Interface crack between two interface deformable piezoelectric layers

Based on an interface deformable piezoelectric bi-layer beam model, a bonded piezoelectric bi-material beam with an interface crack perpendicular to the poling axis is analyzed within the framework of the theory of linear piezoelectricity. The layer-wise approximations of both the elastic displacements and electric potential are employed, and each sub-layer is modeled as a single linearly elastic Timoshenko beam perfectly bonded together through a deformable interface. Using the impermeable crack assumption, the closed form solutions for the energy release rate (ERR) and crack energy density (CED) are derived for the layered piezoelectric beam subjected to combined uniformly distributed electromechanical loading. Based on superposition principle, both the ERR and CED and their components are all reduced to the functions of the crack tip loading parameters. Loading dependence of the total CED with respect to the applied electric field is manifested with the analytical results, showing that there is a transformation from an even dependence to an odd dependence for the normalized CED when the applied mechanical loading increases. Compared with the commonly used equivalent single layer model, the proposed analysis augments the crack driving force by alleviating the stress concentration along the interface and thus increases the loading parameters at the crack tip. The proposed model provides improved solutions for fracture analysis of piezoelectric layered structures and sheds light on the loading dependence of the fracture parameters (i.e., the ERR and CED) with respect to the applied electromechanical loadings.     

Conductive carbon black-filled ethylene acrylic elastomer vulcanizates: physico-mechanical,thermal, and electrical properties

The effect of conductive carbon black (CCB) on the physico-mechanical, thermal, and electrical properties have been investigated by various characterization techniques. Physico-mechanical properties of the vulcanizates were studied with variation of filler loading, which revealed that the tensile strength increased up to 20 phr (parts per hundred rubber) CCB loading, whereas at higher filler loading it decreased marginally. Furthermore, tensile modulus, tear strength, and hardness gradually increased with increase in filler loading. The compression set and abrasion loss decreased with increasing CCB loading. The bound rubber content (Bdr) of unvulcanized rubber was found to increase significantly with increasing CCB content. The crosslink density increased, whereas the swelling decreased with CCB loading. The thermal stability of the vulcanizates evaluated by thermogravimetric analysis (TGA) showed a minor increment with increase in CCB content. It is observed from the dynamic mechanical thermal analysis (DMTA) that the storage modulus (E′), loss modulus (E″), and glass transition temperature (T _g) of ethylene acrylic elastomer (AEM) matrix increased by incorporation of CCB. The dielectric relaxation characteristics of AEM vulcanizates such as dielectric permittivity (ε′), electrical conductivity (σ _ac), and electric moduli (M′ and M″) have been studied as a function of frequency (10¹ to 10⁶ Hz) at different filler loading. The variation of ε′ with frequency and filler loading was explained based on the interfacial polarization of the fillers within a heterogeneous system. The ε′ increased with increasing the CCB loading and it decreased with applied frequency. The frequency dependency of σ _ac was investigated using conduction path theory and percolation threshold limit. The σ _ac increased with increase in both CCB concentration and applied frequency. The M′ increased with applied frequency, however, it decreased above 30 phr filler. The M″ peak shifted towards higher frequency region and above 20 phr filler loading the peaks were not observed within the tested frequency region. The electromagnetic interference shielding effectiveness (EMISE) was studied in the X-band frequency region (8–12 GHz), which significantly improved with increase in CCB loading.     

Analysis of the diametral compression method for determining the tensile strength of transparent magnesium aluminate spinel

Attempts were made to determine the inherent tensile strength of a coarse-grained, hot-pressed magnesium aluminate spinel (MgAl₂O₄) using the diametral compression test. Thick (9.6 mm) disk specimens were machined from a large (356 mm square) plate of spinel. Two pairs of tungsten carbide (WC) platens, one with flat surfaces and the other with a 20° half-arc and radius matched to the disk diameter, were used to transfer the applied load. Specimens tested using the platens with the matched radius had strength values almost 50% higher than those tested using flat platens. Images of the fracture process captured using a high-speed camera showed that irrespective of the type of platens used, fracture consistently initiated at the loading interface, resulting in an invalid test. These results show that the diametral compression test method is not appropriate for determining the tensile strength of this spinel and it raises concerns about the applicability of the method for any advanced ceramic.     

(Bi1/2Na1/2)TiO3 additive effect for improved piezoelectric and mechanical properties in PZT ceramics

Bismuth sodium titanate, (Bi_1/2Na_1/2)TiO₃(BNT) additive effect for the improvement of piezoelectric and mechanical properties in PZT ceramics were discussed from the viewpoint of high-power applications. The addition of 5 wt% BNT in Pb(Zr_0.52Ti_0.48)O₃ ceramics showed suppressive effect for electro-mechanical coupling factor (k _p) value. On the other hand, the addition of 0.5 and 1.0 wt% BNT contributed to improve the four point mechanical bending strength when it was sintered at 1150°C.     

Magnetic and processability studies on rubber ferrite composites based on natural rubber and mixed ferrite

Polycrystalline single phasic mixed ferrites belonging to the series Ni_1–x Zn _x Fe₂O₄ for various values of _x have been prepared by conventional ceramic techniques. Pre-characterized nickel zinc ferrites were then incorporated into a natural rubber matrix according to a specific recipe for various loadings. The processability and cure parameters were then determined. The magnetic properties of the ceramic filler as well as the ferrite loaded rubber ferrite composites (RFC) were evaluated and compared. A general equation for predicting the magnetic properties was also formulated. The validity of these equations were then checked and correlated with the experimental data. The coercivity of the RFCs almost resemble that of the ceramic component in the RFC. Percolation threshold is not reached for a maximum loading of 120 phr (parts per hundred rubber by weight) of the filler. These studies indicate that flexible magnets can be made with appropriate magnetic properties namely saturation magnetisation (M _s) and magnetic field strength (H _c) by a judicious choice of x and a corresponding loading. These studies also suggest that there is no possible interaction between the filler and the matrix at least at the macroscopic level. The formulated equation will aid in synthesizing RFCs with predetermined magnetic properties.     

Crystalline state extrusion of high -density polyethylene as a function of die entrance angle

High-density polyethylene (HDPE) of two different average molecular weights, ¯M _w, has been solid-state extruded in an Instron capillary rheometer through brass capillary dies of several entrance angles from 10 to 180°. Extrusion rates increase substantially at smaller angles whereas the maximum achievable extrusion draw ratio, (R _E), is realized at larger angles. At a constant R _E, maxima are observed in plots of linear expansion coefficient, Young's modulus, tensile strength and elongation at break against die entrance angle. These maxima occur at angles of 20 to 30° for the lower molecular weight HDPE (¯M _w = 59 000). For the higher molecular weight HDPE (¯M _w = 92 000) maxima were at angles of 14 to 20°.     

Piezoelectric and dielectric properties of Bi0.5Na0.5TiO3–Bi0.5K0.5TiO3–Ba0.77Ca0.23TiO3 lead-free piezoelectric ceramics

Lead-free piezoelectric ceramics (1 − x)Bi_0.5(Na_0.84K_0.16)_0.5TiO₃–xBa_0.77Ca_0.23TiO₃ (BNKT–xBCT, x = 0–0.04) were synthesized by conventional solid-state reaction method. The piezoelectric, dielectric, and ferroelectric characteristics of the ceramics are investigated and discussed. The XRD results show that Ba_0.77Ca_0.23TiO₃ (BCT) has diffused into Bi_0.5(Na_0.84K_0.16)_0.5TiO₃ (BNKT) lattices to form a new solid solution. It is shown that moderate additive of BCT (x ≤ 0.025) in BNKT–xBCT ceramics can enhance their piezoelectric and ferroelectric properties. Three dielectric anomalies are observed in BNKT–xBCT (x ≤ 0.03) ceramics. The piezoelectric measurements and P–E hysteresis loops reveal that BNKT–0.025BCT ceramic has the highest piezoelectric performance and strongest ferroelectricity in all the samples. Piezoelectric constants d ₃₃, k _p, and k _t of 175 pC/N, 29.1, and 54% are, respectively, achieved. Remnant polarization P _r and coercive field E _c reach 28.3 μC/cm² and 24.2 kV/cm, respectively.     

The temperature dependence of the strength of adhesion between epoxy-rubber glues and steels

We have studied the temperature dependence of the strength of adhesion between epoxy-rubber glues and steel 45 measured at a fixed loading rate. It is established that the adhesion strength σ exhibits a linear decrease with increasing temperature, predicted by the kinetic theory of fracture, only in the temperature interval between the characteristic values T _t and T _b. Below T _t, the adhesion strength is independent of the temperature, while at T>T _b, the slope of the σ(T) curve decreases with increasing temperature. Deviations from the kinetic theory predictions are explained by a change in the fracture mechanism (with tunneling transitions being involved in the fracture at low temperatures) and by variation of the parameter γ (at elevated temperatures). The values of the activation energy and activation volume of the fracture are determined.     

A study of the effect of molecular weight on the tensile strength of ultra-high modulus polyethylenes

In this paper the influence of molecular weight and molecular weight distribution on the tensile strength (tenacity) of melt spun and drawn linear polyethylene are investigated with the aim of outlining the requirements for a high strength fibre. The tenacity was investigated over the molecular weight average ¯M _w range 60×10³ to 330×10³ with polydispersities ¯M _w/¯M _n ranging from 1.1 to 13.3. It was found that both molecular weight and its distribution affected tensile strength. The drawing conditions were also found to be important, a high draw temperature and a high draw ratio being needed for a high strength, high modulus fibre. By using a polymer of high ¯M _w and low polydispersity, and drawing at the optimum conditions, strengths of 1.65 GPa and moduli of 85 GPa have been achieved for test temperatures of –55° C.     

Energy Analysis for Permeable and Impermeable Cracks in Piezoelectric Materials

This letter deals with an energy analysis for both permeable and impermeable cracks in piezoelectric materials. Computed numerical results are plotted in figures, which support Park-Sun's conclusion (1995a,b) that the total energy release rate (TERR) involving both mechanical and electric parts is not suitable to describe piezoelectric fracture for a plane impermeable crack because the two parts have different signs: the former is positive and the latter is always negative under any kinds of combined mechanical-electric loading. This provides the major reason as why the mechanical part (the mechanical strain energy release rate, MSERR) must be used as a fracture criterion empirically. Whereas the electric part of the TERR for a permeable crack does always vanish whatever the poling direction is oriented with respect to the remote electric loading direction. This finding supports McMeeking's (1990, 1999) conclusion that the TERR could be used as a fracture criterion for permeable cracks.     

Strong and Tough Glass with Self‐Dispersed Nanoparticles via Solidification

Glassy materials can be broadly defined as any amorphous solid, which are important in nature and have significant societal value for their applications in daily life and industry. Although many methods have been applied, the fracture toughness of traditional glasses is still very low due to intrinsic brittleness, significantly limiting their use for structural applications. While nanoelements may be added into glasses and ceramics to form nanocomposites with enhanced properties, it is extremely difficult to distribute and disperse them inside the liquid glass/ceramic matrix with traditional processing methods. It is shown that a strong and tough glass can be fabricated through a direct‐solidification process using a nanoparticle self‐dispersion mechanism in a glass melt (2MgO·2Al₂O₃·5SiO₂) with the assistance of B₂O₃, delivering a 6.1% strain limit and strength up to E/14 (E is elastic modulus), which is close to the theoretical limit of E/10 and one of the highest among all materials reported so far. The fracture toughness of the glass with 30 vol% SiC nanoparticles is significantly higher than any other inorganic glass tested under similar conditions. This new method opens up remarkable opportunities for glass and ceramic research, manufacturing, and applications.     

Crack resistance of ceramic materials with controlled crack growth. Report No. 1. Experimental method

A method is described for testing ceramic materials to fracture with controlled crack growth. The method makes it possible to study the laws which govern the kinetics of fracture with allowance for loading history. The use of an automated system to permit recording in real time makes the test more informative and allows testers to obtain a representative volume of data from a single specimen of standard dimensions. This in turn makes it possible to conduct more detailed studies of the principles underlying the nonequilibrium fracture of new ceramics in which fracture resistance depends on microstructure.Translated from Problemy Prochnosti, No. 5, pp. 69–77, May, 1994.     

The history of ceramic filters

The history of ceramic filters is surveyed. Included is the history of piezoelectric ceramics. Ceramic filters were developed using technology similar to that of quartz crystal and electro-mechanical filters. However, the key to this development involved the theoretical analysis of vibration modes and material improvements of piezoelectric ceramics. The primary application of ceramic filters has been for consumer-market use. Accordingly, a major emphasis has involved mass production technology, leading to low-priced devices. A typical ceramic filter includes monolithic resonators and capacitors packaged in unique configurations.     

Large strain response in acceptor- and donor-doped Bi<Subscript>0.5</Subscript>Na<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript>-based lead-free ceramics

Effects of Fe and La addition on the dielectric, ferroelectric, and piezoelectric properties of Bi_0.5Na_0.5TiO₃–Bi_0.5Li_0.5TiO₃–BaTiO₃–Mn ceramics were investigated. Similar to the doping effect in lead-based piezoelectric materials, here the Fe-doped ceramic created a hard effect with an improved mechanical quality factor (Q _m) ~ 160, coercive field (E _c) ~ 2.9 kV/mm, decreased dielectric constant ( e₃₃^T /e₀ ) ~ 80 3, \left( {\varepsilon_{33}^{T} /\varepsilon_{0} } \right)\sim 80 3, and loss (tanδ) ~ 0.024 while the La-doped one indicated a soft feature with improved piezoelectric constant (d ₃₃) ~ 184 pC/N, e₃₃^T /e₀   ~ 983, \varepsilon_{33}^{T} /\varepsilon_{0} \,\sim { 983}, tanδ ~ 0.033, and decreased E _c ~ 2.46 kV/mm. In addition, the temperature dependence of the ferroelectric hysteresis loops and strain response under unipolar electric field was also studied. Around the depolarization temperature T _d, large strain value was obtained with the normalized d₃₃^* d_{33}^{*} up to ~1,000 pC/N, which was suggested originated from the development of the short-range order or non-polar phases in the ferroelectric matrix. All these would provide a new way to realize high piezoelectric response for practical application in different temperature scale.     

Size and loading mode effects in fracture toughness testing of polymers

Experimental work is described which examines the applicability of plane-strain fracture toughness testing techniques to several polymers. The fracture behaviour of five polymers was studied using pre-notched test specimens and was characterized by the linear elastic fracture parameter,K _c. Two test geometries and loading modes were used; SEN tension and three-point bending have been investigated by varying both thickness and width. It has been established that the ASTM criterion for plane-strain conditions ofB>2.5 (K _c1/σ _y)² is sufficient for SEN bending but not for tension where an extrapolation method is needed. For width effects the BCS model was shown to describe the observations and this with a limiting nominal stress analysis gave quite close agreement with the ASTM criterionW>5 (K _c1/σ _y)². This value was shown to be a good estimate of the practical minimum width. There is some evidence that PP, which gives substantial crazing and whitening, can give satisfactory values at sizes about half these limiting values.     

On saturation-strip model of a permeable crack in a piezoelectric ceramic

Summary. The saturation-strip model for piezoelectric crack is re-examined in a permeable environment to analyze fracture toughness of a piezoelectric ceramic. In this study, a permeable crack is modeled as a vanishing thin but finite rectangular slit with surface charge deposited along crack surfaces. This permeable saturation crack model reveals that there exists a possible leaky mode for electrical field, which allows applied electric field passing through the dielectric medium inside a crack. By taking into account the leaky mode effect, a first-order approximated solution is obtained with respect to slit height, h ₀, in the analysis of electrical and mechanical fields in the vicinity of a permeable crack tip. The permeable saturation crack model presented here also considers the effect of charge distribution on crack surfaces, which may be caused by any possible charge-discharge process in the dielectric medium inside the crack. A closed form solution is obtained for the permeable crack perpendicular to the poling direction under both mechanical as well electrical loads. Both local and global energy release rates are calculated. Remarkably, the global energy release rate for a permeable crack has an expression, where M is elastic modulus, a is the half crack length, is permittivity constant, and e is piezoelectric constant. This result is in a broad agreement with some experimental observations and may be served as the fracture criterion for piezoelectric materials. This contribution elucidates how an applied electric field affects crack growth in piezoelectric ceramic through its interaction with permeable environment surrounding a crack. The author would like to acknowledge the support from the Academic Senate Committee on Research at University of California (Berkeley) through the fund of BURNL-07427-11503-EGSLI.     

Application of a strip-yield model to predict crack growth under variable-amplitude and spectrum loading – Part 1: Compact specimens

Fatigue-crack-growth tests were conducted on compact, C(T), specimens made of D16Cz (clad) aluminum alloy under constant-amplitude loading, a single spike overload, and simulated aircraft spectrum loading. Constant-amplitude tests were conducted to generate crack-growth-rate data from threshold to near fracture over a wide range of stress ratios (R = P_min/P_max = 0.1–0.75) using the new compression pre-cracking test methods. Comparisons were made between test data generated on the C(T) specimens with test data from the literature on middle-crack-tension, M(T), specimens machined from the same sheet. A crack-closure analysis was used to collapse the rate data from both specimen types into a narrow band over many orders of magnitude in rates using proper constraint factors. The constraint factors were established from constant-amplitude (CA) and single-spike overload tests. The life-prediction code, FASTRAN, which is based on the strip-yield model concept, was used to calculate crack-length-against-cycles under CA loading and a single-spike overload (OL) test, and to predict crack growth under simulated aircraft spectrum loading tests on C(T) specimens. The calculated crack-growth lives under CA loading were generally within about ±25% of the test results, but slower crack growth under the double-shear fatigue mode, unlike the single-shear mode (45^o slant crack growth), may be the reason for some of the larger differences. The predicted results under the single-spike overload and the Mini-Falstaff+ spectrum were within 10% of the test data.     

Dynamic behavior of selected ceramic powders

An experimental setup has been developed on the continuous recording of the stress profiles in ceramic powders subject to shock loading with manganin gauges. A series of plate impact experiments on highly porous ceramic powders such as Al₂O₃, SiC and B₄C were conducted at the laboratory's single stage powder gun facility. The relationship between shock wave velocity and particle velocity was measured to obtain the Hugoniot data. Plate impact onto powder sample experiments were conducted at loading stresses ranging from 1.6 to 4.2 GPa. The experimental results show that the shock wave speeds in various ceramic powders vary between 1 and 2 km/s. Linear Hugoniot relations between shock velocity (D) and particle velocity (u) are observed. The loading stress–specific volume form of Hugoniot relations (P–V) was constructed using the data from quasistatic compression test results, Hopkinson bar dynamic compression test results and powder gun plate impact experiment results. The P–V diagram shows that the crush strength of ceramic powders is comparable to the loading stress level. The B₄C and SiC powders with bigger particle size more easily reach the solid state Hugoniot than the powders with smaller particle size at the same loading condition. In the case of Al₂O₃, the material shows less sensitivity to particle size difference at the same level of loading rate as compared to B₄C and SiC.     

The effect of molecular weight on slow crack growth in linear polyethylene homopolymers

The rate of initiation and growth of cracks in linear high-density polyethylene with different molecular weights was observed in single-edge-notched tensile specimens under plane strain condition as a function of applied stress, notch depth and temperature. The initial rates of crack initiation all have the form of C ^m a ₀ ⁿ exp (–Q/RT) or AK ^pexp (–Q/RT) where = stress, a ₀ = notch depth and K= stress intensity factor. For the different molecular weights, m, n, P and Q are almost the same where m=5, n=2, P=4.7 and Q=115 kJ mol^–1, but the constants C and A varied as (¯M _w–¯M _c)^–1 where ¯M_c is a limiting molecular weight for sudden fracture. A molecular model based on tie-molecules has been used to explain the dependence on ¯M _w. The effect of ¯M _w on the fast-fracture strength at low temperature and the relationship to tie-molecules have also been investigated. Quantitative relationships between the concentration of tie-molecules and the fracture behaviour have been obtained.     

Effects of La occupation site on the dielectric and piezoelectric properties of [Bi0.5(Na0.75K0.15Li0.10)0.5]TiO3 ceramics

The crystal structure, phase transition and ferroelectric (FE)/piezoelectric properties were investigated for three types of La-doped [Bi_0.5(Na_0.75K_0.15Li_0.10)_0.5]TiO₃ ceramics. The dielectric measurements showed that the transition between FE and antiferroelectric (AFE) phases near 180 °C became pronounced by La addition, and the maximum permittivity was observed at 360 °C in La-doped samples, whereas at 290 °C in non-doped samples. Normal FE and excellent piezoelectric properties were observed by P–E hysteresis loop and piezoelectric measurements in samples without vacancy. However, when the A-site or B-site vacancies were formed, the temperature range of AFE phase extended even appeared at room temperature, which resulted in the presence of deformed P–E curves and decrease of piezoelectric properties. It was suggested that the AFE phase originated from the decoupling effect between BO₆ octahedra in ABO₃ perovskites due to the A-site and/or B-site vacancies.