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 the10.10direction 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.

Effects of microstructure characteristics on the tensile properties and fracture toughness of TA15 alloy fabricated by hot isostatic pressing

Powder hot isostatic pressing(HIP) is an effective method to achieve near-net-shape manufacturing of high-quality complex thinwalled titanium alloy parts, and it has received extensive attention in recent years. However, there are few reports about the microstructure characteristics on the strengthening and toughening mechanisms of powder hot isostatic pressed(HIPed) titanium alloys. Therefore, TA15powder was prepared into alloy by HIP approach, which was used to explore the microstructure characteristics at different HIP temperatures and the corresponding tensile properties and fracture toughness. Results show that the fabricated alloy has a “basket-like structure” when the HIP temperature is below 950℃, consisting of lath clusters and surrounding small equiaxed grains belts. When the HIP temperature is higher than 950℃, the microstructure gradually transforms into the Widmanstatten structure, accompanied by a significant increase in grain size. The tensile strength and elongation are reduced from 948 MPa and 17.3% for the 910℃ specimen to 861 MPa and 10% for the 970℃ specimen.The corresponding tensile fracture mode changes from transcrystalline plastic fracture to mixed fracture including intercrystalline cleavage.The fracture toughness of the specimens increases from 82.64 MPa·m^(1/2)for the 910℃ specimen to 140.18 MPa·m^(1/2)for the 970℃ specimen.Specimens below 950℃ tend to form holes due to the prior particle boundaries(PPBs), which is not conducive to toughening. Specimens above 950℃ have high fracture toughness due to the crack deflection, crack branching, and shear plastic deformation of the Widmanstatten structure. This study provides a valid reference for the development of powder HIPed titanium alloy.

Size effects on the tensile strength and fracture toughness of granitic rock in different tests

This study investigates the tensile failure mechanisms in granitic rock samples at different scales by means of different types of tests.To do that,we have selected a granitic rock type and obtained samples of different sizes with the diameter ranging from 30 mm to 84 mm.The samples have been subjected to direct tensile strength(DTS)tests,indirect Brazilian tensile strength(BTS)tests and to two fracture toughness testing approaches.Whereas DTS and fracture toughness were found to consistently grow with sample size,this trend was not clearly identified for BTS,where after an initial grow,a plateau of results was observed.This is a rather complete database of tensile related properties of a single rock type.Even if similar databases are rare,the obtained trends are generally consistent with previous scatter and partial experimental programs.However,different observations apply to different types of rocks and experimental approaches.The differences in variability and mean values of the measured parameters at different scales are critically analysed based on the heterogeneity,granular structure and fracture mechanics approaches.Some potential relations between parameters are revised and an indication is given on potential sample sizes for obtaining reliable results.Extending this database with different types of rocks is thought to be convenient to advance towards a better understanding of the tensile strength of rock materials.

Tensile and tear-type fracture toughness of gypsum material:Direct and indirect testing methods

In this context,four specimens,i.e.(i)circumferentially notched cylindrical torsion(CNCT),(ii)circum-ferentially notched cylindrical direct tension(CNCDT),(iii)edge notch disc bend(ENDB)and(iv)three-point bend beam(3PBB),were utilized to measure the modesⅠandⅢfracture toughness values of gypsum.While the CNCT specimen provides pure modeⅢloading in a direct manner,this pure mode condition is indirectly produced by the ENDB specimen.The ENDB specimen provided lower KⅢc and a non-coplanar(i.e.twisted)fracture surface compared with the CNCT specimen,which showed a planar modeⅢfracture surface.The ENDB specimen is also employed for conducting pure modeⅠ(with different crack depths)and mixed modeⅠ/Ⅲtests.KIc value was independent of the notch depth,and it was consistent with the RILEM and ASTM standard methods.But the modeⅢfracture results were highly sensitive to the notch depth.While the fracture resistance against modeⅢwas significantly lower than that of modeⅠ,the greater work of fracture under modeⅢwas noticeable.

Mechanism and Method of Testing Fracture Toughness and Impact Absorbed Energy of Ductile Metals by Spherical Indentation Tests

To address the problem of conventional approaches for mechanical property determination requiring destructive sampling, which may be unsuitable for in-service structures, the authors proposed a method for determining the quasi-static fracture toughness and impact absorbed energy of ductile metals from spherical indentation tests (SITs). The stress status and damage mechanism of SIT, mode I fracture, Charpy impact tests, and related tests were frst investigated through fnite element (FE) calculations and scanning electron microscopy (SEM) observations, respectively. It was found that the damage mechanism of SITs is diferent from that of mode I fractures, while mode I fractures and Charpy impact tests share the same damage mechanism. Considering the diference between SIT and mode I fractures, uniaxial tension and pure shear were introduced to correlate SIT with mode I fractures. Based on this, the widely used critical indentation energy (CIE) model for fracture toughness determination using SITs was modifed. The quasi-static fracture toughness determined from the modifed CIE model was used to evaluate the impact absorbed energy using the dynamic fracture toughness and energy for crack initiation. The efectiveness of the newly proposed method was verifed through experiments on four types of steels: Q345R, SA508-3, 18MnMoNbR, and S30408.

New role of α phase in the fracture behavior and fracture toughness of a β-type bio-titanium alloy

The role of α precipitates formed during aging in the fracture toughness and fracture behavior of β-type bio-titanium alloy Ti–29Nb–13Ta–4.6Zr(TNTZ) was studied. Results showed that the fracture toughness of the TNTZ alloy aged at 723 K decreases to the minimum of 72.07–73.19 kJ·m^(-2)when the aging time is extended to 4–8 h and then gradually increases and reaches 144.89 kJ·m^(-2)after 72 h. The decrease in fracture toughness within the aging time of 4–8 h is caused by the large stress concentration at the tip of acicular α precipitates with a high aspect ratio and the preferential crack propagation along the inhomogeneous acicular α precipitates distributed in “V-shape” and “nearly perpendicular shape”. When the aging time is extended to 8–72 h, the precrack tip is uniformly blunted, and the crack is effectively deflected by α precipitates with multi long axis directions, more high homogeneity, low aspect ratio, and large number density. Analysis of the effect of αprecipitates on the fracture behavior suggested that the number of long axis directions of α precipitates is the key controlling factor for the fracture behavior and fracture toughness of the TNTZ alloy aged for different times.

A modified single edge V-notched beam method for evaluating surface fracture toughness of thermal barrier coatings

The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed(APS)thermal barrier coatings(TBCs).As APS TBCs are typical multilayer porous ceramic materials,the direct applications of the traditional single edge notched beam(SENB)method that ignores those typical structural characters may cause errors.To measure the surface fracture toughness more accurately,the effects of multilayer and porous characters on the fracture toughness of APS TBCs should be considered.In this paper,a modified single edge V-notched beam(MSEVNB)method with typical structural characters is developed.According to the finite element analysis(FEA),the geometry factor of the multilayer structure is recalculated.Owing to the narrower V-notches,a more accurate critical fracture stress is obtained.Based on the Griffith energy balance,the reduction of the crack surface caused by micro-defects is corrected.The MSEVNB method can measure the surface fracture toughness more accurately than the SENB method.

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.

Effects of thawing-induced softening on fracture behaviors of frozen rock

Due to the presence of ice and unfrozen water in pores of frozen rock,the rock fracture behaviors are susceptible to temperature.In this study,the potential thawing-induced softening effects on the fracture behaviors of frozen rock is evaluated by testing the tension fracture toughness(KIC)of frozen rock at different temperatures(i.e.-20℃,-15℃,-12℃,-10℃,-8℃,-6℃,-4℃,-2℃,and 0℃).Acoustic emission(AE)and digital image correlation(DIC)methods are utilized to analyze the microcrack propagation during fracturing.The melting of pore ice is measured using nuclear magnetic resonance(NMR)method.The results indicate that:(1)The KIC of frozen rock decreases moderately between-20℃ and-4℃,and rapidly between-4℃ and 0℃.(2)At-20℃ to-4℃,the fracturing process,deduced from the DIC results at the notch tip,exhibits three stages:elastic deformation,microcrack propagation and microcrack coalescence.However,at-4℃e0℃,only the latter two stages are observed.(3)At-4℃e0℃,the AE activities during fracturing are less than that at-20℃ to-4℃,while more small events are reported.(4)The NMR results demonstrate a reverse variation trend in pore ice content with increasing temperature,that is,a moderate decrease is followed by a sharp decrease and-4℃ is exactly the critical temperature.Next,we interpret the thawing-induced softening effect by linking the evolution in microscopic structure of frozen rock with its macroscopic fracture behaviors as follow:from-20℃ to-4℃,the thickening of the unfrozen water film diminishes the cementation strength between ice and rock skeleton,leading to the decrease in fracture parameters.From-4℃ to 0℃,the cementation effect of ice almost vanishes,and the filling effect of pore ice is reduced significantly,which facilitates microcrack propagation and thus the easier fracture of frozen rocks.

Twinning mediated anisotropic fracture behavior in bioimplant grade hot-rolled pure magnesium

Bioimplant grade hot-rolled magnesium with equiaxed microstructure and basal texture was examined for fracture toughness(FT)anisotropy using fatigue pre-cracked single-edge notch bending specimens with the notch,an||,⊥and 45°to rolling direction(RD).Due to adequate crack-tip plasticity,the size-independent elastic-plastic fracture toughness(JIC)were determined.Anisotropic JIC was ob-served due to different twin lamellae formation w.r.t.notch owing to the initial basal texture with{10¯10}and{11¯20}poles mostlyand⊥to RD.The out-of-plane tensile stresses activated the{10¯12}||10¯11||extension twins(ET)as usual with matrix-ET∑15b coincident site lattice boundary(CSLB)interfaces.While the in-plane tensile stress⊥to the crack-tip activated{10¯11}||10¯12||contraction twins(CT)that transform into{10¯11}-{10¯12}double twins(DT)with matrix-DT∑23b and∑15a CSLBs.For an||RD,large DT lamellae fraction formed at∼30°and few ETs at∼30°and∼90°to the notch with crack growth mainly via the∑23b/∑15a CSLB interfaces during FT.While,significant DT and ET lamellae developed at∼0°and∼60°with cracking via the matrix-DT∑23b/∑15a and matrix-ET||15b CSLBs for an⊥RD.The DT and ET lamellae activated at∼15°,and the crack propagated through∑15b for an∼45°to RD.The JIC and the crack-tip plastic zone decreases,while the elastic component of the J-integral(Jel)and the ET formation increases from an||,⊥,to∼45°to RD.The strain incompatibility of matrices was higher with the geometrically hard ETs than DTs.Thus,brittle interlamellar cracking occurred through the∑15b interfaces.In contrast,almost similar and higher crack-tip plasticity occurred in matrix and DT domains during crack propagation via||23b/||15a CSLBs.Crack growth through∑23b/||15a led to high JIC,both∑15b and||23b/||15a led to moderate JIC,and∑15b least JIC for an||,⊥and 45°to RD,respectively.

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.

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.

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）.

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.

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.

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.