Simulation of Corrosion-Induced Cracking of Reinforced Concrete Based on Fracture Phase Field Method

Accurate simulation of the cracking process caused by rust expansion of reinforced concrete(RC)structures plays an intuitive role in revealing the corrosion-induced failure mechanism.Considering the quasi-brittle fracture of concrete,the fracture phase field driven by the compressive-shear term is constructed and added to the traditional brittle fracture phase field model.The rationality of the proposed model is verified by a mixed fracture example under a shear displacement load.Then,the extended fracture phase model is applied to simulate the corrosion-induced cracking process of RC.The cracking patterns caused by non-uniform corrosion expansion are discussed for RC specimens with homogeneous macroscopically or heterogeneous with different polygonal aggregate distributions at the mesoscopic scale.Then,the effects of the protective layer on the crack propagation trajectory and cracking resistance are investigated,illustrating that the cracking angle and cracking resistance increase with the increase of the protective layer thickness,consistent with the experimental observation.Finally,the corrosion-induced cracking process of concrete specimens with large and small spacing rebars is simulated,and the interaction of multiple corrosion cracking is easily influenced by the reinforcement spacing,which increases with the decrease of the steel bar interval.These conclusions play an important role in the design of engineering anti-corrosion measures.The fracture phase field model can provide strong support for the life assessment of RC structures.

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.

A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.

Review of the experimental studies of the cracking behaviors of fractured rocks under compression

In recent years, many useful experimental results on the cracking behaviors of fractured rocks have been obtainedvia uniaxial, biaxial, triaxial, and Split Hopkinson Pressure Bar (SHPB) tests. In this paper, the influence of theinclination angle of flaws, number of flaws, and patterns of cracks on the mechanical properties during the failureprocess under static loading and dynamic loading conditions is introduced and reviewed. The results show thatthe presence of cracks can decrease the strengths of precracked specimens, and the inclination angles, numbers,and crack patterns of pre-existing flaws can change the mechanical properties and cracking behaviors of precracked specimens. Under static loading, the closer the inclination angle is to 90, the greater the strength, theelastic modulus, and the peak strain of the precracked specimen. However, under dynamic loading, the influenceof the inclination angle varies, and the strength can increase or decrease, possibly in a V-shaped manner. Thischange can be determined by multiple factors, such as the loading path, the materials of the precracked specimen,and the number of pre-existing cracks. Under dynamic loading, the precracked specimen usually exhibits an Xshaped conjugated failure. Additionally, some problems in the study of the cracking behaviors of fractured rocksand related future research are described and presented, and corresponding suggestions and solutions are given.In particular, excavation in deep rock engineering, support of the rock surrounding the tunnel, and mining engineering have important scientific and engineering significance.

Effect of icosahedral phase formation on the stress corrosion cracking(SCC)behaviors of the as-cast Mg-8%Li(in wt.%)based alloys

Through exploring the stress corrosion cracking(SCC)behaviors of the as-cast Mg-8%Li and Mg-8%Li-6%Zn-1.2%Y alloys in a 0.1 M NaCl solution,it revealed that the SCC susceptibility index(I_(SCC))of the Mg-8%Li alloy was 47%,whilst the I_(SCC)of the Mg-8%Li-6%Zn-1.2%Y alloy was 68%.Surface,cross-sectional and fractography observations indicated that for the Mg-8%Li alloy,theα-Mg/β-Li interfaces acted as the preferential crack initiation sites and propagation paths during the SCC process.With regard to the Mg-8%Li-6%Zn-1.2%Y alloy,the crack initiation sites included the I-phase and the interfaces of I-phase/β-Li andα-Mg/β-Li,and the preferential propagation paths were the I-phase/β-Li andα-Mg/β-Li interfaces.Moreover,the SCC of the two alloys was concerned with hydrogen embrittlement(HE)mechanism.

Thermally-induced cracking behaviors of coal reservoirs subjected to cryogenic liquid nitrogen shock

The benefits of using cryogenic liquid nitrogen shock to enhance coal permeability have been confirmed from experimental perspectives.In this paper,we develop a fully coupled thermo-elastic model in combination with the strain-based isotropic damage theory to uncover the cooling-dominated cracking behaviors through three typical cases,i.e.coal reservoirs containing a wellbore,a primary fracture,and a natural fracture network,respectively.The progressive cracking processes,from thermal fracture initiation,propagation or cessation,deflection,bifurcation to multi-fracture interactions,can be well captured by the numerical model.It is observed that two hierarchical levels of thermal fractures are formed,in which the number of shorter thermal fractures consistently exceeds that of the longer ones.The effects of coal properties related to thermal stress levels and thermal diffusivity on the fracture morphology are quantified by the fracture fractal dimension and the statistical fracture number.The induced fracture morphology is most sensitive to changes in the elastic modulus and thermal expansion coefficient,both of which dominate the complexity of the fracture networks.Coal reservoir candidates with preferred thermal-mechanical properties are also recommended for improving the stimulation effect.Further findings are that there exists a critical injection temperature and a critical in-situ stress difference,above which no thermal fractures would be formed.Preexisting natural fractures with higher density and preferred orientations are also essential for the formation of complex fracture networks.The obtained results can provide some theoretical support for cryogenic fracturing design in coal reservoirs.

Dynamic Phase Field Description on Ductile Fracture Process

In comparison to discrete descriptions of fracture process,the recently proposed phase field methodology averts the numerical tracking strategy of discontinuities in solids,which enables the numerical implement simplification.An implicit finite element formulation based on the diffuse phase field is extended for stable and efficient analysis of complex dynamic fracture process in ductile solids.This exhibited formulation is shown to capture entire range of the characteristics of ductile material presenting J2-plasticity,embracing plasticization,cracks initiation,propagation,branching and merging while fulfilling the basic principle of thermodynamics.Herein,we implement a staggered time integration scheme of the dynamic elasto-plastic phase field method into the commercial finite element code.The numerical performance of the present advanced phase field model has been examined through several classic dynamic fracture benchmarks,and in all cases simulation results are in good agreement with the associated experimental data and other numerical results in previous literature.

Peridynamic Study on Fracture Mode and Crack Propagation Path of a Plate with Multiple Cracks Subjected to Uniaxial Tension

How to simulate fracture mode and crack propagation path in a plate with multiple cracks is an attractive but difficult issue in fracture mechanics.Peridynamics is a recently developed nonlocal continuum formulation that can spontaneously predict the crack nucleation,branch and propagation in materials and structures through a meshfree discrete technique.In this paper,the peridynamic motion equation with boundary traction is improved by simplifying the boundary transfer functions.We calculate the critical cracking load and the fracture angles of the plate with multiple cracks under uniaxial tension.The results are consistent with those predicted by classical fracture mechanics.The fracture mode and crack propagation path are also determined.The calculation shows that the brittle fracture process of the plate with multiple cracks can be conveniently and correctly simulated by the peridynamic motion equation with boundary conditions.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Correlative Factors Research of Tibial Shaft Fracture with Ipsilateral Posterior Malleolar Crack Fractures

Background:Missed diagnosis rate of spiral tibia shaft fracture with posterior malleolus crack fracture(PMCF)is high in the clinical.However,the mechanism and related factors of fracture are still unclear.Moreover,PMCF has been observed in other types of tibial shaft fractures.Objective:To explore the correlative factors of tibial shaft fracture with ipsilateral PMCF,decrease the rate of clinical missed diagnosis,strengthen the effective fixation of PMCF,and reduce the incidence of traumatic arthritis.Methods:From September 2014 to May 2019,we collected 137 tibiofibular fracture.Only 68 cases involved in ankle joint CT examination and were retrospectively analyzed.The patients were divided into posterior malleolus group(30 cases)and non-posterior malleolus group(38 cases)according to whether come up PMCF or not.The posterior malleolus group contained 24 males and 6 females,27-77(47.57±11.79)years old,the non-posterior malleolus group contained 23 males and 15 females,18-85(48.71±13.84)years old.The gender,age,location,fibula fracture and tibial shaft fracture classification were observed for univariate and multivariate analysis.Results:The probability of PMCF was higher with right tibial shaft fracture(OR=3.6995%CI:1.13-12.08 P<0.05);the probability of PMCF following distal fibular fracture was higher than that without fibular fracture(OR=11.3695%CI:1.72-75.05 P<0.05);the probability of PMCF with type A tibial shaft fracture was higher than type C(OR=4.8295%CI:1.19-19.58 P<0.05).Conclusion:Right type A tibial shaft fracture accompanied by distal fibular fracture are very important factors related to PMCF,which needs highly attention to avoid clinical missed diagnosis.

Improved Staggered Algorithm for Phase-Field Brittle Fracture with the Local Arc-Length Method

The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling.An improved staggered algorithm with energy and damage iterative tolerance convergence criteria is developed based on the residuals of displacement and phase-field.The improved staggered solution scheme is implemented in the commercial software ABAQUS with user-defined element subroutines.The layered system of finite elements is utilized to solve the coupled elastic displacement and phase-field fracture problem.A one-element benchmark test compared with the analytical solution was conducted to validate the feasibility and accuracy of the developed method.Our study shows that the result calculated with the developed method does not depend on the selected size of loading increments.The results of several numerical experiments show that the improved staggered algorithm is efficient for solving the more complex brittle fracture problems.

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.

Experimental study of multi-timescale crack blunting in hydraulic fracture

Hydraulic fracture is important in unconventional oil and gas exploration.During the propagation of the hydraulic fracture,the crack tip is blunted due to the development of the process zone in the near-tip area.In this study,the blunting of the hydraulic fracture in polymethyl methacrylate specimens due to multi-timescale stress concentration is investigated.The ratio of the initiation toughness to the arrest toughness of the blunted hydraulic fracture is measured using both the dynamic and the static methods.Results show that a hydraulic fracture can be blunted with the time span of stress concentration from 1 ms to 600 s.It is also shown that the blunting of hydraulic fracture is a highly localized process.The morphology of the blunted crack depends on the stress distribution in the vicinity of the crack tip.

Calculation Model of Equivalent Strength for Induced Crack Based on Double-K Fracture Theory and Its Optimizing Setting in RCC Arch Dam

By means of fracture testing on roller-compacted concrete （RCC） three-point bending beams with two different specimen sizes, the P-CMOD complete curve for RCC was gained. Furthermore, by applying double-K fracture theory, KiniⅠC,KunⅠC, as well as the critical effective crack length and the critical crack tip opening displacement, were evaluated. Based on the double-K fracture parameters above, the calculation model of equivalent strength for induced crack was established, thus the calculation method on its initiation, stable propagation and unstable fracture was ascertained. Moreover, the finite element simulation analysis of stress field in ShaPai arch dam and the on-site observational splaying points of induced crack at different altitudes validated the reliability of the model. Finally, crack inducer′s optimal setting in RCC arch dam was studied. It improves the design level of induced crack in RCC arch dam and satisfies the necessity of engineering practice.

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.

THERMAL FRACTURE OF FUNCTIONALLY GRADED PLATE WITH PARALLEL SURFACE CRACKS

This work examines the fracture behavior of a functionally graded material （FGM） plate containing parallel surface cracks with alternating lengths subjected to a thermal shock. The thermal stress intensity factors （TSIFs） at the tips of long and short cracks are calculated using a singular integral equation technique. The critical thermal shock △Tc that causes crack initiation is calculated using a stress intensity factor criterion. Numerical examples of TSIFs and △Tc for an Al2O3/Si3N4 FGM plate are presented to illustrate the effects of thermal property gradation, crack spacing and crack length ratio on the TSIFs and △Tc. It is found that for a given crack length ratio, the TSIFs at the tips of both long and short cracks can be reduced significantly and △Tc can be enhanced by introducing appropriate material gradation. The TSIFs also decrease dramatically with a decrease in crack spacing. The TSIF at the tips of short cracks may be higher than that for the long cracks under certain crack geometry conditions. Hence, the short cracks instead of long cracks may first start to grow under the thermal shock loading.

Fatigue fracture mechanism of AZ31B magnesium alloy and its welded joint

Fatigue test was carried out on AZ31B magnesium alloy. Under 2×10 6 cycle times, the fatigue strengths of base metal （BM）, butt joint （BJ）, transverse cross joint （TJ）, lateral connection joint （LJ） are 66.72, 39.00, 24.38 and 24.40 MPa, respectively. The crack propagation behavior of the alloy was analyzed by optical microscopy. The AZ31B magnesium alloy base metal has a smooth crack propagation macroscopic path. However, the microscopic path is twisted and some cracks have two forks, and the crack propagation is transgranular. The crack initiates in the weld toe and the crack propagates along the HAZ for the BJ and TJ; for the LJ crack initiates in the fillet weld leg. The fatigue fracture mechanisms were analyzed by SEM. The fatigue fracture surface consists of quasi-cleavage patterns or cleavage step and a brittle fracture occurs. Numerous secondary cracks are observed; some fatigue striations exist in butt joint and its size is about 5 μm.

COMPUTER SIMULATED ANALYSES ON DEFORMATION AND FRACTURE OF NON-CRACKED AND CRACKED SPECIMENS

A unified damage and fracture model,the combinatory work density model,which is suitable for ei- ther non-cracked body or cracked body has been suggested.In the present paper,the deformation and fracture of the two kinds of tensile spceimen and TPB specimen made of 40Cr steel have been simulated by using the new mod- el together with the large èlastic-plastic deformation finite element method.The results give a good picture of the whole deformation and fracture processes of the specimens in experiments;especially,the results on the TPB specimen can be used to obtain the relationship between load and displacement at the loading point P-Δ,and between crack ex- tension and displacement at the loading point Δα-Δ,the resistance curve J_R-Δa and the fracture toughness J_(IC).All the results are in remarkable agreement with those obtained by experiments.Therefore the model suggested here can be used to simulate crack initiation and propagation in non-cracked body and fracture initiation and crack stable propa- gation in cracked body.

ON PROBLEMS OF FRACTURE OF MATERIALS IN COMPRESSION ALONG TWO INTERNAL PARALLEL CRACKS

The fracture of materials under the action of compressive forces, directed along cracks which are parallel in plane can,lot be described within the framework of the linear fracture mechanics. The criteria of fracture of the Griffith-Irvin or COC type, used in classical linear fracture mechanics, are not applicable in this problem, since these forces have no influence on stress intensity coefficients and on values of cracks opening([1, 2]). The problems of such a class may be described only by using new approaches. One of possible approaches is presented by the first author, which involves using linearized relations, derived from exact non-linear equations of deformable solid body mechanics([3, 4, 5]). It should be remarked here that this approach has been widely used in problems of deformable bodies stability. As a criterion of the initiation of fracture the criterion of local instability near defects of the crack type is used. In these cases the process of loss of stability initiates the fracture process.

CRACK INITIATION POINT DETERMINATION AND DYNAMIC FRACTURE TOUGHNESS FOR CHARPY PRE-CRACKED SPECIMEN

The method to detect the crack initiation point of Charpy pre-cracked specimen under dy- namie loading was studied using strain gauge.The load-time curve and nominal strain-time curve at the crack tip for impact testing specinens may be shnultaneously measured by twin-channel oscilloscope with high speed sampling and diskette storing.Based on the dynam- ic finite element simulation of impact response of Charpy specimen,the measuring method of dynamic fracture toughness was analysed and some problems in previous dynamic fracture toughness measurement were discussed.