Triaxial Stress State Research Articles

Understanding the deformation and fracture mechanisms in backward flow-forming process of Ti-6Al-4V alloy via a shear modified continuous damage model

A shear modified coupled damage criterion based on continuum damage mechanics has been proposed in this study. Khan-Huang-Liang (KHL) model is implemented to predict the constitutive behavior of Ti-6Al-4 V (Ti64) alloy. A VUMAT subroutine has been developed for the damage model using a stress integration algorithm. Multiple simulations with tensile, compression and shear geometries are carried out in Abaqus/Explicit and compared with the experimental results to benchmark the hardening and damage criteria. The flow forming process involves a complex triaxial state of stress. This study is focused on understanding the contribution of triaxiality and shear during deformation and fracture in the flow-forming process with different roller arrangements. For this purpose, the flow-forming processes with three different roller arrangements, single roller, three roller, and wedge roller, are modeled, and their formability is compared by implementing a shear modified continuous damage model. A single roller flow-forming (SRF) arrangement undergoes high triaxiality due to excessive material displacement by the roller and high strain gradient in the axial direction. The fracture occurs near the interface of the reducing and thinning zone. The three-rollers flow-forming (TRF) provided maximum reduction till fracture and material fails due to excessive strain in the thinning zone at a relatively large percentage reduction. The wedge roller flow-forming (WRF) suffers a lack of uniform material softening, and fracture occurs near the interface of the uplift and reducing zone under high triaxiality. 3-D process maps have been developed for predicting fracture strain as a function of stress triaxiality/Lode parameter and stress triaxiality/thermal softening factor (E/σ¯2). Finally, a summary chart correlating the parameters, and flow-formability has been developed.

Impact of Titanium Dioxide in the Mechanical Recycling of Post-Consumer Polyethylene Terephthalate Bottle Waste: Tensile and Fracture Behavior.

This work provides an experimental analysis regarding the fracture behavior of recycled opaque PET (rPET-O) containing titanium dioxide (TiO2) under plane stress conditions. For this purpose, a commercially post-consumer transparent colored/opaque PET flakes mix was processed using a semi-industrial extrusion calendering process. The manufactured rPET-O sheets had a TiO2 content of 1.45 wt.%. The mechanical and fracture properties of unaged and physically aged (1 year) samples were determined through uniaxial tensile experiments and the Essential Work of Fracture (EWF) methodology, respectively, and were compared to those of recycled transparent PET (rPET-T). Under tensile loading, independently of the aging time, rPET-O samples exhibited similar mechanical behavior as rPET-T up to the yield point. The main differences remained in the post-yielding region. The presence of TiO2 particles allowed reducing the strain energy density up to neck formation in aged samples. Regarding the EWF analysis, it is argued that the energy consumed up to the onset of crack propagation (we) for rPET-T was mainly dependent of the molecular mobility. That is, the we value decreased by 26% when rPET-T was physically aged. Interestingly, we values remained independent of the aging time for rPET-O. In fact, it was highlighted that before crack propagation, the EWF response was principally governed by matrix cavitation ahead of the crack tip, which allowed a significant release of the triaxial stress state independently of the molecular mobility. This property enabled rPET-O to exhibit a resistance to crack initiation 17% higher as compared to rPET-T when the material was physically aged. Finally, independently of the aging time, rPET-O exhibited a resistance to crack growth approximately 21% larger than rPET-T due to matrix fibrillation in large scale deformation.

Numerical investigation of FRP-confined short square RC columns

Finite element (FE) simulation of confined RC columns is a complex task, as it involves the precise representation of a concrete material model that could express the volumetric change of concrete under a triaxial state of stress. The problem of confining RC columns using fiber-reinforced polymer (FRP) is more complex. This is due to the passive nature of FRP containment. Recently, the concrete damage plasticity (CDP) model available in an FE software product (ABAQUS) has been widely used to represent RC columns subjected to axial loading. The present paper aims to calibrate the concrete dilatancy angle and viscoplastic regularization parameters in the CDP model for the applications of square RC columns confined with FRP sheets. Ten experimental FRP-confined RC column specimens are incorporated in the calibration. In addition, a parametric study is investigated, including 96 cases, to obtain the influence of various design variables on the ratio between the confined to unconfined concrete compressive strength (fcc/fc). Four design variables are considered (i.e., the corner radius, concrete compressive strength, FRP reinforcement ratio, and cross-sectional size of columns). The study also focuses on assessing the reliability of four design codes: ACI-440, ECP-208, CSA-S806 and FIB-Bulletin-14. The numerical results show that a viscoplastic regularization with a fixed value equal to 0.0005 could provide accurate behavior. Nevertheless, the dilation angle cannot be considered a fixed value and should be related to the confinement degree coefficient Cd, which depends on the cross-sectional geometrical and FRP properties. Among the four considered design codes, ACI-440 and ECP-208 provide more accurate behavior than CSA-S806 and FIB-Bulletin-14.

Statistical Errors in X-Ray Triaxial Stress Analysis by Cos α Method

Currently, the sin2ψ method is established as an effective technique as how to measure the residual stress state of metal materials non-destructively by X-ray diffraction. In recent years, new X-ray stress measurements with two-dimensional detector are developed and spreading in the world. There is the cosα method as one of the new techniques. However, the research about the statistical errors in the method continues. The measurement theory of the cos α method is reviewed on the triaxial stress state. The triaxial stress analysis by the method is examined and discussed from a viewpoint of the derived errors for the determination.

Micromechanical study on hard rock strainburst using the discrete element method

Rock strainburst is a geological hazard occurred under high triaxial stress states, posing a great threat to the safety of underground constructions. It is well-known that the in-situ axial stress state of hard rock has significant impacts on its strainburst strength and fracture pattern. However, the effects of axial stress on the strainburst process and micro-cracking behavior ofrock have not been well understood. This paper aims to investigate the strainburst mechanism from the micromechanics perspective using Discrete Element Method (DEM). The microscale parameters of rock are obtained through a calibration process with different laboratory tests of hard rock under both tension and compression loadings. Consequently, a series of true strainburst tests of rock under a wide range of axial stresses are simulated, and numerical results show good agreements with experimental data, which verify the capability of the calibrated model in reproducing the mechanical response of rock strainburst. Based on this, the effects of axial stress on cracking behavior are further analyzed. It is found that the crack density and strainburst strength of specimens tend to increase with growing axial stress, and this trend is shown to be independent of sample size and frictional properties. In addition, the strainburst crack mode exhibits a transition from tensile dominated to tensile-shear mixed when the axial stress increases.

Evaluation Method of Rock Brittleness under True Triaxial Stress States Based on Pre-peak Deformation Characteristic and Post-peak Energy Evolution

Deep rock masses are in true triaxial stress (TTS) fields, and few studies have examined the brittleness evaluation of rock under TTS thus far. In particular, research has not been conducted on the brittleness evaluation index and the effect of TTS. Therefore, based on a summary and analysis of pre-existing brittleness indexes, this paper proposes a brittleness index of rock under TTS that considers both stress-induced anisotropy and energy conversion characteristics during Class I behavior and Class II behavior. Meanwhile, the studied brittleness index is analyzed and verified. The brittleness of rock was found to increase with increasing σ2 while σ3 is constant; when σ2 is constant, the rock brittleness decreases with the increase in σ3. When σ3 is high, the increase in the rock brittleness amplitude with increasing σ2 is large; conversely, when σ3 is low, the amplitude is small. For the same σ3 (σ3 = 5 MPa), the order of brittleness of the three rocks is basalt > granite > marble. Finally, this paper shows that the proposed brittleness index can be applied to conventional triaxial and uniaxial stresses. In addition, under different TTS, a brittleness threshold of σ2/σ3 = 5 was found for the rocks, and when σ2/σ3 < 5, the rock brittleness enters a stress sensitive zone. The research results in this study can provide a relevant basis and guidance for the study of the brittle fracture process and the brittleness of rock under TTS.

СОВРЕМЕННЫЕ КРИТЕРИИ ПРОЧНОСТИ ДЛЯ БЕТОНОВ ПРИ ОБЪЕМНЫХ НАПРЯЖЕННЫХ СОСТОЯНИЯХ

Reliable assessment of the strength and deformations of concrete under multiaxial stress states is important for increasing the accuracy of analysis and design. Classical strength theories do not work for such materials as concrete due to the complex shear-pryout mechanism of its structural failure. Description of the key relations of strength criteria established by G.A. Geniev, G.A. Geniev – N.M. Alikova, E.S. Leites, A.V. Yashin, S.F. Klovanich – D.I. Bezushko, K.J. Willam – E.P. Warnke and N.I. Karpenko is given. Assessment of the compliance of the design strength with the experimental data under uni-, bi- and triaxial stress states is made. Strength criteria that most closely describe the experimental data in the specific areas of the stress state are determined. It has been found out that the most developed strength conditions are the ones developed by S.F. Klovanich – D.I. Bezushko, K.J. Willam – E.P. Warnke and N.I. Karpenko. The criteria introduced by E.S. Leites and A.V. Yashin describe the experimental data under conditions of the plane stress state with sufficient accuracy. The strength conditions established by G.A. Geniev and G.A. Geniev – N.M. Alikova require careful use, taking into account their deviations from the experimental data in certain areas of triaxial stress states. Loading programs in the process of experimental research of concrete strength aimed at identifying the forms of functions of meridional and deviatoric curves more accurately have been determined.

Real-time evolution of oil shale meso-structure under triaxial stress condition

It is significant to research the mechanical properties and micro-fracture evolution characteristics of oil shales with different bedding directions under the condition of in-situ triaxial stress loading for understanding the internal micro-characteristics of oil shales. Triaxial stress loading tests of cylindrical oil shales were carried out in two loading directions perpendicular to and parallel to the bedding, which is the S1 and S2 samples. Our results demonstrate that the oil shales are typical anisotropic and brittle fracture characteristics. The triaxial compressive strength of S1 is higher than that of S2, but the elastic modulus is almost the same. Based on the reconstructed 3D-CT image, we analyzed the dynamic evolution law of the fracture inside the sample in the horizontal and vertical directions, and obtained the distribution of the fracture in the loading process, finally revealing the internal micro-characteristics of oil shales under the different loading conditions.

Physical modeling of deformation and filtration processes in low-permeability reservoir rocks when implementing the directional unloading method

This article describes the results of physical modeling of deformation and filtration processes in low-permeability reservoir rocks of the Achimov deposits of the Urengoy gas condensate field. The experiments were carried out on a unique true Triaxial Independent Loading Test System (TILTS) of the Institute for Problems in Mechanics of the Russian Academy of Sciences. The effect of the non-uniform triaxial stress state on the character of deformation and filtration processes in rocks was studied. Real stresses that occur in the bottomhole formation zone when the pressure in the well decreases were created in the rock specimens. Experiments were carried out to simulate the stress state at the walls of the open hole and at the tip of the perforation hole. The geomechanical approach is shown to be promising for creating ways to improve the quality of wells; in particular, the adaptation of the directional unloading method for the conditions of a given reservoir is considered. These studies are essential both in fundamental scientific and practical terms to substantiate technological solutions in the development of fields with low-permeability reservoirs.

Stress-path-dependent effective medium model for granular media — Comparison with experimental data

Modeling velocity changes in response to stress changes plays an important part in understanding seismic responses from the subsurface. One branch of such modeling consists of treating an assemblage of grains as an effective medium and using established grain contact theories to determine the elastic moduli. Such models are commonly limited to hydrostatic or uniaxial strain scenarios, not capable of capturing the anisotropy induced by a general triaxial stress state. A new set of expressions is developed by extending an existing effective medium theory to a general stress state in which the radial (horizontal) stress is different from the axial (vertical) stress. The theory is valid at the limits of slip and no slip. Novel functions to combine the no-slip and slip limits are implemented to match the model to observed laboratory data on glass beads and sand grain assemblages loaded along different stress paths. The new expressions provide a good agreement between the modeled and measured stress and stress path dependence of the compressional wave (P-wave) and shear wave velocities and associated P-wave anisotropy. This stress dependence is of particular interest in rock-physics modeling workflows evaluating time-lapse feasibility for shallow or unconsolidated sand reservoirs or for characterizing burial history.

ЛОКАЛИЗАЦИЯ ПЛАСТИЧЕСКОЙ ДЕФОРМАЦИИ ТЕХНИЧЕСКИ ЧИСТОГО ТИТАНА В СЛОЖНОМ НАПРЯЖЕННОМ СОСТОЯНИИ ПРИ ВЫСОКОСКОРОСТНОМ РАСТЯЖЕНИИ

In this work, the effect of a triaxiality stress state on the mechanical behavior and fracture of commercially pure titanium VT1-0 (Grade 2) in the range of strain rates from 0.1 to 1000 s−1 is studied. Tensile tests are carried out using a servo-hydraulic testing machine Instron VHS 40 / 50-20 on flat specimens with a constant cross-sectional area and on flat specimens with a notch. To study the effect of the complex stress state on the ultimate deformation before fracture, the samples with the notch of various radii (10, 5, 2.5 mm) are used in the experiments. Phantom V711 is employed for high-speed video registration of specimen’s deformation. Deformation fields in a working part of the sample are investigated by the digital image correlation method. It is shown that the effect of the strain rate on the ultimate deformations before fracture has a nonmonotonic behavior. An analysis of strain fields in the working part of the samples shows that the degree of uniform deformation of the working part decreases with an increase in the strain rate. At strain rates above 1000 s−1, the shear bands occur at the onset of a plastic flow. Commercially pure titanium undergoes fracture due to the nucleation, growth, and coalescence of damages in the bands of localized plastic deformation oriented along the maximum shear stresses. The results confirm that the fracture of commercially pure titanium exhibits ductile behavior at strain rates varying from 0.1 to 1000 s−1, at a triaxiality stress parameter in the range of 0.333 ≤ η &lt;0.467, and at a temperature close to 295 K.

Fracture evolution in mudstone specimens containing a pre-existing flaw under true triaxial compression

In this study, a novel true triaxial loading device that can be paired with an X-ray computerized tomography (CT) scanning system was developed. Using this test equipment, a series of in-situ CT scans of mudstone specimens containing a pre-existing flaw were performed under two true triaxial stress states, namely, the intermediate principal stress parallel to the pre-existing flaw (IPSPPF) and the minimum principal stress parallel to the pre-existing flaw (MPSPPF). The results showed that the difference between the two lateral deformations of the specimen under the IPSPPF condition was more significant than that under the MPSPPF condition and that the stress level of the specimen entering the damage stage under the IPSPPF condition was less than that under the MPSPPF condition. Under the IPSPPF condition, two wing cracks formed in the damage stage first, and an anti-wing crack and a far-field crack then formed successively in the post-peak stage. The surfaces of these four cracks were all parallel to the front edge of the pre-existing flaw. After failure, the pre-existing flaw in the specimen remained fully open. Conversely, under the MPSPPF condition, a far-field crack appeared first in the damage stage, which stopped propagating after intersecting the pre-existing flaw. Concurrently, a wing-like crack and an anti-wing-like crack formed at the tips of the pre-existing flaw in the damage stage, and a new far-field crack formed in the post-peak stage. The surfaces of these four cracks were all perpendicular to the front edge of the pre-existing flaw. The pre-existing flaw was cut off at multiple locations by these cracks and eventually collapsed in large areas. Under both conditions, the inclination angles of all of the cracks in the cross sections of the specimens with respect to the direction of the intermediate principal stress were approximately 0°.

Investigating fracture propagation characteristics in shale using sc-CO2 and water with the aid of X-ray Computed Tomography

The further development of unconventional resources is anticipated to increase the intensity of hydraulic fracturing operations. Injecting water-based fracturing fluids into shale formations, especially shales producing gas, may have adverse impacts of water blocking, scale formation, and water-sensitive clay minerals. Accordingly, nonaqueous candidates such as carbon dioxide (CO2) need to be explored to avoid injection of millions of gallons of water and to increase the effectiveness of stimulation jobs. This study investigates fracturing behavior accompanying supercritical carbon dioxide (sc-CO2) injection compared to water. A High Pressure High Temperature (HPHT) triaxial cell was utilized to conduct shale breakdown experiments under reservoir-like conditions. Furthermore, the experimental setup allows continuous monitoring of in situ details using X-ray Computed Tomography (CT). Here, CT images were utilized for the first time to investigate and confirm the breakdown pressure using Fast Iterative Digital Volume Correlation (FIDVC) that permits visualization of in situ deformation and strain. One inch diameter Green River shale samples were fractured under triaxial stress conditions. Results demonstrated a roughly 2 to 3 times greater breakdown pressure for sc-CO2 compared to water for the samples studied. Compressive infiltration stress might explain such behavior, and mineralogy is believed to be a major contributor to such differences between injectants. Under isotropic horizontal stresses, sc-CO2 induces fractures propagating almost independent of bedding planes. This is a promising finding for probable larger stimulated volume achieved by sc-CO2. CT imaging to monitor fracture propagation demonstrated excellent performance in detecting fracture propagation. We anticipate this technique to help significantly when monitoring fracture propagation mechanisms for laboratory samples with slow pressurization as well as studies of slip on pre-existing fractures.

Stress–strain relationship of cement paste under triaxial compression

Understanding the stress–strain behaviour of cement-based materials is important for the performance modelling of concrete structures. This work studied the stress–strain behaviour of cement paste under a triaxial stress state with varying confining pressures. The influence of confining pressure on peak stress, peak strain and volume change was studied using the experimental results obtained from cement paste samples with compressive strengths of 28 and 35 MPa. The samples were tested under four confining pressures (0, 5, 10 and 15 MPa). A simple equation for the strain at peak compressive strength was developed from linear regression analysis of the test data and available results in the literature. The commonly used stress–strain model for concrete was adopted to model the behaviour of cement paste. A functional relationship for model parameters was developed and calibrated using the experimental results. As expected, the obtained results demonstrated that the strength and ductility of cement pastes are significantly improved due to confinement. The relationship between lateral and axial strains was found to be linear. Overall, the proposed model showed good agreement with the experimental results and can be used to numerically analyse structures with cement paste (e.g. oil wells).

Enhancing coalbed methane recovery with liquid CO2 fracturing in underground coal mine: From experiment to field application

CO2 is both a primary greenhouse gas and an available energy source. In this study, a new type of underground coal permeability enhancement technique by liquid CO2 (L-CO2) fracturing is proposed. The key parameters that determine the feasibility of the technique are identified: L-CO2 injection pressure and flow rate. Based on the principle of stress superposition and the experiments for L-CO2 fracturing under true triaxial stress conditions, the calculation models of the initiation pressure and flow were determined. The mathematical model of the initiation pressure of the L-CO2 fracturing of coal is verified, and the quantitative relationship between the injection flow rates of L-CO2 and hydraulic fracturing is derived. Accordingly, a complete set of underground high-pressure (30 MPa) L-CO2 fracturing equipment for coal permeability enhancement is developed. A field test of the coal permeability enhancement by fracturing in an upward cross-borehole was performed. The results confirm that after the fracturing, the gas drainage mixed flow and pure flow of the observation borehole that was located 25 m distant from the fracturing borehole increased by 3.2 and 3.3 times, respectively, and the maximal CO2 concentration in the observation borehole was 40%. The influence radius of the L-CO2 fracturing was determined to be approximately 25 m. Compared with areas with no coal permeability enhancement measures, the average single-borehole gas drainage concentration increased by approximately 1.57 times, and the pure flow increased by approximately 1.82 times within a radius of 25 m after L-CO2 fracturing.

A dynamic constitutive model of ultra high toughness cementitious composites

In this study, an explicit dynamic constitutive model was established for ultra high toughness cementitious composites (UHTCCs). The model, based on the Holmquist–Johnson–Cook (HJC) model, includes tensile and compressive damage evolution, hydrostatic pressure, strain rate, and the Lode angle effect. The proposed model was embedded in LS-DYNA software and then comprehensive tests were carried on a hexahedral brick element formulation under uniaxial, biaxial, and triaxial stress states to verify its rationality through comparisons with results determined by the HJC and Karagozian & Case (K&C) models. Finally, the proposed model was used to simulate the damage caused to UHTCC targets subjected to blast by embedded explosive and projectile penetration, and predictions were compared with corresponding experimental results. The results of the numerical simulations showed that our proposed model was more accurate than the HJC model in predicting the size of the crater, penetration depth, and the distribution of cracks inside the target following the blast or high-speed impact loading.

Study on Mechanical Properties of the Basalt Fiber-Rubber Granular Concrete under Triaxial Stress Condition and Its Application

To reduce the failure probability of rigid supporting structures caused by large deformation of deeply buried high-stress soft rock roadways, the mechanical properties and failure features of basalt fiber-rubber granular concrete (BFRGC) are investigated based on triaxial compression tests. The post-peak strain softening equations of BFRGC, based on the Mohr–Coulomb yield criterion, are deduced and then compiled in the finite-difference software (FLAC3D) to simulate the post-peak strain-softening process of BFRGC. Combined with practical engineering, the supporting effects of BFRGC with different proportions are evaluated by FLAC3D. The results of compression tests show that the yield strength of the BFRGC increases significantly when the mass percentage of basalt fiber is 0.4%. Moreover, mixing basalt fibers into both the plain concrete and rubber concrete can effectively restrain the development of the fractures under three-dimensional stress. The numerical results show that when the mass fractions of basalt fibers and rubber particles are 0.4% and 5–10%, respectively, both the plastic zone in the surrounding rocks and the deformation of the rigid supporting structures decrease obviously. It is indicated that the optimal ratio of BFRGC can effectively reduce the stress concentration around the roadway and improve the overall bearing capacity of the supporting structures.

Considerations when calculating the mechanical properties of single crystals and bulk polycrystals from molecular dynamics simulations

ABSTRACT The choice of a proper interatomic potential is critical to obtaining accurate and realistic molecular dynamics results. However, previous studies that have tested the suitability of a potential to predict mechanical properties often do so using elastic constants from a triaxial stress state that ignores Poisson’s effect. While this method is suitable it is not consistent with macroscale experimental methods and cannot provide the complete loading behaviour. Further, there is a lack of knowledge as to whether accuracy in predicting elastic constants from a fixed volume condition indicates accuracy for elastic moduli from uniaxial tensile simulations. Moreover, those studies that did account for Poisson’s effect studied only one crystal orientation and thus assumed potential accuracy is independent of crystal orientation. Results from the current study demonstrated that accuracy of a potential is dependent on the crystal direction. Further, the most accurate potentials for elastic constants calculated using a fixed volume condition were not necessarily the most accurate at predicting elastic moduli from a physically realisable tension test. Finally, the Voigt Reuss Hill (VRH) method was shown to accurately predict polycrystalline mechanical properties from single crystal data as a function of temperature.

Experimental Testing of Masonry Subjected to Concentrated Load in Direction of Bed Joints

One of the options for rehabilitating existing masonry buildings is a post-tensioning of masonry. The deformation properties of the masonry in the direction parallel to bed joints are essential for the design of a suitable value of the applied force. However, these values are usually not available or are defined only roughly. The aim of this study was to determine, as accurately as possible, the deformation characteristics of the masonry in the direction parallel to the bed joints. Experimental measuring of masonry samples was carried out in laboratory facilities designed specifically for testing the triaxial state of stress of the masonry. The obtained deformations were used to determine the modulus of elasticity of the masonry in the direction of bed joints. Within these experimental tests, laboratory measuring of mechanical masonry properties was carried out, and deformation characteristics were defined on the basis of calculations. The strengths of masonry units and mortar were tested in the laboratory and, according to the tests results, the modulus of elasticity in the direction perpendicular to bed joints was determined. The modulus of elasticity in the direction parallel to bed joints was verified through a simple numerical model. The calculated deformations were compared with the measured values. On the basis of the determination of the deformation characteristics of masonry in the direction of bed joints, the ratios of the modulus of elasticity in the direction perpendicular and parallel to bed joints were concluded.

Behavior of polyethylene under different triaxial stress states: An experimental and numerical study

The behavior of a semi-crystalline polymer under different triaxial stress states is studied through the combination of experimental testing and finite element simulation. Polyethylene round bar specimens with four different notch radii were stretched at crosshead speed of 1 mm/min until fracture. The continuum damage mechanics damage model and Gurson–Tvergaard–Needleman damage model were proposed and applied to the finite element simulation. The results of engineering stress–displacement curves determined from finite element simulation match experimental results. Finite element simulation without considering damage and with the consideration of damage was conducted to determine the damaged and undamaged true stress–strain relationship of polyethylene materials, respectively. Damage evolution model was established based on the degradation of true stress. The finite element model was further applied to study the distribution of stress triaxiality for specimens with different notch radii and the effect of stress triaxiality on damage evolution, critical damage parameters, and fracture strain. The results show that the distribution of the stress triaxiality on the cross section of the specimen is not uniform, and as the stress triaxiality increases, the position where the maximum stress triaxiality occurs moves from the center point to two-third the radius from the center. Furthermore, the damaged true stress and the undamaged true stress increases with the decrease of the stress triaxiality when the strain is below 0.3, but decreases with the increase of stress triaxiality when the strain is larger than 0.3. In addition, it was found that the greater the stress triaxiality, the earlier the onset of damage and the faster the evolution, but the smaller the fracture strain.