SIF-based fracture criterion for interface cracks

The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s^（-iε）, so that K = ■ s^（-iε）, s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin（ASME J. Appl. Mech. 24：361–364, 1957） did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor（SIF）-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.

Towards fully automatic modelling of the fracture process in quasi-brittle and ductile materials:a unified crack growth criterion

Fully automatic finite element(FE) modelling of the fracture process in quasi-brittle materials such as concrete and rocks and ductile materials such as metals and alloys,is of great significance in assessing structural integrity and presents tre-mendous challenges to the engineering community. One challenge lies in the adoption of an objective and effective crack propagation criterion. This paper proposes a crack propagation criterion based on the principle of energy conservation and the cohesive zone model(CZM) . The virtual crack extension technique is used to calculate the differential terms in the criterion. A fully-automatic discrete crack modelling methodology,integrating the developed criterion,the CZM to model the crack,a simple remeshing procedure to accommodate crack propagation,the J2 flow theory implemented within the incremental plasticity framework to model the ductile materials,and a local arc-length solver to the nonlinear equation system,is developed and im-plemented in an in-house program. Three examples,i.e.,a plain concrete beam with a single shear crack,a reinforced concrete(RC) beam with multiple cracks and a compact-tension steel specimen,are simulated. Good agreement between numerical predictions and experimental data is found,which demonstrates the applicability of the criterion to both quasi-brittle and ductile materials.

Crack Propagation Path in Two-Directionally Graded Composites Subjected to Mixed-Mode Ⅰ+Ⅱ Loading

Crack propagation path in two-directionally graded composites was investigated by the finite element method.A graded extended finite element method(XFEM)was employed to calculate displacement and stress fields in cracked graded structures.And a post-processing subroutine of interaction energy integral was implemented to extract the mixed-mode stress intensity factors(SIFs).The maximum hoop stress(MHS)criterion was adopted to predict crack growth direction based on the assumption of local homogenization of asymptotic crack-tip fields in graded materials.Effects of material nonhomogeneous parameters on crack propagation paths were also discussed in detail.It is shown that the present method can provide relatively accurate predictions of crack paths in two-directionally graded composites.Crack propagates in the decreasing direction of effective Young′s modulus.The shape and steepness of property gradient perpendicular to the crack surface have great influences on crack paths.Through redesigning material property reasonably,crack growth in graded material can be changed to improve mechanical behaviours of cracked structures.

A new mixed type crack propagation criterion in shale reservoirs

Hydraulic fracturing is a mainstream technology for unconventional oil and gas reservoirs development all over the world.How to use this technology to achieve high-level oil and gas resource extraction and how to form complex fracture networks as hydrocarbon transportation channels in tight reservoirs,which depends to a large extent on the interaction between hydraulic and pre-existing cracks.For hydraulic fracturing of fractured reservoirs,the impact of natural fractures,perforation direction,stress disturbances,faults and other influencing factors will produce a mixed I&II mode hydraulic fracture.To forecast whether hydraulic fractures cross pre-existing fractures,according to elastic mechanics and fracture mechanics,a stress state of cracks under the combination of tensile(I)and shear(II)is presented.A simple mixed-mode I&II hydraulic fracture's crossing judgment criterion is established,and the propagation of hydraulic fractures after encountering natural fractures is analyzed.The results show that for a given approaching angle there exists a certain range of stress ratio when crossing occurs.Under high approaching angle and large stress ratio,it is likely that hydraulic cracks will go directly through pre-existing cracks.The reinitiated angle is always controlled within the range of approximately 30among the main direction of penetration.

Solidification behaviour and hot cracking susceptibility of a novel Ni-based superalloy

A novel Ni-based superalloy GH4151,with a γ′ volume fraction of about 55%and a service temperature capability up to 8oo oC,was investigated.Due to the different cooling conditions of various regions during the solidification of ingots,significant cooling rate variations may lead to the occurrence of hot cracking.Conventional scanning laser microscope was utilised to investigate the solidification process and phase precipitation behaviour of the GH4151 under wide range cooling rates.The characteristics of L→γ transformation were analysed,and the growth rates of at each stage were calculated.The segregation behaviour was predicted using the Scheil equation,and the predicted results match well with the experimental results.The sensitivity coefficient for hot cracking was modified,and cracking sensitivity coefficient values for the alloy under different cooling rates were computed,revealing that the alloy is most susceptible to hot cracking at 10℃/min cooling rate.Therefore,controlling the cooling rate can reduce the possibility of hot cracking in ingot.

Fracture initiation and propagation in intact rock—A review

The initiation and propagation of failure in intact rock are a matter of fundamental importance in rock engineering. At low confining pressures, tensile fracturing initiates in samples at 40%-60% of the uniaxial compressive strength and as loading continues, and these tensile fractures increase in density, ultimately coalescing and leading to strain localization and macro-scale shear failure of the samples. The Griffith theory of brittle failure provides a simplified model and a useful basis for discussion of this process. The Hoek-Brown failure criterion provides an acceptable estimate of the peak strength for shear failure but a cutoff has been added for tensile conditions. However, neither of these criteria adequately explains the progressive coalition of tensile cracks and the final shearing of the specimens at higher confining stresses. Grain-based numerical models, in which the grain size distributions as well as the physical properties of the component grains of the rock are incorporated, have proved to be very useful in studying these more complex fracture processes.

Fatigue cracking criterion of high-strength steels induced by inclusions under high-cycle fatigue

Fatigue properties of high-strength steels become more and more sensitive to inclusions with enhancing the ultimate tensile strength (UTS) because the inclusions often cause a relatively low fatigue strength and a large scatter of fatigue lives. In this work, four S–N curves and more than 200 fatigue fracture morphologies were comprehensively investigated with a special focus on the size and type of inclusions at the fatigue cracking origin in GCr15 steel with a wide strength range by different heat treatments after high-cycle fatigue (HCF). It is found that the percentage of fatigue failure induced by the inclusion including Al2 O3 and TiN gradually increases with increasing the UTS, while the percentage of failure at sample surfaces decreases conversely and the fatigue strength first increases and then decreases. Besides, it is interestingly noted that the inclusion sizes at the cracking origin for TiN are smaller than that for Al2 O3 because the stress concentration factor for TiN is larger than that for Al2 O3 based on the finite element simulation. For the first time, a new fatigue cracking criterion including the isometric inclusion size line in the strength-toughness coordinate system with specific physical meaning was established to reveal the relationship among the UTS, fracture toughness, and the critical inclusion size considering different types of inclusions based on the fracture mechanics. And the critical inclusion size of Al2 O3 is about 1.33 times of TiN. The fatigue cracking criterion could be used to judge whether fatigue fracture occurred at inclusions or not and provides a theoretical basis for controlling the scale of different inclusion types for high-strength steels. Our work may offer a new perspective on the critical inclusion size in terms of the inclusion types, which is of scientific interest and has great merit to industrial metallurgical control for anti-fatigue design.

New insight into fracturing characterization of shale under cyclic soft stimulation:A lab-scale investigation

The cyclic soft stimulation(CSS)is a new method of reservoir reforming for which the mechanism of fracturing crack propagation is ambiguous with regard to the alternating fluid pressure.This study aims to provide a comprehensive understanding of the fracturing mechanical characterizations of CSS under different magnitudes and amplitudes of the alternating fluid pressure.Acoustic emission(AE)is recorded to investigate the damage evolution under CSS based on the b value analysis of AE.Experimental results reveal the difference of pressure in a crack under different cyclic fluid pressure conditions.The AE results show that the maximum radiated energy under CSS tends to be reduced with the increase in the amplitude and magnitude of the alternating fluid pressure.The finishing crucial touch is that the crack extending criterion under CSS is proposed,which combines the injection parameters,the rock properties and in-situ stress.According to the crack extending criterion,the fluctuation fluid pressure causes the reduction of a critical crack extending pressure,and the CSS causes the crack to initiate and propagate under low fluid pressure.Under a higher-value magnitude of alternating fluid pressure,the cyclic times of CSS is less for the crack initiation.In supplement to the crack extending criterion,a distinct relationship between the radiated energy and the cyclic fluid pressure also is established based on the energy dissipation criterion.These new findings provide an insight into the determination of crack extending criterion under CSS for efficiently implementing shale fracturing.

A Hot Cracking Initiation Criterion Based on Solidification Liquid Film Characteristic and Microstructure

Herein,a hot cracking initiation criterion based on the characteristics of solidification liquid film and the microstructure was proposed,which integrated both the mechanical and non-mechanical factors during solidification.The criterion also took the effect of the shrinkage volume of the solid-liquid two-phase in the mushy zone,the flow behavior of the liquid film and the microstructure on the feeding behavior into account.Meanwhile,the effect factors of hot cracking initiation such as alloy composition,microstructure,mold design and process condition were included in this criterion,and it could quantitatively calculate whether hot cracks occurred under a certain state or not during solidification.The criterion was utilized to predict whether hot cracks occurred in Al-4.0 wt%Cu alloy in different initial solidification states or not,which was consistent with the experimental results and verified its reliability.According to the criterion expression,Vfeeding*was related with five effect factors includingη,ΔP*,l*,r*and n,in which r*and n were in positive correlation with Vfeeding*whileη,ΔP*and l*were in negative correlation with that,which provided a good instructive significance for mold design,process optimization and composition and microstructure regulation of alloys and simultaneously further enriched the mechanism and influencing factors of hot cracking initiation.Furthermore,a multiscale simulation method for calculating the characteristic parameters of hot tearing behavior during solidification was also provided in this study.

Application of viscoelastic continuum damage approach to predict fatigue performance of Binzhou perpetual pavements

For this study, the Binzhou perpetual pavement test sections constructed in Shandong Province, China, were simulated for long-term fatigue performance using the layered viscoelastic pavement analysis for critical distresses （LVECD） finite element software package. In this framework, asphalt concrete was treated in the context of linear visco- elastic continuum damage theory. A recently developed unified fatigue failure criterion that defined the boundaries of the applicable region of the theory was also incorporated. The mechanistic modeling of the fatigue mechanisms was able to accommodate the complex temperature variations and loading conditions of the field pavements in a rigorous manner. All of the material models were conveniently characterized by dynamic modulus tests and direct tension cyclic fatigue tests in the laboratory using cylindrical specimens. By comparing the obtained damage characteristic curves and failure criteria, it is found that mixtures with small aggregate particle sizes, a dense gradation, and modified asphalt binder tended to exhibit the best fatigue resistance at the material level. The 15 year finite element structural simulation results for all the test sections indicate that fa- tigue performance has a strong dependence on the thickness of the asphalt pavements. Based on the predicted location and severity of the fatigue damage, it is recommended that Sections 1 and 3 of the Binzhou test sections be emoloved for perpetual pavement design.