Is Mg_(17)Al_(12) ductile or brittle?A theoretical insight

The Mg_(17)Al_(12)-phase,which is common and important in Mg-Al alloy,has long been regarded as a brittle phase in experiments but theoretical calculations report controversial results.To unravel why theoretical calculations report controversial results and determine whether Mg_(17)Al_(12)is brittle or ductile,density functional theory calculations on atomic level are performed to investigate mechanic properties of Mg_(17)Al_(12)without containing alloying elements and without taking the size effect.The results showed that the parameter k-point played critical role in the DFT-based elastic calculations.The convergent G/B ratio of Mg_(17)Al_(12)was about 0.52,suggesting that the Mg_(17)Al_(12)-phase was theoretically ductile although its ductility was poor.The chemical bonding in Mg_(17)Al_(12)was the mixture of metallic Mg-Mg bond and covalent Al-Al bond.The advantage of metallic bonding over covalent bonding provided a possible explanation for the ductility of Mg_(17)Al_(12).Possible reasons for the brittleness of Mg_(17)Al_(12)in experiments are also discussed.

Quantitative characterization of the brittleness of deep shales by integrating mineral content,elastic parameters,in situ stress conditions and logging analysis

Deep shale reservoirs(3500–4500 m)exhibit significantly different stress states than moderately deep shale reservoirs(2000–3500 m).As a result,the brittleness response mechanisms of deep shales are also different.It is urgent to investigate methods to evaluate the brittleness of deep shales to meet the increasingly urgent needs of deep shale gas development.In this paper,the quotient of Young’s modulus divided by Poisson’s ratio based on triaxial compression tests under in situ stress conditions is taken as SSBV(Static Standard Brittleness Value).A new and pragmatic technique is developed to determine the static brittleness index that considers elastic parameters,the mineral content,and the in situ stress conditions(BIEMS).The coefficient of determination between BIEMS and SSBV reaches 0.555 for experimental data and 0.805 for field data.This coefficient is higher than that of other brittleness indices when compared to SSBV.BIEMS can offer detailed insights into shale brittleness under various conditions,including different mineral compositions,depths,and stress states.This technique can provide a solid data-based foundation for the selection of‘sweet spots’for single-well engineering and the comparison of the brittleness of shale gas production layers in different areas.

Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

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.

Modeling the Interaction between Vacancies and Grain Boundaries during Ductile Fracture

The experimental results in previous studies have indicated that during the ductile fracture of pure metals,vacancies aggregate and form voids at grain boundaries.However,the physical mechanism underlying this phenomenon remains not fully understood.This study derives the equilibrium distribution of vacancies analytically by following thermodynamics and the micromechanics of crystal defects.This derivation suggests that vacancies cluster in regions under hydrostatic compression to minimize the elastic strain energy.Subsequently,a finite element model is developed for examining more general scenarios of interaction between vacancies and grain boundaries.This model is first verified and validated through comparison with some available analytical solutions,demonstrating consistency between finite element simulation results and analytical solutions within a specified numerical accuracy.A systematic numerical study is then conducted to investigate the mechanism that might govern the micromechanical interaction between grain boundaries and the profuse vacancies typically generated during plastic deformation.The simulation results indicate that the reduction in total elastic strain energy can indeed drive vacancies toward grain boundaries,potentially facilitating void nucleation in ductile fracture.

Deformation characteristics of granitic rocks in Erguna ductile shear zone,NE China

The Erguna ductile shear zone is situated in the Erguna Massif,which has been exposed along the eastern bank of the Erguna River in northeastern China.The authors present comprehensive study results on the macro-and micro-structures,finite strain and kinematic vorticity,quartz electron backscatter diffraction(EBSD)fabrics,and geochronology of granitic rocks in the Erguna ductile shear zone.The deformed granitic rocks have experienced significant SE-trending dextral strike-slip shearing.Finite strain and kinematic vorticity in all deformed granitic rocks indicate that the deformation is characterized by simple sheardominated general shearing with S-L tectonites.Mineral deformation behaviors and quartz C-axis textures demonstrate that the deformed granitic rocks developed under greenschist to amphibolite facies conditions at deformation temperatures ranging from 450 to 550℃.New LA-ICP-MS zircon U-Pb ages indicate that these granitic rocks were formed in Early Triassic(~248.6 Ma)and Early Cretaceous(~136.7 Ma).All the evidence indicates that this deformation may have occurred in Early Cretaceous and was related to the compression resulting from the final closure of the Mongol-Okhotsk Ocean.

Analysis of the Application Effect of Structured Healthcare Education in Brittle Diabetic Patients

Objective:To explore the application effect of structured healthcare education in patients with brittle diabetes mellitus.Methods:188 brittle diabetic patients admitted to our hospital from May 2021 to December 2023 were selected as the study subjects,and were divided into the control group(n=94)and the observation group(n=94)according to the random number table method.The control group used conventional nursing intervention and the observation group used structured healthcare education.The general information,glycemic indexes,self-efficacy,compliance,and nursing satisfaction of patients in the two groups were observed.Results:There was no statistical significance in the basic information of the two groups of patients(P>0.05);after the intervention,the fasting plasma glucose,2-hour postprandial blood glucose,and HbA1c of the patients in the observation group were lower than those of the control group(P<0.001);after the intervention,the self-efficacy scores of the patients in the two groups increased,and the scores of the observation group were significantly higher than those of the control group(P<0.001);the total adherence rate of the patients in the observation group(90/95.75%)was significantly higher than that of the control group(80/90.10%)(χ^(2)=6.144,P<0.05);and the total satisfaction rate of patients in the observation group(92/97.87%)was significantly higher than that of the control group(78/82.98%)(χ^(2)=12.042,P<0.05).Conclusion:In patients with brittle diabetes mellitus,structured healthcare education can effectively control patients’blood glucose levels,improve patients’self-efficacy and adherence,and enhance patient satisfaction.

DUCTILEBRITTLETRANSITION OF POLYCRYSTALLINE Ni_3Al WITH VARYING GRAIN SIZE

It is known that in B (un)doped Ni 3Al polycrystals, the dependence of yield strength on grain size follows the Hall Petch relationship: σ y= σ 0+ K y d -1/2 , and the slope K y can be reduced by B doping owing to the lowering of grain boundary resistance to slip transmission. If the intergranular cracking in polycrystalline Ni 3Al occurs from the microcavity along the grain boundaries, the effective external tensile stress for the propagation of the crack like microcavity along the grain boundaries can be deduced as: σ f= σ i+ K u d -1/2 , where K u reflects the effects of such factors as environment, strain rate, boron doping and the orientation of the grain boundary on the trend of intergranular cracking. For loaded polycrystalline Ni 3Al, it should be competitive between the intergranular cracking and slip transmission across the grain boundary. Therefore, comparing the varieties of both σ y and σ f with grain size, the dependence of ductile brittle transition on grain size, and the effects of the above factors on ductile brittle transition can be expected. The model also predicts that there exists a critical grain size for the ductile brittle transition of polycrystalline Ni 3Al alloys, and B doping can increase the critical grain size due to the reduction of the slope K y and the increase of K u. The reported experimental results verified the above model.

Geochronology Constraints on Transformation Age from Ductile to Brittle Deformation of the Shangma Fault and Its Tectonic Significance,Dabieshan,Central China

By a detailed investigation of geometry and kinematics of the Shangma （商麻） fault in Dabieshan （大别山）, three different crust levels of extension movement have been recognized in sequence from the deep to the shallow：① low-angle ductile detachment shearing with top to the NW; ② low-angle normal fault with top to the NW or NWW in brittle or brittle-ductile transition domain; ③ high-angle brittle normal fault with top to the W or NWW. Two samples were chosen for zircon U-Pb age dating to constrain the activity age of the Shangma fault. A bedding intrusive granitoid pegmatite vein that is parallel to the foliation of the low-angle ductile detachment shear zone of the country rock exhibits a lotus-joint type of boudinage deformation, showing syn-tectonic emplacing at the end of the ductile deformation period and deformation in the brittle-ductile transition domain. The zircon U-Pb dating of this granitoid pegmatite vein gives an age of （125.9±4.2） Ma, which expresses the extension in the brittle-ductile transition domain of the Shangma fault. The other sample, which is collected from a granite pluton cutting the foliation of the low-angle ductile detachment shear zone, gives a zircon U-Pb age of （118.8±4.1） Ma, constraining the end of the ductile detachment shearing. Then the transformation age from ductile to brittle deformation can be constrained between 126-119 Ma. Combined with the previous researches, the formation of the Luotian （罗田） dome, which is locatedto the east of the Shangma fault, can be constrained during 150-126 Ma. This study gives a new time constraint to the evolution of the Dabie orogenic belt.

Burial depth interval of the shale brittle–ductile transition zone and its implications in shale gas exploration and production

Brittleness and ductility of shale are closely related to shale gas exploration and production. How to predict brittleness and ductility of shale is one of the key issues in the study of shale gas preservation and hydraulic fracturing treatments. The magnitude of shale brittleness was often determined by brittle mineral content(for example, quartz and feldspars) in shale gas exploration.However, the shale brittleness is also controlled by burial depth. Shale brittle/ductile properties such as brittle, semibrittle and ductile can mutually transform with burial depth variation. We established a work flow of determining the burial depth interval of brittle–ductile transition zone for a given shale. Two boundaries were employed to divide the burial depth interval of shale brittle/ductile properties. One is the bottom boundary of the brittle zone(BZ), and the other is the top boundary of the ductile zone(DZ). The brittle–ductile transition zone(BDTZ) is between them.The bottom boundary of BZ was determined by the overconsolidation ratio(OCR) threshold value combined with pre-consolidation stress which the shale experienced over geological time. The top boundary of DZ was determined based on the critical confining pressure of brittle–ductile transition. The OCR threshold value and the critical confining pressure were obtained from uniaxial strain andtriaxial compression tests. The BZ, DZ and BDTZ of the Lower Silurian Longmaxi shale in some representative shale gas exploration wells in eastern Sichuan and western Hubei areas were determined according to the above work flow. The results show that the BZ varies with the maximum burial depth and the DZ varies with the density of the overlying rocks except for the critical confining pressure.Moreover, the BDTZ determined by the above work flow is probably the best burial depth interval for marine shale gas exploration and production in Southern China. Shale located in the BDTZ is semi-brittle and is not prone to be severely naturally fractured but likely to respond well to hydraulic fracturing. The depth interval of BDTZ determined by our work flow could be a valuable parameter of shale gas estimation in geology and engineering.

PROBABILISTIC MODELING OF BRITTLE FRACTURE WITH PRIOR DUCTILE CRACK EXTENSION

A computation framework for brittle fracture which incorporates weakest link statistics and a microme- chanics model reflecting reflecting local damage of the material is described.The Weibull stress W emerges as a probabilistic fracture parameter to define the condition leading material failure. Unstable crack propa- gation occurs at a critical value of W which may be attained paior to or following some amount of duc- tile crack extension. A realistic model of ductile crack growth using the computation cell methodology is used to define the evolution of near tip stress fields during crack extension. An application of proposed framework to predict the measured geometry and ductile tearing effects on the statistical distributio of fracture toughness for the pipe line steel welded joint is described.

Mechanism of brittle-ductile transition of a glass-ceramic rigid substrate

The hardness, elastic modulus, and scratch resistance of a glass-ceramic rigid substrate were measured by nanoindentation and nanoscratch, and the fracture toughness was measured by indentation using a Vickers indenter. The results show that the hardness and elastic modulus at a peak indentation depth of 200 nm are 9.04 and 94.70 GPa, respectively. These values reflect the properties of the glass-ceramic rigid substrate. The fracture toughness value of the glass-ceramic rigid substrate is 2.63 MPa？m1/2. The material removal mechanisms are seen to be directly related to normal force on the tip. The critical load and scratch depth estimated from the scratch depth profile after scratching and the friction profile are 268.60 mN and 335.10 nm, respectively. If the load and scratch depth are under the critical values, the glass-ceramic rigid substrate will undergo plastic flow rather than fracture. The formula of critical depth of cut described by Bifnao et al. is modified based on the difference of critical scratch depth

Towards understanding the brittle–ductile transition in the extreme manufacturing

The brittle–ductile transition(BDT) widely exists in the manufacturing with extremely small deformation scale, thermally assisted machining, and high-speed machining. This paper reviews the BDT in extreme manufacturing. The factors affecting the BDT in extreme manufacturing are analyzed, including the deformation scale and deformation temperature induced brittle-to-ductile transition, and the reverse transition induced by grain size and strain rate. A discussion is arranged to explore the mechanisms of BDT and how to improve the machinability based on the BDT. It is proposed that the mutual transition between brittleness and ductility results from the competition between the occurrence of plastic deformation and the propagation of cracks. The brittleness or ductility of machined material should benefit a specific manufacturing process, which can be regulated by the deformation scale, deformation temperature and machining speed.

Anisotropic brittle-ductile transition of monocrystalline sapphire during orthogonal cutting and nanoindentation experiments

Single-crystal sapphire is utilized as a high-performance engineering material,especially in extreme and harsh environments.However,due to its extreme hardness and brittleness,the machinability of sapphire is still a challenge.By means of nanoindentation and plunge-cut experiments,the anisotropic brittle-ductile transition of the prismatic M-plane and rhombohedral R-plane is examined by analyzing crack morphologies and the critical depth-of-cut(CDC).The experimental results of the nanoindentation tests are correlated to the plunge-cut experiment.Both the prism plane and the rhombohedral crystal plane exhibit a two-fold symmetry of ductility with various crack patterns along the machined grooves.The direction-dependent plasticity of the hexagonal sapphire crystal is mainly connected to a twinning process accompanied by slip dislocation.

Effect of quenching process on mechanical properties and ductile-brittle transition behavior of 28CrMnMoV steel

Effect of quenching process on the microstructure and mechanical properties of a kind of seamless tubes of steel 28CrMnMoV was investigated.Then,an investigation on the influence of two different quenching processes on the ductile-brittle transition behavior of this steel was undertaken.The ductile-brittle transition temperatures of the steel by two different quenching processes were also determined.The results show that a good combination of mechanical properties can be obtained through austenitizing experimental steel at 800 ℃ or 890 ℃ followed by tempering at 630 ℃.Ductile-to-brittle transition temperature of 28CrMnMoV steel austenitized at 800 ℃ followed by tempering at 640 ℃ is about 73 ℃,which is much lower than the value 37 ℃ when the steel was austenitized at 890℃ and then tempered at 650 ℃.This indicates that subcritical quenching process could decrease largely the ductile-to-brittle transition temperature of 28CrMnMoV steel.

Effect of Graphite Nodule Diameter on Water Embrittlement of Austempered Ductile Iron

Effects of graphite nodule diameter on the water embrittlement of austempered ductile iron (ADI) is studied. The water embrittlement mechanism is discussed. Due to water adhesion, local embrittlement occurs on the surface of ADI specimen, resulting in early fracture and significant reduction in tensile strength and elongation. The water embrittlement is the cracking of stress induced martensite formed during tensile deformation caused by hydrogen diffusion decomposed from water and as a result tensile strength and elongation of ADI are remarkably reduced. The segregation of alloying elements in ductile iron is weakened with decreasing nodule diameter, reducing the residual austenite in grain boundaries, then decreasing the amount of stress induced martensite during tensile plastic deformation and finally restraining ADI water embrittlement.

INVESTIGATION OF HYDROGEN INDUCED DUCTILE BRITTLE TRANSITION IN 7175 ALUMINUM ALLOY

Effects of hydrogen on the mechanical properties of differently aged 7175 aluminum alloys were investigated by using cathodic H-permeation, slow strain rate tension and so on. The results indicate that both the yield stress and the percentage reduction of area decrease with increasing hydrogen charging time, and the degree of reduction decreases as aging time increases for the same hydrogen charging time.

BRITTLE-DUCTILE TRANSITION OF PP/EPDM/ELASTOMERIC NANO-PARTICLE TERNARY BLENDS

The brittle-ductile transition is a very important phenomenon for polymer toughening. Polypropylene （PP） is often toughened by using rubbers, e.g., ethylene-propylene diene monomer （EPDM） has often been used as a modifier. In this article, the toughening of PP by using a new kind of rubber, known as elastomeric nano-particle （ENP）, and the brittleductile transition of PP/EPDM/ENP was studied. Compared to PP/EPDM binary blends, the brittle-ductile transition of PP/EPDM/ENP ternary blends occurred at lower EPDM contents. SEM experiment was carried out to investigate the etched and impact-fractured surfaces. ENP alone had no effect on the impact strength of PP, however, with the same EPDM content, PP/EPDM/ENP ternary blends had smaller particle size, better dispersion and smaller interparticle distance in contrary to PP/EPDM binary blends, which promoted the brittle-ductile transition to occur earlier.

Understanding ductile-to-brittle transition of metallic glasses from shear transformation zone dilatation

A theoretical model that takes into account the flee-volume aided cooperative shearing of shear transformation zones （STZs） is developed to quantitatively understand the ductile-to-brittle transition （DBT） of metallic glasses. The STZ dilatational strain is defined as the ratio of STZ-activated free volume to STZ volume itself. The model demonstrates that the STZ dilatational strain will increase drastically and exceed the characteristic shear strain of STZ as temperature decreases below a critical value. This critical temperature is in good agreement with the experimentally measured DBT temperature. Our results suggest that the DBT of metallic glasses is underpinned by the transition of atomic-cluster motions from STZ-tvpe rearrangements to dilatational processes （termed tension transformation zones （TrZs））.

Fine-tuning the ductile-brittle transition temperature of Mg_2Si intermetallic compound via Al doping

Brittleness is a dominant issue that restricts potential applications of Mg_2Si intermetallic compounds(IMC). In this paper, guided by first-principles calculations, we found that Al doping will enhance the ductility of Mg_2Si. The underlying mechanism is that Al doping could reduce the electronic exchange effect between Mg and Si atoms, and increase the volume module/shear modulus ratio, both of which are beneficial to the deformation capability of Mg_2Si. Experimental investigations were then carried out to verify the calculation results with Al doping contents ranging from Al-free to 10 wt%. Results showed that the obtained ductile-brittle transition temperature of the Mg_2Si–Al alloy decreased and the corresponding ductility increased. Specifically, the ductile-brittle transition temperature could be reduced by about 100℃. When the content of Al reached 6 wt%, α-Al phase started to precipitate, and the ductile-brittle transition temperature of the alloy no longer decreased.