The ultrafine copper wire with a diameter of 18 µm is prepared via cold drawing process from the single crystal downcast billet (Φ8 mm), taking a drawing strain to 12.19. In this paper, in-depth investigation of the microstructure feature, texture evolution, mechanical properties, and electrical conductivity of ultrafine wires ranging from Φ361 µm to Φ18 µm is performed. Specially, the microstructure feature and texture type covering the whole longitudinal section of ultrafine wires are elaborately characterized. The results show that the average lamella thickness decreases from 1.63 µm to 102 nm during the drawing process. Whereas, inhomogeneous texture evolution across different wire sections was observed. The main texture type of copper wires are components of <111>, <001> and <112> orientations. Specifically, the peripheral region is primarily dominated by <111> and <112>, while the central region is <001> and <111>. As the drawing strain increases, the volume fraction of hard orientation <111> with low Schmid factor increase, where notably higher fraction of <111> is result from the consumption of <112> and <001> for the wire of Φ18 µm. For drawn copper wire of 18 µm, superior properties are obtained with a tensile strength of 729.8 MPa and an electrical conductivity of 86.9% IACS. Furthermore, it is found that grain strengthening, dislocation strengthening, and texture strengthening are three primary strengthening mechanisms of drawn copper wire, while the dislocation density is main factor on the reducing of conductivity.

The effects of Yb/Zr micro-alloying on the microstructure, mechanical properties, and corrosion resistance of an Al-Zn-Mg-Cu alloy were systematically investigated. Upon the addition of Yb/Zr to the Al-Zn-Mg-Cu alloy, the grain boundaries were pinned by high-density nanosized Al₃(Yb, Zr) precipitates during extrusion deformation, consequently, the average grain size was significantly reduced from 232.7 µm to 3.2 µm. This grain refinement contributed substantially to the improvement in both strength and elongation. The ultimate tensile strength, yield strength, and elongation of the Yb/Zr modified alloy increased to 705.3 MPa, 677.6 MPa, and 8.7%, respectively, representing enhancements of 16.2%, 19.3%, and 112.2% compared to the unmodified alloy. Moreover, the distribution of MgZn₂ phases along grain boundaries became more discontinuous in the Yb/Zr modified alloy, which effectively retarded the propagation of intergranular corrosion and improved the corrosion resistance.

This study investigates the differences in microstructural control between cryogenic forging combined with pre-deformation (PCF) and traditional thermal forging (TTF) for 7050 aluminum forgings intended for aerospace applications. The PCF process, utilizing cryogenic deformation, significantly refines the coarse grains at the surface of the forgings, resulting in a finer and more uniform microstructure, thereby effectively addressing the issue of surface coarse grains associated with traditional methods. The findings indicate that the PCF process can accumulate higher stored energy, facilitating static recrystallization (SRX) during subsequent heat treatment and enhancing the microstructural uniformity. Utilizing various analytical techniques, including optical microscopy (OM), electron backscatter diffraction (EBSD), and transmission electron microscopy (TEM). This study reveals the superiority of the PCF process in terms of strain accumulation, dislocation density, and grain refinement. In conclusion, this method offers advantages in enhancing the performance and microstructural uniformity of 7050 aluminum forgings, presenting new opportunities for applications in the aluminum forging industry.

Trace amounts of Zr and V can increase the recrystallization temperature of Al-Mg-Si wrought aluminum alloys, which is expected to regulate the recrystallization grain. In this paper, trace amounts of V and Zr were added to recycled Al-Mg-Si alloys, and their effects on the microstructure and mechanical properties of the cast alloys were studied by scanning electron microscopy (SEM) and synchrotron radiation X-ray tomography (SRXT). The results show that the addition of Zr significantly increases the grain sizes due to the “Zr poisoning”; V addition has no significant effect on the grain size. The morphology of Fe-rich phase gradually changes from the large Chinese-script shape to the fine short rod and curved long strip shape, and the distribution uniformity is improved with the combined addition of V and Zr. The three-dimensional (3D) morphology of Fe-rich phase includes granular, short rod-like, simple branch and multi-branch structures. The individual addition of V and Zr has no significant effect on the morphology of Fe-rich phase; but the combined addition of V and Zr significantly increases the number and volume fraction of Fe-rich phase with small size (diameter ≤15 µm), the number of branches in the largest Fe-rich phase is significantly reduced, resulting in the improvement of elongation. This work provides a theoretical basis for the development of new recycled Al-Mg-Si alloys in industrial application.

The commercial ZK60 magnesium alloy with extruded state experienced aging heat treatment (T6) was dynamically loaded at strain rate of 3000 s⁻¹ by means of the split Hopkinson pressure bar (SHPB) in this paper. Transmission electron microscopy (TEM) observations showed that the precipitated β′₁ phases partially dissolved (spheroidized) with blurred interfaces within 160 µs at 3000 s⁻¹. The average length and diameter of the rod-shaped β′₁ phase particles were 48.5 and 9.8 nm after the T6 heat treatment; while the average diameter of the spherical β′₁ phases changed to 8.8 nm after loading. The deformed β′₁ phase generated larger lattice distortion energy than Mg matrix under high strain rate loading. Therefore, the difference of free energy (the driving force of dissolution) between the β′₁ phase and the matrix increased, making the instantaneous dissolution of the β′₁ phase thermodynamically feasible. The dissolution (spheroidization) of the β′₁ phase particles was kinetically promoted because the diffusion rate of the solute Zn atoms was accelerated by combined actions of adiabatic temperature rise, high density of dislocations (vacancies) and high deviatoric stresses during high strain rate loading. The increase in hardness of ZK60-T6 alloy could be attributed to solid solution strengthening, dislocation strengthening and second phase particle strengthening.

High-purity silver (Ag) is extensively utilized in electronics, aerospace, and other advanced industries due to its excellent thermal conductivity, electrical conductivity, and machinability. However, the prohibitive material cost poses substantial challenges for optimizing thermal processing parameters through repetitive experimental trials. In this work, hot compression experiments on high-purity silver were conducted using a Gleeble-3800 thermal simulator. The high-temperature deformation behaviors, dynamic recovery (DRV) and dynamic recrystallization (DRX) of high-purity silver were studied by constructing an Arrhenius constitutive equation and developing thermal processing maps. The results show that plastic instability of high-purity silver occurs at high strain rates and the optimized hot processing parameters are the strain rate below 0.001 s⁻¹ and the temperature of 340–400 °C. Microstructural observations exhibit that DRV prefers to occur at lower deformation temperatures (e.g. 250 °C ). This is attributed to the low stacking fault energy of high-purity silver, which facilitates the decomposition of dislocations into partial dislocations and promotes high-density dislocation accumulation. Furthermore, DRX in high-purity silver becomes increasingly pronounced with increasing deformation temperature and reaches saturation at 350 °C.

The novel magnetic sepiolite/Fe₃O₄/zero-valent iron (nZVI) nanocomposite (nZVI@SepH-Mag) was prepared and used to achieve the removal of Cr(VI) in this work. The nZVI@SepH-Mag composites were characterized by XRD, FTIR, BET, SEM and TEM. The characterization results indicated that the structure of the composite consisted of small nanoscale nZVI and magnetite (Mag) particles uniformly anchoring on the surface of acid-activated sepiolite (SepH). Batch experiments were used to analyze the effects of main factors on Cr(VI) removal. A 100% removal efficiency in 60 min and enhanced reaction ratio were reached by the composite comparing other existing materials. The kinetic of the adsorption and possible Cr(VI) removal mechanism of the hybrids were also evaluated and proposed. Based on the removal products identified by Raman, XRD and XPS, a reduction mechanism was proposed. The results indicated that the SepH and Mag can inhibit the agglomeration and enhance the dispersibility of nZVI, and Mag and nZVI displayed good synergetic effects.

An erratum to this article is available online at https://doi.org/10.1007/s11771-025-6033-0.

This study examines the intricate occurrences of thermal and solutal Marangoni convection in three-layered flows of viscous fluids, with a particular emphasis on their relevance to renewable energy systems. This research examines the flow of a three-layered viscous fluid, considering the combined influence of heat and solutal buoyancy-driven Rayleigh-Bénard convection, as well as thermal and solutal Marangoni convection. The homotopy perturbation method is used to examine and simulate complex fluid flow and transport phenomena, providing important understanding of the fundamental physics and assisting in the optimization of various battery configurations. The inquiry examines the primary elements that influence Marangoni convection and its impact on battery performance, providing insights on possible enhancements in energy storage devices. The findings indicate that the velocity profiles shown graphically exhibit a prominent core zone characterized by the maximum speed, which progressively decreases as it approaches the walls of the channel. This study enhances our comprehension of fluid dynamics and the transmission of heat and mass in intricate systems, which has substantial ramifications for the advancement of sustainable energy solutions.

Al-doped manganese dioxide (MnO₂) was synthesized by simple hydrothermal method, and a controllable phase transition of the MnO₂ crystal phase from β to δ was achieved. The effects of Al doping concentration on the structure and electrochemical properties of electrode materials were studied in detail. The results show that the controlled synthesis requires a synergy between KMnO₄, MnCl₂ and AlCl₃, and that Al³⁺ plays an important role. Compared with the pure phase MnO₂, the crystallinity of Al-doped MnO₂ decreases and the specific surface area increases, which provides more active sites for the electrode material. When 3 mmol Al³⁺ is added, the prepared MnO₂-3 has the largest specific capacitance and the highest rate performance. The energy density of the asymmetric supercapacitor (ASC) with MnO₂-3 as the positive electrode and activated carbon (AC) as the negative electrode can reach 18.4 W·h/kg at the power density of 400 W/kg, and the capacity can maintain 90% of the initial value after 20000 cycles, indicating that Al-doped MnO₂ has certain practical application value. This study provides favorable guidance for MnO₂ as a high performance electrode material.

Developing efficient, durable, and precious metal-free electrocatalysts is currently a huge challenge. In this article, through a simple one-step high-temperature pyrolysis method, by incorporating various non-metallic element atoms, we prepared four different NiX(X=Cl₂, (CH₃COO)₂, (NO₃)₂, SO₄)@CNT catalysts. Additionally, by adjusting the temperature, these four materials were expanded into twelve catalyst materials for comparative optimization of hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) activity. Ultimately, Ni(NO₃)₂@CNT-900 typically exhibits superior OER and HER activity. In 1 mol/L KOH solution with a current density of 10 mA/cm², the overpotentials of HER and OER of Ni(NO₃)₂@CNT-900 are only 145 mV and 300 mV, respectively. Furthermore, the Ni(NO₃)₂@CNT-900 shows excellent durability in both HER and OER.

Nitrogen doping has significant effects on the photocatalytic performance of ceria (CeO₂), and the possible synergistic effect with the inevitably introduced abundant oxygen vacancies (OVs) is of great significance for further investigation, and the specifically exposed crystal faces of CeO₂ may have an impact on the performance of nitrogen-doped CeO₂. Herein, nitrogen-doped CeO₂ with different morphologies and exposed crystal faces was prepared, and its performances in the photocatalytic degradation of tetracycline (TC) or hydrogen production via water splitting were evaluated. Density functional theory (DFT) was used to simulate the band structures, density of states, and oxygen defect properties of different CeO₂ structures. It was found that nitrogen doping and OVs synergistically promoted the catalytic activity of nitrogen-doped CeO₂. In addition, the exposed crystal faces of CeO₂ have significant effects on the introduction of nitrogen and the ease of OV generation, as well as the synergistic effect of nitrogen doping with OVs. Among them, the rod-like nitrogen-doped CeO₂ with exposed (110) face (R-CeO₂-NH₃) showed a photocatalytic degradation ratio of 73.59% for TC and hydrogen production of 156.89 µmol/g, outperforming other prepared photocatalysts.

As the second most important solid waste produced by coal-fired power plants, the improper management of coal-fired slag has the potential to result in environmental pollution. It is therefore imperative that high-value utilization pathways for coal-fired slag should be developed. In this study, modified magnesium slag (MMS), produced by a magnesium smelter, was selected as the alkali activator. The activated silica-aluminum solid wastes, namely coal-fired slag (CFS) and mineral powder (MP), were employed as pozzolanic materials in the preparation of alkali-activated cementitious materials. The alkali-activated cementitious materials prepared with 50 wt% MMS, 40 wt% CFS and 10 wt% MP exhibited favorable mechanical properties, with a compressive strength of 32.804 MPa in the paste sample cured for 28 d. Then, the activated silica-aluminum solid waste consisting of CFS-MP generated a significant amount of C-S(A)-H gels, AFt, and other products, which were observed to occupy the pore structure of the specimen. In addition, the secondary hydration reaction of CFS-MP occurs in high alkalinity environments, resulting in the formation of a mutually stimulated and promoted reaction system between CFS-MP and MMS, this will subsequently accelerate the hydrolysis reaction of MMS. It is important to emphasize that the amount of MMS in alkali-activated cementitious materials must be strictly regulated to avert the potential issue of incomplete depolymerization-repolymerization of active silica-aluminum solid waste containing CFS-MP. This in turn could have a deleterious impact on the late strength of the cementitious materials. The aim of this work is to improve the joint disposal of MMS, CFS and MP and thereby provide a scientific basis for the development of environmentally friendly and low-carbon modified magnesium slag alkali-activated coal-fired slag based cementitious materials for mine backfilling.

Malachite, being highly hydrophilic and difficult to be floated conventionally, is usually beneficiated by sulfidation flotation in industry. However, the complex crystal structure of malachite leads to the formation of various fracture surfaces with distinct properties during crushing and grinding, resulting in surface anisotropy. In this study, we explored the surface anisotropy of malachite and further investigated its sulfidation mechanism from the coordination chemistry perspective, considering the influence of the Jahn-Teller effect on malachite sulfidation. Computational results reveal that the penta-coordinated Cu ions on the malachite (201) and (010) surfaces exhibit stronger activity compared to those on the malachite ($\bar{2}01$) surface. Additionally, the tetra-coordinated structure formed by HS⁻ adsorption on the malachite (010) and (201) surfaces is more stable, with more negative adsorption energy, compared to the hexacoordinated structure formed by HS⁻ adsorption on the ($\bar{2}01$) surface. The sulfidized malachite surface has an additional pair of π electron and smaller HOMO (highest occupied molecular orbital)-LUMO (lowest unoccupied molecular orbital) gap with xanthate molecules, causing stronger π backbonding with xanthate. This study provides new insights into the surface sulfidation mechanism of malachite and offers a theoretical reference for the design of targeted flotation reagents.

The lime-Cu²⁺-xanthate process is commonly used for the flotation separation of sphalerite from pyrite. In this process, lime is added to the pulp to inhibit the floatability of pyrite. However, the excessive use of lime can result in pipeline blockage and inadequate recovery of associated precious metals. Therefore, it is necessary to develop new flotation process that minimizes or eliminates the use of lime. In this paper, a novel Fe³⁺-Cu²⁺-butyl xanthate process was developed as an alternative to lime for separating of sphalerite from pyrite. The flotation results indicated that with the artificially-mixed minerals, the flotation recovery of pyrite was lower than 16% and that of sphalerite was higher than 47% at pH 5.0–10.0. The zeta potential measurements revealed that ferric ion preferred to adsorb on pyrite, and copper ion displaced with zinc ion from the lattice at the interface of sphalerite. The wettability analyses indicated that the hydrophobicity of sphalerite surface increased apparently after being treated with Fe³⁺-Cu²⁺-BX, while the hydrophobicity of pyrite surface remained nearly unchanged. With XPS analysis, Cu—S bond and hydrophilic ferric hydroxide were detected separately on the surface of sphalerite and pyrite after conditioning with Fe³⁺-Cu²⁺-BX, which facilitated the flotation separation of sphalerite from pyrite with butyl xanthate collector.

After excavation, some of the surrounding rock mass is in a state of triaxial extension, exhibiting tensile or shear fracture modes. To study the energy mechanism of tensile fracture turning to shear fracture, a series of triaxial extension tests were conducted on sandstone under confining pressures of 10, 30, 50 and 70 MPa. Elastic energy and dissipated energy were separated by single unloading, the input energy u_t, elastic energy u_e, and dissipated energy u_d at different unloading stress levels were calculated by the integrating stress – strain curves. The results show that tensile cracks dominate fracture under lower confining pressure (10 MPa), and shear cracks play an increasingly important role in fracture as confining pressure increases (30, 50 and 70 MPa). Based on the phenomenon that u_e and u_d increase linearly with increasing u_t, a possible energy distribution mechanism of fracture mode transition under triaxial extension was proposed. In addition, it was found that peak energy storage capacity is more sensitive to confining pressure compared to elastic energy conversion capacity.

Signal filtering and differential acquisition are classic yet challenging issues in control engineering. The discrete-time optimal control (DTOC) based on classic tracking differentiator (TD) can effectively extract differentiation signals and filter signals, while eliminating the chattering problem that arises during the discretization of the continuous solution. However, under external disturbance, the convergence mode may change, leading to overshoot and noise amplification. In this paper, a dual-switching strategy is proposed, which can alternate between the base double-integral system and its dual system according to the quadrant of the system’s state. And a novel linearized control law is also introduced, deriving a novel dual-switch tracking differentiator. Further analysis of system convergence and time optimality is provided. Simulation results show that the application of this dual-switching strategy notably reduces overshoot in both tracking and differential signals while enhancing noise filtering performance. Moreover, experiments conducted on a permanent magnet synchronous motor (PMSM) platform, where the proposed TD acts as a filter in the speed feedback loop, demonstrate that the standard deviation between the reference speed and the target speed (at a constant speed of 378 r/min) decreased from 5.63 r/min to 4.93 r/min, compared to the moving average algorithm.

The electricity-hydrogen integrated energy system (EH-IES) enables synergistic operation of electricity, heat, and hydrogen subsystems, supporting renewable energy integration and efficient multi-energy utilization in future low-carbon societies. However, uncertainties from renewable energy and load variability threaten system safety and economy. Conventional chance-constrained programming (CCP) ensures reliable operation by limiting risk. However, increasing source-load uncertainties that can render CCP models infeasible and exacerbate operational risks. To address this, this paper proposes a risk-adjustable chance-constrained goal programming (RACCGP) model, integrating CCP and goal programming to balance risk and cost based on system risk assessment. An intelligent nonlinear goal programming method based on the state transition algorithm (STA) is developed, along with an improved discretized step transformation, to handle model nonlinearity and enhance computational efficiency. Experimental results show that the proposed model reduces costs while controlling risk compared to traditional CCP, and the solution method outperforms average sample sampling in efficiency and solution quality.

Heat transfers at the interface of adjacent saturated soil primarily through the soil particles and the water in the voids. The presence of water induces the contraction of heat flow lines at the interface, leading to the emergence of the thermal contact resistance effect. In this paper, four thermal contact models were developed to predict the thermal contact resistance at the interface of multilayered saturated soils. Based on the theory of thermal-hydro-mechanical coupling, semi-analytical solutions of thermal consolidation subjected to time-dependent heating and loading were obtained by employing Laplace transform and its inverse transformation. Thermal consolidation characteristics of multilayered saturated soils under four different thermal contact models were discussed, and the effects of thermal resistance coefficient, partition thermal contact coefficient, and temperature amplitude on the thermal consolidation process were investigated. The outcomes indicate that the general thermal contact model results in the most pronounced thermal gradient at the interface, which can be degenerated to the other three thermal contact models. The perfect thermal contact model overestimates the deformation of the saturated soil during the thermal consolidation. Moreover, the effect of temperature on consolidation properties decreases gradually with increasing interfacial contact thermal resistance.

This paper proposes a longitudinal vulnerability-based analysis method to evaluate the impact of foundation pit excavation on shield tunnels, accounting for geological uncertainties. First, the shield tunnel is modeled as an Euler-Bernoulli beam resting on the Pasternak foundation incorporating variability in subgrade parameters along the tunnel’s length. A random analysis method using random field theory is introduced to evaluate the tunnel’s longitudinal responses to excavation. Next, a risk assessment index system is established. The normalized relative depth between the excavation and the shield tunnel is used as a risk index, while the maximum longitudinal deformation, the maximum circumferential opening, and the maximum longitudinal bending moment serve as performance indicators. Based on these, a method for analyzing the longitudinal fragility of shield tunnels under excavation-induced disturbances is proposed. Finally, the technique is applied to a case study involving a foundation pit excavation above a shield tunnel, which is the primary application scenario of this method. Vulnerability curves for different performance indicators are derived, and the effects of tunnel stiffness and subgrade stiffness on the tunnel vulnerability are explored. The results reveal significant differences in vulnerability curves depending on the performance index used. Compared to the maximum circumferential opening and the maximum longitudinal bending moment, selecting maximum longitudinal deformation as the control index better ensures the tunnel’s usability and safety under excavation disturbances. The longitudinal vulnerability of the shield tunnel nonlinearly decreases with the increase of the tunnel stiffness and subgrade stiffness, and the subgrade stiffness has a more pronounced effect. Parametric analyses suggest that actively reinforcing the substratum is more effective at reducing the risk of tunnel failure due to adjacent excavations than passive reinforcement of the tunnel structure.

To address the issue of extreme thermal-induced arching in CRTS II slab tracks due to joint damage, an optimized joint repair model was proposed. First, the formula for calculating the safe temperature rise of the track was derived based on the principle of stationary potential energy. Considering interlayer evolution and structural crack propagation, an optimized joint repair model for the track was established and validated. Subsequently, the impact of joint repair on track damage and arch stability under extreme temperatures was studied, and a comprehensive evaluation of the feasibility of joint repair and the evolution of damage after repair was conducted. The results show that after the joint repair, the temperature rise of the initial damage of the track structure can be increased by 11 °C. Under the most unfavorable heating load with a superimposed temperature gradient, the maximum stiffness degradation index SDEG in the track structure is reduced by about 81.16% following joint repair. The joint repair process could effectively reduce the deformation of the slab arching under high temperatures, resulting in a reduction of 93.96% in upward arching deformation. After repair, with the damage to interfacing shear strength, the track arch increases by 2.616 mm.

To investigate the mechanical response during failure and the impact tendency characteristics of gangue-coal combined structure, uniaxial compression tests were conducted on nine groups of combined structures, each with varying gangue thicknesses and positions. The response patterns of compressive strength, elastic modulus, pre-peak accumulated energy, elastic energy index, and impact energy index were systematically analyzed. Furthermore, a new index for evaluating the impact tendency of gangue-containing coal was proposed, and its effectiveness was verified. The findings are as follows: (1) As the gangue thickness increases, both the compressive strength and the pre-peak energy of the combined structure decrease, whereas the elastic modulus increases accordingly. When the gangue is located in the lower-middle position, the combined structure exhibits the lowest compressive strength and elastic modulus but the highest pre-peak energy. (2) As the gangue shifts toward the middle position of the combined structure, the failure mode gradually transitions from complete “crushing” failure to an incomplete “point-type” failure. As gangue thickness further increases, the failure region evolves from overall failure to localized failure, with the degree of failure shifting from complete to incomplete. The K_crc value corresponding to “crushing” complete failure is higher and has a stronger impact tendency compared to “point-type” incomplete failure. (3) The proposed comprehensive impact instability evaluation index K_crc for the gangue-coal combined structure has shown a significant positive correlation with compressive strength (R_c) and impact energy index (K_E), further verifying its rationality in comprehensively assessing the impact tendency of gangue-containing coal bodies. Applying this index to the evaluation of gangue-containing coal seams provides a more accurate reflection of their impact tendency compared with the residual energy index, which has a wide range of potential applications and practical significance.

The undrained mechanical behavior of unsaturated completely weathered granite (CWG) is highly susceptible to alterations in the hydraulic environment, particularly under uniaxial loading conditions, due to the unique nature of this soil type. In this study, a series of unconfined compression tests were carried out on unsaturated CWG soil in an underground engineering site, and the effects of varying the environmental variables on the main undrained mechanical properties were analyzed. Based on the experimental results, a novel constitutive model was then established using the damage mechanics theory and the undetermined coefficient method. The results demonstrate that the curves of remolded CWG specimens with different moisture contents and dry densities exhibited diverse characteristics, including brittleness, significant softening, and ductility. As a typical indicator, the unconfined compression strength of soil specimens initially increased with an increase in moisture content and then decreased. Meanwhile, an optimal moisture content of approximately 10.5% could be observed, while a critical moisture content value of 13.0% was identified, beyond which the strength of the specimen decreases sharply. Moreover, the deformation and fracture of CWG specimens were predominantly caused by shear failure, and the ultimate failure modes were primarily influenced by moisture content rather than dry density. Furthermore, by comparing several similar models and the experimental data, the proposed model could accurately replicate the undrained mechanical characteristics of unsaturated CWG soil, and quantitatively describe the key mechanical indexes. These findings offer a valuable reference point for understanding the underlying mechanisms, anticipating potential risks, and implementing effective control measures in similar underground engineering projects.

Rocks will suffer different degree of damage under FT (freeze-thaw) cycles, which seriously threatens the long-term stability of rock engineering in cold regions. In order to study the mechanism of rock FT damage, energy calculation method and energy self-inhibition model are introduced to explore their energy characteristics in this paper. The applicability of the energy self-inhibition model was verified by combining the data of FT cycles and uniaxial compression tests of intact and pre-cracked sandstone samples, as well as published reference data. In addition, the energy evolution characteristics of FT damaged rocks were discussed accordingly. The results indicate that the energy self-inhibition model perfectly characterizes the energy accumulation characteristics of FT damaged rocks under uniaxial compression before the peak strength and the energy dissipation characteristics before microcrack unstable growth stage. Taking the FT damaged cyan sandstone sample as an example, it has gone through two stages dominated by energy dissipation mechanism and energy accumulation mechanism, and the energy rate curve of the pre-cracked sample shows a fall-rise phenomenon when approaching failure. Based on published reference data, it was found that the peak total input energy and energy storage limit conform to an exponential FT decay model, with corresponding decay constants ranging from 0.0021 to 0.1370 and 0.0018 to 0.1945, respectively. Finally, a linear energy storage equation for FT damaged rocks was proposed, and its high reliability and applicability were verified by combining published reference data,the energy storage coefficient of different types of rocks ranged from 0.823 to 0.992, showing a negative exponential relationship with the initial UCS (uniaxial compressive strength). In summary, the mechanism by which FT weakens the mechanical properties of rocks has been revealed from an energy perspective in this paper, which can provide reference for related issues in cold regions.