RANDOM-FUZZY MODEL FOR THE DUCTILE/BRITTLE TRANSITION

Based on a large experimental sample, the influence of stress triaxiality and temperature have been studied on the growth of micro voids and the ductile/brittle transition (DBT) of 40Cr steel. Ductile and brittle fractures have been investigated simultaneously. The experiments show that the ductile fracture is controlled by the micro void mechanism,and the critical void growth ratio can be used as the criterion of ductile fracture. The brittle fracture is modeled by an embedded penny crack, and a micro stress intensity with a characteristic length can be used as the criterion of the brittle fracture. The DBT is the result of the competition of the two mechanisms. Which exists in the fracture of all specimens simultaneously. The distributions of model parameters were measured experimentally. A random model and a random-fuzzy model for DBT were presented. The comparison between the calculated and experimental results shows that the random-fuzzy model can model the DBT satisfactorily.

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.

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.

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.

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.

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.

CRACK TIP STRUCTURE AND DUCTILE-BRITTLE TRANSITION IN BULK SINGLE CRYSTALS

Based on the crack tip structure a new model of ductile -brittle transition was proposed. Using this new model we calculated the dependence of the transition temperature-strain rate over a wide range of strain rate. Finally the significance of this new model is discussed in detail.

EFFECTS OF INTERPARTICLE DISTANCE,TEMPERATURE AND INTERFACIAL ADHESION ON BRITTLE-DUCTILE TRANSITION FOR NYLON 6/ABS BLENDS

The toughness of blends composed of nylon 6 and acrylonitrile-butadiene-styrene(ABS) compatibilized by using styrene-maleic anhydride(SMA) as a compatibilizer was measured over a wide temperature region.Results reveal that the combining effects of particle size and volume fraction of ABS on the toughness of nylon 6/ABS/SMA blends can be described through plotting brittle-ductile transition of the impact strength versus the interparticle distance(ID) on the assumption that ABS domains relieve the triaxial te...

BRITTLE-DUCTILE TRANSITION OF POLYMERS AND ITS PERCOLATION MODEL

The brittle-ductile transition (BDT) of particlc toughened polymers was extensively studied in terms ofmorphology, strain rate, and temperature. The calculation results showed that both the critical interparticle distance (ID_c) andthe brittle-ductile transition temperature (T_(BD)) of polymers were a function of strain rate. The ID_c reduced nonlinearly withincreasing strain rate, whereas T_(BD) increased considerably with increasing strain rate. The effects of temperature andplasticizer concentration on BDT were discussed using a percolation model. The results were in agreement with theexperiments.

EFFECT OF LOADING RATE AND TEMPERATURE ON DUCTILE-BRITTLE TRANSITION OF A CARBON STEEL

The dynamic fracture toughness of a mild steel has been studied at different loading rates and temperatures.The material exhibits a transition from tough to brittle fracture with the chang- ing loading rate alone.Analysis of the fracture process by the theory of thermal activation suggests that the fracture activation energy approximates to the bond energy of the{100}of a unit cell.The toughness can be resolved into two parts,J-(fd)=J_a+J_l,where J_a is the athermal part,being independent on temperature and loading rate,while J_l=(K/K_o)^(1/n)exp(Q_f/nkT),which controls the fracture process is temperature and load- ing rate dependent.The transition of fracture mechanism caused by both temperature and loading rate is associated with the thermal movement of atoms.

The Ductile to Brittle Transition Behavior of the Modified 9Cr-1Mo Steel and Its Laser Welds

The ductile to brittle transition temperature (DBTT) of the modified 9Cr-1Mo steel and its laser welds was studied. The increase in grain size of the weld structure ascended the DBTT of the steel significantly. The transformation of retained austenite at martensite interlath boundaries into untempered and/or twinned martensite could also contribute to increased DBTTs of the steel and its welds tempered at 540℃.

A statistical damage-based constitutive model for shearing of rock joints in brittle drop mode

Some rock joints exhibit significant brittleness,characterized by a sharp decrease in shear stress upon reaching the peak strength.However,existing models often fail to accurately represent this behavior and are encumbered by numerous parameters lacking clear mechanical significance.This study presents a new statistical damage constitutive model rooted in both damage mechanics and statistics,containing only three model parameters.The proposed model encompasses all stages of joint shearing,including the compaction stage,linear stage,plastic yielding stage,drop stage,strain softening stage,and residual strength stage.To derive the analytical expression of the constitutive model,three boundary conditions are introduced.Experimental data from both natural and artificial rock joints is utilized to validate the model,resulting in average absolute relative errors ranging from 3%to 8%.Moreover,a comparative analysis with established models illustrates that the proposed model captures stress drop and post-peak strain softening more effectively,with model parameters possessing clearer mechanical interpretations.Furthermore,parameter analysis is conducted to investigate the impacts of model parameters on the curves and unveil the relationship between these parameters and the mechanical properties of rock joints.Importantly,the proposed model is straightforward in form,and all model parameters can be obtained from direct shear tests,thus facilitating the utilization in numerical simulations.