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Showing papers on "Deformation (engineering) published in 2021"


Journal ArticleDOI
TL;DR: In this paper, a superhydrophobic micro-cracked conductive paper-based strain sensor was fabricated by coating conductive Ti3C2Tx MXene on printing paper via dip-coating process and followed by depositing super-hydrophilic candle soot layer on its surface.
Abstract: With the rapid development of wearable intelligent devices, low-cost wearable strain sensors with high sensitivity and low detection limit are urgently demanded. Meanwhile, sensing stability of sensor in wet or corrosive environments should also be considered in practical applications. Here, superhydrophobic microcracked conductive paper-based strain sensor was fabricated by coating conductive Ti3C2Tx MXene on printing paper via dip-coating process and followed by depositing superhydrophobic candle soot layer on its surface. Owing to the ultrasensitive microcrack structure in the conductive coating layer induced by the mismatch of elastic modulus and thermal expansion coefficient between conductive coating layer and paper substrate during the drying process, the prepared paper-based strain sensor exhibited a high sensitivity (gauge factor, GF = 17.4) in the strain range of 0–0.6%, ultralow detection limit (0.1% strain) and good fatigue resistance over 1000 cycles towards bending deformation. Interestingly, it was also applicable for torsion deformation detection, showing excellent torsion angle dependent, repeatable and stable sensing performances. Meanwhile, it displayed brilliant waterproof, self-cleaning and corrosion-resistant properties due to the existence of micro/nano-structured and the low surface energy candle soot layer. As a result, the prepared paper-based strain sensor can effectively monitor a series of large-scale and small-scale human motions even under water environment, showing the great promising in practical harsh outdoor environments. Importantly, it also demonstrated good applicability for spatial strain distribution detection of skin upon body movement when assembled into electronic-skin (E-skin). This study will provide great guidance for the design of next generation wearable strain sensor.

139 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of grain size on the strength and ductility of Mg alloys are summarized and fine-grained Mg-alloys with high strength and high ductility developed by various severe plastic deformation technologies and improved traditional deformation methods are introduced.
Abstract: Magnesium (Mg) alloys, as the lightest metal engineering materials, have broad application prospects. However, the strength and ductility of traditional Mg alloys are still relativity low and difficult to improve simultaneously. Refining grain size via the deformation process based on the grain boundary strengthening and the transition of deformation mechanisms is one of the feasible strategies to prepare Mg alloys with high strength and high ductility. In this review, the effects of grain size on the strength and ductility of Mg alloys are summarized, and fine-grained Mg alloys with high strength and high ductility developed by various severe plastic deformation technologies and improved traditional deformation technologies are introduced. Although some achievements have been made, the effects of grain size on various Mg alloys are rarely discussed systematically and some key mechanisms are unclear or lack direct microscopic evidence. This review can be used as a reference for further development of high-performance fine-grained Mg alloys.

111 citations


Journal ArticleDOI
TL;DR: Transmission electron microscopy reveals the electroplastic effects in a Ti–Al alloy, which can be uncoupled from Joule heating effects, and enhances wavy slip of dislocations, reconfiguring the dislocation pattern, and hence increases the ductility.
Abstract: It has been known for decades that the application of pulsed direct current can significantly enhance the formability of metals. However, the detailed mechanisms of this effect have been difficult to separate from simple Joule heating. Here, we study the electroplastic deformation of Ti–Al (7 at.% Al), an alloy that is uniquely suited for uncoupling this behaviour because, contrary to most metals, it has inherently lower ductility at higher temperature. We find that during mechanical deformation, electropulsing enhances cross-slip, producing a wavy dislocation morphology, and enhances twinning, which is similar to what occurs during cryogenic deformation. As a consequence, dislocations are prevented from localizing into planar slip bands that would lead to the early failure of the alloy under tension. Our results demonstrate that this macroscopic electroplastic behaviour originates from defect-level microstructural reconfiguration that cannot be rationalized by simple Joule heating. Transmission electron microscopy reveals the electroplastic effects in a Ti–Al alloy, which can be uncoupled from Joule heating effects. Electropulsing during deformation enhances wavy slip of dislocations, reconfiguring the dislocation pattern, and hence increases the ductility.

110 citations


Journal ArticleDOI
TL;DR: In this paper, three categories of samples with different interlayer deformation strains were fabricated by cold metal transfer (CMT) based wire-arc additive manufacturing (WAAM) technology and they were further investigated to evaluate the effects of inter layer deformation on the mechanical properties, microstructural evolution, and the underlying strengthening mechanism.
Abstract: The cold metal transfer (CMT) based wire-arc additive manufacturing (WAAM) technology has been widely recognized as a suitable method for fabricating large-sized aluminum alloy components. However, the poor mechanical properties of the as-deposited aluminum alloys prevent their wide application in the aerospace industry. In this paper, three categories of samples with different interlayer deformation strains were fabricated by WAAM. These samples were further investigated to evaluate the effects of interlayer deformation on the mechanical properties, microstructural evolution, and the underlying strengthening mechanism. The grain size distribution and internal sub-microstructure were characterized by electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). As compared to the as-deposited samples, the yield strength and ultimate tensile strength of the 50.8% deformed sample increased from 148.4 to 240.9 MPa and from 288.6 to 334.6 MPa, respectively. The microstructure of the samples with interlayer hammering exhibited highly refined grain, which is a combined result of deformation and subsequent intrinsic in-situ heat treatment induced by the next deposition layer. The recrystallized grains can be further deformed with subsequent hammering, which leads to an increase in dislocation density and contributes to an increase in ultimate tensile strength of the additively manufactured 2319 aluminum alloys with interlayer hammering.

93 citations


Journal ArticleDOI
Yang Wei1, Jiawen Bai1, Yirui Zhang1, Kunting Miao1, Kaiqi Zheng1 
TL;DR: In this article, a new high-strength seawater and sea sand concrete (HSSC)-filled circular FRP-steel composite tube (HFSCT) structure consisting of an internal FRP, carbon steel tube and external FRP was investigated.

69 citations


Journal ArticleDOI
TL;DR: In this article, 2195 aluminum alloy was compressed at 300-520°C using a Gleeble 3500-GTC thermo-mechanical testing system and the discontinuous dynamic recrystallization (DDRX) and continuous dynamic re-structure (CDRX), and the results demonstrated that during medium temperatures (300-360°C) deformation the main softening mechanism was DDRX, and at high temperatures (420-520 °C), it was CDRX.
Abstract: The 2195 aluminum alloy has been widely utilized in the aerospace field, of which dynamic recrystallization microstructures have a substantial effect on the mechanical properties of aerospace parts. In this study, 2195 aluminum alloy was compressed at 300–520 °C using a Gleeble 3500-GTC thermo-mechanical testing system. The discontinuous dynamic recrystallization (DDRX) and continuous dynamic recrystallization (CDRX) behavior of 2195 aluminum alloy at medium/high temperature was studied. The results demonstrated that during medium temperatures (300–360 °C) deformation the main softening mechanism was DDRX, and at high temperatures (420–520 °C), it was CDRX. CDRX of 2195 aluminum alloy involved three types of subgrain-forming mechanisms: dislocation tangling to form subgrains, microscopic shear bands to form subgrains, and the coalescence of two small subgrains to form larger subgrains. In addition, several recrystallized grains underwent geometric dynamic recrystallization (GDRX) at high temperature and extensive deformation (480 °C-80% or 520 °C-60%).

68 citations


Journal ArticleDOI
TL;DR: In this paper, a high-nitrogen duplex alloy design strategy was proposed to produce ultrastrong, tough, and low-cost high-entropy alloys.

67 citations


Journal ArticleDOI
Dan-Li Zhang1, Junshi Zhang1, J. Kuang1, Guozhi Liu1, J. Sun1 
TL;DR: In this paper, the authors developed a novel (NiCoCr)92Al6Ta2 medium-entropy alloy (MEA) towards superior cryogenic mechanical properties via elaborating the chemical composition designing and the thermo-mechanical processing.

67 citations


Journal ArticleDOI
TL;DR: In this article, the influence of selective laser melted (SLM) on the microstructure, deformation behavior, and mechanical properties of the Cu-Ni-Sn alloy compared with their cast (CC) counterparts was examined.

67 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigate the strain rate and dislocation density dependence of the strength of bulk copper and aluminum single crystals, and propose an analytical relationship between material strength, dislocations density, strain rate, and dislocations mobility.
Abstract: Dislocation glide is a general deformation mode, governing the strength of metals. Via discrete dislocation dynamics and molecular dynamics simulations, we investigate the strain rate and dislocation density dependence of the strength of bulk copper and aluminum single crystals. An analytical relationship between material strength, dislocation density, strain rate and dislocation mobility is proposed, which agrees well with current simulations and published experiments. Results show that material strength displays a decreasing regime (strain rate hardening) and then increasing regime (classical forest hardening) as the dislocation density increases. Accordingly, the strength displays universally, as the strain rate increases, a strain rate-independent regime followed by a strain rate hardening regime. All results are captured by a single scaling function, which relates the scaled strength to a coupling parameter between dislocation density and strain rate. Such coupling parameter also controls the localization of plasticity, fluctuations of dislocation flow and distribution of dislocation velocity. The relationship between the strain rate and micro-scale deformation in metals is still poorly understood. Here the authors use discrete dislocation dynamics and molecular dynamics to establish a universal relationship between material strength, dislocation density, strain rate and dislocation mobility in fcc metals.

66 citations


Journal ArticleDOI
TL;DR: In this article, the influence of cyclic wetting-drying weathering on mechanical behavior of a medium-grained sandstone is experimentally investigated, and the results show that the water absorption of the rock monotonically increases with the increase of the number of wettingdrying cycle in the treatment.

Journal ArticleDOI
TL;DR: In this paper, a multi-layered Zr-based BMGC with a well-controlled gradient in volume fraction of the crystalline dendrites via laser additive manufacturing (LAM) was designed to allow site-specific control of the cooling rate and the resultant microstructure.

Journal ArticleDOI
TL;DR: In this article, variations in the stress-strain curves, irreversible strain, elastic modulus, and Poisson's ratio are discussed and explained under triaxial cyclic unloading and loading conditions.
Abstract: In recent years, many studies have shown that it is meaningful to place rocks under stress paths corresponding to various loading and unloading conditions. However, the deformation evolution of rock under cyclic loading with consideration of the mechanical behavior and characteristics has rarely been studied under triaxial cyclic unloading and loading conditions. In practical engineering, particularly in underground or mining engineering, the stress increase in the rock mass in areas affected by mining is mainly caused by crack initiation and development when the rock is subjected to the effects of cyclic unloading and loading. In this study, variations in the stress–strain curves, irreversible strain, elastic modulus, and Poisson’s ratio are discussed and explained. The test results demonstrate that in comparison with a lower initial confining stress, increasing the initial confining pressure restrains the radial deformation of sandstone samples, and the degree of compaction of the sandstone samples rapidly increases in the failure stage. This results in the loss of the failure buffering process of the sandstone sample. Changes in the degree of compaction of the rock samples lead to obvious differences in the irreversible strain of the rock under different initial confining pressures and different limit unloading and loading cyclic confining stresses. The scanning electron microscopy and analysis results demonstrate that the macroscopic mechanical and microscopic physical properties of sandstone show different characteristics under different initial confining stresses.

Journal ArticleDOI
TL;DR: In this article, the authors showed that dislocations in AM metallic materials are self-stabilized even without the alloying effect, by forming Lomer locks and a complex dislocation network.

Journal ArticleDOI
TL;DR: In this paper, a high-entropy alloy with enhanced fatigue life by ductile transformable multicomponent B2 precipitates is reported, which is attributed to the high elasticity, plastic deformability and martensitic transformation of the B2-strengthening phase.
Abstract: Catastrophic accidents caused by fatigue failures often occur in engineering structures. Thus, a fundamental understanding of cyclic-deformation and fatigue-failure mechanisms is critical for the development of fatigue-resistant structural materials. Here we report a high-entropy alloy with enhanced fatigue life by ductile-transformable multicomponent B2 precipitates. Its cyclic-deformation mechanisms are revealed by real-time in-situ neutron diffraction, transmission-electron microscopy, crystal-plasticity modeling, and Monte-Carlo simulations. Multiple cyclic-deformation mechanisms, including dislocation slips, precipitation strengthening, deformation twinning, and reversible martensitic phase transformation, are observed in the studied high-entropy alloy. Its improved fatigue performance at low strain amplitudes, i.e., the high fatigue-crack-initiation resistance, is attributed to the high elasticity, plastic deformability, and martensitic transformation of the B2-strengthening phase. This study shows that fatigue-resistant alloys can be developed by incorporating strengthening ductile-transformable multicomponent intermetallic phases. A fundamental understanding of fatigue-failure mechanisms is key to develop robust structural materials. Here the authors report a high entropy alloy with enhanced fatigue life by ductile transformable multicomponent B2 precipitates, as revealed by combined experimental and simulation methods.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the hot deformation behavior and mechanism of the Ti-6554 alloy in the β single phase region, and found that the instability region was mainly concentrated in the high strain rate area, and the peak efficiency of power dissipation (η) region occurs in the temperature range of 913-928 ǫ c and the strain rate of 0.001−10 s−1 on the Gleeble-3500 thermal simulation machine.
Abstract: A new metastable β titanium alloy Ti–6Cr–5Mo–5V–4Al (Ti-6554) has shown good application potential in large parts. In order to study the hot deformation behavior and mechanism of the Ti-6554 alloy in the β single phase region, hot compression tests were carried out at temperatures of 800–950 °C and strain rates of 0.001–10 s−1 on the Gleeble-3500 thermal simulation machine. Strain-compensated Arrhenius constitutive model was used to predict the flow behavior of the alloy, and the correlation coefficient between the experimental and predicted values reached 0.982. Based on the hot processing map, it was found that the instability region was mainly concentrated in the high strain rate area, and the peak efficiency of power dissipation (η) region occurs in the temperature range of 913–928 °C and the strain rate of 0.001–0.0025 s-1. There was an obvious DRX phenomenon in the stability region, while the instability region was dominated by deformation band (DB) and flow localization (FL). The continuous dynamic recrystallization (CDRX) by progressive rotation of subgrains and discontinuous dynamic recrystallization (DDRX) by grain boundaries bulging could be observed. DDRX mainly occurred in high temperature and low strain rate regions, while the CDRX process occurred in the high strain rate region. As the η decreased, the deformation mechanism changed from DDRX to CDRX and further to dynamic recovery (DRV), DB, FL.

Journal ArticleDOI
TL;DR: Li et al. as discussed by the authors developed a new elastoplastic model for describing diffusion-induced deformation in the framework of high-density dislocation defects generated due to the migration of Li atoms.

Journal ArticleDOI
TL;DR: In this paper, a multiple level cyclic compressive loading experiments were conducted using GCTS RTR 2000 rock mechanics system on marble with F-T treatment of 0, 20, 40 and 60 cycles, and fracture evolution and energy dissipation mechanism were analyzed as well as the damage evolution characteristics.

Journal ArticleDOI
TL;DR: In this article, the deformation behavior of single crystals of the equiatomic Cr−Mn−Fe−Co−Ni high-entropy alloy (HEA) with the face-centered cubic structure has been investigated in tension and compression as a function of crystal orientation and temperature from 10 k to 13 k.

Journal ArticleDOI
TL;DR: In this paper, in situ straining transmission electron microscopy (TEM) experiments reveal a crystalline-to-amorphous phase transformation in an ultrafine-grained Cantor alloy.
Abstract: The Cantor high-entropy alloy (HEA) of CrMnFeCoNi is a solid solution with a face-centered cubic structure. While plastic deformation in this alloy is usually dominated by dislocation slip and deformation twinning, our in situ straining transmission electron microscopy (TEM) experiments reveal a crystalline-to-amorphous phase transformation in an ultrafine-grained Cantor alloy. We find that the crack-tip structural evolution involves a sequence of formation of the crystalline, lamellar, spotted, and amorphous patterns, which represent different proportions and organizations of the crystalline and amorphous phases. Such solid-state amorphization stems from both the high lattice friction and high grain boundary resistance to dislocation glide in ultrafine-grained microstructures. The resulting increase of crack-tip dislocation densities promotes the buildup of high stresses for triggering the crystalline-to-amorphous transformation. We also observe the formation of amorphous nanobridges in the crack wake. These amorphization processes dissipate strain energies, thereby providing effective toughening mechanisms for HEAs.

Journal ArticleDOI
TL;DR: In this article, a new Al0.9CoFeNi2 eutectic high entropy alloy (EHEA) was designed, and the microstructures as well as the deformation behavior were investigated.

Journal ArticleDOI
30 Aug 2021
TL;DR: In this paper, the surface deformation structures of turbine blade root of single crystal nickel-based superalloy produced under different creep feed grinding conditions were investigated and clarified and composed of a severely deformed layer with nano-sized grains (48-67 nm) at the topmost surface, a DFL with submicron sized grains (66-158 nm) and micron-sized laminated structures at the subsurface, and a dislocation accumulated layer extending to the bulk material.
Abstract: The service performance of the turbine blade root of an aero-engine depends on the microstructures in its superficial layer. This work investigated the surface deformation structures of turbine blade root of single crystal nickel-based superalloy produced under different creep feed grinding conditions. Gradient microstructures in the superficial layer were clarified and composed of a severely deformed layer (DFL) with nano-sized grains (48–67 nm) at the topmost surface, a DFL with submicron-sized grains (66–158 nm) and micron-sized laminated structures at the subsurface, and a dislocation accumulated layer extending to the bulk material. The formation of such gradient microstructures was found to be related to the graded variations in the plastic strain and strain rate induced in the creep feed grinding process, which were as high as 6.67 and 8.17×107 s-1, respectively. In the current study, the evolution of surface gradient microstructures was essentially a transition process from a coarse single crystal to nano-sized grains and, simultaneously, from one orientation of a single crystal to random orientations of polycrystals, during which the dislocation slips dominated the creep feed grinding induced microstructure deformation of single crystal nickel-based superalloy.

Journal ArticleDOI
TL;DR: In this paper, a stretchable rough filament strain sensor with dentate groove structure was designed to eliminate the shoulder peak phenomenon and improve recoverability, which can accurately and stably monitor both large and subtle human motions (such as body motion, expression and phonation).
Abstract: Stretchable strain sensors based on conductive polymer composites commonly utilize elastic polymers as the matrix. However, elastic polymers always show strong mechanical hysteresis effect leading to shoulder peak phenomenon and thereby poor recoverability of strain sensors. Herein, we design a stretchable rough filament strain sensor with dentate groove structure to eliminate the shoulder peak phenomenon and improve recoverability. The filament strain sensor is fabricated by the extrusion of poly(styrene-b-ethylene-b-butylene-b-styrene) (SEBS) filament constructing dentate groove structure and the subsequent ultrasonic treatment decorating carbon nanotubes (CNTs) on the surface of the SEBS filament. It is interesting to find that the strain sensing range of rough SEBS/CNTs filaments with dentate groove structure is wider than that of smooth filaments. More importantly, the rough filament strain sensors exhibit significantly enhanced recoverability without shoulder peak during the releasing process while the rough dentate groove structure has minor effects on the mechanical properties of SEBS filaments. The great improvement is ascribed to the uniform distribution of deformation because of the dentate groove structure, which induces reduction of the mechanical hysteresis effect and thereby decreases residual strain. Moreover, the rough filament strain sensors have a favorable integration of good stability, fast response time of 300 ms (0.5% strain is applied with a high strain rate of 500 mm/min) and excellent durability (1976 cycles at the strain of 50%). The rough filament strain sensors can accurately and stably monitor both large and subtle human motions (such as body motion, expression and phonation), showing broad application prospects in wearable devices.

Journal ArticleDOI
TL;DR: The microstructural and texture evolutions of as-cast AlCoCrFeNi2.1 eutectic high entropy alloy (EHEA) have been investigated in the course of thermomechanical processing at the temperature range of 25-500°C.
Abstract: The microstructural and texture evolutions of as-cast AlCoCrFeNi2.1 eutectic high entropy alloy (EHEA) have been investigated in the course of thermomechanical processing at the temperature range of 25–500 °C. Interestingly, compared with other conventional casting structures, significant strength-ductility ratio has been achieved at room temperature. In addition, the volume fractions of the constituent phases: soft FCC (face-centered cubic), and the hard BCC (body-centered cubic) phases, do not significantly change from room to elevated deformation temperatures. In fact, the strength and ductility have not been decreased at higher temperatures which represent the mechanical stability of the alloy in the examined temperature range. From room temperature up to 300 °C, the dendrites have been stretched and broken with a slight deviation from the load direction, whereas at higher temperature of 500 °C the dendrites have been rotated relative to the direction of load before fracture. Texture examination reveals the formation of a random texture in the initial and deformed states due to simultaneous contribution of different influencing factors such as stretching of dendrites during deformation, the dendrite morphology changes, and the presence of hard and soft phases and their interaction with each other.

Journal ArticleDOI
TL;DR: In this paper, the effects of heat treatment on the mechanical response of a WE43 Mg alloy using an integrated framework of SEM-DIC experiment and CPFE simulation were investigated.

Journal ArticleDOI
TL;DR: In this article, a non-equiatomic CoCrFeMnNi high-entropy alloy was used to achieve a yield strength of 750 MPa, a tensile strength of 1050 MPa and tensile uniform elongation of 27.5%.

Journal ArticleDOI
TL;DR: In this paper, two types of heterostructures, grain-size gradient structure and heterolamellar structure, are studied and the issues, concerns, and progress are reviewed with the emphasis on the synergistic effect of mechanical properties, the fundamentals of several special plastic behaviors (e.g., strain gradient, HDI hardening and strain hardening), the relationship between the microstructure and properties.
Abstract: Heterostructured (HS) materials are a novel class of materials with mechanical properties that are superior over their conventional homogeneous counterparts. They are composed of HS zones with a dramatic difference in mechanical behaviors, which produces a synergistic effect on mechanical properties that are above the prediction by the rule-of-mixtures. Among all heterostructures, the two most studied are grain-size gradient structure and heterolamellar structure. These two heterostructures produce typical heterogeneous deformation during tensile deformation, producing long-range back stress in the soft zones and forward stress in the hard zones, which collectively produces hetero deformation-induced (HDI) stress to enhance the yield strength before yielding, and HDI hardening after yielding to retain ductility. In this article, we will focus on these two types of heterostructures. The issues, concerns, and progress are reviewed with the emphasis on the synergistic effect of mechanical properties, the fundamentals of several special plastic behaviors (e.g., strain gradient, HDI hardening and strain hardening), the plastic deformation mechanism, and the relationship between the microstructure and properties.

Journal ArticleDOI
TL;DR: In this paper, the authors showed that the dislocation network consisted of the cellular boundaries provided a high density of interfaces that significantly inhibited the dislocations motion, resulting in higher yield strength.
Abstract: The cellular sub-grain was widely reported as the main contributor to the high yield strength of selective laser melted stainless steels, but its underlying strengthening mechanism was still unclear. In this study, the high yield strength of selective laser melted 316L stainless steel was studied by manipulating the cellular sub-grain through various heat treatments. Although the cellular sub-grain still existed in the heat-treated samples, the yield strength decreases significantly after heat treatment. This study firstly demonstrated that the high density of dislocations at the cellular boundary played a key role in the interfacial strengthening effect. Despite the small misorientation between the neighbouring cellular sub-grain, the cellular boundary acted as the high-angle grain boundary during deformation. The dislocation network consisted of the cellular boundaries provided a high density of interfaces that significantly inhibited the dislocation motion, resulting in higher yield strength.

Journal ArticleDOI
TL;DR: In this article, the evolution of statistically stored dislocation and geometrically necessary dislocation during tensile tests was investigated in CoCrFeMnNi high-entropy alloys (HEAs) with 0 and 0.52% nitrogen.
Abstract: In this study, the evolution of statistically stored dislocation (SSD) and geometrically necessary dislocation (GND) during tensile tests was investigated in CoCrFeMnNi high-entropy alloys (HEAs) with 0 and 0.52 at. % nitrogen. The microstructure characterization indicated that the plastic deformation of the alloys was dominated by dislocation slip below 20% true strain. Nitrogen alloying increased the total dislocation density and the strain-hardening rate during deformation, which could be explained by the interaction between nitrogen atoms and dislocations. The higher fraction of soft orientation zones for 0.52 N HEA was conducive for strain accommodation, resulting in a reduced GND density. Hence, SSDs contributed primarily to the increase of the total dislocation density and the higher strain-hardening rate of nitrogen-doped CoCrFeMnNi.

Journal ArticleDOI
Liming Zhang1, Cong Yu1, Fanzhen Meng1, Zaiquan Wang1, Peng Zhang1, Gao Su1 
TL;DR: In this article, a nonlinear energy evolution model of rock was established based on the interaction mechanism of energy accumulation and energy dissipation, and a strain value corresponding to the energy iterative growth factor at the first bifurcation of the energy equation was chosen as the initiation criterion for rock failure.
Abstract: Triaxial loading and unloading tests on marble specimens under different stress paths were conducted to investigate the characteristics of energy evolution in rock deformation process. Results show that tensile failure occurred in rock specimens under uniaxial compression, while shear failure dominated under triaxial loading and unloading. The energy storage limit of rock specimens under triaxial loading was higher than that under uniaxial compression or triaxial unloading. A nonlinear energy evolution model of rock was established based on the interaction mechanism of energy accumulation and energy dissipation. Results from the theoretical model are in good agreement with the test results. Since the evolution of energy was characterised by bifurcation and chaos, a strain value corresponding to the energy iterative growth factor at the first bifurcation of the energy equation was chosen as the initiation criterion for rock failure. The critical strain accounted for 77%, 72–76%, and 72–81% of the peak strain under uniaxial compression, triaxial loading, and unloading, respectively.