practical importance in open up its new applications.
本文以国产高密度(7.76 g/cm~3)PZT 95/5陶瓷作为研究对象,在一级气体炮上开展了一维应变平面冲击波加载实验。
通过研究冲击波传播过程中陶瓷的Hugoniot性能、高压声速及冲击去极化释放的电性能,提出了一种弹性区不可逆相变本构模型,深入分析了相变与冲击轴向应力、冲击释电的关系。本文的主要工作及创新点归纳如下:
1.在逆向碰撞实验中,使用含熔石英窗口的激光速度干涉测量技术(VISAR),精确测试了0.48-3.78 GPa压力范围内PZT 95/5陶瓷的轴向应力-粒子速度Hugoniot关系。与未极化陶瓷在弹性区的线性冲击轴向应力-粒子速度Hugoniot关系明显不同的是,弹性区内极化陶瓷的冲击轴向应力-粒子速度Hugoniot关系可以用三段式折线表示。综合Setchell(J Appl Phys,2003,94(1)573)对PZT 95/5陶瓷屈服起始应力和Avdeev(Phys Rev B,2006,73:064105)对PZT 95/5陶瓷F_R→A_O相变前后晶格参数变化的研究结果,得到了国产高密度PZT 95/5陶瓷在大约0.5-2.0 GPa应力范围发生了弹性区一级结构相变的结论。研究结果为建立弹性应力区内包含相变的材料的本构关系奠定了基础。
2.利用上述逆向碰撞实验中得到的PZT 95/5陶瓷粒子速度剖面,计算了在弹性区内的纵波声速。结果表明,PZT 95/5陶瓷在弹性区内的纵波声速随冲击加载应力的增加而增大。纵波声速随冲击加载应力的变化的斜率因相变而发生拐折,也可以用三段折线描写。
3.对国产高密度PZT 95/5陶瓷的相变引起的去极化过程和电流释放性能进行了研究。首先,通过比较冲击释放剩余极化强度P_(rs)与陶瓷的初始剩余极化强度P_r,确定了该陶瓷材料相变起始应力为(0.30±0.15)GPa,相变完成应力为(1.90±0.15)GPa。实验结果表明:在陶瓷相变区内,冲击轴向应力幅值越大,电流幅值越大。其次,对于完全相变后的PZT 95/5陶瓷,研究了外电路负载对陶瓷电流输出性能的影响。通过等效电路的计算分析,并经实验验证表明:完全相变后的PZT 95/5陶瓷可等效为脉冲恒流源,释放的电流为恒定值;释放的电流受外电路的RLC负载参数影响:电感负载导致电流幅值增加,波形振荡;纯电阻负载的电流幅值稳定,电流响应时间随负载电阻的增加而增加。
4.在高密度PZT 95/5陶瓷Hugoniot性能、声速、弹性模量的实验研究基础上,将唐志平等人提出的描写一维应力加载下弹性区不可逆相变本构模型拓展到本文研究的一维应变加载条件下,建立了PZT 95/5陶瓷F_R→A_O相变本构模型:
式中,σ_A、ε_A分别表示相变起始点的冲击轴向应力和应变,σ_B、ε_B分别表示相变完成点的冲击轴向应力和应变。根据本文对国产高密度PZT 95/5陶瓷实验的研究结果,σ_A=0.23 GPa,ε_A=1.48×10~(-3),σ_B=1.94 GPa,ε_B=1.34×10~(-2)。
5.根据实验测量的PZT 95/5陶瓷在相变过程中释放的电荷,提出了用冲击相变过程中陶瓷的A_O相的体积分数ξ来描述陶瓷的动态相变特性,A_O相的体积分数ξ定义为陶瓷冲击释放的剩余极化强度P_(rs)和陶瓷初始剩余极化强度P_r的比值。由于F_R相和A_O相的密度已知,相变过程中A_O相的质量分数可以通过体积分数ξ确定。结合实验测得的PZT 95/5陶瓷的σ-u Hugoniot性能和电释放性能,描写国产高密度PZT 95/5陶瓷的A_O相体积含量ξ随冲击轴向应力σ的变化的关系式如下:
根据相变体积含量关系式,极化高密度PZT 95/5陶瓷的相变起始应力为0.23 GPa,相变结束应力为1.94 GPa。
综上所述,本文发展了一种一维应变条件下研究弹性区相变材料的本构关系的实验研究方法,并确定了国产高密度PZT 95/5陶瓷的冲击相变动力学模型。本实验研究方法采用逆向碰撞实验技术和带窗VISAR测试技术,用于获取“样品/透明窗口界面”的粒子速度和冲击加载下的声速。本方法可用于其它材料的本构关系及低压相变研究。本研究获得的国产高密度PZT 95/5陶瓷的冲击动力学参数、冲击相变动力学特性,对于拓展该材料的应用,具有重要价值。
The polarized PZT 95/5 ferroelectric ceramics with a rhombohedral structure (F_R) will transform into the antiferroelectric phase with an orthorhombic structure(A_O) when subjecting to proper shock loadings. This Phase transition will result in a rapidly depolarizing process, in which the dramatic releasing of the surface charges bounded in the ceramics happens. This kind of ceramics has been successfully used in the United States, United Kingdoms and Russia as the promising pulsed power supplies to provide large amplitude current. Studies of the phase transition mechanism and electric current generation behavior are of essential importance for exploiting and developing applications of the materials. Furthermore, the accurate identify of the F_R to A_O phase transition is also a challenge to the experimental researchers, both in method and diagnosis techniques, for it occurs below the Hugoniot elastic limits of the ceramics and the phase transition process would be seriously affected by its constitutive behavior, and the construction of the constitutive relations in the elastic stress region involving phase transition is not yet an easy job.
In this paper, the domestic PZT 95/5 ceramic with a density of 7.76g/cm~3 was chosen as our test sample and the one-stage gas gun at LSD was used as the planar shock-loading tools to create the one-dimensional strain states in the ceramics. Based on the measured Hugoniot data, the sound velocities at the Hugoniot states and the depoling current profiles determined from the experiments, a constitutive model involving the irreversible phase transition in the elastic stress region was proposed; behavior of the phase transition related with the shock loading stresses and the shock-depoling properties was carefully analyzed. Main results are as follows:
1. The axial stress(σ) to particle velocity(u) relation, i.e. the Hugoniot of the polarized high density PZT 95/5 ceramics at stresses ranging from 0.48 GPa to 3.78 GPa, were measured via reverse-impact experiments, by using the VISAR instrumentation techniques coupled with a fused quartz window. The elasticσ-u Hugoniot of the polarized ceramics behaves totally different from that of the un-polarized ones in that the former can be characterized by a three-sections broken-line while the latter is linear. These results provided a basis for establishing a constitutive relation involving the phase transition in the elastic stress regions. In reference to the dynamic yielding threshold stress data for low density PZT 95/5 ceramics by Setchell et al and to the crystal lattice parameter changes before and after the phase transition by Avdeev et al, it is concluded that the phase transformation of domestic high density PZT 95/5 is a first order phase transition occurring in the stress region, roughly from about 0.5 GPa to about 2.0 GPa.
2. Sound velocities were calculated from the particle velocity profile of PZT 95/5 ceramic, which is obtained from the reverse-impact experiments. Result shows that the longitudinal sound velocity increase with shock stress, it can also be expressed by a three-sections broken line. It is the phase transition that results in the inflections in the slopes of the sound velocity versus stress curve.
3. Shock-induced depoling process and electric current releasing of the high density PZT 95/5 ceramics were studied. Firstly, the current-releasing behavior in the phase transition stress region was studied by comparing the released polarization (P_(rs)) under shock compression and the initial remanent polarization (P_r). Results show that the magnitude of the current released increases with the shock stress. Analysis of the current data further confirms that the phase transition should start at stress about 0.30±0.15 GPa and almost complete at 1.90±0.15 GPa. Secondly, the influence of the circuit loads on the output currents at stresses where phase transition completes was discussed. Analyses of the equivalent circuit and the experiment results show that the current magnitude will keep constant when phase transition has completed. The current in circuit will only be influenced by RLC loads such that: the inductance loads will induce a rising current magnitude and a oscillatory profile, the pure resistance loads will induce a stable current output and the response time will increase with the resistance magnitude.
4. By using the experiment data of the Hugoniot, the sound velocity ,and the elastic modulus at ambient conditions for the high density PZT 95/5 ceramics, and by expanding Tang Zhiping's irreversible phase transition model for 1-D stress loading conditions to 1 -D strain conditions of this study, a new constitutive model for F_R→A_O phase transition of the high density PZT 95/5 ceramics was proposed: whereσ_A andε_A are threshold stress and strain, andσ_B andε_B are ending stress and strain of the phase transition, respectively. All of them were determined from F_R→A_O phase transition experiment:σ_A=0.23 GPa,ε_A=1.48×10~(-3),σ_B=1.94 GPa,ε_B=1.34×10~(-2).
5. Based on the experimentally measured electric charges released during the phase transition, a volume fraction function,ξof the A_O phase due to the phase transition is introduced to describe the dynamic phase transition behavior by definition, the volume fraction fuctionξcan be expressed as the ratio of the released polarization P_(rs) to the remanent polarization P_r Since the density of the F_r phase and A_O phase have been precisely determined, the mass fraction change of the A_O phase due to the phase transition can easily be calculated from the volume fractionξ. By combination of theσ-u Hugoniot and the measured electric charges released, the volume fraction parameterξcan further be expressed as the function of the shock stress (σ) such that:This also implies that the phase transition of the polarized high density PZT 95/5 ceramics initiates at stress of 0.23 GPa and completes at 1.94 GPa.
In conclusion, a method for studying experimentally the constitutive relations under 1-D strain condition and a model for describing the dynamic phase transition behavior of the domestic high density PZT 95/5 ceramics have been developed. The method mainly includes two basic experimental techniques-the reverse impact techniques and the VISAR instrumentation techniques coupled with a transparent window, to obtain the particle velocity profile at the sample-window interface and the sound velocity profile of the sample under shock loadings. These methods should be applicable to other materials for constitutive measurement and phase transition study. The authors believe that the shock dynamic parameters and the characteristics of the shock-induced phase transition of the domestic high density PZT 95/5 ceramics obtained in this study would be of practical importance in open up its new applications.
引文
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