Static fatigue behavior of cracked piezoelectric ceramics in three-point bending under electric fields

This paper describes an experimental and analytical study on the static fatigue behavior of piezoelectric ceramics under electromechanical loading. Static fatigue tests were carried out in three-point bending with the single-edge precracked-beam specimens. The crack was created perpendicular to the poling direction. Time-to-failure under different mechanical loads and dc electric fields were obtained from the experiment. Microscopic examination of the fracture surface of the piezoelectric ceramics was performed as well. A finite element analysis was also made, and the applied energy release rate for the permeable crack model was calculated. The effect of applied dc electric fields on the energy release rate versus lifetime curve is examined. The most important conclusion we reach is that the lifetimes for the piezoelectric specimens under a positive electric field are much shorter than the failure times of specimens under a negative electric field for the same mechanical load level.     

Fracture behavior of poled piezoelectric PZT under mechanical and electrical loads

Four point bending samples were poled parallel to the long axis, notched and fractured. During mechanical loading, a constant electric field was applied parallel or antiparallel to the poling direction (perpendicular to the crack surface). Assuming electrical crack boundary conditions of (i) an impermeable or (ii) a completely permeable crack, the stress intensity factors K_I and the field intensity factors K_IV at failure were determined by linear-piezoelectric finite element calculations. The fracture curve K_IC(K_IV) for the impermeable crack model does not comply to fracture criteria based on the total energy release rate or on the mechanical energy release rate. Within the completely permeable crack model, it appears generally impossible to describe electric field effects on the fracture resistance. Some theoretical extensions of the crack models are discussed which might contribute to resolve the aforementioned problems.     

Evaluation of Electric Fracture Properties of Piezoelectric Ceramics Using the Finite Element and Single-Edge Precracked-Beam Methods

Single-edge precracked-beam (SEPB) tests were performed on a commercial lead zirconate titanate (PZT) ceramic. Mechanical loading was applied by the crosshead displacement control of a screw-driven electromechanical test machine. The fracture toughness parameter K _C was determined for various electric fields. A finite element analysis was also done to calculate the total potential energy release rate, mechanical strain energy release rate, and stress intensity factor for three-point flexure piezoceramic specimens with permeable and impermeable cracks under displacement and load control conditions. Numerical investigation and comparison with test data indicate that the energy release rate, upon application of the permeable model, is useful for predicting crack growth in PZT ceramic under electromechanical loading. Based on current findings, we suggest that the energy release rate criteria for the permeable crack are superior to fracture criteria for the impermeable crack.     

Dynamic fatigue behavior of cracked piezoelectric ceramics in three-point bending under AC electric fields

This paper describes an experimental and analytical study on the dynamic fatigue behavior of cracked piezoelectric ceramics under AC electric fields. Constant load-rate testing was conducted in three-point bending with the single-edge precracked-beam specimens. The crack was created normal to the poling direction. The effects of AC electric fields and loading-rate on the fracture load were examined. A phenomenological model of domain wall motion was also used in finite element computation, and the energy release rate for the permeable crack model was calculated. The effect of AC electric fields on the critical energy release rate was then examined. The results suggest that (1) the fracture load of PZT ceramics decreases as the load-rate decreases; (2) an overall decrease in the fracture load occurs when testing under AC electric fields; and (3) the critical energy release rate is not very affected by the AC electric fields.     

Reliability Analysis of Structural Ceramics Subjected to Biaxial Flexure

Sintered alumina and silicon nitride were tested in uniaxial (four-point and three-point bend) and biaxial (uniformpressure-on-disk) flexure tests in inert conditions. Fracture origins were identified to be surface flaws in alumina and subsurface pores in silicon nitride. Batdorf's statistical fracture theory and two different fracture criteria, the critical normal stress criterion and a noncoplanar strain energy release rate criterion, were used to examine size and stress-state effects on fracture strengths of the two ceramics. Size effects assessed in four-point and three-point bend tests were in good agreement with the theoretical predictions for both ceramics. Measured biaxial strengths of alumina were in good agreement with the prediction when a noncoplanar strain energy release rate criterion and random surface flaw orientations were assumed. On the other hand, biaxial fracture strength of the silicon nitride was consistent with a prediction based on preferred flaw orientation (i.e., normal to the principal stress in the disks) and the normal stress fracture criterion. Orientation distributions of the fracture planes assessed from the fracture patterns of the disks supported the assumptions of random flaw orientations (alumina) and the preferred flaw orientations (silicon nitride), respectively, for the two ceramics. The preferred flaw orientation in silicon nitride is suggested to originate at subsurface pores as a result of crack nucleation in the plane of maximum tensile stress concentration, i.e., a diametral plane normal to the maximum principal stress.     

平纹编织C/SiC复合材料的断裂韧性

采用紧凑拉伸试件进行循环加载,研究了化学气相渗透工艺制备的二维平纹编织碳布增强碳化硅(C/SiC)复合材料的断裂韧性.基于实验结果,应变能释放率可分为弹性应变能释放率和不可逆应变能释放率,分别分析了弹性应变能释放率和不可逆应变能释放率随裂纹扩展的变化规律.发现在裂纹扩展初始阶段,裂纹分叉引起不可逆应变能释放率远高于弹性应变能释放率.随裂纹进一步扩展,不可逆应变能释放率迅速下降;最终两部分能量释放率都达到相近的平稳值,且不可逆应变能释放率大于弹性应变能释放率.对试件断裂表面进行扫描电镜分析,发现在裂纹尖端区域基体主要是剪切损伤,纤维具有很长的拔出长度.     

The mixed-mode fracture behavior of epoxy by the compact tension shear test

In this study, pure mode I, pure mode II and mixed mode fracture behavior of an epoxy were investigated. Specifically, the mixed mode values of fracture toughness and critical strain energy release rate (CSERR) were measured. Specimens were subjected to mixed mode loading using compact tension shear (CTS) test. Some experimental modifications were found to be necessary to eliminate rotation and ensure crack propagation at the notch when testing epoxy specimens at high mode II loading. A failure criterion for the mixed mode loading of polymer is developed and its predictions are compared with the experimental results. The crack propagation direction in epoxy was investigated in this research as well. A detailed study of failure mechanisms on the fracture surface was performed. The results indicate that the increase in the value of toughness can be directly related to the fracture morphology.     

Double torsion tests for studying slow crack growth of portland cement mortar

For studying slow crack growth in portland cement mortar 32″ (812.8 mm) long double torsion specimens were tested. During testing, the loading and reloading compliances, permanent (or inelastic) deformations and crack growth were measured. It was observed that the strain energy release rates calculated from elastic, secant or reloading compliances do not accurately represent the fracture behavior of this material. A modified definition of the strain energy release rate is developed here to include both the elastic and the inelastic strain energy absorbed during crack extension. For this method, in addition to the reloading compliance, the knowledge of the rate of change of permanent deformations with crack growth is necessary. Details of the analytical and experimental procedure are described in this paper.     

Analytical estimation of fracture toughness for circumferential cracks in thin hard films on ductile substrates

In this study, the fracture toughness of circumferential crack caused by indentation effect of a rigid indenter on a thin and elastic coating deposited on the elastic substrate was calculated. In the coating and substrate, the analytical solution of displacement and stress field was used. The complete adhesion was considered for the coating on the substrate. The location of maximum circumferential stress was investigated using the analytical calculation of the stress and it was found that this place was located at a distance away from the center of the indenter. Then, the stress intensity factor and energy release rate for plane strain state was determined, and consequently, the energy release rate for a channel crack was calculated. Finally, the fracture toughness was calculated with energy release rate curves for plane strain crack and crack channeling. This method was used to calculate the fracture toughness of TiN/TiCrN ceramic multilayer coating which was deposited on the GTD450 substrate using the Cathodic Arc PVD method. To validate the results, the analytically calculated crack radius was compared with the experimental crack radius in the fracture load and the difference between the radiuses was in the acceptable range.     

金属基聚合物复合材料短纤维桥接界面强化机理

针对金属基聚合物复合材料易诱发界面剥离损伤失效的共性问题,研究了通过多层复合组装注射成型,在聚合物复合层与粘接层界面形成短纤维桥接,实现复合界面强化.基于内聚力剥离损伤模型,构建了短纤维桥接强化界面剥离裂纹扩展断裂失效过程的模拟仿真技术,模拟建立了界面剥离裂纹快速失稳扩展断裂损伤失效临界载荷—桥接纤维特性—界面剥离断裂...     

Fatigue Crack Growth in Structural Adhesives

Fatigue crack growth rate studies of two high temperature structural adhesives, EA-9649 and AF-163, are described. It is shown that crack closure loads develop as a result of fatigue crack propagation. The fatigue crack propagation rates have been correlated with the strain energy release rate range, AG and with an effective strain energy release, ΔG_aff. The effective strain energy release rate range subtracts the strain energy due to crack closure from the applied strain energy release rate range.     

Cyclic Fatigue Crack Growth in Three-Point Bending PZT Ceramics under Electromechanical Loading

This paper investigates experimentally and analytically the cyclic fatigue crack growth in piezoelectric ceramics under electromechanical loading. Cyclic crack growth tests were conducted on lead zirconate titanate (PZT) ceramics subjected to dc electric fields, and a finite element analysis was used to calculate the maximum energy release rate for the permeable crack model. Based on bending experiments using single-edge precracked-beam specimens, cyclic fatigue crack growth rates are found to be sensitive to the maximum energy release rate and applied dc electric fields. Possible mechanisms for crack growth were discussed by scanning electron microscope examination of the fracture surface of the PZT ceramics.     

Fracture behavior of magnesia refractory materials under combined cyclic thermal shock and mechanical loading conditions

To investigate the effect of cyclic thermal shock and mechanical loading on the fracture behavior of magnesia refractories showing different brittleness, the as-received and cyclic thermally shocked specimens are subjected to monotonic and cyclic wedge splitting test. The whole duration of test is monitored by digital image correlation and acoustic emission. Both thermal and mechanical fatigue resistance increase with the reduction of brittleness. Repetitive thermal shock results in pronounced reduction of strength. However, the specific fracture energy and nonlinearity increase after exposure to thermal shock due to the expanded micro-crack network inducing the development of a significant fracture process zone. Periodic loading mainly leads to the decrease of strain bearing capacity, as the fatigue loads favor the extension of crack tip instead of fracture process zone expansion. The combined application of periodic thermal shock and mechanical loads gives a new insight into the progressive damage behavior of refractory under critical conditions.     

直流电场对LiNbO3晶体亚临界裂纹扩展的影响

本工作采用双扭曲试验法(DT法),着重研究了极化条件、直流电场的强度和取向对晶体学取向不同的LiNbO_3晶体中裂纹亚临界扩展行为的影响,并对晶体由裂纹临界扩展导致断裂的形貌作了分析。实验结果表明:LiNbO_3晶体试样的裂纹亚临界扩展方程指数n随晶体学取向的不同而不同,这与裂纹扩展所沿晶面的断裂能有关。未极化的LiNbO_3晶体受直流电场作用时,其亚临界裂纹扩展的加快,系压电晶体电致伸缩效应所致;极化的LiNbO_3晶体试样在直流电场作用下,其亚临界裂纹扩展主要是受晶体的逆压电效应的影响。     

Applying fractography and fracture mechanics to the energy and mass of crack growth for glass in the mirror region

The mirror region following the fracture initiation site is considered by applying fracture mechanics principles along with experimental observations of the crack velocity at the formation of the mirror mist boundary. Several issues regarding this crack growth in glass are addressed after considering the terminal velocity of crack growth and the mirror mist boundary information on silicate glasses. A strain energy release rate criterion is applied to estimate the kinetic energy of an advancing crack in glass at the mirror/mist boundary. This energy is then utilized to estimate the effective mass of the crack at the mirror/mist boundary. It is compared with material volumes in the vicinity of the crack.     

A micro/macro approach to fracture in composites

The results of an integrated microscopic/macroscopic finite element analysis of fracture in fiber-reinforced composites are presented. A macroscopic analysis of a composite double-cantilever-beam (DCB) fracture toughness test specimen was carried out using a singular finite element method. The effects of fiber layup angle on strain energy release rate are discussed. Results from this analysis were input as boundary conditions to a microscopic model used to calculate J-integral values in the crack tip region. Nonhomogeneity in this region causes the elastic strain energy release rate to vary with crack tip location and geometry. Elastic-plastic calculations showed that significant matrix plasticity occurs near fibers away from the crack tip region. The constitutive equation chosen for the matrix plasticity was shown to have an important effect on the J-integral value. The results show how the microscopic J-integral is related to the macroscopic strain energy release rate.     

Temperature effect on impact fracture toughness and fracture mechanism of phenolphthalein poly(ether ketone)

Phenolphthalein poly(ether ketone) (PEK-C) was tested using an instrumented impact tester to determine the temperature effect on the fracture toughness K_c and critical strain energy release rate G_c. Two different mechanisms, namely the relaxation processes and thermal blunting of the crack tip were used to explain the temperature effect on the fracture toughness. Examination of the fracture surfaces revealed the presence of crack growth bands. It is suggested that these bands are the consequence of variations in crack growth along crazes that are formed in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances.     

The Fracture Toughness of Adhesive-Bonded Joints

Fracture mechanics is related to adhesion theory and the testing of adhesive-bonded joints in the lap-shear configuration. The complexity of the stress field necessitates the strain energy release rate approach, which is followed to derive the relation for a lap-shear sample: G_c = P_c²/4b (dC/da). G_c is the fracture toughness (critical strain energy release rate), P_c is the breaking or crack instability load, a and b are crack lengths and widths, respectively, and C is the sample compliance for the Tap-shear sample with a crack of these dimensions at each loading edge. It was found that G_c ranged from 1.18 to 1.42 with an average value of 1.34 in.-lb./in.² for epoxy bonded aluminum strips (EPON 934 and Alcald 2024-T3). Evidence, in the form of photoelastic stress patterns, suggesting that crack extension occurs in the opening mode in lap-shear samples is presented and discussed.     

Failure load prediction of structural adhesive joints : Part 2: Experimental study

The objective of this study was to determine how the fracture of adhesive joints depends on elastic beam parameters describing the adherends and the applied loads. The basic specimen geometry was the cracked lap shear joint constructed of aluminium alloy with various adherend and bondline thicknesses. Loads were applied in different combinations of bending, tension and shear to generate a failure envelope for each adhesive and specimen geometry. It was found that crack propagation for precracked specimens occured at a critical strain energy release rate but was also a function of the G_I/G_II ratio and the bondline thickness. The experiments also showed that the loads required to propagate a crack in a precracked specimen were always lower than the loads required to break the fillet. Hence, by treating uncracked joints as being cracked, where the fictitious crack tip is assumed to coincide with the location of the fillet, a conservative estimate of the failure load is obtained.     

Correlation between nodular morphology and fracture properties of cured epoxy resins

Various bulk epoxy resin formulations, based on diglycidyl ether of bisphenol A (DGEBA) and cured with diethylene triamine (DETA) were studied. Methods of linear elastic fracture mechanics were employed and all systems were characterized by the corresponding values of the critical strain energy release rate for crack initiation and crack arrest. Fracture morphology was studied by scanning electron microscopy and transmission electron microscopy of carbon—platinum surface replicas. An apparent correlation between morphology and ultimate mechanical properties has been found. All fracture surfaces are shown to be characterized by distinct nodular morphology. Nodules, ranging in size from 15–45 nm, represent the sites of higher crosslink density in an inhomogeneous network structure. Fracture surfaces were further characterized by three crack propagation zones. A smooth, brittle fracture zone was preceded and followed by crack initiation and crack arrest zones, respectively. An apparent plastic flow was confined to the initiation and arrest regions. No crazing phenomenon was seen in the initiation zone; instead a step-like fracture was observed, typified by the ‘flow’ of internodular matrix during step formation. Local plastic deformation in the initiation zone and the corresponding value of critical strain energy release rate, G_Ic, were correlated with the nodular morphology. The size of nodules was found to vary with the curing agent concentration, thus allowing us to establish a fundamental correlation between the nodular morphology and the ultimate mechanical properties of epoxy resins.