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In the present study, a physics-informed neural network model based on Bayesian hyperparameter optimization is proposed for the prediction of short crack growth paths. A large number of cyclic loadings at a lower amplitude were applied to an α titanium sample by an ultrasonic fatigue machine to ensure a sufficient amount of data for machine learning. The grain size, grain orientation and grain boundary direction on the path, as well as crack growth direction, were selected as feature data for training the prediction model. The optimizations of the size ratio and the angle operation were conducted to compare different data processing methods, respectively. After evaluation, eventually, a model for predicting crack growth path is obtained with a reliable performance of 10% tolerance on the path angle at each grain boundary. And the prediction effect of the proposed model is better than that of some classic machine learning models and slip trace analysis. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'. [ABSTRACT FROM AUTHOR]

A non-destructive thermographic methodology based on the temperature field is utilized to determine the crack tip position during the very high cycle fatigue (VHCF) test of pure iron and deduce the corresponding fatigue crack growth rate (FCGR). To this end, a piezoelectric fatigue machine is employed to test 1 mm thick pure iron samples at 20 kHz in push–pull fatigue loading. Two cameras are placed on each side of the plate sample, an infrared one for measuring the temperature fields on the specimen surface and an optical one for visualizing the crack tip verification. The centre section of the specimen is notched to initiate the crack. The temperature field is converted into intrinsic dissipation to quantify the inelastic strain energy according to energy conservation. The maximum value of intrinsic dissipation in each thermal image is related to the position of the crack tip and thus allows monitoring of the crack evolution during the fatigue test. The obtained results show that one specific specimen broke at 7.25 × 107 cycles in the presence of a very low-stress amplitude (122 MPa). It is observed that the intrinsic dissipation has a low-constant level during the initiation and the short cracking, then sharply grows during the long cracking. This transition is visible on the polished surface of the sample, where the plasticity appears during the long cracking and slightly before. The material parameters in the Paris equation obtained from the intrinsic dissipation in the short crack growth are close to the results available in the literature as well as those obtained by the optical camera. [ABSTRACT FROM AUTHOR]

Structural components with different scales normally show different fatigue behaviors, which are virtually dominated by defects originated from multiple sources, including manufacturing processes. This paper reviews three types of size effects (statistical, geometrical, technological) as well as their recent advances in metal fatigue, aiming to provide a guide for fatigue strength assessment of engineering components containing defects, inclusions and material inhomogeneity. Firstly, the background of inherent defects and defect-based failure mechanism are briefly outlined, and fatigue failure analysis based on fracture mechanics as well as statistics theory are emphasized. Then, two approaches commonly applied in statistical size effect modeling, i.e. critical defect method and weakest link method, are elaborated. In addition, the highly stressed volume method is introduced for considering the geometrical size effects, and the technological (production and surface) size effect is briefly overviewed. Finally, further directions on size effect in metal fatigue under defects are explored. [ABSTRACT FROM AUTHOR]

The study on the interaction between defects and dislocation emission is of significance to predict the behaviors of fracture and plastic deformation in crystalline metals; however, the multiscale interaction mechanism has not been well understood. In this work, based on molecular dynamics simulation and distributed dislocation technique, the interaction mechanism between dislocation emission and a crack or a void is studied at the atomic and continuum scales. The results show that dislocation emission can change the mode of crack growth, i.e., from brittle to ductile, and the emitted dislocations cause crack‐tip blunt and decrease stress concentration near the defects. The increment of void growth is completely contributed by dislocation emission, and it can be predicted by the characteristics of dislocation emission. This work reveals the influence mechanism of dislocation emission on failure behaviors and deepens the understanding of the interaction between dislocation emission and defects. Highlights: Interaction between defects and dislocation emission is analyzed at different scales.Dislocation emission changes crack growth mode and improves the resistance of fracture.Mechanism of void growth by dislocation emission is proposed based on MD simulations.Dislocation density and stress field are obtained by distributed dislocation modeling. [ABSTRACT FROM AUTHOR]

In this work, ferroelastic domain switching and R‐curve behavior in lead zirconate titanate (Nb/Ce co‐doped Pb(Zr0.52Ti0.48)O3, ab. PZT‐NC)‐based ferroelectric ceramics were investigated, using the indentation‐strength‐in‐bending (ISB) method. Firstly, Vickers indentation test examined the notable fracture anisotropy of PZT‐NC ceramics between the poling direction and its perpendicular direction, and the crack open displacement (COD) profiles in the two directions were also theoretically calculated from the indentation fracture mechanics. And then two kinds of ferroelastic domain switching modes (in‐plane and out‐of‐plane) were used for explaining such anisotropic propagation behavior of indentation cracks. The subsequent three‐point bending test illustrated the dependence of fracture strength on indentation load and the rising crack growth resistance curves (R‐curves) in two directions. The resulted R‐curves were fitted by the Hill's type Growth Function successfully, giving the reasonable values of crack extension exponential (n), plateau fracture toughness (Kmax), and initial fracture toughness (Kini). The in‐plane ferroelastic domain switching was identified as a more significant toughening mechanism for PZT‐NC ceramics than the out‐of‐plane switching due to more switchable domains. [ABSTRACT FROM AUTHOR]

The purpose of this study was to evaluate rotary bending high-cycle fatigue properties and crack growth of Nimonic 80A-based metal and electron beam-welded joints. All the tests were performed at room temperature. Fracture surfaces under high-cycle fatigue and fatigue crack growth were observed by scanning electron microscopy. Microstructure, hardness and tensile properties were also evaluated in order to understand the effects on the fatigue results obtained. It was found that the tensile properties, hardness and high-cycle fatigue properties of the welded joint are lower than the base metal. The fracture surface of the high-cycle fatigue shows that fatigue crack initiated from the surface under the high stress amplitude and from the subsurface under the low stress amplitude. The effect of the welding process on the statistical fatigue data was studied with a special focus on probabilistic life prediction and probabilistic lifetime limits. The fatigue crack growth rate versus stress intensity factor range data were obtained from the fatigue crack growth tests. From the results, it was evident that the fatigue crack growth rates of the welded are higher than the base metal. The mechanisms and fracture modes of fatigue crack growth of welded specimens were found to be related to the stress intensity factor range ΔK. In addition, the effective fatigue crack propagation thresholds and mismatch of welded joints were described and discussed. [ABSTRACT FROM AUTHOR]

In this paper, the influence of Cr2O3 additive ( y = 0~0.4 wt%) on fracture behaviors, ferroelastic deformation, and mechanical strengths of Bi4Ti2.95W0.05O12.05 ( BTW) Aurivillius ceramics was investigated. For these W/Cr co-doped Bi4Ti3O12 ceramics (BTW- yC), SEM analysis on their fractured surfaces demonstrate that the transgranular fracture is the main fracture mechanism, however, the intergranular fracture also exists in the sample at y = 0.3. Impedance analyses based electrical resonance show that their Poisson's ratio and Young's modulus vary with y in a similar trend, while the frequency constant and elastic compliance exhibit a contrary varying trend with y. On the other hand, under the Vickers indentation, the crack propagation in BTW- yC ceramics takes the form of the long-straight extension, small-angle deflection, and short-distance branching at y = 0, 0.2, and 0.4, respectively. In the uniaxial compression tests, the stress-strain behavior of ceramics consist of three stages, i.e., linear elastic deformation, ferroelastic domain switching, and microcrack propagation. The ferroelastic domain switching tends to form the resistance for the microcrack propagation. Furthermore, uniaxial bending tests prove that the fracture strength is dependent on the grain size and fracture toughness, Overall, the sample at y = 0.1 gains a better mechanical strength among BTW- yC ceramics. [ABSTRACT FROM AUTHOR]

Fatigue properties of Ti-6Al-4V (TC4) subjected to 0.9% physiological saline solutions were presented in this paper. The ultrasonic fatigue test method has been used to investigate the very high cycle fatigue properties of commercial titanium alloy TC4 with the microstructure of tramsformed lamellar dipped into 0.9% physiological saline solution prior to testing. Three estimated times have been decided for subjecting at 37 °C, such as 24 hours, 2 weeks and 4 weeks. The results show that physiological saline solution treatment makes a little influence on the ultrasonic fatigue life of TC4. The slope of S-N curve decreases as the dipping time increases. Dipping tests for three estimated times also have been performed. When TC4 has been dipped into physiological saline solution for 4 weeks, homogeneous white points have been observed on specular facet specimen. And in the fracture surface of which has been dipped for 4 weeks, new inclusion sized 5-10 µm in the crack initiation has been observed. The fractography pictures show the fracture to be transcrystalline plastic. Cracks are initiated because of the subsurface inclusion and the facet slip of α-phase. [ABSTRACT FROM AUTHOR]

Effects of the stress ratio on the very high cycle fatigue behaviors of 9%Cr turbine steel have been investigated at 630 °C. The experimental results show that the S–N curve has a continuous downward trend and has no fatigue limit with the increasing in the cycles at 630 °C. Meanwhile, according to the analysis of microstructure, there are two failure modes that were observed at different stress ratios (R = −1 and 0.1), including surface crack failure and internal crack failure, respectively. Besides, the theoretical threshold value of the crack growth is compared with the calculated value of the fracture surface. To decrease the difference between the threshold value of internal crack initiation and the corresponding theoretical value, a new model for the crack growth threshold of the interior-induced fracture at different stress ratios is proposed and discussed. [ABSTRACT FROM AUTHOR]

In this paper, the thermo-elastic fracture problems of functionally graded materials (FGMs) are thoroughly investigated based on a modified phase field model. In this model, the material constants and fracture toughness vary along a specified direction, the thermal conductivity and stiffness constants in the damaged regions are degraded by the phase-field variable, and the crack evolution is driven by the variation of elastic energy induced by the thermo-mechanical loading. Therefore, the temperature, mechanical and damage fields are coupled with each other. The validation of the present approach has been checked by comparing the present results with the analytical, numerical, and experimental results in literature. The examples of thermo-elastic tensile fracture and thermal shock cracking of FGMs are performed to investigate the influence of material heterogeneity and external thermal loading. Furthermore, the experimental phenomenon of crack deflection in FGMs has been captured by the present simulations. The present study provides a guidance for understanding the fracture mechanism, material design and safety assessment of FGM structures in engineering practice. • The thermo-elastic fracture of FGMs is studied based on a phase-field model. • Both the tensile fracture and thermal shock cracking of FGMs can be simulated. • Effects of material heterogeneity and heat load on fracture behavior are studied. • The present study guides the structural design of FGMs in engineering practice. [ABSTRACT FROM AUTHOR]

• Very high cycle fatigue behavior of titanium alloy welded joints under asymmetric loading was investigated. • Mean stress causes the fatigue failure to transfer from the FZ to the BM. • The size of the plastic zone at the crack tip for FGA is related to the lamella α structures in FZ. • The crack non-propagation region and critical safe size of welded pores are obtained. Very high cycle fatigue behavior of electron beam welded TC17 titanium alloy joints under different stress ratios was investigated. The results revealed that the welded joints exhibited different failure modes depending on the stress ratios applied. As the stress ratio increased, the failure probability attributed to welded pores in the fusion zone (FZ) gradually decreased, shifting the failure mode towards fatigue failure induced by the primary α phase in the base metal (BM). Moreover, the stress intensity factor at the edge of fine granular area (FGA) was determined to be the threshold of long crack growth. It was observed that the size of the plastic zone at the crack tip of FGA was related to the acicular α phase structures precipitated through recrystallization in the FZ. The influence of effective size and location of welded pores on fatigue life was further discussed. To gain further insights, improvements were made to the K-T diagram. Consequently, the non-crack propagation zone and the critical safety size of welded pores responsible for initiating cracks in the welded joint were identified. Additionally, the Weibull probability function was employed to determine the average size of welded pores that led to fatigue failure in the welded joints. [ABSTRACT FROM AUTHOR]

• Applied surface replica technique to study small cracks in dual-phase Mg alloy, revealing relations between crack growth and microstructure. • Rolling process led to distinct microstructures and deformation textures in specimens sampled along the transverse and extrusion directions. • Higher proportion of α-Mg grains with favorable orientation reduced fatigue crack initiation forms. • Denser grain boundaries and strong cylindrical deformation texture of the α-Mg phase severely impeded early growth of small fatigue cracks. This study investigated the high-cycle fatigue behavior of an extruded dual-phase magnesium-lithium (Mg-Li) alloy using ultrasonic fatigue experiments and surface replica techniques. Specimens along the extrusion and transverse directions were compared. The α-Mg phase was found to significantly affect fatigue crack behaviors, with different deformation textures and microstructures in ED and TD specimens. ED specimens exhibited a stronger cylindrical texture, which impeded crack initiation within the basal plane of the α-Mg grain, resulting in higher fatigue strength than TD specimens. This study highlights the importance of microstructure and deformation texture in determining the fatigue behavior of dual-phase Mg-Li alloys. [ABSTRACT FROM AUTHOR]

• The fatigue crack growth tests of 9%Cr martensitic steel are conducted under R = 0.1, 0.3 and 0.5 at 630 ℃. • The FCG path and secondary crack growth behavior under different stress ratios are discussed. • The martensitic lath structures can lead to a more tortuous crack growth path. • The finite element method is introduced to calculate the evolution of the plastic zone and the secondary crack growth behavior. To understand the effect of mean stress and microstructure on the fatigue crack growth (FCG) behavior of 9%Cr martensitic steel under high temperatures, the FCG experiments are conducted on three stress ratios (R = 0.1, 0.3, and 0.5) at 630 ℃. The results indicate that the high-stress ratios have a higher fatigue crack growth rate, and the Paris region can be divided into two regions by the transition point (da / d N = 1 × 10 - 4 mm/Cycle) with different fracture morphology. For da / d N > 1 × 10 - 4 mm/Cycle, due to the influence of high crack driving force and the microstructure, the FCG path presents in a zigzag way. For da / d N ⩽ 1 × 10 - 4 mm/Cycle, the FCG path presents the characteristic of purely horizontal and no obvious crack deflection. Meanwhile, the martensitic lath fracture angles near the FCG path have an obvious statistical relationship with the stress ratio, which is mainly concentrated at 60° to 80° and 100° to 130°. Additionally, according to the EBSD map of secondary cracks, when the secondary cracks encounter the HAGBs, the larger angle of secondary crack deflection occurs. [ABSTRACT FROM AUTHOR]

In this paper, a series of Aurivillius phase Bi 4 Ti 2.95 W 0.05 O 12.05 + 0.2 wt% Cr 2 O 3 (ab. BTWC) ceramics were prepared by a solid-reaction process and sintered at different temperatures (1050 ℃~1150 ℃), their microstructures, fracture mechanisms and fatigue behaviors were investigated under three-point-bending mode. The results show that the grain size of BTWC ceramics increases with increasing the sintering temperature. The typical transgranular mode dominates the fracture behavior of the samples sintered at lower temperatures, while the intergranular fracture can be also observed in the samples sintered at higher temperatures. Besides, the storage modulus ( E’ ) and mechanical loss (tan m δ ) of BTWC ceramics have a subtle variation with the increase of sintering temperature. In addition, the high-temperature environment could not only decrease the fracture toughness and bending strength of ceramics but also change their fracture mode. On the other hand, the bending strength also decreases with the decrease of loading rates, which could be attributed to the slow crack growth referring to the dynamic fatigue behavior of brittle materials. The slow crack growth parameter ( n ) of BTWC ceramics shows a downtrend with increasing their sintering temperature, indicating that those high temperature sintering samples possess a higher susceptibility when subjected to the long-term stress corrosion. Furthermore, the sample sintered at 1125 ℃ exhibits an excellent fatigue resistance when subjected to the cyclic stress. The corresponding fatigue mechanism is not only related to the ferroelectric domain configuration but also involved with the pores or impurities. [ABSTRACT FROM AUTHOR]

• With a small part of online data, the final fatigue failure was predicted with reasonable accuracy. • The crack growth rate was practically estimated for an inner crack at a very high cycle regime. • The initiation site of an inner crack with eccentricity was detected from the thermographic analysis. • A combined approach of simulation and measurement was introduced to study the propagation rate of internal crack. This paper presents a thermodynamic characterization method for estimating the internal crack growth rate, which has been a puzzle in very high cycle fatigue research. A theoretical approach of surface temperature is discussed with crack size, initiation site, and time for thin sheet material. Infrared thermography is used to study the inner crack behavior and the heat dissipation phenomenon under 20 kHz vibration loading on high-strength stainless steel. A numerical simulation reveals the consequent temperature elevation on the surfaces by the heat generation at the crack tip and the heat conduction. Ultimately, the internal crack growth rate and final fatigue failure prediction are obtained by combining the calculation of heat dissipation and the observed evolution of the surface temperature field. [ABSTRACT FROM AUTHOR]

• A comprehensive review on phase-field models for fracture and fatigue is presented. • The theory fundamentals and implementation approaches are provided and compared. • All the phase field models for fatigue failure are summarized and discussed. • The future research directions of phase field fatigue models are pointed out. Phase field fracture models have demonstrated great capacities in simulating crack nucleation, propagation, branching, and joining in brittle and ductile materials subjected to external stimulations. Because of their great flexibility, phase field fracture models can incorporate various material properties including anisotropy, elastoplasticity, viscoelasticity, hyperelasticity, piezoelectricity, etc. Recently, the models have been extended to fatigue, one of the most common material failure mechanisms in structural engineering. The purpose of this paper is to provide a comprehensive review of recent work on phase field models for fatigue damage and failures. Following a brief introduction to the development of phase field fracture models as well as the theories and models of fatigue, the fundamentals of the models for elastic and elasto-plastic cases are presented, including basic theories, formulas, tension–compression splits, and numerical implementations. Then, the emphasis is placed on different aspects of the phase field models for fatigue fracture involving the approaches of introducing fatigue damage, the descriptions of crack nucleation and propagation, the coupling of cyclic plasticity and phase field models, and the acceleration algorithms. Finally, the future research directions of phase field models for fatigue fracture and the major challenges to be conquered in their engineering applications are discussed. [ABSTRACT FROM AUTHOR]

• A general phase field framework for brittle fracture in quasi-crystals is proposed. • The effect of phason wall on the fracture toughness is taken into consideration. • A new numerical implementation approach in Comsol Multiphysics is developed. • Influence of phason field on the fracture behavior of QCs is thoroughly studied. Most of quasi-crystals are brittle at room temperature due to their specific cluster structures. Phase-field fracture models have demonstrated a powerful ability to predict brittle crack evolution. This paper develops a phase-field framework for modeling macroscopic brittle fracture in quasi-crystal solids. The kind of quasi-crystals is not preset in the phase-field model; therefore, this model is valid for almost all quasi-crystal solids. The phase-field model for the first time introduces a volume fraction parameter into the fracture toughness to reflect the effect of phason wall. Furthermore, a new numerical implementation approach of phase-field fracture models in C omsol M ultiphysics is presented. Several examples of 1D hexagonal and 2D decagonal quasi-crystals are performed. The developed model is validated against the reported results of benchmark problems. Further investigations indicate that the phason field peculiar to quasi-crystals has a certain influence on the crack paths in asymmetric fracture problems and on the force–displacement curves in both symmetric and asymmetric fracture problems. When the fracture toughness is fixed, the increase of the volume fraction parameter results in the decrease of the peak force and the increase of the failure displacement. When the influence of the phason field on the fracture toughness is considered, both the peak force and failure displacement would sharply decrease, which indicates that the degradation of fracture toughness due to the phason field plays a more important role than the phason elastic energy in the fracture of quasi-crystals. Furthermore, the relation between the phonon-phason energy transformation and the elastic constants of QCs has been qualitatively analyzed. The developed phase-field modeling framework provides a guidance for understanding the fracture mechanism of quasi-crystals and assessing the safety of quasi-crystal structures in engineering practice. [ABSTRACT FROM AUTHOR]

• Two physics-guided machine learning (ML) frameworks for fatigue life prediction of AM materials; • The hybrid ML model based on the morphological details of critical defects for fatigue life prediction; • In serial physics-guided ML framework, ANN presents better prediction accuracy compared with SVR; • Under limited data condition, the serial physics-guided ML framework with ANN is recommended. Introducing random defects is a type of the dominant causes of fatigue scatter of additive manufacturing (AM) materials. The fracture mechanics-based models oversimplify the fatigue damage process and ignore the key influencing factors. Given data-driven nature of machine learning (ML), sufficient samples are required to train, which generally cannot be met in practice. In view of this, this work develops two physics-guided machine learning frameworks which combine physics-based models and ML algorithms, for improving the prediction ability. In the proposed framework, ML models can consider those factors ignored by physics-based models and physics-based models can ensure the consistency with physical results. Finally, fatigue data of three AM materials are used for model evaluation and comparison. The results show that, physics-based models lack sufficient explanatory power for scatter of fatigue life. Moreover, compared with the purely data-driven methods, the proposed framework can maintain high accuracy and alleviate the over fitting phenomenon under insufficient fatigue data sources. [ABSTRACT FROM AUTHOR]

A series of tests with centrally cracked Brazilian disc and un-cracked Brazilian disc specimens were conducted to investigate the relation between the mode II fracture toughness K IIC and tensile strength σ t of sandstone under different treatment conditions. The results indicated that there was a good linear relation between these two rock parameters. Further, this conclusion was also validated by theoretical analysis based on the generalized maximum tangential stress criterion. Moreover, an empirical formula K IIC = 0.2159 σ t was obtained using linear regression analysis, which can be confidently used to estimate the mode II fracture toughness with tensile strength of rocks. [ABSTRACT FROM AUTHOR]

• TMAZ consists of needle-like α precipitates and elongated α p within β grains. • Fine β grains in SZ contribute to the highest strength in the 3rd layer. • Cracks tend to nucleate from HAGBs and {1 1 2} 〈1 1 1〉 slip deformation of β structure. • Fatigue cracks initiate from the 2nd layer of SZ below 210 MPa. • Crack growth exhibits a higher crack growth rate in HAZ than SZ. Heterogeneities of microstructure, tensile and fatigue behavior of FSWed titanium alloy joint were in-situ studied by utilizing replica, DIC and electron back-scattered diffraction methods. Banded TMAZ consisting of needle-like α precipitates and elongated α p within DRXed β grains bridges the HAZ and SZ. Fine β grains in SZ contribute to the highest tensile strength in the 3rd layer. Fatigue cracks prefer to nucleate from HAGBs and {1 1 2} 〈1 1 1〉 slip deformation of β structure in the 2nd layer of SZ below 210 MPa and 3rd layer of HAZ otherwise. Transgranular crack propagation along the {1 1 2} planes exhibits a higher crack growth rate in HAZ than SZ. [ABSTRACT FROM AUTHOR]

• Slip bands initiated inside martensitic laths, are oriented parallel to the lath. • Internal slip bands of the martensitic laths cause cracks to initiate. • Crack are more likely to propagation along the martensitic laths. • The complex structure of martensite has a greater resistance to small crack growth. Martensitic steel presents high fatigue crack resistance due to its complex and hierarchical microstructure, but its mechanisms are unclear. This work experimentally investigated effect of the lath and the prior austenitic grain (PAGs) on crack initiation and the early propagation behavior in high cycle fatigue. It is found that micro cracks initiated from the slip bands in the interior of thin monocrystalline laths, in which the dislocation intensity zones deflected the crack path. Subsequently, the micro cracks coalesced through the lath boundaries, and resulted in an intermittent and staggered appearance of crack path in the PAGs. Finally, the crack propagation across the boundaries of the primary PAG are extremely slow and presents significant zigzag manners due to the misorientation of the laths in neighboring PAGs. The above observations demonstrate that the crack initiation and early propagation are significantly hindered by the multi-scaled microstructure of the martensitic steel. [ABSTRACT FROM AUTHOR]

• Four kinds of defects responsible for axle failures are reviewed. • Mechanisms of surface hardening techniques and their applications to axles are explored. • Induction hardening and anti-corrosion/impact coating are recommended with regard to structural integrity of railway axles. Fatigue is a classic and longstanding issue, which challenges railway axles' structural integrity. In spite of its almost 200 years of research history, it has always been a hot topic considering the increasing service speed and safety concern. Except for inclusions, defects from axle steel ingot, corrosion pit, fretting and flying ballast impact damage also bring potential failure risk. A broad overview on the four kinds of defects responsible for axle failures is given in present paper. Surface hardening techniques are utilized during axle manufacturing aiming to improve surface integrity of railway axles by means of both retarding crack initiation and decelerating crack growth rate due to introduction of residual compressive stress and formation of hardened layer. Mechanisms of surface hardening techniques, including shot peening, deep rolling and induction hardening, are briefly introduced and their applications to axles are reviewed. Based on state-of-the-art of axle manufacturing, induction hardening and anti-corrosion/impact coating is recommended as an efficient and prospective combination with regard to structural integrity of railway axles. [ABSTRACT FROM AUTHOR]

For Aurivillius phase Bi 4 Ti 3 − x W x O 12 + x + 0.2 wt.% Cr 2 O 3 (BTW x -C, x = 0–0.1) ceramics prepared by a conventional ceramic process, plate-like grains with random orientations are formed there. The aspect ratio of grains increases after the doping of W for ceramics, at the same time the bulk density of ceramics decreases. The change of Poisson's ratio may be related to the change of bulk density, whilst the change of bond strength could be responsible for the change of Young's modulus. The large-grained samples tend to possess a lower frequency constant but a higher elastic compliance, as well as a lower hardness. Especially, a larger grain size provides a higher fracture toughness for the sample at x = 0.05 due to the mechanism of crack deflection. The stress–strain curves of BTW x -C ceramics under a uniaxial compression load are characterized as three stages: linear elastic deformation, ferroelastic domain switch and microcrack propagation. The microcrack propagation along grain boundaries results in the final axial flerry of ceramics. Additionally, the fracture strength of ceramics may be largely influenced by the internal stress resulted from the paraelectric–ferroelectric phase transformation during sintering. [ABSTRACT FROM AUTHOR]

Highlights: [•] Very high cycle fatigue behaviors of HAZ and FZ for Q345 welded joints. [•] The association between frequency variation and crack growth under ultrasonic loading condition. [•] A nonlinear fatigue model based on natural frequency changes for very high cycle fatigue. [ABSTRACT FROM AUTHOR]