Fatigue crack growth driven by electric fields in piezoelectric ceramics and its governing fracture parameters

Fatigue crack growth test for piezoelectric ceramics was performed under cyclic electric loading. Double cantilever beam specimen, which was made of two different piezoelectric ceramics, with a through notch was used. The specimens were, varying the amplitude and the mean value, subjected to various cyclic electric fields. It was found that crack growth behavior is greatly dependent on the amplitude and mean value of cyclic electric field and materials. Crack growth rate decreased as electric field increased and finally stopped. Crack growths under the positive, the negative and the shifted electric field were very slow compared to that under fully reversed electric field. However, threshold for the crack propagation did not depend greatly on materials. Then, as possible governing fracture parameters, CED and electric displacement intensity factor were chosen based on the results of electromechanical finite element analysis within linear framework and their closed form equations were also obtained considering the influences of electric boundary conditions inside the notch. Finally, the parameters were correlated with crack growth rate measured experimentally by employing Paris law type equation.     

On the fracture toughness anisotropy of mechanically poled ferroelectric ceramics

In this paper an incremental constitutive theory for the deformation due to switching in ferroelectrics is applied to predict the fracture toughness anisotropy in these materials after mechanical poling. Mechanical poling of an initially unpoled specimen differs from electrical poling in that only mechanical stresses are applied to the material. Therefore, no electrical polarization can develop. After mechanical poling, for example by a uniaxial applied stress, the fracture toughness of a ferroelectric ceramic for cracks running parallel or orthogonal to the poling direction will differ. Finite element computations of the steady crack growth process have been carried out to quantify these differences. Results are generated for a range of constitutive properties for three crack growth directions with respect to the initial mechanical poling direction. The results are discussed in relation to available experimental data and to the toughness anisotropy due to electrical poling.     

极化电场取向对应力诱发PZT畴转向增韧的影响

研究了ＰＺＴ压电陶瓷断裂韧性Ｋ１ｃ随温度、特别是铁电相变的变化。探讨了极化电场与外应力的相对取向对材料Ｋ１ｃ的影响。结果表明，断裂韧性随温度升高而下降至居里点处的最低值，然后略有回升。基于裂纹尖端应力诱发畴转向的增韧机理，极化取向垂直于外张应力时的Ｋ１ｃ比平行取向的高。     

On the electrical boundary conditions on the crack surfaces in piezoelectric ceramics

This paper investigates a cracked piezoelectric ceramic under remote electro-mechanical loads. The ideal crack boundary conditions for electrically impermeable and permeable crack assumptions, and the deformed crack with a yet-to-be-determined crack shape are considered. The last is referred to as the “natural boundary condition (NBC)”. Closed-form solutions to the crack-tip field intensity factors are obtained. The analysis shows that traditional approaches to the electric boundary conditions on the crack faces, that is, either the impermeable crack assumption or the permeable crack assumption, produce significantly different results for the crack-tip quantities such as electric displacement intensity factor, energy release rate and crack opening displacement. There are also considerable differences between the results obtained from traditional impermeable and permeable crack analyses and those obtained from the proposed NBC. The difference increases with applied electric loads.     

Effect of electric field on fracture of piezoelectric ceramics

Closed form solutions for all three modes of fracture for an infinite piezoelectric medium containing a center crack subjected to a combined mechanical and electrical loading were obtained. The explicit mechanical and electrical fields near the crack tip were derived, from which the strain energy release rate and the total potential energy release rate were obtained by using the crack closure integral. The suitability in using the stress intensity factor, the total energy release rate, or the mechanical strain energy release rate as the fracture criterion was discussed.     

On scattering of measured values of fracture toughness parameters

The values of fracture toughness K _1C of C-Mn steels and weld metal were calculated from values of COD measured in standard specimens tested at low temperatures. The analysis of scattering of 42 values of K _1C measured in normalized C-Mn steel showed that the highest value of K _1C could be as large as 360 percent of the lowest. The factors affecting the scattering were investigated in detail and it was found that the scattering was mainly caused by the variation of locations of cleavage initiation. The local fracture stress σ was found to be the most stable parameter and combined with the minimum cleavage distance min which is determined by the triaxiality of stress reaching a critical value, it could be used to characterize the lower boundary of fracture toughness of steels. This revised version was published online in July 2006 with corrections to the Cover Date.     

Some effects of an electric field on the plastic deformation of metals and ceramics

 The external parameters generally considered in the plastic deformation of metals and ceramics are the temperature, pressure or stress and time. Usually neglected are the effects of electric and magnetic fields. However, such fields can often have a significant influence, especially when applied concurrently with the more common parameters. Some examples of the effects of an electric field on the plastic deformation of metals and ceramics found by the author and his coworkers are presented. Included are the following: (a) the influence of electropulsing on the flow stress of metals at 78–300 K, (b) the effect of an external electric field (surface charge) on the superplastic deformation of the 74754 Al alloy, (c) the influence of an electric field on the flow stress and ductility of polycrystalline NaCl at 0.28–0.75 T_M and (d) the effect of an electric field on the superplastic deformation of 3Y-TZP. Mechanisms responsible for the observed effects are considered. Received: 1 January 1998 / Accepted: 1 March 1998     

On the effect of remanent polarization on electro-mechanical fields near an elliptic cavity in poled or depolarized piezoelectric ceramics

In this paper the effect of remanent polarization on electric-mechanical fields near an elliptic cavity in piezoelectric ceramics is studied. The analysis is based on the application of exact electric boundary conditions at the rim of the elliptic cavity, thus avoiding the common assumption of electric impermeability. Expressions for electromechanical fields near the elliptic cavity are derived in a closed form in terms of complex potentials. The result shows that the problem of remanent polarization is similar to the problem of general strain mismatch and the effect of remanent polarization on fracture in poled or depolarized piezoelectric ceramics can not be omitted. When the permitivity of the medium in a cavity is small, the effect of remanent polarization is identical to the effect of a considerable strong positive electric field and the tangent stress at the major axial apex of the elliptical cavity is tensile. Such behavior explains why the positive electric field promotes the crack growth while the negative electric field retards the crack growth and accounts for the anisotropy of fracture toughness under mechanical loads. The results show that the effect of remanent polarization on electromechanical fields near an elliptic cavity depends not only on the geometry of the elliptic cavity, i.e. the ratio of the minor semi-axis to major semi-axis, but also on the ratio of permitivity of the medium in the cavity to permitivity of the piezoelectric ceramic.     

The influence of magnetic field on the fracture toughness of soft ferromagnetic materials

This paper studies the effect of magnetic fields on the fracture toughness in nickel iron soft ferromagnetic materials. Tensile tests were conducted on single-edge cracked plate specimens in the bore of a superconducting magnet at room temperature, and the critical load was determined. The magnetoelastic analysis of a soft ferromagnetic strip with a single-edge crack was also performed, and the magnetic stress intensity factor was calculated. Based on the magnetic stress intensity factor, the fracture toughness was then obtained.     

铬掺杂的PSN-PZN-PZT四元系压电陶瓷材料的研究

用传统固相合成方法制备了Pb(sn1/3Nb2/3)O3-Pb(Zn1/3Nb2/3)O3-PbZrO3-PbTiO3(简写为PSN-PZN-PZT)四元系压电陶瓷材料,主要研究Cr离子掺杂对此材料的微观结构以及压电、介电性能的影响.通过对XRD衍射谱图分析可知,随着Cr的掺杂量的增大,该系统材料的三方相的含量减少,准同相界的位置向三方相移动;SEM照片显示,晶粒尺寸随Cr的量增大而增大,在0.5wt%含量时晶粒分布均匀且大小较为一致;ERP结果表明,Cr2O3在材料中主要以Cr3 、Cr5 存在.且结合材料的性能参数分析,增加Cr的含量会促使Cr离子由高价向低价转化.当Cr2O3的掺杂量为0.5wt%时,PSN-PZN-PZT材料的综合性能较好.     

Computational evaluation of flexural toughness of FRC and fracture properties of plain concrete

In this paper, a computational tool concerning the computation of flexural and fracture toughness of cement based composites is presented. Firstly, RILEM’s (Réunion Internationale des Laboratoires d’Essais de Matériaux) recommendations related to the analysis of FRC in three-point bend tests are discussed in their relevant aspects regarding the computational implementations. The determination of other mechanical properties such as the Young modulus has been added to the program. Taking this into account, a new formulation based on displacements is used. In the second part of the paper, the determination of fracture properties of concrete, such as the fracture energy, G _F , and the fracture toughness, K _IC ^S , is discussed regarding the computational strategies used in the implementations. Several features whereby anterior data can be reanalyzed, obtained from other standards and recommendations, have been incorporated into the program, therefore allowing comparative studies and back analysis activities.     

Electrical failure of piezoelectric ceramics with a conductive crack under electric fields

The failure behavior of piezoelectric ceramics with a conductive crack under purely electric loading is investigated. Electrical fracture tests are conducted to study the influence of the directions of poling and electric loading. Two failure modes of piezoelectric materials are observed: fracture that is accompanied with dielectric discharging and the formation of tubular channels without fracture. The critical J integrals at the onset of both fracture and breakdown are calculated numerically via finite element analysis. The effects of both the direction of the electric field and the poling direction on both fracture and breakdown resistance are discussed.     

Effect of aging treatment on fracture toughness in ZM61 magnesium alloy

The effect of aging treatment on fracture toughness in Mg–6Zn–1Mn (wt-%) was investigated by optical microscopy, scanning electron microscopy, transmission electron microscopy, scanning transmission electron microscopy, uniaxial tensile and fracture toughness tests, respectively. The results showed that the fracture toughness of Mg–6Zn–1Mn alloy can be enhanced by aging treatment. The fracture toughness and strength showed a reverse trend in single aged and double aged alloy. Synergetic effect of fine grains and precipitates improved the fracture toughness more sharply than aging treatment. The precipitate free zones and grain boundary precipitates made the largest contribution to the reduction of toughness. Under as extruded and aged conditions, the main origins of cracks were elastic incompatibility and plastic deformation.     

Experimental research on the compressive fracture toughness of wing fracture of frozen soil

It is commonly found that not only bending fracture but also compressive fracture occur frequently in compression, furthermore, in some specific conditions, compressive fracture sometimes has dominant effect on frozen soil. Therefore, it is extremely necessary to study the mechanical characteristics of the compressive fracture of frozen soil and to investigate the damage and fracture mechanism of frozen soil based on the previous research on frozen soil damage in compression. This study draws on the ideas and methods used in compression fracture research on ice that is very similar to frozen soil, and specific clay in Shenyang region was adopted as the experimental material, to make compressive specimens containing tilted wing crack of different angles, and uniaxial unconfined compression fracture experiments were conducted at different temperatures and loading rates. The fracture toughness K_IC and K_IIC of the main crack tip of the specimens are calculated with obtained experimental results and the law of K_IC and K_IIC changing with tilted angles, temperatures and loading rate is obtained to gain an insight to damage mechanism of frozen soil in compression. This paper presents a meaningful attempt for the research on compressive fracture of frozen soil, so as to better solve practical engineering problems.     

On the self-consistent, energetically consistent, and electrostatic traction approaches in piezoelectric fracture mechanics

In terms of crack opening, the present work studies the self-consistent, energetically consistent, and electrostatic traction approaches. In the self-consistent approach, crack will not open if no mechanical load is applied. The energetically consistent approach under a given electric field yields a threshold stress for crack opening and a bifurcation stress, which is higher than the threshold stress. Between the bifurcation and threshold points there are two solutions for crack opening. The electrostatic traction approach considers electrostatic tractions along crack faces and infinite boundaries. The electrostatic traction along infinite boundaries is equivalent to an additional mechanical load for a given electric field, which is tensile and promotes crack opening, if the dielectric constant of the infinite medium is smaller than that of the material. Energy release rate is also comprehensively analyzed in each of the three approaches.     

陶瓷材料动态断裂韧性测试

为了测试陶瓷材料动态断裂韧性,利用Hopkinson压杆实验原理和改装的Hopkinson压杆装置,并将试件加工成单边切口梁进行了三点弯曲动态试验.利用改装的Hopkinson压杆装置可直接测得透射应力波,从而直接得到试件变形过程中作用在试件上的支反力.本文定义了无量纲挠度和挠度变化率,给出了几种陶瓷材料在不同挠度变化...     

Modified transformation formulae between fracture toughness and CTOD of ductile metals considering pre-deformation effects

Strengthening action and degrading action are proposed to describe influences of plastic deformation on fracture toughness in ductile metals. Strengthening effect represents the shield operation of dislocation from crack and degrading effect displays the emergence of damage. In order to demonstrate two effects, the existing transform equation between fracture toughness and crack-tip opening displacement is modified based on a novel damage variable. The modified transform formulae can help to find the maximum of fracture toughness for metals and keep safer performance for structural components.     

On fracture toughness of nano-particle modified epoxy

A systematic study on the effects of silica and rubber nano-particles on the fracture toughness behavior of epoxy was conducted. Mode I fracture toughness (G_IC) of binary silica/epoxy, binary rubber/epoxy and ternary silica/rubber/epoxy nanocomposites with different particle weight fractions was obtained by compact tension tests. It is found that G_IC of epoxy can be significantly increased by incorporating either rubber or silica nano-particles. However, hybrid nanocomposites do not display any “synergistic” effect on toughness. Microstructures before and after fracture testing were examined to understand the role of nano-particles on the toughening mechanisms.     

On fracture initiation toughness and crack sharpness for Mode II cracks

Fracture toughness of brittle materials is calibrated in experiments where a sample with a preexisting crack is loaded up to a critical point of the onset of static instability. Experiments with ceramics, for example, exhibit a pronounced dependence of the toughness on the sharpness of the crack/notch: the sharper is the crack the lower is the toughness. These experimental results are not entirely compatible with the original Griffith theory of brittle fracture and Linear Elastic Fracture Mechanics which both ignore the crack sharpness.To explain the experimental observations qualitatively we earlier considered Mode I cracks [Volokh KY, Trapper P. Fracture toughness from the standpoint of softening hyperelasticity. J Mech Phys Solids 2008;56:2459-72.] and in the present work we extend our considerations to Mode II cracks. We simulate pure shear of a thin plate with a small crack of a finite and varying sharpness. In simulations we introduce the failure energy as a limiter for the stored energy of the Hookean solid. The energy limiter induces softening, indicating material failure. Thus, elasticity with softening allows capturing the critical point of the onset of static instability of the cracked plate, which corresponds to the onset of the failure propagation at the tip of the crack. In numerical simulations we find that the magnitude of the fracture toughness can not be determined uniquely because it depends on the sharpness of the crack: the sharper is the crack the lower is the toughness.Based on the obtained results we argue that a stable magnitude of the toughness of brittle materials can only be reached when a characteristic size of the crack tip is comparable with a characteristic length of the material microstructure, e.g. grain size, atomic distance etc. In other words, the toughness can be calibrated only under conditions where the hypothesis of length-independent continuum fails.