Triaxial creep damage characteristics of sandstone under high crustal stress and its constitutive model for engineering application

The creep characteristics of rock under high crustal stress are of important influence on the long‐term stability of deep rock engineering.To study the creep characteristics and engineering application of sandstone under high crustal stress,this study constructed nonlinear creep damage(NCD)constitutive mode based on the triaxial graded loading‒unloading creep test of sandstone in the Yuezhishan Tunnel.A numerical NCD constitutive model and a breakable lining(BL)model were developed based on FLAC3D and then applied to the stability analysis of the Yuezhishan Tunnel.Based on the creep test results of sandstone,a power function of creep rate and stress level was constructed,by which the long‐term strength was solved.The results show that the long‐term strength of the red sandstone based on the related function of the steady‐state creep rate and stress level is close to the measured stress value in engineering.The NCD model considering damage factors reflects the instantaneous and viscoelastic plasticity deformation characteristics of the red sandstone.The numerical NCD constitutive model and the BL model can reflect surrounding rock deformation characteristics and lining failure characteristics in practical engineering.The research results provide theoretical references for long‐term stability analysis of rock engineering and the deformation control of surrounding rock under high crustal stress.

A DCPD TECHNIQUE FOR LOCALIZED CREEP DAMAGE IN NOTCHED BARS

Localized creep damage in a notched round specimen has been investigated in this paper based on the creep damage mechanics and the DCPD technique. Expressions of creep damage equivalent stress under multi-axial state are given to describe the validity for localized damage in ductile materials. A DCPD method is introduced into the measurement of local creep damage near the tip of V-type notch of round bar. The technique with instrument configuration, selection of probe position and measuring calibration is also presented in the paper. Some results of creep damage estimation are shown on 2.25Cr-1Mo at 550℃.

Non-linear creep damage model of sandstone under freeze-thaw cycle

To study rock damage characteristics under long-term freeze-thaw cycles and loads,rock freeze-thaw and creep damage factors were defined based on nuclear magnetic resonance porosity and volume strain,respectively.The damage factor is introduced into the basic rheological element,and the non-linear creep damage constitutive model and freeze-thaw rock equation are established to describe non-linear creep characteristics under a constant load.Simultaneously,the creep test of freeze-thaw rock under step loading is performed.Based on the test data,the applicability and accuracy of the creep damage freeze-thaw rock model are analyzed and verified.The results show that freeze-thaw cycles result in continuous rock pore structure damage and deterioration,and nuclear magnetic resonance porosity enhancement.The constant load induces increasing rock plastic deformation,volume,and creep aging damage.As the loading stress increases,the instantaneous rock elastic parameters increase,and the rheological elastic and viscosity parameters decrease.Furthermore,the damage degradation of freeze-thaw cycles weakens the rock viscoplasticity,resulting in a rapid decrease in the viscosity parameter with an increase in freeze-thaw cycles.Generally,the continuous damage of the rock is degraded,and the long-term strength decreases continuously.

Creep damage properties of sandstone under dry-wet cycles

Rock creep properties can be used to predict the long-term stability in rock engineering.In reservoir bank slopes,sandstones which are frequently used in the bank slope undergoing longterm effects of dry-wet(DW) cycles due to periodic water inundation and drainage may gradually accumulate creep deformation,resulting in rock structure’s damage or even geological hazards such as landslides.To fully investigate the effect of DW cycles on the creep damage properties of sandstone,triaxial creep tests were conducted on saturated sandstone with different DW cycles by using a triaxial rheometer apparatus.The experimental results show that both the instantaneous strain and the stabilized strain increase with the DW cycles.In addition,using the Burgers model,four kinds of functions including an exponentially decreasing function,a linearly decreasing function,a linearly increasing function and an exponentially increasing function were proposed to express the relationships between the shear modulus,viscoelastic parameters of the Burgers model and the deviatoric stress under different DW cycles.Through comparative analysis,it is found that the theoretical curves generated using proposed four kinds of functions are in good agreement with the experimental data.Furthermore,macromorphological and microstructural observations were performed on specimens after various triaxial rheological tests.For samples with small number of DW cycles,approximately X-shaped fracture surfaces were observed in shear failure zones,whereas several shear fractures including obvious axial and horizontal tensile cracks,and flaws were found for samples with relatively large DW cycles due to long-term propagation and evolution of micro-fissures and micro-pores.Furthermore,as the DW cycles increases,the variation in micro-structure of samples after creep failure was summarized into three stages,namely,a stage with good and dense structure,a stage with pore and fissure propagation,and a stage with extensive increase of pores,fissures and loose particles.It is concluded that the combination effect of permeation of water molecules through pores and fissures within sandstone,and the propagation of preexisting pores and fissures owing to the dissolution of mineral particles leads to further deterioration of the mechanical properties of sandstone as the number of DW cycles increases.This study provides a fundamental basis for evaluating the long-term stability of reservoir bank slopes under cyclic fluctuations of water level.

Research on the creep damage and interfacial failure of dissimilar metal welded joint between 10Cr9Mo1VNbN and 12Cr1MoV steel

The mechanical properties, creep damage, creep rupture strength and features of interfacial failures of welded joints between martensite (SA213T91) and pearlite steel (12Cr1MoV) have been investigated by means of argon tungsten pulsed arc welding, high temperature accelerated simulation, creep rupture, mechanical property tests and scanning electronic microscope (SEM). The research results indicate that the mechanical properties of overmatched and medium matched joint deteriorate obviously, and they are susceptible to creep damage and failure after accelerated simulation operation 500 h, in the condition of preheat 250℃, and post welding heat treatment 750℃×1 h. However, the mechanical properties of undermatched joint are the best, the interfacial failure tendency of undermatched welded joint is less than those of medium and overmatched welded joint. Therefore, it is reasonable that low alloy material TR31 is used as the filler metal of weld between SA213T91and 12Cr1MoV steel.

Influence of Creep Strength of Weld on Interfacial Creep Damage of Dissimilar Welded Joint between Martensitic and Bainitic Heat-Resistant Steel

The mechanical properties, creep rupture strength, creep damage and failure characteristics of dissimilar metal welded joint （DMWJ） between martensitic （SA213T91） and bainitic heat-resistant steel （12Cr2MoWVTiB（G102）） have been investigated by means of pulsed argon arc welding, high temperature accelerated simulation, mechanical and creep rupture test, and scanning electronic microscope （SEM）. The results show that there is a marked drop of mechanical properties of undermatching joint, and low ductility cracking along weld/G102 interface is induced due to creep damage. Creep rupture strength of overmatching joint is the least. The mechanical properties of medium matching joint are superior to those of overmatching and undermatching joint, and creep damage and failure tendency along the interface of weld/G102 are lower than those of overmatching and undermatching joint after accelerated simulation for 500 h, 1 000 h, 1 500 h, and the creep rupture strength of medium matching joint is the same as that of undermatching joint. Therefore, it is reasonable that the medium matching material is used for dissimilar welded joint between martensitic and bainitic steel.

COMPUTER SIMULATION OF CREEP DAMAGE AT CRACK TIP IN SHORT FIBRE COMPOSITES

Creep damage at crack tip in short fibre composites has been sim- ulated by using the finite element method(FEM).The well-known Schapery non- linear viscoelastic constitutive relationship was used to characterize time-dependent behaviour of the material.A modified recurrence equation was adopted to accelerate the iteration.Kachanov-Rabotnov's damage evolution law was employed.The growth of the damage zone with time around the crack tip was calculated and the results were shown with the so-called 'digit photo',which was produced by the printer.

Nonlinear creep damage model for soft rock under uniaxial compression

A nonlinear creep-damage model for soft rock under uniaxial compression waspresented,which takes into account both nonlinear creep and damage growth with time.The model is based on the hardening theory,The model is validated through comparisonwith experimental results.

MESO APPROACHES FOR THE CREEP DAMAGE BEHAVIOR OF NICKEL-BASE DIRECTIONALLY SOLIDIFIED SUPERALLOYS

A self-consistent creep damage constitutive model and a finite element model have been developed for nickel-base directionally solidified superalloys. Grain degradation and grain boundary voiding are considered. The model parameters are determined from the creep test data of a single crystal and a directionally solidified superalloy with a special crystallographic orientation. The numerical analysis shows that the modeled creep damage behaviors of nickel-base directionally solidified super-alloys with different crystallographic orientations are in good agreement with the experimental data.

Creep damage constitutive model of rock based on the mechanisms of crack-initiated damage and extended damage

Since the classical element model cannot describe the nonlinear characteristics of rock during the entire compressive creep process,nonlinear elements and creep damage are generally introduced in the model to resolve this issue.However,several previous studies have reckoned that creep damage in rock only occurs in the accelerated creep stage and is only described by the Weibull distribution.Nevertheless,the creep damage mechanism of rocks is still not clearly understood.In this study,a reasonable representation of the damage variables of solid materials is presented.Specifically,based on the Gurson damage model,the damage state functions reflecting the constant creep stage and accelerated creep stage of rock are established.Further,the one-dimensional and three-dimensional creep damage constitutive equations of rock are derived by modifying the Nishihara model.Finally,the creep-acoustic emission tests of phyllite under different confining pressures are conducted to examine the creep damage characteristics of phyllite.And the proposed constitutive model is verified by analyzing the results of creep tests performed on saturated phyllite.Overall,this study reveals the relationship between the creep characteristics of rocks and the corresponding damage evolution pattern,which bridges the gap between the traditional theory and the quantitative analysis of rock creep and its damage pattern.

Coupling phase field with creep damage to study γ’evolution and creep deformation of single crystal superalloys

A phase-field model coupling with elastoplastic de fo rmation and creep damage has been built to study the micro structural evolution and deformation behavior for Ni-Al single crystal alloy during the whole creep processing.The relevant experiments were conducted to verify the model validity.The simulation re sults show that under the tensile creep at 1223 K/100 MPa,cubic γ’phases coarsen along the direction parallel to the axis of tensile stress during the first two creep stages;and spindle-shaped and wavy γ’phases are fo rmed during tertiary creep,similar to the experimental results.The evolution mechanism of γ’phases is analyzed from the perspective of changes of stress and strain fields.The"is land-like"γ phase is observed and its formation mechanism is discussed.With the increase of creep stress,the directional coarsening of γ’phase is accelerated,the steady-state creep rate is increased and the creep life is decreased.The comparison between simulated and experimental creep curves shows that this phase-field model can effectively simulate the performance changes during the first two creep stages and predict the influence of creep stresses on creep properties.Our work provides a potential approach to synchronously simulate the creep microstructure and property of superalloys strengthened by γ’precipitates.

A 2-D mesoscopic model for the evaluation of creep damage induced by void growth in polycrystalline metals

At elevated temperature, creep failures of polycrystalline metals after long-term constant loading are often caused by the nucleation, growth and coalescence of creep voids on the grain boundaries. Void h＇action is an important parameter for the evaluation of creep damage level of structural materials operating at high temperature. In this paper, a 2-D numerical simulation method was developed for analyzing the void fraction evolution during the process of creep, based on some hypothesis from experiments. The model was implemented and then was used to predict the evolution of void fraction in the 2.25Cr-1Mo steel of uniaxial creep experiment at 570 ℃, in which the simulation results showed good agreement with the experimental results.

MICRO-MACRO DAMAGE SIMULATION OF LOW-ALLOY STEEL WELDS SUBJECT TO TYPE IV CREEP FAILURE

A simulation method for microscopic creep damage at grain boundaries in the fine-grain heat-affected zone of low-alloy steel welds involving high energy piping was proposed on the basis of the combination of elastic-creep FEM (finite element method) analysis and random fracture resistance modeling of the materials. The procedure to determine the initiation and growth-driving forces of small defects were briefly described. Then, a simulation procedure combining the stress distribution from elastic-creep FEM and the random fracture resistance model was proposed, and Ms procedure was applied to the simulation of the microscopic damage progress in a welded joint model test and in actual power piping. The results in terms of the simulated number density of small defects throughout the wall thickness were in good agreement with the observed results.

TENSILE CREEP DEFORMATION AND DAMAGE BEHAVIOR IN A NICKEL-BASE SUPERALLOY AT 900℃

The tensile creep deformation and damage evolution in a Ni-base superalloy at 900℃/170MPa were investigated. At the first creep stage, abnormal creep occured due to the resolution of fine particles, and the deformation initiated from grain boundary areas. It is evident that nearly all of the dislocations were in γ matrix channels in form of dislocation pairs and the dislocations were impeded at γ/γ' interfaces, thus the dislocation networks developed deformation. At the steady creep stage, impeded dislocations atγ/γ' interfaces climbed over γ' phases by diffusion-dominant mechanism. At the last creep stage, voids were formed around carbides at grain boundary which leaded to accumulated damage and caused creep rate accelerated. With the dislocation networks being broken, the voids connected and grew into micro-cracks gradually. Finally the cracks propagated along grain boundary area and resulted in failure.

Creep properties and permeability evolution in triaxial rheological tests of hard rock in dam foundation

Triaxial creep tests were carried out under seepage pressure by using rock servo-controlled triaxial rheology testing equipment. Based on experimental results, rock rheological properties influenced by seepage-stress coupling were studied, and variations of seepage rate with time in complete creep processes of rock were analyzed. It is shown that, when the applied stress is less than failure stress level, the creep deformation is not obvious, and its main form is steady-state creep. When applied stress level is greater than or less than but close to fracture stress, it is easier to see the increase of creep deformation and the more obvious accelerative creep characteristics. The circumferential creep deformation is obviously higher than the axial creep deformation. At the stage of steady-state creep, the average of seepage flow rate is about 4.7×10-9 rn/s at confining pressure （tr3） of 2 MPa, and is about 3.9×10-9 m/s at a3 of 6 MPa. It is seen that the seepage flow rate at or3 of 2 MPa in this case is obviously larger than that at tr3 of 6 MPa. At the stage of creep acceleration, the seepage flow rate is markedly increased with the increase of time. The variation of rock permeability is directly connected to the growth and evolution of creep crack. It is suggested that the permeability coefficient in complete creep processes of rock is not a constant, but is a function of rock creep strain, confining pressure, damage variable and pore water pressure. The results can be considered to provide a reliable reference for the establishment of rock rheological model and parameter identification.

A power function model for simulating creep mechanical properties of salt rock

In this paper,a new micro-creep model of salt rock is proposed based on a linear parallel bonded model(LPBM)using the two-dimensional particle flow code(PFC2D).The power function weakening form is assumed to describe the variation of the parallel bonded diameter(PBD)over time.By comparing with the parallel-bonded stress corrosion(PSC)model,a smaller stress fluctuation and smoother creep strain−time curves can be obtained by this power function model at the same stress level.The validity and adaptability of the model to simulate creep deformation of salt rock are verified through comparing the laboratory creep test curves and the Burgers model fitting result.The numerical results reveal that this model can be capable of capturing the creep deformation and damage behavior from the laboratory observations.

Low Cycle Fatigue, Creep-Fatigue and Relaxation-Fatigue Tests on P91

Creep-fatigue is a damage mechanism where cyclic deformation damage （fatigue） is enhanced by creep damage and vice versa. Factors affecting the creep-fatigue damage are stress level （or, equivalently, strain range）, temperature, hold time period, material softening/hardening and number of cycles. Moreover, environmental effects can accelerate the creep-fatigue interaction （oxidation, hot corrosion, irradiation, etc.）. The activity described in this paper was planned to perform tests on 9Cr-lMo ferritic/martensitic steel （P91） combining fatigue cycles and constant tensile and compressive holding periods. A preliminary basic fatigue characterization campaign in the LCF （low cycle fatigue） regime was carried out by performing a series of strain controlled tests, each at the same temperature （550 ℃）, using two different values for the total strain range （1% and 0.6%） and the same total strain rate （2×10^-3 s^-1）. The tests were carried out with a strain ratio of-l, i.e., in fully reversed cyclic conditions. In this paper we illustrate the results obtained by testing in air P91 （9Cr-lMo） ferritic/martensitic steel, introducing different dwell periods （either in strain or load control） and obsetwing how these affect the fatigue life of the specimens. The final aim of the activity is to investigate how much detrimental is the effect of the holding periods on the fatigue life in order to validate the creep-fatigue interaction diagram presently adopted in RCC-MRx code for the P91 steel.

CREEP BEHAVIOR MODELING OF UDIMET 720Li SUPERALLOY

Constant load creep tests on isothermally forged Udimet 720Li, an advanced superalloy for gas turbine disc application, were run in the stress/temperature field 900-450MPa/650-700 ℃ producing rupture times in the 20-5000h range. The creep curves have shown a predominant accelerating creep stage, that has been described by the following equation: where ε min depends on stress and temperature, while parameter C depends mainly on stress. A strain dependent damage, defined by the parameter C, causes the accelerating creep stage at stresses lower than 750MPa, whilst its contribution to the creep strain acceleration is less important at higher stresses. The model rationalizes the different behaviors at high and low stress and has been validated with variable stress and temperature creep behavior.

ON INTEGRITY ASSESSMENT OF AXISYMMETRIC COMPONENTS OPERATING WITHIN CREEP REGIME

A multiaxial paradigm for predicting creep damage/lives of components is described. Although in principle the paradigm is general, it is verified using axisymmetric experimental data. It is shown that the proposed paradigm is capable of predicting creep lives with an error of less than 2%. It is also shown that the proposed paradigm is more accurate than the reference stress method.

Study on creep-fatigue damage evaluation for advanced 9%–12% chromium steels under stress controlled cycling

Creep-fatigue interaction is one of the main damage mechanisms in high temperature plants and their components. Assessment of creep-fatigue properties is of practical importance for design and operation of high temperature components. However, the standard evaluation techniques, i.e. time fraction rule and ductility exhaustion one have limitations in accounting for the effects of control mode on the cyclic deformations. It was found that conventional linear cumulative damage rule failed in accurately evaluating the creep-fatigue life under stress controlled condition. The calculated creep damages by time fraction rule were excessively high, which led to overly conservative prediction of failure lives. In the present study, it was suggested that such over estimation of creep damage was mainly caused by anelastic strain upon stress loading. For precise assessment under conditions of stress control, a modified creep damage model accounting for the effect of anelastic creep was proposed. The assessments of creep fatigue data under stress controlled condition were performed with the new approach developed in this paper for a rotor material and a boiler material used in ultra supercritical power plants. It was shown that a more moderate amount of creep damage was obtained by the new model, which gave better predictions of failure life.