Hydraulic fracturing behaviors of shale under coupled stress and temperature conditions simulating different burial depths

Fracture propagation in shale under in situ conditions is a critical but poorly understood mechanical process in hydraulic fracturing for deep shale gas reservoirs. To address this, hydraulic fracturing experiments were conducted on hollow double-wing crack specimens of the Longmaxi shale under conditions simulating the ground surface(confining pressure σ_(cp)=0, room temperature(Tr)) and at depths of 1600 m(σ_(cp)=40 MPa, Ti=70 ℃) and 3300 m(σ_(cp)=80 MPa, high temperature Ti=110 ℃) in the study area.High in situ stress was found to significantly increase fracture toughness through constrained microcracking and particle frictional bridging mechanisms. Increasing the temperature enhances rather than weakens the fracture resistance because it increases the grain debonding length, which dissipates more plastic energy and enlarges grains to close microdefects and generate compressive stress to inhibit microcracking. Interestingly, the fracture toughness anisotropy in the shale was found to be nearly constant across burial depths, despite reported variations with increasing confining pressure. Heated water was not found to be as important as the in situ environment in influencing shale fracture. These findings emphasize the need to test the fracture toughness of deep shales under coupled in situ stress and temperature conditions rather than focusing on either in situ stress or temperature alone.

A modified 3D mean strain energy density criterion for predicting shale mixed-mode Ⅰ/Ⅲ fracture toughness

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a significant role in fracture mechanics and hydraulic fracturing.The edge-notched disk bending(ENDB)specimens are employed to measure the entire range of mixed-modeⅠ/Ⅲfracture toughness of Longmaxi shale.To theoretically interpret the fracture mechanisms,this research first introduces the detailed derivations of three established fracture criteria.By distinguishing the volumetric and distortional strain energy densities,an improved three-dimensional mean strain energy density(MSED)criterion is proposed.As the critical volumetric to distortional MSED ratio decreases,the transition from tensiondominated fracture to shear-dominated fracture is observed.Our results indicate that both peak load and applied energy increase significantly with the transition from pure mode I(i.e.,tension)to pure modeⅢ(i.e.,torsion or tearing)since mode-Ⅲcracking happens in a twisted manner and mode-Ⅰcracking occurs in a coplanar manner.The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing.The average ratio of pure mode-Ⅲfracture toughness to pure mode-Ⅰfracture toughness is 0.68,indicating that the obtained mode-Ⅲfracture resistance for a tensionbased loading system is apparent rather than true.Compared to the three mainstream fracture criteria,the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-modeⅠ/Ⅲfracture toughness of distinct materials and loading methods.

Effects of multimodal microstructure on fracture toughness and its anisotropy of LPSO-type extruded Mg-1Zn-2Y alloys

The fracture toughness of extruded Mg-1Zn-2Y(at.%)alloys,featuring a multimodal microstructure containing fine dynamically recrystallized(DRXed)grains with random crystallographic orientation and coarse-worked grains with a strong fiber texture,was investigated.The DRXed grains comprised randomly oriented equiaxedα-Mg grains.In contrast,the worked grains includedα-Mg and long-period stacking ordered(LPSO)phases that extended in the extrusion direction(ED).Both types displayed a strong texture,aligning the(10.10)direction parallel to the ED.The volume fractions of the DRXed and worked grains were controlled by adjusting the extrusion temperature.In the longitudinal-transverse(L-T)orientation,where the loading direction was aligned parallel to the ED,there was a tendency for the conditional fracture toughness,KQ,tended to increase as the volume fraction of the worked grains increased.However,the KQ values in the T-L orientation,where the loading direction was perpendicular to the ED,decreased with an increase in the volume fraction of the worked grains.This suggests strong anisotropy in the fracture toughness of the specimen with a high volume fraction of the worked grains,relative to the test direction.The worked grains,which included the LPSO phase and were elongated perpendicular to the initial crack plane,suppressed the straight crack extension,causing crack deflection,and generating secondary cracks.Thus,these worked grains significantly contributed to the fracture toughness of the extruded Mg-1Zn-2Y alloys in the L-T orientation.

Effect of heat treatment on stress corrosion cracking, fracture toughness and strength of 7085 aluminum alloy

The influences of heat treatment on stress corrosion cracking （SCC）, fracture toughness and strength of 7085 aluminum alloy were investigated by slow strain rate testing, Kahn tear testing combined with scanning electron microscopy （SEM） and transmission electron microscopy （TEM）. The results show that the fracture toughness of T74 overaging is increased by 22.9% at the expense of 13.6% strength, and retrogression and reaging （RRA） enhances fracture toughness 14.2% without reducing the strength compared with T6 temper. The fracture toughness of dual-retrogression and reaging （DRRA） is equivalent to that of T74 with an increased strength of 14.6%. The SCC resistance increases in the order： T6〈RRA〈DRRA≈T74. The differences of fracture toughness and SCC were explained on the basis of the role of matrix precipitates and grain boundary orecioitates.

Microstructure and fracture toughness of a TiAl-Nb composite consolidated by spark plasma sintering

A TiAl-Nb composite was prepared by spark plasma sintering （SPS） at 1250 °C and 50 MPa for 5 min from prealloyed TiAl powder and elemental Nb powder in a molar ratio of 9：1 for improving the fracture toughness of TiAl alloy at room temperature. The microstructure, phase constitute, fracture surface and fracture toughness were determined by X-ray diffractometry, electron probe micro-analysis, scanning and transmission electron microscopy and mechanical testing. The results show that the sintered samples mainly consist of γ phase, O phase, niobium solid solution （Nbss） phase and B2 phase. The fracture toughness is as high as 28.7 MPa？m1/2 at room temperature. The ductile Nbss phase plays an important role in absorbing the fracture energy in front of the cracks. Moreover, B2 phase can branch the propagation of the cracks. The microhardness of each phase of the composite was also tested.

INTERLAMINAR FRACTURE TOUGHNESS OF MULTI-DIRECTIONAL LAMINATES

Based on the conventional compliance and area methods, a high precision method named the angle method is presented in this work. The interlaminar fracture toughness is determined by measurement of the load and the bending angle at the loading point without measurement of the crack length, and the improvement of the conventional compliance method is made, which is more precise and can be used to general DCB specimen with unequal flexural stiffness of the cantilevers. The interlaminar fracture toughness in 0/ θ(θ =0°,30°,60°,90°) interfaces of two epoxy composites, one being the carbon fibre reinforced brittle matrix T300/4211, the other the carbon fibre reinforced tough matrix T300/3261, is measured by both compliance and angle methods, and the relationship between fracture toughness and the ply angle θ is obtained. It is found that the interlaminar fracture toughness is correlated with the type of matrix and the ply angles near the crack front.

Microstructure-fracture toughness relationships and toughening mechanism of TC21 titanium alloy with lamellar microstructure

The independent influence of microstructural features on fracture toughness of TC21alloy with lamellar microstructure was investigated.Triple heat treatments were designed to obtain lamellar microstructures with different parameters,which were characterized by OM and SEM.The size and content ofαplates were mainly determined by cooling rate from singleβphase field and solution temperature in two-phase field;while the precipitation behavior of secondaryαplatelets was dominantly controlled by aging temperature in two-phase field.The content and thickness ofαplates and the thickness of secondaryαplatelets were important microstructural features influencing the fracture toughness.Both increasing the content ofαplates and thickeningαplates(or secondaryαplatelets)could enhance the fracture toughness of TC21alloy.Based on energy consumption by the plastic zone of crack tip inαplates,a toughening mechanism for titanium alloys was proposed.

Improvement of Toughness of Ultrahigh Strength Steel Aermet 100

The influence of double aging on the microstructure and mechanical properties of ultrahigh strength steel Aermet 100 was analyzed. Under the double aging, there is no apparent decrease in the strength of steel. However, the impact fatigue life can be prolonged by 35.5% and dynamic fracture toughness be raised by 22.6% respectively, as compared with the normal aging. Based on the observation of microscopic structure, the physical mechanism of the prolongation of impact fatigue life and the enhancement of stability of the reverted austenite, AR, is analyzed further. The results show that this new technique is a breakthrough of combination optimization between strength and toughness for Aermet 100 steel. In the light of the current understanding on this subject, the volume fracture of soften and tough AR formed in process of heat preservation at higher temperature of double aging increases drastically. Moreover, during the treatment of lower temperature of double aging, the carbon separating from the martensitic ferrite will diffuse into AR, resulting that the martensitic brittleness decreases and the stability of AR increases.

Effects of Microstructure on the Tensile, Fracture Toughness and Fatigue Behaviour of Gamma Titanium Aluminides

The effects of microstructure on the deformation and fracture behaviour of two-phase TiAl alloys were investjgated under monotonic and cyclical loading conditions, over a range of temperatu res.The tensile behaviour is analyzed for deformation temperatures between RT and 950℃, Fracture resistance behaviour and toughening mechanisms at RT and 800℃ are analyzed. and the inverse relationship botween ductility and toughness is explained using the crack initiation toughness. The preliminary results of load-controlled fatigue behaviour at 800℃ are interpreted using the tensile behaviour because deformation structure and fracture modes are similar under these two loading conditions

3D Lamellar-Structured Graphene Aerogels for Thermal Interface Composites with High Through-Plane Thermal Conductivity and Fracture Toughness

Although thermally conductive graphene sheets are efficient in enhancing in-plane thermal conductivities of polymers,the resulting nanocomposites usually exhibit low through-plane thermal conductivities,limiting their application as thermal interface materials.Herein,lamellarstructured polyamic acid salt/graphene oxide(PAAS/GO)hybrid aerogels are constructed by bidirectional freezing of PAAS/GO suspension followed by lyophilization.Subsequently,PAAS monomers are polymerized to polyimide(PI),while GO is converted to thermally reduced graphene oxide(RGO)during thermal annealing at 300℃.Final graphitization at 2800℃ converts PI to graphitized carbon with the inductive effect of RGO,and simultaneously,RGO is thermally reduced and healed to high-quality graphene.Consequently,lamellar-structured graphene aerogels with superior through-plane thermal conduction capacity are fabricated for the first time,and its superior through-plane thermal conduction capacity results from its vertically aligned and closely stacked high-quality graphene lamellae.After vacuum-assisted impregnation with epoxy,the resultant epoxy composite with 2.30 vol% of graphene exhibits an outstanding through-plane thermal conductivity of as high as 20.0 W m^−1 K^−1,100 times of that of epoxy,with a record-high specific thermal conductivity enhancement of 4310%.Furthermore,the lamellar-structured graphene aerogel endows epoxy with a high fracture toughness,~1.71 times of that of epoxy.

Effects of precipitates and inclusions on the fracture toughness of hot rolling X70 pipeline steel plates

In order to investigate the fracture toughness, crack tip opening displacement （CTOD） experiments were conducted on two X70 pipeline steel plates with different rolling processes. Atter the experiments, optical microscopy （OM）, scanning electron microscopy （SEM） and transmission electron microscopy （TEM） were employed to observe the microstructure and fracture morphology. The effects of precipi- tates on the fracture toughness and the crack initiation mechanism induced by inclusions were analyzed. The CTOD result shows that the steel with a lower finishing cooling temperature has a higher fracture toughness. Inchisiom with different shapes and two kinds of precipi- tates with different sizes were observed. It can be concluded that precipitates with different sizes have different effects and mechanisms on the fracture toughness. Distinguished fi＇om the earlier researches, inclusions enriched in silicon can be also served as the crack initiation.

Mechanical properties and fracture toughness of rail steels and thermite welds at low temperature

Brittle fracture occurs frequently in rails and thermite welded joints, which intimidates the security and reliability of railway ser- vice. Railways in cold regions, such as Qinghai-Tibet Railway, make the problem of brittle fi＇acture in rails even worse. A series of tests such as uniaxial tensile tests, Charpy impact tests, and three-point bending tests were carried out at low temperature to investigate the mechanical properties and fracture toughness of U71Mn and U75V rail steels and their thermite welds. Fracture micromechanisms were analyzed by scanning electron microscopy （SEM） on the fracture surfaces of the tested specimens. The ductility indices （percentage elongation aider frac- ture and percentage reduction of area） and the toughness indices （Charpy impact energy Ak and plane-strain fracture toughness Kic） of the two kinds of rail steels and the corresponding thermite welds all decrease as the temperature decreases. The thermite welds are more critical to fracture than the rail steel base metals, as indicated by a higher yield-to-ultimate ratio and a much lower Charpy impact energy. U71Mn rail steel is relatively higher in toughness than U75V, as demonstrated by larger Ak and Klc values. Therefore, U71Mn rail steel and the corresponding thermite weld are recommended in railway construction and maintenance in cold regions.

Test of subcritical crack growth and fracture toughness under water-rock interaction in three types of rocks

The subcritical crack growth and fracture toughness in peridotite, lherzolite and amphibolite were investigated with double torsion test. The results show that water-rock interaction has a significant influence on subcritical crack growth. With water-rock interaction, the crack velocity increases, while the stress intensity factor declines, which illustrates that water-rock interaction can decrease the strength of rocks and accelerate the subcritical crack growth. Based on Charlse theory and Hilling & Charlse theory, the test data were analyzed by regression and the correlation coefficients were all higher than 0.7, which shows the correlation is significant. This illustrates that both theories can explain the results of tests very well. Therefore, it is believed that the subcritical crack growth attributes to the breaking of chemical bond, which is caused by the combined effect of the tensile stress and the chemical reaction between the material at crack tip and the corrosive agent. Meanwhile, water-rock interaction has a vital effect on fracture toughness. The fracture toughness of samples under atmospheric environment is higher than that of samples immersed in water. And water-rock interaction has larger influence on fracture toughness in amphibolite than that in peridotite and lherzolite.

Effect of Aging on Fracture Toughness and Stress Corrosion Cracking Resistance of Forged 7475 Aluminum Alloy

The effects of two-stage aging and retrogression and reaging heat treatment on the fracture toughness and stress corrosion cracking resistance of 7475 alloy were studied. The fracture toughness, conductivity and strength of samples of nine groups under duplex aging conditions and three retrogression and reaging heat treatments were also measured. Incorporating the microstructure and property, we found that when the condition of the first order aging kept identical, the fracture toughness and stress corrosion cracking resistance increase with aging time and the second aging temperature. The optimal treatment conditions are （ 115℃×7h ＋ 185 ℃×13h） among all tested two-stage aging treatments. Although the 7475 alloy treated by RRA method shows the highest strength and its stress corrosion cracking resistance after twenty minutes retrogression can also reach the same level as those by the optimal treatment of （115℃×7h＋ 185℃×13h ）, the fracture toughness is even low.

Fatigue Crack Growth Rate of Ti-6Al-4V Considering the Effects of Fracture Toughness and Crack Closure

Fatigue fracture is one of the main failure modes of Ti-6A1-4V alloy,fracture toughness and crack closure have strong effects on the fatigue crack growth（FCG）rate of Ti-6A1-4V alloy.The FCG rate of Ti-6A1-4V is investigated by using experimental and analytical methods.The effects of stress ratio,crack closure and fracture toughness on the FCG rate are studied and discussed.A modified prediction model of the FCG rate is proposed,and the relationship between the fracture toughness and the stress intensity factor（SIF）range is redefined by introducing a correcting coefficient.Notched plate fatigue tests（including the fracture toughness test and the FCG rate test）are conducted to investigate the influence of affecting factors on the FCG rate.Comparisons between the predicted results of the proposed model,the Paris model,the Walker model,the Sadananda model,and the experimental data show that the proposed model gives the best agreement with the test data particularly in the near-threshold region and the Paris region,and the corresponding calculated fatigue life is also accurate in the same regions.By considering the effects of fracture toughness and crack closure,the novel FCG rate prediction model not only improves the estimating accuracy,but also extends the adaptability of the FCG rate prediction model in engineering.

Improvement of Fracture Toughness Lanthanum Zirconate

La2Zr2O7 （LZ） is a promising thermal barrier coating material for the high temperature applications. The fracture toughness and microhardness of nanocrystalline LZ （n-LZ）, microcrystalline LZ （m-LZ） and LZ-5mol%8YSZ （LZ-5-8YSZ） composite （8YSZ for zirconia stabilized by 8 mol% ytrria） were studied. The n-LZ had a thermal expansion coefficient of （9.6±0.4）×10 -6 K -1 （200～1000℃） and fracture toughness of （1.98±0.07） MPa·m 1/2 which are obviously higher than those of the m-LZ （ （9.1±0.4）×10 -6 K -1 and （1.40±0.23） MPa·m 1/2, respectively）, indicating that nanofication was an efficient way to increase the toughness and thermal expansion coefficient of LZ. The composite LZ-5-8YSZ had a higher fracture toughness （（1.88±0.30） MPa·m 1/2） than LZ, which was close to that of 8YSZ densified by superhigh pressure （SHP）.

Fracture Toughness Properties of Three Different Biomaterials Measured by Nanoindentation

The fracture toughness of hard biomaterials, such as nacre, bovine hoof wall and beetle cuticle, is associated with fibrous or lamellar structures that deflect or stop growing cracks. Their hardness and reduced modulus were measured by using a nanoindenter in this paper. Micro/nanoscale cracks were generated by nanoindentation using a Berkovich tip. Nanoindentation of nacre and bovine hoof wall resulted in pile-up around the indent. It was found that the fracture toughness （Kc） of bovine hoof wall is the maximum, the second is nacre, and the elytra cuticle of dung beetle is the least one.

Dynamic fracture toughness of TA15ELI alloy studied by instrumented impact test

The dynamic fracture toughness of TA15ELI alloy with two types of microstructures was studied by instrumented impact test.Charpy specimens with both the 0.2 mm U-notch and the a/W = 0.2 pre-crack were adopted to compare notch sensitivity in the two microstructures.The result shows that the specimen with Widmanst？tten microstructure exhibits a better dynamic fracture toughness and lower notch sensitivity than that with lath-like microstructure.Fracture surfaces in the case of the two microstructures are analyzed to have a ductile and brittle mixed feature under dynamic loading.The fracture surface of lath-like microstructure is composed of dimples and tear ridges,while that of Widmanst？tten microstructure is covered with rough block-like facets and dimples and tear ridges.The α phase boundaries and α/β interfaces act as locations for void nucleation and crack arrest and deviation.The decrease in width of α phase lamellae leads to the increase in the amount of boundaries and interfaces,which causes the increase in the consumption of impact energy and results in the improvement in dynamic fracture toughness.

A NOVEL METHOD FOR MEASURING AND CHARACTERIZING DYNAMIC FRACTURE-INITIATION TOUGHNESS OF ELASTIC-PLASTIC MATERIALS

The characterization and testing methods of the dynamic fractureinitiation toughness of elas- tic-plastic materials under tensileimpact are studied. By using the self-designed bar-bar tensile impactappa- ratus, a novel test method for studying dynamicfracture-initiation ahs been proposed based on the one-di- mensionaltest principle. The curve of average load v. s. displacement (P-δ)is smooth until unstable crack propagation, and the kinetic energywhich does not contribute to the crack growth can be removed fromtotal work done by external-force to the specimen.

Correlating mode-I fracture toughness and mechanical properties of heat-treated crystalline rocks

For the effect of thermal treatment on the mode-I fracture toughness(FT), three crystalline rocks(two basalts and one tonalite) were experimentally investigated. Semi-circular bend specimens of the rocks were prepared following the method suggested by the International Society for Rock Mechanics(ISRM)and were treated at various temperatures ranging from room temperature(25 ℃) to 600 ℃. Mode-I FT was correlated with tensile strength(TS), ultrasonic velocities, and Young’s modulus(YM). Additionally,petrographic and X-ray diffraction analyses were carried out to find the chemical changes resulting from the heat treatment. Further, scanning electron microscopy(SEM) was conducted to observe the micro structural changes when subjected to high temperatures. These experiments demonstrate that heat treatment has a strong negative impact on the FT and mechanical properties of the rocks. From room temperature to 600 ℃, mode-I FT values of massive basalt, giant plagioclase basalt, and tonalite were reduced by nearly 52%, 68%, and 64%, respectively. Also, at all temperature levels, FT and mechanical properties are found to be exponentially correlated. However, the exact nature of the relationship mainly depends on rock type. Besides, TS was found to be a better indicator of degradation degree than the mode-I FT. SEM images show that micro crack density and structural disintegration of the mineral grains increase with temperature. These physical changes confirm the observed reduction in the stiffness of heat-treated crystalline rocks.