Frequency effects on fatigue crack growth and crack tip domain-switching behavior in a lead zirconate titanate ceramic

The microstructural origins of the effect of frequency on the electrical fatigue behavior of pre-cracked soft ferroelectric Pb(Zr_0.48Ti_0.52)O₃ is investigated by means of a high spatial resolution hard X-ray synchrotron source. It is found that there is a strong link between the frequency of the applied bipolar field, domain-switching behavior in terms of ferroelastic reorientation of the domains around the crack tip and the resultant crack growth. The crack growth is accentuated under increased ferroelastic switching and, in particular, found to be more pronounced under low-frequency loading. The concept of domain wall viscoelasticity is applied to explain why lower frequencies accelerate crack growth under a bipolar electric field.     

Effect of switching stresses on domain evolution during quasi-static crack growth in a ferroelastic single crystal

The present paper demonstrates the effect of switching stresses on domain evolution and fracture toughening during quasi-static crack growth in elastically isotropic ferroelastic single crystals with transversally isotropic ferroelastic strains. With a simple switching algorithm and crack propagation procedure, domain evolution is simulated in an exemplary material with semi-infinite crack under mode I loading, starting from a mono-domain configuration. Domain reorientation is found to be strongly affected by switching stresses, which therefore have to be considered in the context of domain evolution modelling and fracture toughening. Before the onset of crack growth a needle-like domain is formed at the tip of the stationary crack, but this does not effect the crack tip stress intensity factor. Elongation of this domain during the onset of crack growth causes a large increase of the fracture toughness. Domain separation in a later stage results in toughness reduction. The subsequent domain evolution indicates a periodic formation of needle-like domains as observed in soft ferroelastic materials.     

Phase field simulations of ferroelastic toughening: The influence of phase boundaries and domain structures

Limited reliability of ferroelectric-based actuators restricts their use in high-performance applications, where stress-induced cracking of ferroelectric ceramics often leads to fatal failure. The main limiting factors are the relatively small fracture toughness and the brittle nature of ferroelectrics. However, ferroelectrics naturally exhibit fracture toughening (so called ferroelastic toughening) due to stress induced reorientation of non-180° domains that inhibits crack propagation. Here we present a phase-field study of ferroelastic toughening based on Landau–Ginzburg–Devonshire theory. The primary qualitative factors that control the magnitude of ferroelastic toughening are identified and discussed.     

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.     

Interactions between domain switching and crack propagation in poled BaTiO3 single crystal under mechanical loading

In this paper, the interactions between the crack propagation and corresponding domain switching in ferroelectric single crystal under mechanical loading were investigated. An experimental setup with a polarized light microscope (PLM) was designed and constructed to in situ observe the crack propagation in poled BaTiO₃ specimens subjected to three-point-bending loading. The observed domain switching was stimulated by the intensive stress field near the crack tip, and the theoretical R-curve taking into account the domain switching toughening agrees well with the experimental results quantitatively. It is confirmed from the actual switched zone that the 90° domain switching is the major mechanism of the fracture toughening, and the apparent fracture toughness increases by 150% in the BaTiO₃ single crystal specimen.     

Quasi-dynamic visualization of crack propagation and bridging evolution in Si3N4 and SiC ceramics by mechano-luminescence

The propagations of macro-scale cracks were visualized in Si₃N₄ and SiC ceramics using a mechano-luminescence (ML) of SrAl₂O₄:Eu,Dy. The bridging zones behind the crack tip were also clearly detected in the crack path within realistic time frames. The ML made it possible to detect cracks propagating within a speed range of 200 m/s to 250 m/s, thereby realizing so-called quasi-dynamic R-curves. The magnitudes and shapes of the bridging stress distributions were found to change with the advancing cracks, continuing to change as the applied load changes, even after the cessation of crack propagation. The effective toughening then commenced and the applied stress intensity factors increased dramatically up to ∼120 MPa√m in Si₃N₄ and 150 MPa√m in SiC. The K_Tip values expected on the basis of the instantaneous bridging stress distributions obtained from ML observations deviated greatly from those measured using the conventional crack tip lengths; rather, the values support the results obtained by using bridging tips in quasi-dynamic crack propagations.     

Evaluation of crack-tip stress fields on microstructural-scale fracture in Al–Al2O3 interpenetrating network composites

The influence of local microstructure on the fracture process at the crack tip in a ceramic–metal composite was assessed by comparing the measured stress at a microstructural level and analogous finite element modelling (FEM). Fluorescence microprobe spectroscopy was used to investigate the influence of near-crack-tip stress fields on the resulting crack propagation at the microstructural scale. The high spatial resolution was effective at mapping the localized crack-tip stress distributions within the complex Al–Al₂O₃ phase morphologies, where the localized stress distribution about the crack tip within the Al₂O₃ phase could be measured. Regions of high-localized tensile stress within the microstructure resulting from a combination of applied load and thermal residual stress were identified and could be used in predicting the subsequent crack extension direction. Stress distributions calculated from spectroscopy results were compared with microstructural level FEM of the same structure and general agreement between the two techniques was observed.     

Crack tip process zone domain switching in a soft lead zirconate titanate ceramic

Non-180° domain switching leads to fracture toughness enhancement in ferroelastic materials. Using a high-energy synchrotron X-ray source and a two-dimensional detector in transmission geometry, non-180° domain switching and crystallographic lattice strains were measured in situ around a crack tip in a soft tetragonal lead zirconate titanate ceramic. At K_I = 0.71 MPa m^1/2 and below the initiation toughness, the process zone size, spatial distribution of preferred domain orientations, and lattice strains near the crack tip are a strong function of direction within the plane of the compact tension specimen. Deviatoric stresses and strains calculated using a finite element model and projected to the same directions measured in diffraction correlate with the measured spatial distributions and directional dependencies. Some preferred orientations remain in the crack wake after the crack has propagated; within the crack wake, the tetragonal 0 0 1 axis has a preferred orientation both perpendicular to the crack face and toward the crack front.     

Study on crack propagation in ferroelectric single crystal under electric loading

The crack propagation in ferroelectric single crystals subjected to electric fields was studied experimentally and theoretically. An in situ observation of crack propagation and domain switching near the crack tip in a poled PMN–PT62/38 single crystal was carried out using polarized optical microscopy. It was found that a pure negative electric field leads to a larger domain switching zone near the crack tip than a positive one does. A negative electric field below the coercive field can cause crack propagation, while no crack growth was observed for a positive electric field far larger than the coercive field. A fracture model based on energy analysis was developed which indicates that the energy variation due to the domain switching provides the thermodynamic driving force for the crack propagation under pure electric loading. The critical electrical loading for the crack growth determined by this model agrees well with experiments.     

层状组织对双相TiAl合金裂纹扩展的影响

在ＴＥＭ下原位观察了双相ＴｉＡｌ层状组织对裂纹扩展的影响，发现了裂纹尖端的钝化以及裂纹的扩展方式与裂纹和片层界面的夹角有关。当裂纹接近平行片层界面时，主裂纹前端有微裂纹产生，此时剪切带韧化机制起主导作用。而当裂纹垂直于片层界面以及介于平等我恶性循环之间进，片支界面对扩展裂纹的阻碍，界面滑移造成的裂纹尖端钝化是层状组织韧化ＴｉＡｌ合金的主要原因，依据裂纹形核的位错理论地上述现象进行了分析。     

Toughening effects quantification in glass matrix composite reinforced by alumina platelets

A borosilicate glass matrix composite containing alumina platelets was considered to investigate toughening mechanisms and crack tip behavior in dispersion reinforced brittle matrix composites. Fracture toughness was determined by applying the chevron notched specimen technique, and fractographic analysis was employed to reveal the active toughening mechanisms with increasing content of reinforcement. A roughness-induced shielding effect has been quantified to prove the relation between fracture toughness and fracture surface roughness. Theoretical calculations of the fracture toughness enhancement based on a modified crack deflection model developed by Faber and Evans, combined with the influence of the increase in Young’s modulus, were found to be in good agreement with experimental data. An effect of residual stresses upon toughening of the investigated composite is discussed.     

Phase field simulations of polarization switching-induced toughening in ferroelectric ceramics

Polarization switching-induced shielding or anti-shielding of an electrically permeable crack in a mono-domain ferroelectric material with the original polarization direction perpendicular to the crack is simulated by a phase field model based on the time-dependent Ginzburg–Landau equation. The domain wall energy and the long-range mechanical and electrical interactions between polarizations are taken into account. The phase field simulations exhibit a wing-shape-switched zone backwards from the crack tip. The polarization switching-induced internal stresses shield the crack tip from applied mechanical loads. A local J-integral is numerically calculated and used as a failure criterion to illustrate the polarization switching-toughening. The result indicates that an applied uniform electric field parallel to the original polarization direction reduces the apparent fracture toughness, while an applied uniform electric field anti-parallel to the original polarization direction enhances it.     

Magnetoelastic interactions in a cracked ferromagnetic body

The stress–strain state associated with a moving crack in a ferromagnetic material is investigated. The model considers a soft magnetic ferroelastic body and incorporates a realistic (nonlinear) susceptibility. The moving crack propagates in a direction perpendicular to the magnetic field. A closed-form solution yields the magnetoelastic stresses and a stress intensity factor. An applied magnetic field makes the stress intensity factor depend upon the crack velocity. The nonlinear susceptibility produces a completely different magnetoelastic stress state than a constant susceptibility, and the stress intensity is highly sensitive to material properties. The stresses around the crack are largely insensitive to the external magnetic field and crack speed except at critical combinations for which the stresses are singular. Some combinations of magnetic field and crack velocity cause the stress components ahead of the crack tip to change sign.     

Elucidating the variables affecting accelerated fatigue crack growth of steels in hydrogen gas with low oxygen concentrations

The objective of this study was to quantify the effects of mechanical and environmental variables on oxygen-modified accelerated fatigue crack growth of steels in hydrogen gas. Experimental results show that in hydrogen gas containing up to 1000 v.p.p.m. oxygen fatigue crack growth rates for X52 line pipe steel are initially coincident with those measured in air or inert gas, but these rates abruptly accelerate above a critical ΔK level that depends on the oxygen concentration. In addition to the bulk gas oxygen concentration, the onset of hydrogen-accelerated crack growth is affected by the load cycle frequency and load ratio R. Hydrogen-accelerated fatigue crack growth is actuated when threshold levels of both the inert environment crack growth rate and K_max are exceeded. The inert environment crack growth rate dictates the creation of new crack tip surface area, which in turn determines the extent of crack tip oxygen coverage and associated hydrogen uptake, while K_max governs the activation of hydrogen-assisted fracture modes through its relationship to the crack tip stress field. The relationship between the inert environment crack growth rate and crack tip hydrogen uptake is established through the development of an analytical model, which is formulated based on the assumption that oxygen coverage can be quantified from the balance between the rates of new crack tip surface creation and diffusion-limited oxygen transport through the crack channel to this surface. Provided K_max exceeds the threshold value for stress-driven hydrogen embrittlement activation, this model shows that stimulation of hydrogen-accelerated crack growth depends on the interplay between the inert environment crack growth increment per cycle, load cycle frequency, R ratio and bulk gas oxygen concentration.     

Compositionally graded materials with cracks normal to the elastic gradient

Mixed-mode crack tip deformations and fracture parameters in glass-filled epoxy beams with cracks normal to the elastic gradient are studied. Crack tip fields are optically measured for different crack locations in the elastic gradient when subjected to symmetric pure bending. A companion finite element model is developed and validated by the measurements. The numerical model is then used to examine the influence of the elastic gradient on crack location by evaluating stress intensity factor, mode-mixity and energy release rate. For certain crack locations, computed stress intensity factors and energy release rates in the graded material exceed that of the bimaterial counterpart. However, when reconciled with measured critical values of the fracture parameters, graded beams show consistently better performance for all crack locations in the graded region. Crack kinking due to compositional gradients are examined and are successfully compared with the vanishing K_II criterion based on a locally homogeneous material behavior.     

Aging and fracture of human cortical bone and tooth dentin

Mineralized tissues, such as bone and tooth dentin, serve as structural materials in the human body and, as such, have evolved to resist fracture. In assessing their quantitative fracture resistance or toughness, it is important to distinguish between intrinsic toughening mechanisms, which function ahead of the crack tip, such as plasticity in metals, and extrinsic mechanisms, which function primarily behind the tip, such as crack bridging in ceramics. Bone and dentin derive their resistance to fracture principally from extrinsic toughening mechanisms, which have their origins in the hierarchical microstructure of these mineralized tissues. Experimentally, quantification of these toughening mechanisms requires a crack-growth resistance approach, which can be achieved by measuring the crack-driving force (e.g., the stress intensity) as a function of crack extension (“R-curve approach”). Here this methodology is used to study the effect of aging on the fracture properties of human cortical bone and human dentin in order to discern the microstructural origins of toughness in these materials.     

Influence of pores distribution on fracture toughness of FeSi/Si3N4 composite

FeSi/Si₃N₄ ceramic composite was fabricated by hot pressing technique, using α-Si₃N₄ and Fe₃Al. The toughening effect of Fe₃Al on the Si₃N₄ matrix is explained on the basis of microstructural characterizations and schematic representations. Results indicate that the reaction between α-Si₃N₄ and Fe₃Al results in the formation of FeSi and sialon phases at the interface. Both phases effectively restrain coalescence and movement of the gaseous reaction product, N₂, retaining it in situ to form small separated pores. The dominant toughening effect of these pores reduces the interface bonding strength, consumes the crack propagation energy, and decreases the stress-concentration at the crack tip, thereby improving the fracture toughness of the matrix.     

脉冲放电裂纹止裂处的热处理研究

对含有裂纹的金属构件进行脉冲放电止裂时，裂纹尖端由于电流的绕流热集中效应，在瞬间使裂尖熔化形成焊口。由于裂尖附近超快速加热和冷却，金属材料完成了一次超高速冲击淬火。采用数值模拟计算了脉冲放电超快速加热时裂纹尖端温度、温度梯度场；通过脉冲放电止裂试验研究了裂尖超高速淬火全过程。通过对止裂后裂尖的金相组织观察和微观机理分析发现；超细化的条状马氏体、极少量残留奥氏体和细颗粒碳化物的出现明显提高了裂纹尖端的硬度、韧性和耐磨性。     

A plasticity-corrected stress intensity factor for fatigue crack growth in ductile materials

In this paper, a plasticity-corrected stress intensity factor range ΔK_pc is developed on the basis of plastic zone toughening theory. Using this new mechanical driving force parameter for fatigue crack growth (FCG), a theoretical correlation of Paris’s law with the crack tip plastic zone is established. Thus, some of the important phenomena associated with the plastic zone around the fatigue crack tip, such as the effects of load ratio R, overload and T stress on the FCG behavior, can be incorporated into the classical Paris’s law. Comparisons with the experimental data demonstrate that ΔK_pc as a single and effective mechanical parameter is capable of describing the effects of the load ratio, T stress and overload on the FCG rate. The FCG rate described as a function of ΔK_pc tested under a simple loading condition can also be used for other complex loading conditions of the same material.     

An experimental observation of dislocation nucleation based on the peierls concept

The HREM-moiré method developed by Dai and Xing [1] is an experimental technique which allows for the direct measurement of such parameters as displacement, strain and dislocation in the nanoscopic range. This technique was used to measure the nanoscopic deformation field near the tip of a quasi-cleavage crack in silicon. A process of dislocation nucleation was observed. A long dislocation extending about 600 burgers vectors was found at the crack tip and the slip distribution along it was measured. This distributed dislocation has a similar slip structure to the one based on the Peierls concept described by Rice [2], but has a much longer slip range. The nanoscopic strain distribution near the crack tip was obtained. There is a strain field controlled by linear elastic fracture mechanics at the very vicinity of the crack tip. This article based on a presentation made in the symposium “The 4th International Conference on Fracture and Strength of Solid”, held at POSTECH, Pohang, Korea, August 16–18 under the auspices of Far East and Ocean Fracture Society (FEOFS),et al.