Effect of domain switching on kinking of a crack in a ferroelectric material

Summary Crack kinking induced by domain switching in a ferroelectric material under purely electric loading is investigated. Boundaries of domain switching zones for the asymptotic problem of a semi-infinite crack under the small scale conditions are determined based on the nonlinear electric theory. Stress intensity factors induced by the domain switching are numerically evaluated using the solution of the switching zone. Numerical results of the kink angle are obtained as a function of the ratio of the coercive electric field to the yield electric field for various polarization angles. Crack kinking in ferroelectric materials subjected to a cyclic electric field is also examined. The crack in the fully poled materials branches with different directions at application of the positive and negative electric fields, respectively. The electric fatigue crack is shown to have a forked crack pattern in the fully poled materials.     

NUCLEATION AND SHORT CRACK GROWTH IN FATIGUED POLYCRYSTALLINE COPPER

Surface evolution in polycrystalline copper specimens with a shallow notch has been studied in interrupted constant strain amplitude cyclic loading. The inhomogeneous strain distribution close to stress amplitude saturation leads to the formation of extrusions and intrusions along persistent slip bands within the grain and also in suitably oriented grain boundaries. Numerous primary cracks within a grain or at a grain boundary are nucleated. Some cracks can grow further either by linking with existing cracks or by nucleation of new elementary cracks ahead of the crack tip. Crack growth rates of individual cracks fluctuate considerably but for each strain amplitude, which results in a saturated plastic strain amplitude, a crack growth rate of an equivalent crack can be established. This crack growth rate was found to depend strongly on the plastic strain amplitude in agreement with the Manson-Coffin law.     

FATIGUE CRACK GROWTH IN DUCTILE MATERIALS UNDER CYCLIC COMPRESSIVE LOADING

Abstract— Mode I fatigue crack growth has been studied in notched specimens of 7017-T651 aluminium alloy subjected to fully compressive cyclic loads. The specimens were first subjected to a deliberate compressive preload which causes plastic deformation at the notch tip. On unloading, this region developed a residual tensile stress field and on subsequent compressive cyclic loading in laboratory air, a fatigue crack was nucleated at the notch and grew at a diminishing rate until it stopped. The final crack length increased with an increase in the value of the initial compressive preload and with an increase in the negative value of the applied cyclic mean load. To gain a better understanding of crack growth in residual stress fields, the magnitude and extent of residual stress induced from compressive preloads have been analysed. This was achieved when extending the notch by cutting while recording the change in the back face strain. From residual strain models it was found that the fatigue crack growth was confined to a region of tensile cyclic stress within the residual stress field. The effective stress intensity range was investigated at selected mean loads and amplitudes, for correlating purposes, using both the compliance technique and by invoking the crack growth rate behaviour of the alloy. Finally, a brief discussion of the fracture morphology of cracks subjected to cyclic compression is presented.     

Crack growth in ferroelectric ceramics under electric loading

Summary A crack with growth in ferroelectric ceramics under purely electric loading is analyzed. The crack tip stress intensity factor for the growing crack under small scale conditions is evaluated by employing the model of nonlinear domain switching. The electrical fracture toughness is obtained from the result of the stress intensity factor. It is shown that the ferroelectric material can be either toughened or weakened as the crack grows. Fatigue crack growth in a ferroelectric material under cyclic electric loading is also examined. The incremental fatigue crack growth under cyclic electric loading is obtained numerically. The fatigue crack growth rate is affected strongly by the electrical nonlinear behavior. It is found that the curve of fatigue crack growth rate versus electric field intensity factor is linear on the log-log plot at intermediate values of the electric field intensity factor.     

Influence of loading path on fatigue crack growth under multiaxial loading condition

In this study, the specimens made of carbon steel S45 with an initial surface straight edge notch were subjected to combined cyclic axial‐torsion loading at room temperature. The fatigue life, surface crack extension direction and crack length were experimentally investigated. The effects of loading path, stress amplitude ratio and phase angle on the crack growth behaviour were also discussed. The results showed that, under the combination of cyclic axial and torsion loading, the tension stress amplitude had more effect on the initial crack growth path than the latter. The shear stress amplitude contributed mainly to the latter crack extension. The crack extension path was mainly determined by the stress amplitudes and the ratio of the normal stress to the shear stress, and almost independent of the mean stresses. The increase of the tension stress amplitude and shear stress amplitude would both accelerate the crack growth rate.     

Notch effect on torsional fatigue of austenitic stainless steel: Comparison with low carbon steel

Notch effect in austenitic stainless steel under cyclic torsion is quite different depending on the superposition of static tension. In pure torsion, the rubbing of the serrated factory-roof type crack faces delays the crack growth along the notch root. Thus, the lifetime in notched specimen becomes longer than in smooth specimen. However, in cyclic torsion with static tension, the flat crack path and mean tensile stress reduce the influence of the crack face contact. Accordingly, shorter lifetime resulted from higher strain concentration at the notch root. Crack growth in low carbon steel under cyclic torsion is highly affected by the ferrite/pearlite banded microstructure besides the addition of static tension. Because of a small amount of the crack face contact, the reduction of lifetime in notched specimen is revealed irrespective of superposition of static tension.     

循环压缩载荷下缺口残余拉应力场的X射线分析

用细束 x 射线研究了循环压缩载荷下缺口残余拉应力的分布及变化。试验表明,循环压缩加载后形成的残余拉应力大于一次压缩加载后的数值,压缩应力幅对残余拉应力分布的影响大于压缩平均应力的影响,其原因除了加载-降载过程中形成的残余应力直接与应力幅有关外,尚与应力幅加剧材料循环软化程度有关。形成疲劳裂纹后,在完全卸载的裂纹面上,残余拉应力基本松弛,但垂直于裂纹面稍远处的残余拉应力仍保持有相当大的数值,这部分残余应力是否对裂纹扩展起作用,在计算残余应力的应力强度因子时如何予以考虑值得注意。     

Measurement of Structural Changes in Tetragonal PZT Ceramics under Static and Cyclic Electric Fields Using a Laboratory X-ray Diffractometer

In situ structural characterization techniques that are capable of characterizing piezoelectric ceramics under different electrical loading conditions are important to understand the behavior of materials during their use. In this work, we report the use of a laboratory X-ray diffractometer for the measurement of various structural changes in tetragonal La-doped lead zirconate titanate (PZT) ceramics under the application of static and cyclic electric fields. The changes in the volume fractions of the 90° domains parallel to the electric field direction are calculated from the intensities of the {002} diffraction peaks. In addition, the components of lattice strains are monitored from the changes in the (111) crystallographic planes. It is observed that, under the application of static electric fields, both 90° domain switching and the 111 lattice strains showed similarity with the macroscopic strainelectric field hystersis loop. To measure the structural changes under cyclic electric fields, a time-resolved X-ray diffraction technique was used. Under application of a square-wave electric field of amplitude ±650 V/mm and frequency 0.3 Hz, a change of ~5% in the volume fraction of the 90° domains and ~0.07% strain of the 111 lattice planes are observed. Both the amount of 90° domain switching and the 111 lattice strains are observed to increase with an increase in the amplitude of the cyclic electric field. The implications of the measured structural changes for the macroscopic piezoelectric properties of ceramics are discussed.     

Simplified analysis of steady-state crack growth of piezoelectric ceramics based on the continuum damage mechanics

Summary A simplified analysis of crack growth of piezoelectric ceramics was performed by using the double cantilever beam (DCB) model. The analysis was intended for the crack growth in a steady state by using some assumptions to simplify the analysis. In the present paper, damage within piezoelectric ceramics was represented by a damage variable based on the continuum damage mechanics, and the effect of the damage on material properties was taken into account in a constitutive equation of the piezoelectric ceramics. The constitutive equation and an evolution equation of the damage variable were applied to the DCB model. Then, the crack growth in the DCB model was dealt with within the framework of the continuum damage mechanics. As a result of the analysis, a constant crack growth rate and distribution of stress, strain and damage variable in front of the crack tip were elucidated, and the effects of the applied electric field on the crack growth were discussed in particular.     

Effects of electric field and poling on the mode I energy release rate in cracked piezoelectric ceramics at cryogenic temperatures

We discuss the mode I energy release rate of a rectangular piezoelectric material with a crack under electromechanical loading at cryogenic temperatures. A crack was created normal or parallel to the poling direction, and electric fields were applied parallel or normal to the poling. A plane strain finite element analysis was carried out, and the effects of electric field and localized polarization switching on the energy release rate were discussed for the piezoelectric ceramics at cryogenic temperatures.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

Effect of microstructural stability on fatigue crack growth behaviour of nanostructured Cu

Constant amplitude fatigue crack growth tests were carried out on commercial and high purity nanostructured copper processed by High Pressure Torsion (HPT). Due to strong grain refinement the HPT processed materials show higher tensile strength but also faster crack growth rates when compared to coarse grained material. Crack growth curves of nanostructured copper determined at different stress levels, however, showed that the occurrence of grain coarsening at low stress amplitudes leads to a retardation of crack growth in commercial and high purity HPT Cu. This effect was not observed for high purity HPT Cu with a bimodal microstructure. Crack propagation rates depend significantly on the coarsening phenomenon which on the other hand depends on the applied stress amplitude. A comparison of these results with cyclic deformation tests in the high cycle fatigue regime suggests that grain coarsening during crack growth depends more on the stored energy of the materials while a similar coarsening during cyclic deformation depends more on the activation enthalpy for annealing of defects.     

Variable amplitude crack growth in notched specimens

Predictions of variable amplitude fatigue crack growth in notched tensile specimens at an elevated temperature and relative high loads were conducted. The predictions were based on constant amplitude fatigue data and mean crack growth rates were calculated. Crack closure levels were calculated by comparison of crack closure free experimental data obtained with the so called constant K_I,max-method and nominal data. Also, numerical simulations of the closure level throughout the specimens were performed. Although experimental data showed rather large a scatter it was concluded that variable amplitude crack growth rates can be predicted with reasonable agreement using constant amplitude fatigue data. Also, crack growth rates cannot be predicted by LEFM in the inelastic notch affected zone, even if absence of crack closure is assumed.     

Growth of cracks under far-field cyclic compressive loads: Numerical and experimental results

Crack growth from a notch tip, under the influence of fully compressive far-field cyclic loads, is investigated both numerically and experimentally in notched specimens of a lower strength steel and an aluminum alloy. Such cracks, emanating from the root of the notch, progressively decelerate until complete crack arrest occurs. Analyses of the stress state along the crack plane indicate that while the extent of the residual tensile stress field diminishes with an increase in crack length, there is a progressive increase in crack closure during crack advance. Approximate numerical calculations of the crack closure loads are in reasonable agreement with experimental results.     

FATIGUE CRACK GROWTH UNDER AN EQUIVALENT FALSTAFF SPECTRUM

Abstract—Optical fractography was used to estimate growth of small cracks at notches under programmed FALSTAFF loading in an Al-Cu alloy. Crack sizes as low as 25 microns and growth rates over two orders of magnitude could be resolved using this technique. Randomized MiniFALSTAFF load sequence was modified into a programmed load equivalent with major loads either preceding or following marker loads. Crack growth rate under programmed FALSTAFF spectrum as estimated by optical fractography conformed to compliance based estimates on a SE(T) specimen. Long crack growth rates under programmed and randomized MiniFALSTAFF spectrum were essentially similar. Spectrum load fatigue crack growth was studied in central hole coupons under notch inelastic conditions. Scatter in growth rates for small notch cracks was found to be of the same magnitude as that of long cracks. Multiple fatigue cracks are observed at the notch root, and they appear to influence each other.     

Crack Initiation under Cyclic Compression

The crack initiation behaviour under cycliccompression foy the notched specimen wasinvestigated. It has been found that the cyclesfor crack initiation increase with the increaseof compressive mean stress, and the decreaseof stress amplitude. The stress amplitude playsa more important role than the mean stress does.Photoelastic coating and finite element methodswere employed to measure and calculate the stressfield in the notched part. The resul ts showthat the crack initiation under compressionis attributed to the tensile stress which mayexist during unloadtng. If the true stress statein the notch is compressive, no crack initiates.     

NOTCH ROOT CRACK CLOSURE UNDER CYCLIC INELASTICITY

Aluminium alloy sheet coupons with a central hole were tested in fatigue under specially designed programmed load sequences. Electron microscopy of the fatigue fracture surfaces showed striation mode fatigue crack extension up to more than a millimeter before onset of rapid failure. Crack opening stress was determined from striation patterns. Under variable amplitude loading and conditions of notch root cyclic inelasticity, crack opening stress exhibits noticeable hysteresis. The hysteresis is attributed to a difference between crack closure and opening stresses. A linear model of this phenomenon appears to describe observed behaviour.     

A material and environment-dependent criterion for the prediction of fatigue crack paths in metallic structures

Crack growth under mode II cyclic loading was investigated in maraging steel, ferritic–pearlitic steel and TA6V. When ΔK_II exceeds a threshold value, cracks do not bifurcate but grow in mode II over a distance which increases with ΔK_II. Shear mode crack growth was much more extensive in maraging steel than in TA6V and ferritic–pearlitic steel. This result is discussed in relation with the cyclic behaviour of the materials and the importance of friction along the crack faces. The maximum growth rate criterion is shown to be suitable for the prediction of crack paths when shear mode crack growth is likely to occur.     

Effect of Pre-loading on Short Fatigue Crack Growth at a Notch

Results indicate that under cyclic tension thegrowth rate of short fatigue crack from notch rootwill be lowered greatly by tensile pre-loading,butonly a little change by compressive pre-loading.The effect of tensile pre-loading will decrease withthe increase of stress ratio.The variation of shortfatigue crack growth rate is related to the residualstress distribution around notch root.     

Linear electro-elastic fracture mechanics of piezoelectric materials

The concepts of linear elastic fracture mechanics, generalized to treat piezoelectric effects, are employed to study the influence of the electrical fields on the fracture behavior of piezoelectric materials. The method of distributed dislocations and electric dipoles, already existing in the literature, is used to calculate the electro-elastic fields and the energy-release rate for a finite crack embedded in an infinite piezoelectric medium which is subjected to both mechanical and electric loads. The energy-release rate expressions show that the electric fields generally tend to slow the crack growth. It is shown that the stress intensity factor criterion and the energy-release rate criterion differ when the energetics of the electric field is taken into account. The study of crack tip singular stress field yields a possible explanation for experimentally observed crack skewing in the presence of a strong electric field.