Origin of nucleation and growth of extension twins in grains unsuitably oriented for twinning during deformation of Mg-1%Al

A large number of anomalous extension twins,with low or even negative twinning Schmid factors,were found to nucleate and grow in a strongly textured Mg-1Al alloy during tensile deformation along the extruded direction.The deformation mechanisms responsible for this behaviour were investigated through in-situ electron back-scattered diffraction,grain reference orientation deviation,and slip trace-modified lattice rotation.It was found that anomalous extension twins nucleated mainly at the onset of plastic deformation at or near grain boundary triple junctions.They were associated with the severe strain incompatibility between neighbour grains as a result from the differentbasal slip-induced lattice rotations.Moreover,the anomalous twins were able to grow with the applied strain due to the continuous activation ofbasal slip in different neighbour grains,which enhanced the strain incompatibility.These results reveal the complexity of the deformation mechanisms in Mg alloys at the local level when deformed along hard orientations.

Flow characteristics and hot workability of a typical low-alloy high-strength steel during multi-pass deformation

Heavy components of low-alloy high-strength(LAHS) steels are generally formed by multi-pass forging. It is necessary to explore the flow characteristics and hot workability of LAHS steels during the multi-pass forging process, which is beneficial to the formulation of actual processing parameters. In the study, the multi-pass hot compression experiments of a typical LAHS steel are carried out at a wide range of deformation temperatures and strain rates. It is found that the work hardening rate of the experimental material depends on deformation parameters and deformation passes, which is ascribed to the impacts of static and dynamic softening behaviors. A new model is established to describe the flow characteristics at various deformation passes. Compared to the classical Arrhenius model and modified Zerilli and Armstrong model, the newly proposed model shows higher prediction accuracy with a confidence level of 0.98565. Furthermore, the connection between power dissipation efficiency(PDE) and deformation parameters is revealed by analyzing the microstructures. The PDE cannot be utilized to reflect the efficiency of energy dissipation for microstructure evolution during the entire deformation process, but only to assess the efficiency of energy dissipation for microstructure evolution in a specific deformation parameter state.As a result, an integrated processing map is proposed to better study the hot workability of the LAHS steel, which considers the effects of instability factor(IF), PDE, and distribution and size of grains. The optimized processing parameters for the multi-pass deformation process are the deformation parameters of 1223–1318 K and 0.01–0.08 s^(-1). Complete dynamic recrystallization occurs within the optimized processing parameters with an average grain size of 18.36–42.3 μm. This study will guide the optimization of the forging process of heavy components.

Liquefaction susceptibility and deformation characteristics of saturated coral sandy soils subjected to cyclic loadings-a critical review

Coral sandy soils widely exist in coral island reefs and seashores in tropical and subtropical regions.Due to the unique marine depositional environment of coral sandy soils,the engineering characteristics and responses of these soils subjected to monotonic and cyclic loadings have been a subject of intense interest among the geotechnical and earthquake engineering communities.This paper critically reviews the progress of experimental investigations on the undrained behavior of coral sandy soils under monotonic and cyclic loadings over the last three decades.The focus of coverage includes the contractive-dilative behavior,the pattern of excess pore-water pressure(EPWP)generation and the liquefaction mechanism and liquefaction resistance,the small-strain shear modulus and strain-dependent shear modulus and damping,the cyclic softening feature,and the anisotropic characteristics of undrained responses of saturated coral sandy soils.In particular,the advances made in the past decades are reviewed from the following aspects:(1)the characterization of factors that impact the mechanism and patterns of EPWP build-up;(2)the identification of liquefaction triggering in terms of the apparent viscosity and the average flow coefficient;(3)the establishment of the invariable form of strain-based,stress-based,or energy-based EPWP ratio formulas and the unique relationship between the new proxy of liquefaction resistance and the number of cycles required to reach liquefaction;(4)the establishment of the invariable form of the predictive formulas of small strain modulus and strain-dependent shear modulus;and(5)the investigation on the effects of stress-induced anisotropy on liquefaction susceptibility and dynamic deformation characteristics.Insights gained through the critical review of these advances in the past decades offer a perspective for future research to further resolve the fundamental issues concerning the liquefaction mechanism and responses of coral sandy sites subjected to cyclic loadings associated with seismic events in marine environments.

Coseismic deformation and fault slip distribution of the 2023 M_(W)7.8 and M_(W)7.6 earthquakes in Türkiye

On February 6,2023,a devastating earthquake with a moment magnitude of M_(W)7.8 struck the town of Pazarcik in south-central Türkiye,followed by another powerful earthquake with a moment magnitude of M_(W)7.6 that struck the nearby city of Elbistan 9 h later.To study the characteristics of surface deformation caused by this event and the influence of fault rupture,this study calculated the static coseismic deformation of 56 stations and dynamic displacement waveforms of 15 stations using data from the Turkish national fixed global navigation satellite system(GNSS)network.A maximum static coseismic displacement of 0.38 m for the M_(W)7.8 Kahramanmaras earthquake was observed at station ANTE,36 km from the epicenter,and a maximum dynamic coseismic displacement of 4.4 m for the M_(W)7.6 Elbistan earthquake was observed at station EKZ1,5 km from the epicenter.The rupture-slip distributions of the two earthquakes were inverted using GNSS coseismic deformation as a constraint.The results showed that the Kahramanmaras earthquake rupture segment was distinct and exposed on the ground,resulting in significant rupture slip along the Amanos and Pazarcik fault segments of the East Anatolian Fault.The maximum slip in the Pazarcik fault segment was 10.7 m,and rupture occurred at depths of 0–15 km.In the Cardak fault region,the Elbistan earthquake caused significant ruptures at depths of 0–12 km,with the largest amount of slip reaching 11.6 m.The Coulomb stress change caused by the Kahramanmaras earthquake rupture along the Cardak fault segment was approximately 2 bars,and the area of increased Coulomb stress corresponded to the subsequent rupture region of the M_(W)7.6 earthquake.Thus,it is likely that the M_(W)7.8 earthquake triggered or promoted the M_(W)7.6 earthquake.Based on the cumulative stress impact of the M_(W)7.8 and M_(W)7.6 events,the southwestern segment of the East Anatolian Fault,specifically the Amanos fault segment,experienced a Coulomb rupture stress change exceeding 2 bars,warranting further attention to assess its future seismic hazard risk.

Room and cryogenic deformation behavior of AZ61 and AZ61-xCaO(x=0.5,1 wt.%)alloy

This study investigates the influence of CaO(0.5,1(wt.%))alloying on the microstructural evolution,texture development and deformation behavior of AZ61 magnesium alloy.The uniaxial tension tests at room(RT)and cryogenic(CT,-150℃)temperature were performed to investigate the twinability and dislocation behavior and its consequent effect on flow stress,ductility and strain hardening rate.The results showed that the AZ61-1CaO exhibited superior strength/ductility synergy at RT with a yield strength(YS)of 223 MPa and a ductility of 23% as compared to AZ61(178 MPa,18.5%)and AZ61-0.5CaO(198 MPa,21%).Similar trend was witnessed for all the samples during CT deformation,where increase in the YS and decrease in ductility were observed.The Mtex tools based in-grain misorientation axis(IGMA)analysis of RT deformed samples revealed the higher activities of prismatic slip in AZ61-CaO,which led to superior ductility.Moreover,subsequent EBSD analysis of CT deformed samples showed the increased fraction of fine{10-12}tension twins and nucleation of multiple{10-12}twin variants caused by higher local stress concentration at the grain boundaries,which imposed the strengthening by twin-twin interaction.Lastly,the detailed investigations on strengthening contributors showed that the dislocation strengthening has the highest contribution towards strength in all samples.

Mechanical Behavior and Microstructure Evolution during Tensile Deformation of Twinning Induced Plasticity Steel Processed by Warm Forgings

The mechanical behavior and microstructural evolution of an Fe-30Mn-3Al-3Si twinninginduced plasticity(TWIP)steel processed using warm forging was investigated.It is found that steel processed via warm forging improves comprehensive mechanical properties compared to the TWIP steel processed via cold rolling,with a high tensile strength(R_(m))of 793 MPa,a yield strength(R_(P))of 682 MPa,an extremely large R_(P)/R_(m)ratio as high as 0.86 as well as an excellent elongation rate of 46.8%.The microstructure observation demonstrates that steel processed by warm forging consists of large and elongated grains together with fine,equiaxed grains.Complicated micro-defect configurations were also observed within the steel,including dense dislocation networks and a few coarse deformation twins.As the plastic deformation proceeds,the densities of dislocations and deformation twins significantly increase.Moreover,a great number of slip lines could be observed in the elongated grains.These findings reveal that a much more dramatic interaction between microstructural defect and dislocations glide takes place in the forging sample,wherein the fine and equiaxed grains propagated dislocations more rapidly,together with initial defect configurations,are responsible for enhanced strength properties.Meanwhile,larger,elongated grains with more prevalently activated deformation twins result in high plasticity.

Kinematic deformation and intensity assessment of the 2021 Maduo M_(S)7.4 earthquake in Qinghai revealed by high-frequency GNSS

Rapid acquisition of the kinematic deformation field and seismic intensity distribution of large earthquakes is crucial for postseismic emergency rescue,disaster assessment,and future seismic risk research.The advancement of GNSS observation and data processing makes it play an important role in this field,especially the high-frequency GNSS.We used the differential positioning method to calculate the 1 HZ GNSS data from 98 sites within 1000 km of the M_(S)7.4 Maduo earthquake epicenter.The kinematic deformation field and the distribution of the seismic intensity by using the peak ground velocity derived from displacement waveforms were obtained.The results show that:1)Horizontal coseismic response deformation levels ranging from 25 mm to 301 mm can be observed within a 1000 km radius from the epicenter.Coseismic response deformation on the east and west sides shows bilateral asymmetry,which markedly differs from the symmetry presented by surface rupture.2)The seismic intensity obtained through high-frequency GNSS and field investigations exhibits good consistency of the scope and orientation in the high seismic intensity area,although the former is generally slightly smaller than the latter.3)There may exist obstacles on the eastern side of the seismogenic fault.The Maduo earthquake induced a certain tectonic stress loading effect on the western Kunlun Pass-Jiangcuo fault(KPJF)and Maqin-Maqu segment,resulting in higher seismic risk in the future.

Operando measurement of lattice deformation profiles of synchrotron radiation monochromator

This study presents a new method for characterizing the thermal lattice deformation of a monochromator with high precision under service conditions and first reports the operando measurements of nanoscale thermal lattice deformation on a double-crystal monochromator at different incident powers.The nanoscale thermal lattice deformation of the monochromator first crystal was obtained by analyzing the intensity of the distorted DuMond diagrams.DuMond diagrams of the 333 diffraction index,sensitive to lattice deformation,were obtained directly using a 2D detector and an analyzer crystal orthogonal to the monochromator.With increasing incident power and power density,the maximum height of the lattice deformation increased from 3.2 to 18.5 nm,and the deformation coefficient of the maximum height increased from 1.1 to 3.2 nm/W.The maximum relative standard deviation was 4.2%,and the maximum standard deviation was 0.1 nm.Based on the measured thermal deformations,the flux saturation phenomenon and critical point for the linear operation of the monochromator were predicted with increasing incident power.This study provides a simple solution to the problem of the lower precision of synchrotron radiation monochromator characterizations compared to simulations.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids with Rheology

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.

Impact of initial fluctuations and nuclear deformations in isobar collisions

Relativistic isobar^(96)_(44)Ru+^(96)_(44)Ru and^(96)_(40)Zr+^(96)_(40)Zrcollisions have revealed intricate differences in their nuclear size and shape,inspiring unconventional studies of nuclear structure using relativistic heavy ion collisions.In this study,we investigate the relative differences in the mean multiplicityR_(<Nch>)and the secondR_(ε2)and third-order eccentricityR_(ε3)between isobar collisions using initial state Glauber models.It is found that initial fluctuations and nuclear deformations have negligible effects on R_(<Nch>)in most central collisions,while both are important for the R_(ε2)and R_(ε3),the degree of which is sensitive to the underlying nucleonic or sub-nucleonic degree of freedom.These features,compared to real data,may probe the particle production mechanism and the physics underlying nuclear structure.

InSAR-derived surface deformation characteristics and mining subsidence parameters in mountain coal mines

Mining-induced surface deformation disrupts ecological balance and impedes economic progress.This study employs SBAS-InSAR with 107-view of ascending and descending SAR data from Sentinel-1,spanning February 2017 to September 2020,to monitor surface deformation in the Fa’er Coal Mine,Guizhou Province.Analysis on the surface deformation time series reveals the relationship between underground mining and surface shifts.Considering geological conditions,mining activities,duration,and ranges,the study determines surface movement parameters for the coal mine.It asserts that mining depth significantly influences surface movement parameters in mountainous mining areas.Increasing mining depth elevates the strike movement angle on the deeper side of the burial depth by 22.84°,while decreasing by 7.74°on the shallower side.Uphill movement angles decrease by 4.06°,while downhill movement angles increase by 15.71°.This emphasizes the technology's suitability for local mining design,which lays the groundwork for resource development,disaster prevention,and ecological protection in analogous contexts.

Hot deformation behavior and hot-metal-gas-forming process of V micro-alloyed high manganese steel

The hot deformation behavior of a newly designed V micro-alloyed high manganese steel(HMnS)was investigated in order to guide the development of the hot-metal-gas-forming process.Single-pass hot compression experiments were conducted in the temperature range of 950–1100°C and the strain rate range of 0.05–10 s^(−1),and the stress–strain curves and the corresponding softening mechanism of the V micro-alloyed HMnS were analyzed.Results show that two types of stress–strain curves,representing the work hardening(WH)-dynamic recovery(DRV)-dynamic recrystallization(DRX)mechanism and the WH–DRV mechanism,respectively,occur during the deformation process.Moreover,the WH–DRV–DRX mechanism gradually transforms into the WH–DRV mechanism with the increasing strain rate and decreasing deformation temperature.Two types of constitutive models considering the softening mechanism difference were established and verified by additional hot-deformation experiments.Hot processing map of the HMnS was established and correlated well with the microstructure evolution result.Based on the constitutive models and processing map,the optimal processing parameter range and flow stress of HMnS for the hot-metal-gas-forming were determined.

Spatiotemporal deformation characteristics of Outang landslide and identification of triggering factors using data mining

Since the impoundment of Three Gorges Reservoir(TGR)in 2003,numerous slopes have experienced noticeable movement or destabilization owing to reservoir level changes and seasonal rainfall.One case is the Outang landslide,a large-scale and active landslide,on the south bank of the Yangtze River.The latest monitoring data and site investigations available are analyzed to establish spatial and temporal landslide deformation characteristics.Data mining technology,including the two-step clustering and Apriori algorithm,is then used to identify the dominant triggers of landslide movement.In the data mining process,the two-step clustering method clusters the candidate triggers and displacement rate into several groups,and the Apriori algorithm generates correlation criteria for the cause-and-effect.The analysis considers multiple locations of the landslide and incorporates two types of time scales:longterm deformation on a monthly basis and short-term deformation on a daily basis.This analysis shows that the deformations of the Outang landslide are driven by both rainfall and reservoir water while its deformation varies spatiotemporally mainly due to the difference in local responses to hydrological factors.The data mining results reveal different dominant triggering factors depending on the monitoring frequency:the monthly and bi-monthly cumulative rainfall control the monthly deformation,and the 10-d cumulative rainfall and the 5-d cumulative drop of water level in the reservoir dominate the daily deformation of the landslide.It is concluded that the spatiotemporal deformation pattern and data mining rules associated with precipitation and reservoir water level have the potential to be broadly implemented for improving landslide prevention and control in the dam reservoirs and other landslideprone areas.

Superplasticity of fine-grained Mg-10Li alloy prepared by severe plastic deformation and understanding its deformation mechanisms

The superplastic behavior and associated deformation mechanisms of a fine-grained Mg-10.1 Li-0.8Al-0.6Zn alloy(LAZ1011)with a grain size of 3.2μm,primarily composed of the BCCβphase and a small amount of the HCPαphase,were examined in a temperature range of 473 K to 623 K.The microstructural refinement of this alloy was achieved by employing high-ratio differential speed rolling.The best superplasticity was achieved at 523 K and at strain rates of 10^(-4)-5×10^(-4)s^(-1),where tensile elongations of 550±600%were obtained.During the heating and holding stage of the tensile samples prior to tensile loading,a significant increase in grain size was observed at temperatures above 573 K.Therefore,it was important to consider this effect when analyzing and understanding the superplastic deformation behavior and mechanisms.In the investigated strain rate range,the superplastic flow at low strain rates was governed by lattice diffusion-controlled grain boundary sliding,while at high strain rates,lattice diffusion-controlled dislocation climb creep was the rate-controlling deformation mechanism.It was concluded that solute drag creep is unlikely to occur.During the late stages of deformation at 523 K,it was observed that grain boundary sliding led to the agglomeration of theαphase,resulting in significant strain hardening.Deformation mechanism maps were constructed forβ-Mg-Li alloys in the form of 2D and 3D formats as a function of strain rate,stress,temperature,and grain size,using the constitutive equations for various deformation mechanisms derived based on the data of the current tests.

Characterization of local chemical ordering and deformation behavior in high entropy alloys by transmission electron microscopy

Short-range ordering(SRO)is one of the most important structural features of high entropy alloys(HEAs).However,the chemical and structural analyses of SROs are very difficult due to their small size,complexed compositions,and varied locations.Transmission electron microscopy(TEM)as well as its aberration correction techniques are powerful for characterizing SROs in these compositionally complex alloys.In this short communication,we summarized recent progresses regarding characterization of SROs using TEM in the field of HEAs.By using advanced TEM techniques,not only the existence of SROs was confirmed,but also the effect of SROs on the deformation mechanism was clarified.Moreover,the perspective related to application of TEM techniques in HEAs are also discussed.

Deformation mechanism and roof pre-splitting control technology of gob-side entry in thick hard main roof full-mechanized longwall caving panel

This paper explores the deformation mechanism and control technology of roof pre-splitting for gob-side entries in hard roof full-mechanized longwall caving panel(LTCC).The investigation utilizes a comprehensive approach that integrates field monitoring,theoretical analysis,and numerical simulation.Theoretical analysis has illuminated the influence of the length of the lateral cantilever beam of the main roof(LCBM)above the roadway on the stability of the gob-side entry behind the panel.Numerical simulations have further revealed that the longer LCBM results in heightened vertical stress within the coal pillar,developed cracks around the roadway,and more pronounced damage to the roadway.Moreover,numerical simulations also demonstrate the potential of roof pre-splitting technology in optimizing the fracture position of the hard roof.This technology significantly reduces the length of the LCBM,thereby alleviating stress concentration in the coal pillars and integrated coal rib while minimizing the destruction of the gob-side entry.Therefore,this manuscript first proposes the use of roof pre-splitting technology to control roadway deformation,and automatically retain the entry within a hard roof LTCC panel.Field implementation has demonstrated that the proposed automatically retained entry by roof pre-splitting technology effectively reduces gob-side entry deformation and achieves automatically retained entry.

Microstructural evolution and deformation mechanisms of superplastic aluminium alloys:A review

Aluminium alloy is one of the earliest and most widely used superplastic materials.The objective of this work is to review the scientific advances in superplastic Al alloys.Particularly,the emphasis is placed on the microstructural evolution and deformation mechanisms of Al alloys during superplastic deformation.The evolution of grain structure,texture,secondary phase,and cavities during superplastic flow in typical superplastic Al alloys is discussed in detail.The quantitative evaluation of different deformation mechanisms based on the focus ion beam(FIB)-assisted surface study provides new insights into the superplasticity of Al alloys.The main features,such as grain boundary sliding,intragranular dislocation slip,and diffusion creep can be observed intuitively and analyzed quantitatively.This study provides some reference for the research of superplastic deformation mechanism and the development of superplastic Al alloys.

Effect of annealing temperature on microstructure and mechanical properties of Mg-Zn-Zr-Nd alloy with large final rolling deformation

In this study,the Mg-3Zn-0.5Zr-χNd(χ=0,0.6)alloys were subjected to final rolling treatment with large deformation of 50%.The impact of annealing temperatures on the microstructure and mechanical properties was investigated.The rolled Mg-3Zn-0.5Zr-0.6Nd alloy exhibited an ultimate tensile strength of 386 MPa,a yield strength of 361 MPa,and an elongation of 7.1%.Annealing at different temperatures resulted in reduced strength and obviously increased elongation for both alloys.Optimal mechanical properties for the Mg-3Zn-0.5Zr-0.6Nd alloy were achieved after annealing at 200℃,with an ultimate tensile strength of 287 MPa,a yield strength of 235 MPa,and an elongation of 26.1%.The numerous deformed microstructures,twins,and precipitated phases in the rolled alloy could impede the deformation at room temperature and increase the work hardening rate.After annealing,a decrease in the work hardening effect and an increase in the dynamic recovery effect were obtained due to the formation of fine equiaxed grains,and the increased volume fraction of precipitated phases,which significantly improved the elongation of the alloy.Additionally,the addition of Nd element could enhance the annealing recrystallization rate,reduce the Schmid factor difference between basal and prismatic slip systems,facilitate multi-system slip initiation and improve the alloy plasticity.

Exploring the Implications of the Deformation Parameter and Minimal Length in the Generalized Uncertainty Principle

The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.

Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.