Fracture Energy Dissipation Research Articles

Ordered stereom structure in sea urchin tubercles: High capability for energy dissipation

Tubercles in sea urchin shells serve as a base on the test plates connecting the spine; these undergo compressive or impact stress from the spines. As the volume fraction of the ordered stereom structure in a tubercle increases, the compressive load–displacement curves are gradually characterized by the typical behavior of ceramic foams. Although this ordered stereom structure only exhibits an average porosity of 50.6%, it also exhibits high fracture resistance and energy dissipation capacity. Such remarkable behavior of the ordered stereom structure is attributed to its unique hierarchical microstructure. Specifically, at the macroscale, the stereom structure is periodic. It has uniformly distributed pores that are typically round, which can effectively reduce the stress concentration around the pores, and the ordered arrangement of the trabeculae along the axial direction of the tubercle bears the most compressive stress. The trabeculae present a bottleneck shape with a specific dimension, ensuring the best fracture resistance with a relatively higher porosity. Furthermore, crack deflection in the trabeculae changes the local fracture mode of the mineral, thereby increasing the crack surface area. Statement of significanceThe connecting bases of the spines in sea urchin shell, known as tubercle, effectively undergo the compressive stress or impact stress from the spines. An ordered stereom structure is found in the tubercle, and it shows an excellent fracture resistance and energy dissipation capacity. Such a fantastic behavior of the ordered stereom structure mainly takes advantage of its unique hierarchical microstructure. The stereom structure presents a periodic structure on macroscale, the trabeculae show a bottleneck shape with a specific dimension to guarantee the best fracture resistance with a relatively higher porosity, and the soft fillers among CaCO3 nanoparticles in a trabecula cause consecutive crack deflections.

Strong-Weak Response Network-Enabled Ionic Conductive Hydrogels with High Stretchability, Self-Healability, and Self-Adhesion for Ionic Sensors.

The requirement of ionic conductive hydrogels with tailor-made superelasticity and high chain mobility is highly desired while meeting a challenge. Herein, ionic conductive hydrogels with the design of strong-weak response networks were synthesized via the free-radical copolymerization of monomers of 1-methyl-3-(4-vinylbenzyl)imidazolium chloride and sodium 2-acrylamino-2-methylpropanesulfonate in water. The as-formed strong-weak response networks in ionic conductive hydrogels included binary interactions of strong electrostatic forces and weak hydrogen bonds. The electrostatic forces imparted excellent mechanical elasticity, and the hydrogen-bonded interactions served as highly active and reversible networks to dissipate fracture energy during the deformation. Importantly, the resultant ionic conductive hydrogels exhibited high toughness of ∼2205 kJ m-3, satisfying fatigue resistance, and excellent healing efficiency of >90%. Moreover, the tailoring of counterion concentrations in hydrogels by adding various concentrations of inorganic salts could regulate the electrostatic forces within hydrogels as well as the finally mechanical strengths. Ascribing to the combination of large stretchability and large chain mobility, the resultant ionic conductive hydrogels could directly act as a stretchable ionic conductor for the assembly of self-healable and self-adhesive capacitance-type ionic sensors which are capable of detecting large and tiny human activities. This study could offer a promising strategy for the design and manufacturing of emerging ionic conductors with high mechanical elasticity and large segment mobility.

Extended finite element modeling of hot mix asphalt based on the semi-circular bending test

Semi-circular bending (SCB) test is widely used to characterize the fracture behaviors of asphalt mixtures. In this study, heterogeneous models of SCB specimens were prepared with the difference in aggregate shape. Asphalt concrete was composed of coarse aggregate and fine aggregate matrix (FAM). Extended finite element modeling (XFEM) was utilized to capture the fracture behaviors of asphalt mixtures under −10 and 20 °C. The initiation and propagation of cracks under different temperatures were observed. Local cracking was mainly initiated around the aggregates or on the aggregates. Statistical analysis of the failure loads and the displacements corresponding to the peak loads were obtained, and comparison was made with the laboratory test results. SCB tests with the round particles presented the greatest failure load, followed by convex, ellipse and concave particles. The effect of aggregate shape on dissipated fracture energy was the same as the effect of particle shape on failure load. Laboratory results were consistent with the simulation results, proving the reliability of the numerical model.

Investigation of the mechanical response and deformation mechanism of cortical bone material under combined compression and bending loads

Objective service load is the load pattern of cortical bone in practical conditions. The objective service load conditions of cortical bone are complicated, usually including two or more load patterns. The mechanical behavior and deformation mechanism of cortical bone material under coupling load pattern and single load pattern are diametrically different. However, nowadays, researches on the mechanical response of cortical bone have been heavily focused on the single load pattern, which couldn’t reveal the potential deformation mechanism accurately. For the purpose of obtaining the objective mechanical properties under complicated loading patterns, the mechanical response and deformation mechanism of bone material under compression-bending coupling load were investigated by in-situ test. The research shows that bending strength increased under the compression-bending coupling load than the single bending load. By in-situ observation, the variations of surface strain distribution and cracks directions were the potential reasons for the increase of the bending strength. It was found that the cracks changed from transverse fracture to integrated patterns with transverse fracture and longitudinal fracture. Larger fracture range and tortuous crack propagation increased the fracture energy dissipation, which led to an enlarged bending strength under the compression-bending coupling load. Through theoretical analysis and numerical calculation, the impeded effect to the increasing of bending deflection was dominant before the final fracture with the adding of the compression load. The numerical calculation result was consistent with the result of the experiment. This present work would provide new references to further studies on the mechanical behavior of cortical bone under complicated loading patterns.

In situ transmission electron microscopy observation of the deformation and fracture processes of an epoxy/silica nanocomposite.

Herein, we report the in situ transmission electron microscopy observation of the deformation and fracture processes of an epoxy resin thin film containing silica nanoparticles under tensile strain. Under tensile strain, the dispersed silica nanoparticles in the composite arrest the progress of the crack tip and prevent crack propagation. Concomitantly, the generation and growth of nanovoids at the epoxy matrix/nanoparticle interfaces were clearly observed, particularly in the region near the crack tip. These nanovoids contribute to the dissipation of fracture energy, thereby enhancing the fracture toughness. We also analyzed the local distributions of the true strain and strain rate in the nanocomposite film during tensile testing using the digital image correlation method. In the region around the crack tip, the strain rate increased by 3 to 10 times compared to the average of the entire test specimen. However, the presence of large filler particles in the growing crack suppressed the generation of strain, potentially contributing to hindering crack growth.

Study on the Fractal Characteristics of the Pomegranate Biotite Schist under Impact Loading

In order to study the fractal characteristics of the pomegranate biotite schist under the effect of blasting loads, a one-dimensional SHPB impact test was carried out to test the dynamic compressive strength, damage morphology, fracture energy dissipation density, and other parameters of the rocks under different strain rates; besides, sieve tests were conducted to count the mass fractal characteristics of the crushed masses under different strain rates to calculate the fractal dimension of the crushed rock D . Finally, the relationships between fractal dimension and dynamic compressive strength, crushing characteristics, and energy dissipation characteristics were analysed. The results show that under different impact loads, the strain rate effect of the rock is significant and the dynamic compressive strength increases with the increasing strain rate, and they show a multiplicative power relationship. The higher the strain rate of the rock, the deeper the fragmentation and the higher the fractal dimension, and the fractal dimension and rock crushing energy density are multiplied by a power relationship. By performing the comparative analysis of the pomegranate biotite schist, a reasonable strain rate range of 78.75 s-1~82.51 s-1 and a reasonable crushing energy consumption density range of 0.78 J·cm-3~0.92 J·cm-3 were determined. This research provides a great reference for the analysis of dynamic crushing mechanism, crushing block size distribution, and crushing energy consumption of the roadway surrounding rock.

Effect of build orientation and raster pattern on the fracture behavior of carbon fiber reinforced polymer composites fabricated by additive manufacturing

Additive manufacturing (AM) process parameters highly affect the mechanical and fracture properties of additively manufactured carbon fiber reinforced polymer (CFRP) composites. In this work, we study the effect of two process parameters, including build orientation (XYZ, XZY, and ZXY) and raster pattern ( ± 45º and 0º/90º), on the fracture behavior of the CFRP composites fabricated by fused filament fabrication (FFF). The mode I fracture toughness and effective fracture energy of the CFRP composite materials are measured on compact tension samples. The crack growth direction in the FFF-fabricated CFRP composites is found to be controlled by both build orientation and raster pattern. The fracture toughness of the examined CFRP material is sensitive to build orientation, while the effective fracture energy reveals significant dependence on both build orientation and raster pattern. The samples fabricated with the XYZ and ZXY build orientations exhibit 5-fold greater effective fracture energy than the ones with the XZY build orientation. A wide range of fracture energy dissipation mechanisms, including fiber-bridging and fiber pull-out, are identified depending on the process parameters. The reported fracture trends in this study have the potential to provide guidelines for the development of FFF-fabricated CFRP composites with high fracture resistance.

Directional hydraulic fracturing (DHF) using oriented perforations: The role of micro-crack heterogeneity

This study presents numerical investigations about the role of micro-crack heterogeneity in hydraulic fracture (HF) development and directional hydraulic fracturing (DHF) creation. By comparing the results of heterogeneous models (named DFN models) with the associated homogeneous models, the behavior is categorized into three modes: DFN models, which consume more (A), comparable (B), and much lower (C) energy than the associated homogeneous models. Variation of micro-crack distributions, which determines HFs interaction in the stress shadow zone, contributes to the difference in HF morphologies and injection energy consumption. The connection process, where one HF connects the other, predominates the energy cost in the DHF. Offset-related interactions usually occur between HFs and DFN in case of favorable distribution of micro-cracks, which guides the HFs to propagate through the interaction zone, thus favoring the connection process and improving the DHF efficiency. Adverse distribution of local cracks (even a single crack) with dilation-related interactions near the connection zone can produce extremely high stress due to the opening of the cracks, which significantly deteriorates the connection process and reduces the DHF efficiency. Therefore, a limited variation of crack distribution near the connection zone could cause a pronounced effect on HF connection and the associated energy consumption. Due to the limited sizes and shear slips of the micro-cracks in these simulations, deformation energy and fracture energy dissipation dominate the energy conversion during the injection, while frictional energy consumption plays a secondary role. The two-stage injection strategy can be a promising method to weaken the stress shadow effect, i.e., subsequent HFs extend directly to the previous one by taking advantage of the stress state produced in the first stage. The frictional resistance of micro-cracks also plays a significant role in DHF creation. Weak cracks allow the HFs to go through the interaction zone and avert the strict connection process, consequently improving the DHF efficiency.

Crack propagation simulation without crack tracking algorithm: Embedded discontinuity formulation with incompatible modes

We show that for the simulation of crack propagation in quasi-brittle, two-dimensional solids, very good results can be obtained with an embedded strong discontinuity quadrilateral finite element that has incompatible modes. Even more importantly, we demonstrate that these results can be obtained without using a crack tracking algorithm. Therefore, the simulation of crack patterns with several cracks, including branching, becomes possible. The avoidance of a tracking algorithm is mainly enabled by the application of a novel, local (Gauss-point based) criterion for crack nucleation, which determines the time of embedding the localisation line as well as its position and orientation. We treat the crack evolution in terms of a thermodynamical framework, with softening variables describing internal dissipative mechanisms of material degradation. As presented by numerical examples, many elements in the mesh may develop a crack, but only some of them actually open and/or slide, dissipate fracture energy, and eventually form the crack pattern. The novel approach has been implemented for statics and dynamics, and the results of computed difficult examples (including Kalthoff’s test) illustrate its very satisfying performance. It effectively overcomes unfavourable restrictions of the standard embedded strong discontinuity formulations, namely the simulation of the propagation of a single crack only. Moreover, it is computationally fast and straightforward to implement. Our numerical solutions match the results of experimental tests and previously reported numerical results in terms of crack pattern, dissipated fracture energy, and load–displacement curve.

Fracture Behavior of Single-Crystal Sapphire in Different Crystal Orientations

In order to study the anisotropy of fracture toughness and fracture mechanism of single-crystal sapphire, the three-point bending tests and the single-edge V-notch beam (SEVNB) were used to test the fracture toughness of A-plane, C-plane, and M-plane sapphire, which are widely used in the semiconductor, aerospace, and other high-tech fields. Fracture morphology was investigated by a scanning electron microscope and three-dimensional video microscopy. The fracture toughness and fracture morphology of different crystal planes of sapphire showed obvious anisotropy and were related to the loading surfaces. C-plane sapphire showed the maximal fracture toughness of 4.24 MPa·m1/2, and fracture toughness decreases in the order of C-plane, M-plane, and A-plane. The surface roughness is related to the dissipation of fracture energy. The surface roughness of the fracture surface is in the same order as C-plane > M-plane > A-plane. The fracture behavior and morphology of experiments were consistent with the theoretical analysis. C-plane sapphire cleavages along the R-plane with an angle of 57.6 degrees and the rhombohedral twin were activated. M-plane and A-plane sapphire cleavages along their cross-section.

Dynamic fracture mechanics and energy distribution rate response characteristics of coal containing bedding structure.

To investigate the influence of bedding structure and different loading rates on the dynamic fracture characteristics and energy dissipation of Datong coal, a split Hopkinson bar was used to obtain the fracture characteristics of coal samples with different bedding angles. The process of crack initiation and propagation in Datong coal was recorded by the high-speed camera. The formula for the model I fracture toughness of the transversely isotropic material is obtained on the basis of the finite element method (FEM) together with the J-integral. By comparing the incident energy, absorbed energy, fracture energy and residual kinetic energy of Datong coal samples under various impact speeds, the energy dissipation characteristics during the dynamic fracture process of coal considering the bedding structure is acquired. The experimental results indicate that the fracture pattern of notched semi-circular bending (NSCB) Datong coal is tensile failure. After splitting into two parts, the coal sample rotates approximately uniformly around the contact point between the sample and the incident rod. The dynamic fracture toughness is 3.52~8.64 times of the quasi-static fracture toughness for Datong coal. Dynamic fracture toughness increases with increasing impact velocity, and the effect of bedding angle on fracture toughness then decreases. In addition, the residual kinetic energy of coal samples with the same bedding angle increases with the increase of impact speed. The energy utilization rate decreases continuously, and the overall dispersion of statistical data decreases gradually. In rock fragmentation engineering, the optimum loading condition is low-speed loading regardless of energy utilization efficiency or fracture toughness. These conclusions may have significant implications for the optimization of hydraulic fracturing process in coal mass and the further understanding of crack propagation mechanisms in coalbed methane extraction (CME). The anisotropic effect of coal should be fully considered in both these cases.

Effects of characteristic element length on fracture energy dissipation in continuum damage mechanics models

Progressive damage finite element (FE) analysis methods based on continuum damage mechanics (CDM) use mesh regularization algorithms to ensure that fracture energy dissipation predictions are independent of problem discretization. Mesh regularization algorithms require some geometric input related to the discretization. When using crack band theory for mesh regularization, a characteristic element length is used to approximate the width of the region affected by the continuum crack, i.e., the crack band width. Inaccuracy in representing the crack band width significantly affects predictions in terms of fracture energy dissipation. For square elements misaligned by 45°, using a typical line length across an element rather than the crack band width overestimates dissipated fracture energy by 41%. Not accounting for element aspect ratio underestimates dissipated fracture energy by 29% and 50% for ratios of two and four, respectively. Herein, methods for calculating characteristic element lengths in fiber-reinforced materials are presented that account for meshes being misaligned with respect to material directions, element aspect ratio, and element skew. The limits of applicability of different crack band width approximations are explored through numerical crack growth studies and center notch tension FE analyses for different discretizations. Results are compared in terms of fracture energy dissipation to linear elastic fracture mechanics. Analyses with the proposed characteristic element lengths predict consistent fracture energy dissipation with various meshes. The proposed methods and the included studies on potential error in fracture energy dissipation provide analysts the basis to better understand error in CDM model predictions associated with simplified FE model preprocessing.

Modulating Mechanical and Shape-Memory Properties while Mitigating Degradation-Induced Inflammation of Polylactides by Pendant Aspirin Incorporation.

Synergistically modulating mechanical properties and improving shape-memory performance while mitigating degradation-induced chronic inflammation of polylactide (PLA)-based implants for biomedical applications remain elusive. We test the hypothesis that copolymerizing aspirin-functionalized glycolide with d,l-lactide could enhance the thermal processing, toughness, and shape-memory efficiency of the copolymer while mitigating local inflammatory responses upon its degradation. The content of pendant aspirin was readily modulated by monomer feeds during ring-opening polymerization, and the copolymers with ∼10% or less aspirin pendants exhibited gigapascal-tensile moduli at body temperature and significantly improved fracture toughness and energy dissipation that positively correlated with the aspirin pendant content. The copolymers also exhibited excellent thermal-healing and shape-memory efficacy, achieving a >97% temporary shape fixing ratio at room temperature and facile shape recovery at 50-65 °C. These drastic improvements were attributed to the dynamic hydrophobic aggregations among aspirin pendants that strengthen glassy-state physical entanglement of PLA while readily dissociating under stress/thermal activation. When subcutaneously implanted, the copolymers mitigated degradation-induced inflammation due to concomitant hydrolytic release of aspirin without suppressing early acute inflammatory responses. The incorporation of aspirin pendants in PLA represents a straightforward and innovative strategy to enhance the toughness, shape-memory performance, and in vivo safety of this important class of thermoplastics for biomedical applications.

Experimental study on influence of wetting-drying cycle on dynamic fracture and energy dissipation of red-sandstone

To study the influence of the wetting-drying cycles and loading rate on dynamic fracture toughness and energy dissipation of rocks under the dynamic loads, the split Hopkinson pressure bar (SHPB) system was used to perform the dynamic impact tests on NSCB specimens of red sandstone after different wetting-drying cycles. The loading rate response characteristics of fracture toughness of specimens after different wetting-drying cycles were analyzed, and the energy dissipation law of dynamic fracture under the impact loads was obtained. The results show that under a given number of wetting-drying cycles, with the increase of loading rate, the dynamic fracture toughness shows an overall trend of increasing. When the critical loading rate K˙IC is exceeded, the dynamic fracture toughness no longer increases. At the fixed loading rate, the dynamic fracture toughness of red sandstone decreases linearly with the increase of wetting-drying cycles, and the higher the loading rate, the more sensitive the fracture toughness to the wetting-drying cycle. With the increase of the loading rate, the dynamic fracture energy increases exponentially and becomes more sensitive to the loading rate. Under the fixed wetting-drying cycles, the dynamic fracture toughness of red sandstone has a logarithmic relationship with the increase of fracture energy.

Peridynamic analysis of dynamic fracture: influence of peridynamic horizon, dimensionality and specimen size

In peridynamic models for fracture, the dissipated fracture energy is regularized over a non-local region denoted as the peridynamic horizon. This paper investigates the influence of this parameter on the dynamic fracture process in brittle solids, using two as well as three dimensional simulations of dynamic fracture propagation in a notched plate for two loading cases. The predicted crack speed for the various scenarios of the initially stored energy, also known as the velocity toughening behavior as well as characteristics of the crack surface topology obtained in different crack propagation regimes in 3D computational simulations are compared with the experimentally observed crack velocity and fracture surfaces for Polymethyl Methacrylate (PMMA) specimens. In addition, we investigate the influence of the specimen size on the dynamic fracture process using two dimensional peridynamic simulations. The fracture strengths and the velocity toughening relationship obtained from different specimen sizes are compared with the Linear Elastic Fracture Mechanics (LEFM) size effect relationship and with results from experiments, respectively.

Fracture Characteristics and Energy Dissipation of Textile Bamboo Fiber Reinforced Polymer.

The fracture theory of fiber-reinforced polymer (FRP) composites is complicated compared to that of homogeneous materials. Textile FRPs need to consider crimp, fiber off-axis and various weaving parameters in a two-dimensional scale, which makes research of failure and fracture difficult. The objective and main contribution of the present research lie in taking textile bamboo FRP as an example and using tools such as toughness, load and deflection curves analysis, energy analysis, and first-order derivative signals to establish the preliminary information needed for fracture theory. This is followed by observing the fracture characteristics of the material under bending. The identification of fracture modes, corresponding energy, and energy dissipation are all prerequisites for developing fracture models in the future. Differences in the direction of force, weaving method, and number of laminates will cause the amount and direction of fibers to vary, which makes the type and progression of fracture different. Combining signal analysis, fracture images and energy dissipation curves, there are different modes of fracture between various groups due to different energy storage forms and crack types, which ultimately lead to different energy dissipation behaviors.

Research on triaxial compression failure characteristics and meso-simulation of brittle gypsum material

The laboratory tests and Particle Flow Code numerical simulation of triaxial compression are conducted to analyze fractal dimensions of fracture surface, strength properties, energy dissipation, damage laws and crack evolution. Under low confining pressure, the fracture surface of the brittle specimen is rough and the angle relative to the maximum principal stress is small. The specimen eventually exhibits local tensile-shear failure mode. With the increase of confining pressure, the strength of the specimen increases and yield platform for the stress–strain curve is more obvious. The main fracture surface becomes increasingly flatter and the fracture angle increases with the increase of confining pressure. The specimen exhibits a shear failure mode macroscopically. With the increase of confining pressure, the trend of transgranular shear failure becomes obvious and the micro-fracture surface has a smaller fractal dimension. In the triaxial compression test, energy storage, dissipation and release occur. When the storage limit is reached, the internal elastic strain energy releases sharply and the damage variable increases rapidly. As the confining pressure increases, the number of tensile and shear cracks is accumulated in an ‘S’ shape. Meanwhile, the proportion of shear cracks increases gradually.

Low-velocity impact response and breakage characteristics of hollow brittle particles

Low-velocity impact responses of typical hollow brittle particles (HBPs) were tested with a strain-limited loading technique to investigate the particle breakage characteristics at both macro and particle levels. The quasi-static compressions were also conducted for comparison. Effects of strain rate and particle size distribution on the stress-strain response, particle breakage and macro deformation behaviors were discussed. Results show that the strength, plateau stress and energy dissipation of hollow brittle particles all exhibited significant strain rate sensitivity. The particle size gradations after single-impact compression were obtained through the laser diffraction technique. Quantitative analysis on the fragmentations and the Hardin relative breakage shown that the dynamic breakage ratio and the breakage extent of the hollow particles at the same strain were larger than that under quasi-static compressions. Moreover, it was found that the Hardin relative breakage generated by specific energy dissipation decreased with the strain rate. The reduction of fracture energy dissipation efficiency and the rate-dependent breakage response of particle breakage are the intrinsic reasons for bulk-scale strain rate effects of HBPs. Finally, the macro deformation behaviors of hollow brittle particles were analyzed through digital image correlation (DIC) technique. It was observed that there exists a competition mechanism between the boundary effect and the inertial effect in dominating the compression patterns. The deformation mechanism was sensitive to the loading velocity.

Characterization and mesosimulation of the triaxial compression failure of rock-like materials

The laboratory tests and the numerical simulation of the particle flow code of triaxial compression are conducted to analyze the fractal dimensions of fracture surface, strength properties, energy dissipation, damage patterns, and crack evolution. The following results are obtained. (1) Under low confining pressure, the fracture surface of a brittle specimen is rough, and the angle relative to the maximum principal stress is small. The specimen eventually exhibits a local tensile–shear failure mode. As the confining pressure increases, the strength of the specimen increases, and the yield platform for the stress–strain curve is more obvious. The main fracture surface flattens, and the fracture angle increases as the confining pressure increases. The specimen macroscopically exhibits a shear failure mode. (2) As the confining pressure increases, the trend of transgranular shear failure becomes obvious, and the microfracture surface has a smaller fractal dimension. (3) In the triaxial compression test, energy is stored, dissipated, and released. When the storage limit is reached, the internal elastic strain energy becomes released sharply, and the damage variable increases rapidly. (4) As the confining pressure increases, the number of tensile and shear cracks accumulates in an “S” shape, and the proportion of shear cracks increases gradually.

Energy dissipation and damage evolution for dynamic fracture of marble subjected to freeze-thaw and multiple level compressive fatigue loading

For rock engineering in cold regions, rock is often subjected to coupled fatigue conditions of freeze-thaw (F-T) and stress disturbance. Rock fracture evolution and energy mechanism under room temperature and constant stress amplitude loading condition have been widely investigated. Yet the rock energy dissipation and damage evolution characteristics subjected to multiple level cyclic loading conditions are not well understood. In this work, 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. The fracture evolution and energy dissipation mechanism were analyzed as well as the damage evolution characteristics. The results indicate that F-T treatment strongly influences the fatigue mechanical behaviors of marble, with both fatigue strength and strain energy decreases and irreversible volumetric deformation increases with increasing F-T cycles. The incremental rate of dissipated energy becomes faster as cyclic loading level grows. In addition, a F-T-fatigue loads coupling damage variable was proposed by using the input total strain energy and the dissipated strain energy to describe the rock damage evolution after F-T treatment and experiencing fatigue loading. Moreover, a damage evolution model was first established based on the obtained coupling damage variable to describe the two-phase damage accumulation characteristics. Damage accumulation curve presents a first steady increase and then faster increase trend, the damage evolution model can good fit the experimental data.