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℃.

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.

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.

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 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.

Determination of multiaxial stress rupture criteria for creeping materials:A critical analysis of different approaches

Materials in engineering applications are rarely uniaxially-loaded.In reality,failures under multiaxial loading has been widely observed in engineering structures.The life prediction of a component under multiaxial stresses has long been a challenging issue,particularly for high temperature applications.To distinguish the mode of failure ranging from a maximum principal stress intergranular damage to von Mises effective stress rupture mode a multiaxial stress rupture criterion(MSRC)was originally proposed by Sdobyrev and then Hayhurst and Leckie(SHL MSRC).A multiaxial-factor,α,was developed as a result which was intended to be a material constant and differentiates the bias of the MSRC between maxi-mum principal stress and effective stress.The success of the SHL MSRC relies on accurately calibrating the value ofαto quantify the multiaxial response of the material/geometry combination.To find a more suitable approach for determining MSRC,the applicability of different methods are evaluated.Given that the resulting analysis of the various approaches can be affected by the creep failure mechanism,princi-ples in the determination of MSRC with and without using continuum damage mechanics approaches are recommended.The viability of uniaxial material parameters in correlating withαthrough the analysis of available data in literature is also presented.It is found that the increase of the uniaxial creep dam-age tolerance parameterλis accompanied bythe decreaseof theα-value,whichimplies thatthe creep ductility plays an important role in affecting the multiaxial rupture behavior of materials.

TWO METHODS FOR ASSESSMENT OF RESIDUAL LIFE OF HK-40 FURNACE TUBES

Two methods for predicting residual life of high temperature furnace tubes are studied. One is testanalysis method that is mainly based on the creep rupture tests on postservice specimens. Specimens were taken from the tubes, which had been in service for different times. KachanovRobinsons damage summation concept is employed, however with a modified factor K(ts) to account for prior damage in the specimens. If the foregone total life corresponds with real condition, all of the test data modified by K(ts) should be distributed uniformly nearby the master curve of the new material. The other iscomputer simulation method that considers all of the operating conditions that influence the life. The finite element method (FEM) with iterative calculation is used in the analysis. The variation rates of critical damage element along the wall thickness are determined as a function of the service temperature and current damage. A special program designed based on the method predicts well the residual life of furnace tubes, so long as the maximum depth of critical damage in radius direction of tubes has been detected by ultrasonic techniques.

Evolution of micro-pores in a single crystal nickel-based superalloy during 980℃ creep

The evolution of micro-pores in a single crystal nickel-based superalloy during creep at 980 ℃/220 MPa was investigated by X-ray computed tomography. Time-dependent ex-situ 3D information including the number, volume fraction, distribution and morphology of micro-pores was analyzed. The results reveal that the signifi cant formation and growth of micro-pores occur at the end of secondary/beginning of tertiary creep stage. The irregular large pores as well as high density pores located at strain concentration region are the major detrimental factors facilitating the creep damage. Creep failure is resulted from the connection of surface cracks induced by oxidation, and the internal cracks generated from growth and merging of micro-pores.

Geometry independent C^(*)-T_(z) dominance of three-dimensional quasistatic growing crack-tip fields in creeping solids

In creeping solids,plane stress and plane strain solutions for asymptotic singular crack-tip fields have been first put forward by Riedel and Rice with C^(*)as the dominating parameter and developed by Xiang and Guo into three-dimensional solution(3D)for stationary cracks under the domination of C^(*)with the constraint factor Tz.However,how to characterize the 3D crack-tip fields under creep damage-induced quasistatic growing conditions remains challenging.In this study,we reveal that,for 3D quasistatic growing cracks,the leading singular solution can effectively characterize the crack-tip stress distributions with relative errors less than 10.8%for relative creep time up to 0.8 in various specimens with finite thickness.For a given relative time,Tz distributions can be unified by the equivalent thickness concept,Beq.The results show that C^(*)-T_(z) can effectively quantify both the load and constraint effects on the crack-tip fields.Such geometry independent dominance can considerably simplify the treatments of load and constraint effects,thereby promoting the application of fracture mechanics in high-temperature damage tolerance designs.

EBSD parameter assessment and constitutive models of crept HR3C austenitic steel

Creep damage and evolution of HR3C steel at 650℃ were investigated using electron backscatter diffraction(EBSD),and EBSD-based parameter assessments were conducted.EBSD analyses show that the grain size is almost unchanged and no obvious texture formed after creep at different creep rates.The lowest proportion of low Σ coincidence site lattice grain boundaries under 150 MPa implies that the primary twin structures are preserved under the low stress level,while some twin structures evolved into general grain boundaries at the high creep level.Two main damage features of microcracks and cavities can be seen along the grain boundaries:the former emerged at higher stress levels,while the latter appeared at the lower stress level,and both were shown under medium stress.Band contrast shows that the most severe creep damage is present at 170 MPa.It implies that the creep mechanism differs distinctly under different stress levels,and the transition point is around 170 MPa.Kernel average misorientation is better to describe the local plastic deformation related to the strain distribution while grain reference orientation deviation describes the inhomogeneous strain distribution.Creep lifetime prediction models including the isothermal method,Larson-Miller parameter method and Monkman–Grant relation were evaluated by the experimental data and literature data,and they are valid for predicting creep behavior.

Carbides Evolution in 12Cr Martensitic Heat-resistant Steel with Life Depletion for Long-term Service

Evaluating the residual life of exposed components in power industry is a very important procedure inroutine examination. The microstructures of a series of X20CrMoV12.1 martensitic superheater tube samples in a boiler in different service periods were investigated extensively to extract a quantitative relationship. During long-term service from start to rupture, hardness decreased monotonically with life depletion, and the decrease of hardness in prior austenite grain boundary was steeper than that in the matrix. Microstructure observation showed obvious damage characteristics, including carbide coarsening and martensite decomposing, and the martensite structure decomposed completely in rupture state. The morphology, distribution and composition of the main precipitates M23 C6 varied distinctly. The aspect ratio of coarsened carbides along grain boundary increased several fold with respect to their original size. The composition of coarsened M23 C6 carbide shows the most regular trend of Cr enrichment and the statistical result of Cr enrichment in M23 C6 shows a linear correlation between the ratio of Cr to Fe and service time to the power of 3/2, which may be considered as an index of material degradation due to long-term service exposure.