Novel damage constitutive models and new quantitative identification method for stress thresholds of rocks under uniaxial compression

Four key stress thresholds exist in the compression process of rocks,i.e.,crack closure stress(σ_(cc)),crack initiation stress(σ_(ci)),crack damage stress(σ_(cd))and compressive strength(σ_(c)).The quantitative identifications of the first three stress thresholds are of great significance for characterizing the microcrack growth and damage evolution of rocks under compression.In this paper,a new method based on damage constitutive model is proposed to quantitatively measure the stress thresholds of rocks.Firstly,two different damage constitutive models were constructed based on acoustic emission(AE)counts and Weibull distribution function considering the compaction stages of the rock and the bearing capacity of the damage element.Then,the accumulative AE counts method(ACLM),AE count rate method(CRM)and constitutive model method(CMM)were introduced to determine the stress thresholds of rocks.Finally,the stress thresholds of 9 different rocks were identified by ACLM,CRM,and CMM.The results show that the theoretical stress−strain curves obtained from the two damage constitutive models are in good agreement with that of the experimental data,and the differences between the two damage constitutive models mainly come from the evolutionary differences of the damage variables.The results of the stress thresholds identified by the CMM are in good agreement with those identified by the AE methods,i.e.,ACLM and CRM.Therefore,the proposed CMM can be used to determine the stress thresholds of rocks.

3D digital-image correlation insight into generalized relaxation behavior of sandstone under stress and pore pressure coupling

The occurrence of geological hazards and the instability of geotechnical engineering structures are closely related to the time-dependent behavior of rock.However,the idealization boundary condition for constant stress in creep or constant strain in relaxation is not usually attained in natural geological systems.Therefore,generalized relaxation tests that explore the simultaneous changes of stress and strain with time under different stress levels with constant pore-water pressure are conducted in this study.The results show that in area Ⅰ,area Ⅱ,and area Ⅲ,the stress and strain both change synchronously with time and show similar evolutionary laws as the strain-time curve for creep or the stress-time curve for relaxation.When the applied stress level surpasses the δ_(ci) or δ_(cd) threshold,the variations in stress and strain and their respective rates of change exhibit a significant increase.The radial deformation and its rate of change exhibit greater sensitivity in response to stress levels.The apparent strain deforms homogeneously at the primary stage,and subsequently,gradually localizes due to the microcrack development at the secondary stage.Ultimately,interconnection of the microcracks causes the formation of a shear-localization zone at the tertiary stage.The strain-time responses inside and outside the localization zone are characterized by local strain accumulation and inelastic unloading during the secondary and tertiary stages,respectively.The width of the shear-localization zone is found to range from 4.43 mm to 7.08 mm and increased with a longer time-to-failure.Scanning electron microscopy(SEM)reveals a dominant coalescence of intergranular cracks on the fracture surface,and the degree of physiochemical deterioration caused by water-rock interaction is more severe under a longer lifetime.The brittle sandstone’s time-dependent deformation is essentially controlled by microcrack development during generalized relaxation,and its expectancy-life is determined by its initial microstructural state and the rheological path.

A novel binary effective medium model to describe the prepeak stressstrain relationship of combined bodies of rock-like material and rock

Combined bodies of rock-like material and rock are widely encountered in geotechnical engineering,such as tunnels and mines.The existing theoretical models describing the stress-strain relationship of a combined body lack a binary feature.Based on effective medium theory,this paper presents the governing equation of the“elastic modulus”for combined and single bodies under triaxial compressive tests.A binary effective medium model is then established.Based on the compressive experiment of concretegranite combined bodies,the feasibility of determining the stress threshold based on crack axial strain is discussed,and the model is verified.The model is further extended to coal-rock combined bodies of more diverse types,and the variation laws of the compressive mechanical parameters are then discussed.The results show that the fitting accuracy of the model with the experimental curves of the concretegranite combined bodies and various types of coal-rock combined bodies are over 95%.The crack axial strain method can replace the crack volumetric strain method,which clarifies the physical meanings of the model parameters.The variation laws of matrix parameters and crack parameters are discussed in depth and are expected to be more widely used in geotechnical engineering.

A Comprehensive Review of Experience with the Application of the Mechanical Threshold Stress Model

Accurate prediction of stress-strain behavior of metals as a function of arbitrary temperature and strain rate paths has remained a challenge. The Mechanical Threshold Stress constitutive model is one formalism that has emerged following several decades of research. Vast experience has accumulated with the application of the Mechanical Threshold Stress model over a wide variety of pure metals and alloys. Out of this has arisen common trends across metal systems. The magnitude of activation energies presents one example of this, where these variables consistently increase in magnitude as the obstacle to dislocation motion transitions from short range to long range. Trends in strain hardening are also observed. In Face-Centered Cubic metals the magnitude of strain hardening scales with the stacking fault energy;trends in Body-Centered Cubic metals are less clear. Model parameters derived for over twenty metals and alloys are tabulated. Common trends should guide future application of the MTS model and further model development.

Stress triggering of the Lushan M7. 0 earthquake by the Wenchuan Ms8. 0 earthquake

The Wenchuan Ms8.0 earthquake and the Lushan M7.0 earthquake occurred in the north and south segments of the Longmenshan nappe tectonic belt, respectively. Based on the focal mechanism and finite fault model of the Wenchuan Ms8.0 earthquake, we calculated the coulomb failure stress change. The inverted coulomb stress changes based on the Nishimura and Chenji models both show that the Lushan MT. 0 earth- quake occurred in the increased area of coulomb failure stress induced by the Wenchuan Ms8. 0 earthquake. The coulomb failure stress increased by approximately 0. 135 - 0. 152 bar in the source of the Lushan M7.0 earthquake, which is far more than the stress triggering threshold. Therefore, the Lushan M7.0 earthquake was most likely triggered by the coulomb failure stress change.

Application of the Mechanical Threshold Stress Model to Large Strain Processing

Large-strain deformations introduce several confounding factors that affect the application of the Mechanical Threshold Stress model. These include the decrease with the increasing stress of the normalized activation energy characterizing deformation kinetics, the tendency toward Stage IV hardening at high strains, and the influence of crystallographic texture. Minor additions to the Mechanical Threshold Stress model are introduced to account for variations of the activation energy and the addition of Stage IV hardening. Crystallographic texture cannot be modeled using an isotropic formulation, but some common trends when analyzing predominantly shear deformation followed by uniaxial deformation are described. Comparisons of model predictions with measurements in copper processed using Equal Channel Angular Pressing are described.

Characteristic stress and strain precursor information for fine-grained granite during failure process under triaxial loading and unloading conditions

The unloading effect by excavation may cause irreversible and severe damage to the surrounding rock masses in underground engineering.In this paper,both conventional triaxial compression(CTC)tests and triaxial unloading confining pressure(TUCP)tests were conducted on fine-grained granite to study its triaxial compression failure processes due to unloading.Based on the crack volumetric strain(CVS)method,the crack axial strain(CAS)method and crack radial area strain(CRAS)method were proposed to identify the failure precursor information(including stress thresholds and axial strain at the initiation point of crack connectivity stage)during the rock failure processes.The results of the CTC tests show that the stable crack development stressσsd,unstable crack development stressσusd,and crack connectivity stressσct identified by the CAS method are 6%,74%–84%,and 86%–97%of the peak stress,respectively.For the TUCP cases,as the confining pressure increases,the stress thresholds,axial pressure at failure and axial strain at the start of the crack connectivity stage increase,while the time ratio of the crack connectivity stage to the entire unloading stage decreases.This indicates that fine-grained granite is prone to generate more cracks and leads to fail suddenly under high confining pressure.Furthermore,this new method demonstrates that the point at which the derivative of the radial crack area strain transitions from stable to a sudden increase or decrease is defined as the precursor point of rock failure.The results of axial strain at the starting point of the crack connectivity stage are very close to those predicted by the AE method,withβ1 no more than 11%.

Crack Growth Rate Model Derived from Domain Knowledge-Guided Symbolic Regression

Machine learning(ML)has powerful nonlinear processing and multivariate learning capabilities,so it has been widely utilised in the fatigue field.However,most ML methods are inexplicable black-box models that are difficult to apply in engineering practice.Symbolic regression(SR)is an interpretable machine learning method for determining the optimal fitting equation for datasets.In this study,domain knowledge-guided SR was used to determine a new fatigue crack growth(FCG)rate model.Three terms of the variable subtree ofΔK,R-ratio,andΔK_(th)were obtained by analysing eight traditional semi-empirical FCG rate models.Based on the FCG rate test data from other literature,the SR model was constructed using Al-7055-T7511.It was subsequently extended to other alloys(Ti-10V-2Fe-3Al,Ti-6Al-4V,Cr-Mo-V,LC9cs,Al-6013-T651,and Al-2324-T3)using multiple linear regression.Compared with the three semi-empirical FCG rate models,the SR model yielded higher prediction accuracy.This result demonstrates the potential of domain knowledge-guided SR for building the FCG rate model.

Creep mechanism and creep constitutive model of aluminum silicate short-fiber-reinforced magnesium matrix composite

By the constant stress tensile creep test method, creep tests were performed on aluminum silicate short fiber-reinforced AZ91D magnesium matrix composite with volume fraction of 30% and its matrix alloy AZ91D under different temperatures and stresses. The results indicate that the composite and the matrix have the same true stress exponent and true activation energy for creep, which are 3 and 144.63 kJ/mol, respectively. The creep of the composite is controlled by the creep of its matrix, which is mainly the controlling of viscous slip of dislocation, and the controlling of grain boundary slippage as a supplement. The creep constitutive model obtained from the experiment data can well describe the creep deformation pattern of the composite.

Effects of water intrusion and loading rate on mechanical properties of and crack propagation in coal–rock combinations

Tackling the problems of underground water storage in collieries in arid regions requires knowledge of the effect of water intrusion and loading rate on the mechanical properties of and crack development in coal–rock combinations. Fifty-four coal–rock combinations were prepared and split equally into groups containing different moisture contents(dry, natural moisture and saturated) to conduct acoustic emission testing under uniaxial compression with loading rates ranging from 0.1 mm/min to 0.6 mm/min. The results show that the peak stress and strength-softening modulus, elastic modulus, strain-softening modulus, and post-peak modulus partly decrease with increasing moisture content and loading rate. In contrast, peak strain increases with increasing moisture content and fluctuates with rising loading rate. More significantly, the relationship between stiffness and stress, combined with accumulated counts of acoustic emission, can be used to precisely predict all phases of crack propagation. This is helpful in studying the impact of moisture content and loading rate on crack propagation and accurately calculating mechanical properties. We also determined that the stress thresholds of crack closure, crack initiation, and crack damage do not vary with changes of moisture content and loading rate, constituting 15.22%, 32.20%, and 80.98% of peak stress, respectively. These outcomes assist in developing approaches to water storage in coal mines, determining the necessary width of waterproof coal–rock pillars, and methods of supporting water-enriched roadways, while also advances understanding the mechanical properties of coal–rock combinations and laws of crack propagation.

Quantitative analysis of influence of α-Al(MnFeCr)Si dispersoids on hot deformation and microstructural evolution of Al-Mg-Si alloys

The microstructural evolution of AA6061 and Mn-bearing Al-Mg-Si-Cu alloys was studied by compression tests that were carried out between 300 and 500 °C with a wide range of strain rates. Compared to the AA6061 alloy, the large amount of α-Al(MnFeCr)Si dispersoids in the Mn-bearing alloy yielded a significant increase in the flow stress under all deformation conditions. The effects of the deformation parameters on the evolution of the microstructure were studied using electronic backscatter diffraction measurements. The predominant softening mechanism of both alloys was dynamic recovery. The presence of α dispersoids in Mn-bearing alloys effectively refined the size of substructures with misorientation angles in the range of 2°-5°, which retarded the dynamic recovery. To predict the subgrain size under various deformation conditions, the threshold stresses that were caused by α dispersoids were calculated by the modified Orowan equation and incorporated into a conventional constitutive equation. The subgrain size that was predicted by the modified constitutive equation showed satisfactory agreement with the experimental measurements.

GROWTH OF SHORT CRACKS OF A537CLI STEEL UNDER FATIGUE LOADING IN 3.5% NaCl SOLUTION

The effects of environmental media,both in atmosphere and in 3.5% NaCl aqueous solution, on the growth of short cracks in comparison with the long ones have been investigated under fatigue loading on the specimens of single-edge crack about 0.05—0.15 mm for A537CLI steel.The growth rate of short cracks is faster than those of long ones around the threshoht stress intensity.The threshold stress intensity for short crack growth decreases with de- creasing crack length.The acceleration effect of the salt water,as compared with atmosphere environment,on the growth of short cracks under fatigue is much greater than that on the growth of long cracks.

FATIGUE FRACTURE BEHAVIOR OF LOW CARBON MARTENSITE AND MARTENSITE/BAINITE DUPLEX STRUCTURE IN STEEL 20CrMnMo

Fatigue crack propagation rate,da/dN,and threshold stress intensity range,ΔK_(th),of steel 20CrMnMo containing low carbon martensite or low carbon martensite/bainite(LCM/B) duplex structure,obtained by oil quenching and austempered at 360℃,have been measured using specimens under four-point bending.Observation was also made of the crack path and fracture morphology with relation to microstructure.The formation of LCM/B duplex structure,which caused by 20% lower bainite after short-time isothermal treatment,may re- markably increase ΔK_(th)and considerably decrease da/dN.The effect of microstructure on da/dN and ΔK_(th)was discussed with the emphasis on the crack propagation path.

Unraveling the threshold stress of structural rejuvenation of metallic glasses via thermo-mechanical creep

The competition between physical aging and structural rejuvenation determines the physical and mechanical properties of glassy materials.Thus,the rejuvenation-aging boundary must be identified quantitatively.In this work,we unravel a stress boundary to distinguish rejuvenation from aging via the thermo-mechanical creep of a typical Zr-based metallic glass.The crept glasses were rejuvenated into high-enthalpy disordered states when the applied stress exceeded a threshold that was numerically close to the steady-state flow stress;otherwise,the glasses were aged.A theoretical model for glass creep was adopted to demystify the observed stress threshold of rejuvenation.The model revealed that the thermo-mechanical creep beyond the threshold stress could activate sufficient shear transformations to create a net free volume,thus leading to structural rejuvenation.Furthermore,we derived the analytical expressions for the threshold and flow stresses.Both stresses can act as the rejuvenation-aging boundary,which is well supported by experimental creep data.The present work procures a deeper understanding of the rejuvenation mechanism of glasses and provides useful implications for abstaining from glass aging.

Effect of Threshold Stress on Anisotropic Creep Properties of Single Crystal Nickel-Base Superalloy SRR99

The influence of orientation on the creep properties of the nickel-base single crystal superalloy SRR99 was investigated at 760℃ and various levels of applied stress.It was found that the effect of anisotropy was strikingly prominent at this temperature.Deformation mechanisms of single crystals with three principal orientations at 760℃/790 MPa were explained according to detailed observations of dislocation arrangements by means of transmission electron microscopy （TEM）.Liability to shearing γ＇ precipitates for [011] orientation and co-planar slip for [111] orientation resulted in poor creep strength and short stress rupture life.It was also found that the apparent primary creep strain could be measured when the applied stress was increased to 565 MPa.Modified power law equation was adopted and the concept of a threshold stress σ 0 which determines dislocation looping or shearing to be activated was then involved.Through detailed calculations,the threshold stress was obtained to further analyse the distribution of the applied stress and better rationalize the anisotropic creep behaviour in the stereographic triangle in combination with TEM observations.

Steady-State Creep Behavior of Super304H Austenitic Steel at Elevated Temperatures

Creep behavior of Super304H austenitic steel has been investigated at elevated temperatures of 923-973 K and at applied stress of 190-210 MPa. The results show that the apparent stress exponent and activation energy in the creep deformation range from 16.2 to 27.4 and from 602.1 to 769.3 kJ/mol at different temperatures, respectively. These high values imply the presence of a threshold stress due to an interaction between the dislocations and Cu-rich precipitates during creep deformation. The creep mechanism is associated with the dislocation climbing governed by the matrix lattice diffusion. The origin of the threshold stress is mainly attributed to the coherency strain induced in the matrix by Cu-rich precipitates. The theoretically estimated threshold stresses from Cu-rich precipitates agree reasonably with the experi- mental results.