电场、残余应力和介质对PZT-5H铁电陶瓷压痕裂纹扩展的耦合作用

通过在硅油中加恒电场实验,研究了PZT-5H铁电陶瓷Vickers压痕裂纹的扩展行为,探讨了电场、残余应力以及介质间的耦合作用.结果表明,残余应力不足以使压痕裂纹在硅油中发生滞后扩展,只有外加恒电场E>0.2 kV/cm,电场、残余应力和介质的耦合才能使压痕裂纹在经过一个孕育期tp后发生滞后扩展.由于有效应力强度因子随裂纹扩展而下降,故压痕裂纹扩展10-30 μm后就将止裂.压痕裂纹在硅油中滞后扩展的门槛电场强度EDp=0.2 kV/cm.如外加电场大于临界电场Ep=5.25 kV/cm,电场和残余应力的耦合可使压痕裂纹瞬时扩展;保持恒电场,裂纹能继续扩展,然后止裂.如外加电场大于12.6 kV/cm,不需要残余应力协助,电致裂纹也能在光滑试样上形核、长大、连接,导致试样断裂.试样发生电致滞后断裂的门槛电场EDF=12.6 kV/cm,发生瞬时断裂的临界电场EF=19.1 kV/cm.     

BaTiO3单晶压痕裂纹的畴变和裂纹扩展的原位观察

金相显微镜原位观察了面内极化的BaTiO3单晶在瞬时电场作用下的畴变和裂纹形核、扩展的关系以及未极化BaTiO3单晶在恒电场下Vickers压痕裂纹扩展和电致畴变的关系.结果表明,畴变是裂纹形核、扩展的先决条件,但不存在直接的关系.在恒电场下,未极化的BaTiO3单晶卸载压痕裂纹的滞后扩展可以导致畴变区的扩大.     

电场对铁电陶瓷压痕裂纹的作用

研究了极化锆钛酸铅（PZT-5）铁电陶瓷压痕裂纹在硅油中电场作用下的扩展过程。结果表明,当外加电场强度大于裂纹瞬时扩展临界电场强度（Eip=5.25kv/cm）,压痕裂纹能够发生瞬时扩展,继续保持恒电场,裂纹会继续扩展。当外加电场强度小于裂纹瞬时扩展临界电场强度,裂纹不发生瞬时扩展,但保持恒定电场,裂纹会发生滞后扩展。同时,裂纹扩展量显示各向异性,与垂直于电场方向裂纹相比,平行于电场方向的裂纹扩展量很小。     

环境断裂研究进展

本文介绍了环境断裂近年来的研究进展.第一部分是功能材料的环境断裂.研究发现,铁电陶瓷如PZT和Ba-TiO3在有水或无水环境中,应力能使压痕裂纹发生滞后扩展(即存在应力腐蚀).恒电场能引起铁电陶瓷的畴变,不协调畴变会产生内应力,电场和应力场对环境断裂存在耦合作用,因此,恒电场下环境断裂的本质是内应力引起的环境断裂;对磁致伸缩材料如(ThDy)Fe2,应力和磁场均能引起畴变,卸载压痕裂纹在湿空气中的滞后扩展以及恒磁场引起的滞后畴变及滞后开裂均能发生.第二部分是关于氢压裂纹(白点)的再认识.氢压裂纹形核前是一个内壁光滑的空腔,微裂纹从空腔壁产生,而后连接形成白点.白点断口和含白点试样的断口概念不同,对车轮钢,前者为准解理的穿晶断裂,和氢致滞后开裂断口相同,但后者则依赖断裂方式和试样厚度.钢中白点除了产生二次裂纹外,对各种断口形貌均没有影响.车轮钢的滞后断裂由原子氢引起,与白点无关.     

垂直电场下BaTiO_3单晶的畴变与压痕裂纹的演化

利用微分干涉相衬显微镜,在垂直于极化方向的电场下,对BaTiO_3单晶的畴变过程和单晶上压痕裂纹的变化过程进行了原位观察.通过对压痕周围和远离压痕区畴变过程的对比,研究了压痕对其周围畴变的影响.结果显示,面内极化试样在垂直于极化方向的面内电场作用下,原有压痕和压痕裂纹随整个试样经历90°畴变后也要发生变化,变化后其形貌与在新的极化状态下重新压制的压痕相似;对离面极化试样加面内电场时,畴变速度先增大后减小,畴变完成一半时,速度最大;而且畴变初始阶段速度呈现大小相间的振荡性.     

PLZT铁电陶瓷维氏压痕裂纹尖端的原位Raman观测

通过对预先切向极化和纵向极化的PLZT铁电陶瓷试样表面引入维氏压痕,在压痕引入前后以及外加电场作用下原位记录维氏压痕裂纹尖端处的Raman光谱变化。结果表明：裂纹尖端的Raman光学模的强度与90°畴变、试样的预先极化方向以及裂纹尖端的空间分布位置密切相关。当试样的极化方向与外加电场方向垂直时,极化试样的维氏压痕裂纹尖端发生90°畴变,抑制裂纹的生长,此时观测到的Raman光谱强度变化最显著。当试样的极化方向与外加电场方向平行时,几乎不发生90°畴变,将导致裂纹尖端的裂纹生长。     

恒电场下BaTiO3陶瓷压痕裂纹的滞后扩展

在硅油中加恒电场,研究了BaTiO3铁电陶瓷上维氏压痕裂纹的瞬时扩展和滞后扩展的规律.结果表明,当电场E≥2 kV/mm时,压痕裂纹能发生瞬时扩展,瞬时扩展量随外电场升高而升高.当E≤1.5 kV/mm后,裂纹不能瞬时扩展,但在恒电场下保持一定时间后,就开始滞后扩展,大约60 h后将止裂.电场愈小,发生滞后扩展的孕育期ti愈长;当E≤0.8 kV/mm后,压痕裂纹不发生滞后扩展.随电场升高,裂纹扩展量及平均扩展速率均升高.     

外场作用下BaTiO_3单晶裂纹扩展和畴变

通过偏振光显微镜对连续应力和恒电场作用下的BaTiO_3单晶中的裂纹扩展和畴变过程进行原位观察.结果表明.在连续应力的作用下,裂尖处应力集中导致出现畴变带,裂纹与畴变带垂直相交,畴带和裂纹一起向前移动,畴变在先,裂纹扩展在后;在恒电场作用下,畴变引起的不协调应变导致电致裂纹扩展,畴变始终发生在裂纹扩展之前.裂纹向前扩展时不断的切过前方的畴带,直到不再有畴变发生时裂纹停止扩展.     

PZT-5铁电陶瓷恒载荷压痕裂纹在空气和水中的扩展过程

用Vickers硬度计作为加载装置,研究了极化锆钛酸铅(PZT-5)铁电陶瓷压痕裂纹恒载荷下在室温空气和水中的扩展规律.结果表明,恒载荷下,压痕裂纹在空气和水中不断扩展, 120 h后趋于稳定,从而就可获得裂纹扩展速率和裂纹止裂的门槛应力强度因子KISCC,它们均显示各向异性.研究表明,裂纹扩展速率和KISCC的各向异性与铁电陶瓷断裂韧性的各向异性有关,即裂纹扩展速率随KIC的增加而降低,而KISCC随KIC的增加而升高.平行极化方向裂纹的断裂韧性比垂直极化方向高,即KCICdn/dt;与在空气中相比,在水中应力腐蚀更敏感,即裂纹扩展速率更高、门槛值更低.     

浸蚀促进BaTiO3单晶的畴变和裂纹扩展的研究

研究了浸蚀对极化和未极化的BaTiO3单晶中畴变和压痕裂纹扩展的影响.结果表明,对面内极化试样(即极化方向[001],压痕面(100)),用HCl+HF水溶液浸蚀20 s,其压痕裂纹的平均长度由(140±17)μm扩展至(211±26)μm,即增长50%,同时压痕裂纹所围的90°畴变区也明显增大;先浸蚀再打压痕和压痕后再浸蚀所得的结果相同.其原因和浸蚀剂分子吸附降低表面能有关.对离面极化试样(即压痕面(001)垂直于极化方向[001]),则浸蚀对其裂纹长度和畴变区基本没有影响.对未极化试样,浸蚀使其裂纹长度从(150±21)μm增至(182±30)μm,即增长约20%,同时畴变区亦增大.     

湿空气中恒磁场导致(Tb,Dy)Fe2合金的滞后开裂

对（Tb,Dy）Fe2超磁致伸缩合金,用微分相衬显微镜原位研究了应力和磁场引起的畴变、卸载压痕裂纹在湿空气中的滞后扩展以及在湿空气中恒磁场引起的滞后畴变及滞后开裂．结果表明,当磁场大于门槛值上Hth后就能使压痕裂纹发生瞬时扩展;在湿空气中,残余应力能使（Tb,Dy）Fe2发生滞后扩展,当裂纹止裂后,恒磁场（H〈Hth）能使磁畴发生滞后变化,并能使压痕裂纹进一步发生滞后扩展．     

The electrical potential difference across cracks in PZT measured by Kelvin Probe Microscopy and the implications for fracture

An indentation crack in a poled PZT ceramic subjected to an electric field is investigated using AFM and KFM to determine the crack opening displacement and the electrical potential difference across the crack. The experimental results are used to calculate the crack tip stress and dielectric displacement intensity factors and the crack tip energy release rate. From the applied electric field and the measured field interior to the crack, the dielectric constant of the crack interior is determined to be 40. The consequences of this permittivity on the crack tip energy release rate are illustrated for a Griffith crack. The theoretically predicted effect of an applied electric field in retarding crack growth decreases significantly with increasing permittivity. In practical situations in terms of crack length, applied load and electric field level, the retardation of crack growth is negligible when the dielectric constant of the crack interior is higher than 20.     

A fracture criterion for conducting cracks in homogeneously poled piezoelectric PZT-PIC 151 ceramics

A fracture criterion for conducting cracks in piezoelectric ceramics under combined electrical and mechanical loads is proposed in connection with a measured material specific fracture curve of PZT-PIC 151. The characteristic fracture curve of the investigated material is a function of the stress intensity factor, K_I, which is known from fracture mechanical concepts, and the recently defined electric field intensity factor, K_E, for conducting cracks. A four-point-bending device for fracture tests under combined electrical and mechanical loads serves as the experimental set-up. The measured quantities, force, displacement, applied voltage and crack length, are used to evaluate the experiments. The finite element method (FEM) was used to determine the mechanical stress intensity factor, K_I, and the electric field intensity factor, K_E, taking into account linear piezoelectric coupling in the material. A qualitative process zone model is proposed for a physical interpretation of the fracture curve.     

圆柱平压头压电陶瓷压痕过程中接触应力和电场的奇异性

采用有限元方法,针对横观各向同性压电材料进行轴对称纳米压痕的机电耦合响应数值仿真。结果表明：当压入过程中不施加预设电压,压痕载荷与压痕位移之间呈线性关系;导电压头上电势与压痕位移也呈现相似关系,压头边缘附近的接触应力和电场存在奇异性,且二者均随压头下固体厚度呈指数变化。通过对不同压痕深度和材料厚度下,从压头内部到接触边缘向应力、法向电势和切向电势分布情况的拟合公式得到了不同压电材料厚度下电场和应力场的奇异常数,并对其变化规律进行了分析。     

The effect of an electric current on the nanoindentation behavior of tin

Electrical–thermal–mechanical interactions determine the reliability and performance of microelectromechanical devices and systems. Using the nanoindentation technique the effect of an electric current on the indentation deformation of Sn strips was studied for an indentation load in the range 50–200 μN. During the indentation an electric current density in the range 993.05–4087.89 A cm^?2 was passed through the Sn strips, which introduced electrical–thermal–mechanical interactions. The experimental results showed that the reduced contact modulus decreased with increasing electric current density. For an electric current density less than 4087.89 A cm^?2 the decrease in the reduced contact modulus with increasing electric current density was mainly controlled by Joule heating due to an electrothermal interaction. The electrothermal interaction caused surface softening of the Sn strips. A simple relation is proposed to describe the dependence of the reduced contact modulus on the electric current density. The indentation hardness decreased with increasing indentation load, showing a normal indentation size effect. Using the relationship between indentation hardness and indentation depth from strain gradient plasticity theory we curve fitted the experimental data and found that both the indentation hardness at the limit of infinite depth and the characteristic length were dependent on the electric current density. Finite element analysis was performed to analyze the indentation deformation of a two-dimensional tin strip under the simultaneous action of an electric current. The simulation results showed that the contact modulus of tin decreased linearly with the square of the electric current density, qualitatively in accordance with experimental observations for an electric current density ? 2803.7 A cm^?2.     

Cohesive interface simulations of indentation cracking as a fracture toughness measurement method for brittle materials

Cracks in brittle solids induced by pyramidal indenters are ideal for toughness evaluation since the indentation stress fields decay rapidly from the contact center and any cracks will be eventually arrested. Thus, if the applied energy release rate can be determined analytically, the material toughness can be deduced by measuring the crack length. However, such a driving force calculation is a nontrivial task because of the complex stress fields; only a number of limit cases can be solved, such as the long half-penny cracks (at least two times larger than the contact size) in the classic Lawn–Evans–Marshall (LEM) model. Important questions such as the evolution from short cracks to median/radial and then to half-penny cracks, the form of the scaling relationship that relates fracture toughness to material hardness and indenter angles, the threshold load for indentation cracking, etc., cannot easily be answered without a detailed knowledge of the co-evolution history of the stress fields and crack morphology. To this end, a finite element model of four-sided pyramidal indentation adopting cohesive interface elements is developed to study the effects of indenter geometry, load, cohesive interface parameters, and material properties on the initiation and propagation of the median/radial/half-penny crack systems. The validity and artifacts of the cohesive interface model are carefully examined, and the crack morphologies under various indentation and material parameters are systematically studied. Numerical predictions lead to a quantitative evaluation of the threshold load for indentation fracture, and an improved method for the evaluation of material toughness from the indentation load, crack size, hardness, elastic constants, and indenter geometry, which compare favorably to a large set of experiments in the literature. It is also found that the toughness evaluation method is very sensitive to Poisson’s ratio – an observation that has previously received little attentions. An approximate analysis for short cracks is developed based on the fracture mechanics of annular cracks and the embedded-center-of-dilatation model for indentation-induced residual stress fields.