Increase In Σ3 Research Articles

Failure characteristics and brittleness index establishment based on marble energy evolution mechanism

The “carbon peak” and “carbon neutrality” require a continuous increase of clean energy supply, and hydropower shares a big portion of clean energy in China. The Jinping II Hydropower station is the biggest one and its main surrounding rock is marble. Thus, the failure characteristics of its marble holds great significance in safely and economically devising support measures of tunnel groups in this station. In this study, triaxial compression tests were conducted on the deep-buried marble to elucidate their formation mechanism and failure characteristics. Further, the 3D CT reconstruction was conducted for the evolution of microstructures. Finally, a new brittleness evaluation index (BNew) was formulated based on the pre-peak energy evolution and the post-peak stress drop to accurately evaluate the influence of confining pressure (σ3) on rock brittleness. The test results indicate that the strength values (σP and σeh) at segment points increase linearly with the increase of σ3, while the corresponding axial strains (ɛP and ɛeh) at these strength points also show a linear increase. The 3D CT reconstruction results reveal that the failure characteristics of the marble mainly have four types: ‘I’ type shear, ‘II’ type tensile–shear, ‘III’ type tensile–shear, and ‘y’ type conjugate shear. With the increase of σ3, the spatial distribution of crack characteristics in samples gradually shifts from complexity to simplicity and then back to complexity. The accumulated volume of cracks first decreases and then increases.

Plastic deformation behavior and strengthening mechanism of SLM 316L reinforced by micro-TiC particles

In this work, the integrated study on the microstructure evolution, plastic deformation behavior, and strengthening mechanism of Selective Laser Melting (SLM) 316L austenitic stainless steel (ASS) reinforced with micro-TiC particles was investigated. The results indicated that there were lots of small angle grain boundaries in SLM 316L ASS, and the high dislocation density and component segregation of the cellular dislocation structure resulted in a good combination of high strength and good elongation in performance. The tensile strength, yield strength, and elongation of SLM 316L ASS were 682 MPa, 571 MPa, and 49.9%, respectively. The addition of TiC reinforced particles induced microstructure evolution, including grain refinement, reduction of epitaxial columnar dendrites, reduction of low angle grain boundary (LAGB) ratio and increase of Σ3 (60°/<111>) twin boundaries. Through the effects of grain refinement strengthening, Orowan strengthening, and dislocation strengthening, SLM 316L-2TiC showed a higher tensile strength of 1021 MPa and higher yield strength of 809 MPa, while maintaining an elongation of 30.8% due to the suppression of plasticity by twinning induced plasticity (TWIP) effect. Although nano-reinforced particles were commonly used to improve mechanical properties, in our work, we chose to add micrometer-sized TiC particles, and the strength of the SLM 316L-2TiC metallic matrix composites (MMCs) exceeded the previous reports of adding nanoparticles. The reason was that the small contact angle between TiC and 316L provides good wettability between the particles and the melt, and the selection of laser processing parameters ensures good bonding between TiC particles and the substrate.

Failure mode and the mechanism of methane hydrate-bearing clayey sand sediments under depressurization

Failure mode prediction of hydrate-bearing sediments (HBSs) is crucial for accurate evaluation of reservoir mechanical properties and safe exploitation of hydrate resources. In this study, the variation of HBS failure mode with hydrate dissociation degree (Dhd) and effective confining stress (σ3′) and its micro-mechanism were investigated. The results show that the stress-strain curve of HBS shifts from strain-softening to strain-hardening as Dhd and σ3′ increase. The failure strength and residual strength of the sample are negatively correlated with Dhd but positively correlated with σ3′. The increase of Dhd results in a reduction in the cohesion of HBS from 608.74 to 2.49 kPa and a shift in the internal friction angle from increasing to decreasing. The post-shear sample indicates a minimum porosity of 11.47% under the highest Dhd and σ3′ conditions. The increased pore volume available for particle rearrangement resulting from the increase in Dhd, and the enhanced confining effect on the sample due to the increase in σ3′, result in a volume shrinkage characterized by plastic strain-hardening failure mode. A prediction model of HBS failure mode based on the classification of strain-hardening and strain-softening degrees of stress-strain curves was developed and verified using published results.

Study on Dynamic Modulus and Damping Characteristics of Modified Expanded Polystyrene Lightweight Soil under Cyclic Load.

In recent years, expanded polystyrene (EPS) lightweight soil has been widely used as subgrade in soft soil areas because of its light weight and environmental protection. This study aimed to investigate the dynamic characteristics of sodium silicate modified lime and fly ash treated EPS lightweight soil (SLS) under cyclic loading. The effects of EPS particles on the dynamic elastic modulus (Ed) and damping ratio (λ) of SLS were determined through dynamic triaxial tests at various confining pressures (σ3), amplitudes, and cycle times. Mathematical models of the Ed of the SLS, cycle times, and σ3 were established. The results revealed that the EPS particle content played a decisive role in the Ed and λ of the SLS. The Ed of the SLS decreased with an increase in the EPS particle content (EC). The Ed decreased by 60% in the 1-1.5% range of the EC. The existing forms of lime fly ash soil and EPS particles in the SLS changed from parallel to series. With an increase in σ3 and amplitude, the Ed of the SLS gradually decreased, the λ generally decreased, and the λ variation range was within 0.5%. With an increase in the number of cycles, the Ed of the SLS decreased. The Ed value and the number of cycles satisfied the power function relationship. Additionally, it can be found from the test results that 0.5% to 1% was the best EPS content for SLS in this work. In addition, the dynamic elastic modulus prediction model established in this study can better describe the varying trend of the dynamic elastic modulus of SLS under different σ3 values and load cycles, thereby providing a theoretical reference for the application of SLS in practical road engineering.

Three-Parameter Twin τ2 Strength Theory for Brittle Materials under Multiaxial Stress State and Its Application

The strength failure of brittle materials under complex stress is an important problem. Herein, we propose a novel three-parameter twin τ2 strength theory considering the influence of hydrostatic pressure and normal stress on the principal shear-stress surface, derive a mathematical expression for the strength theory, and compare the theoretical predictions under several stress states with existing experimental data. The results show that different ultimate stress ratios, α and β, correspond to different strength theories for brittle materials. The principal stress σ1 increases gradually with an increase in σ2 (=σ3) under the stress state σ1 &gt; σ2 = σ3; σ1 (=σ2) increases gradually with an increase in σ3 under the stress state σ1 = σ2 &gt; σ3. Furthermore, the biaxial compressive strength is considerably higher than the uniaxial compressive strength under the biaxial compressive stress for σ1 &gt; 0, σ2 &gt; 0, and σ3 = 0. When σ3 is fixed and σ2 is relatively small under the stress states of σ1 &gt; 0, σ2 &gt; 0, and σ3 &gt; 0, the maximum principal stress σ1 increases with the increasing σ2. When σ2 is relatively large and as σ1 gradually decreases with the increasing σ2, the effect law of intermediate principal stress σ2 is obtained.

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.

Experimental Study on Mesodamage of Migmatite Under Cyclic Loading and Unloading

To study the mesodamage of migmatite under cyclic loading, single cycle loading and unloading tests of migmatite were carried out under different confining pressures (σ3) and stress ratios (p), and acoustic emission (AE) technology was used to monitor the evolution of microcracks. Additionally, the mesodamage of migmatite was analyzed from the porosity and T2 spectrum distribution measured by nuclear magnetic resonance (NMR) spectroscopy. The results show that the peak stress ratios (pmax) of migmatite under different σ3 are different, and as the value of σ3 increases, the migmatite gradually undergoes a change from tension to shear failure. Moreover, with the increase in σ3, high-frequency signals gradually appeared, indicating that the increase of σ3 to a certain extent limited the generation of large size microcracks. The variations in damage variables defined by the number of AE hits and porosity are the same, “steep increment type,” and increase suddenly when approaching pmax. Furthermore, σ3 slightly affects the pore throat distribution of migmatite. In addition, σ3 has a certain inhibitory effect on the porosity of migmatite and accumulation of mesodamage. However, when σ3 exceeds a critical value, the inhibitory effect becomes a promoting effect.

Failure properties of cubic granite, marble, and sandstone specimens under true triaxial stress

Cubic specimens of granite, marble, and sandstone, with side lengths of 50 mm, were prepared in the laboratory. True triaxial compression tests were conducted on each rock type with minor principal stress (σ3) magnitudes of 10, 20, 30, 50, and 100 MPa and the intermediate principal stress (σ2) varying from σ2 = σ3 to σ2 = σ1 (where σ1 represents the major principal stress). The experimental results demonstrated that the failure strength, fracture dip angle, non-linear behavior and failure mode of these rocks under true triaxial conditions were affected by both σ2 and σ3, as well as by the rock lithology. When σ3 was kept constant and σ2 increased, failure strength showed an initial increase followed by a decrease, whereas the fracture dip angle increased monotonically. The non-linear behavior before the peak strength point of granite became more apparent by the increase of σ3, whereas σ2 had an opposite effect on the non-linear behavior of granite under high σ3 (e.g. 100 MPa). The non-linear behavior before the peak strength point was always found in marble and sandstone for all of the stress state conditions. Analyses of fracture dip angle and failure mode showed that when σ3 = 10, 20, and 30 MPa and σ2/σ3 ≥ 5, 7.5, and 10, respectively, the failure mode of granite changed from shear to slabbing, whereas marble and sandstone always fractured in the shear direction. This study confirms that rocks may experience slabbing failure under true triaxial stress, and slabbing failure mode is likely to be induced in high-strength and brittle rocks under low σ3 with the stress ratio of σ2/σ3 exceeding a particular threshold value.

Damage Ratio Based on Statistical Damage Constitutive Model for Rock

The study of damage characteristics of rock mass is of great significance to the analysis of rock mass structure. According to the characteristics of the microscopic unit strength of rock with random distribution, the Weibull distribution is widely used as the statistical functions of the strength of the microunit of rock to establish the damage constitutive model. The concepts of damage ratio De and damage index Cc are proposed. Damage ratio is mainly used to describe the law of damage evolution in rock. Damage index can be used to evaluate the damage degree of rock. The influence of confining pressure on distribution parameters and damage ratio is analyzed through uniaxial and triaxial compression tests of sandstone. The results show that damage ratio is an index of structural characteristics of rock damage, which can reflect the evolution characteristics of microcracks in rock under spatial stress. Critical damage ratio refers to the damage ratio corresponding to the peak stress of rock and can be used as a parameter to characterize the strength of rock for corresponding to the peak strain one to one. The critical damage ratio is linearly related to the logarithmic function of confining pressure. Its relationship is as follows: Der=Ccln⁡σ3+b. With the increase of σ3, the increasing trend of Der slows down and gradually tends to a certain value. The larger the damage index is, the more serious the damage of rock is. The smaller the damage index is, the less serious the damage of rock is. Therefore, the damage index can be used to evaluate the damage degree of rock. It will be an important direction of rock damage mechanics research to distinguish the severity of rock damage by using damage index as the limit value.

DEM simulations of sandstone under true triaxial compressive tests

Numerically simulated true triaxial compression tests (σ 1 ≥ σ 2 ≥ σ 3) are conducted in this study to elucidate the failure mechanism of sandstone using 3D discrete element method (DEM), in particular the effect of the intermediate principal stress (σ 2). Eight series of tests (σ 3 = 0, 10, 20, 30, 40, 50, 70, and 100 MPa) are conducted. Within each series, σ 2 is varied from σ 2 = σ 3 to σ 2 = σ 1 from test to test. For each test, σ 1 is raised monotonically to failure while keeping σ 2 and σ 3 constant. The DEM simulations reveal the effect of σ 2 on the variations of peak stress, Young’s modulus, failure plane angles, the brittle–ductile transition, and the evolution of failure modes, the effect beyond the well-understood effect of σ 3. The simulation is in qualitative agreement with the results obtained experimentally. Detailed analyses performed on the particle-scale responses further the understanding of the microscopic mechanisms. The distribution of contact force becomes more homogeneous with the increase of σ 3, which leads to the resulting damage being more localized rather than diffused. The interaction between contact force distribution and coalescence of cracks determines the processes and patterns of fracturing in the sample scale. σ 2 is found to affect the microscopic stress distribution as well as structure evolution, and this effect weakens with the increase of σ 3.

Effects of thermomechanical treatment on the occurrence of coincident site lattice boundaries in high strength low alloy steel

Many studies propose thermomechanical routes to improve HSLA (high strength low alloy) steels by microstructural modification but ignore the study of occurrence of CSL boundaries. The occurrence of these special boundaries is influenced by thermomechanical treatment in which the modification of misorientation profile is related with the increase of Σ3 and Σ11 boundaries and inhibition of Σ5 Σ7 and Σ9 ones. The formation of Σ3 boundaries, beneficial to improve strength, is highly stimulated by this treatment in which deformation plays an important role in the development of CSL boundaries.

Study of acoustic emission during deformation of rocks under conditions of a complex axisymmetric stressed state

1. A study of the laws for AE behavior with a complex stressed state has shown that the nature of the dependence for the number of AE signals depends markedly on the ratio of stressed state components for the specimen. 2. Localization is detected for the maximum AE intensity in a specific and quite narrow range of axial strains. The position of this range is almost independent of the level of side pressure and it corresponds to the transition zone from material densification to loosening. 3. The existence of a range for the maximum AE intensity is due to formation of cracks of tensile origin. The range of minumum AE intensity corresponds to the shear mechanism of deformation with a growing residual increase in material volume (quasiplastic deformation). 4. The amount and nature of AE behavior in the range of maximum intensity depends on material structure. For plastic materials the maximum is expressed more weakly than for more brittle materials. Material porosity leads to expansion of the zone of the maximum and to asymmetry of its shape. 5. The dependence of maximum AE intensity on the amount of specimen side pressure has been analyzed. It has been shown that for plastic materials the logarithm of AE intensity falls linearly with an increase in σ3.

ポリスチレン粉体圧縮成形体の三軸圧縮特性

Powdered polystyrene which was prepared by grinding at a temperature of liquid nitrogen was compacted into a cylindrical shape for a triaxial compression test. These specimens having various void fractions n0 were compressed at various confining pressures σ3.The mode of fracture of the specimens changed with an increase in σ3 or n0 from axial cleavage fracture to typical shear fracture, and then to shear fracture accompanied by consolidation. Yield loci were obtained from Mohr's stress circles using σ3 and the axial stress σ1 corrected by Taylor-Bishop's method. The yield criterion was expressed by τ2=μt2σ2+4σt(1+μt2)(σ+σt), where τ is shear stress, σ is the normal stress, μt is a constant, which is related to the sliding friction between particles and is close to the coefficient of effective internal friction, and σt is a constant corresponding to the tensile strength of the powder compact. The criterion can be related to the mechanisms of fracture of powder compacts. The second term of the criterion is larger than the first one under the condition where n0 and σ3 are small; in this case the specimens showed axial cleavage fracture which is characteristic of brittle materials. For larger values of n0 and σ3, on the other hand, the first term is larger than the second, and the specimens showed shear fracture.