Local Deformation Research Articles

On the contribution of local anisotropic creep to macroscopic irradiation-induced growth in zirconium alloy polycrystals

ABSTRACT Zirconium alloys used in nuclear reactor exhibit, under fast neutron flux, a macroscopic deformation even without applied stress called irradiation induced growth. Because of the polycrystalline nature of the material, the local growth of individual grains results in strain incompatibilities yielding to intergranular stresses and thus to local creep. In order to study and understand the influence of the local anisotropic creep on the macroscopic growth behaviour, an analytical and a numerical study have been undertaken, using Voigt and self-consistent estimates and also fast Fourier transform simulations. It is shown that the anisotropic local creep has a strong influence on the effective macroscopic growth strain of the polycrystal. Especially, when the deformation is difficult along the 〈 c 〉 axis, a growth enhancement effect is observed. This phenomenon is well explained in the frame of the Voigt estimate using a reduced fibre texture. Computations conducted using a texture representative of the industrial material provide a quantitative confirmation of this enhancement effect. This work demonstrates the significant contribution of the local anisotropic creep to the macroscopic in-reactor growth strain of zirconium alloys. Highlights The local creep anisotropy has a strong influence on macroscopic irradiation growth of polycrystalline zirconium tubes. The macroscopic axial growth can be significantly enhanced by the interactions between grains when local creep deformation is prevented along the 〈 c 〉 axis. A simplified representation of grain interactions (reduced fibre texture and Voigt estimate) offers a qualitative understanding of this phenomenon. Refined estimates of the effective growth strain are provided for realistic crystallographic texture using polycrystalline unit-cell FFT computations.

Discovery of white etching areas in high nitrogen bearing steel X30CrMoN15-1: A novel finding in rolling contact fatigue analysis

White etching areas (WEA) and white etching cracks (WEC) are frequently linked to premature bearing failure in conventional high carbon bearing steels like 100Cr6 (SAE 52100). In contrast, no WEA/WEC has yet been reported for the high nitrogen bearing steel X30CrMoN15-1 (SAE AMS 5898). Thus, the present study proves for the first time that X30CrMoN15-1 is also susceptible to develop WEA/WEC under rolling contact fatigue (RCF) when pre-charged with hydrogen. RCF tests conducted in parallel without hydrogen pre-charging resulted in RCF damage only, which identifies hydrogen as an active agent for WEA/WEC formation in X30CrMoN15-1. These findings correspond to the fact that hydrogen diffusion during RCF is often considered to cause or accelerate the formation of WEA/WEC. Additionally, it is observed that the M2(C, N) and M23C6 precipitates of the martensitic microstructure of the X30CrMoN15-1 do not entirely decompose during the WEA formation process as observed for M3C precipitates in 100Cr6. In conclusion, the results for X30CrMoN15-1 strongly suggest that the formation of WEA is driven by a hydrogen-activated local severe plastic deformation process, which initiates continuous dynamic recrystallisation, leading to the characteristic nano-ferritic grains observed in WEA. Also, the highly stable and self-regenerating passive chromium-oxide layer of X30CrMoN15-1 mitigates the risk of WEA/WEC failure during typical RCF operation by hindering the formation and adsorption of ionic hydrogen. Hence, this study emphasises the importance of protecting the base material against hydrogen ingress to delay WEA/WEC formation.

A homogenized anisotropic constitutive model of perforated sheets for numerical simulation of stamping

Perforated sheets exhibit strong anisotropy related to the arrangement of holes during plastic deformation, which poses significant challenges for accurate prediction of the macroscopic plastic behavior in stamping. Addressing this, unit cell simulations were conducted to determine the homogenized yielding and hardening behaviors of perforated sheets with hexagonal or square arrays of circular holes under in-plane loading conditions. The local deformation mode, which determines the macroscopic anistropy, is unveiled. A mechanism-motivated homogenized yield criterion was proposed based on the local deformation modes, which provides a concise yet unified approach to modeling complex material anisotropic behavior with high accuracy. Additionally, a mixed hardening strategy was developed to capture the evolution of yield loci in term of size and shape. The proposed constitutive model demonstrates precise predictions of flow stress variations and the apparent r-value with loading angles during uniaxial tension. Furthermore, it successfully forecasts two distinct types of earing profiles in the deep drawing of perforated sheets with square arrays of circular holes at different hole fractions. This modeling approach provides a feasible way for predicting the deformation behavior of perforated sheets during stamping with high computational efficiency.

Energy absorption performance of Kresling origami tubes under impact loading

Thin-walled tubes with an origami design, particularly the Kresling pattern, exhibit superior mechanical properties compared to traditional straight tubes, including a more constant reaction force and predictable deformation. Despite their potential, research on these patterned structures, especially when made from structural materials like metal and tested under dynamic conditions, remains limited. This study investigates the compressive performance of aluminium Kresling origami tubes (KOTs) under quasi-static and impact scenarios (up to 30 m/s) in the axial direction. Results show that increased impact velocity leads to more localized deformation and improved energy absorption metrics. A validated numerical model was used to analyze the influence of hierarchy rotation, sector angles, and loading velocity on mechanical performance. Comparisons with Miura-ori patterned tubes and hexagonal cross-section straight tubes of the same relative density revealed that KOTs have superior energy absorption performance. An empirical model was developed to effectively predict the mean crushing stress of KOTs. In addition. a generative machine learning model was introduced to synthesize a large dataset from initial simulations, providing an efficient and reliable solution for energy absorption analysis in origami structures, addressing the challenge of limited specimen datasets.

Strain localisation and grain boundary-mediated deformation in pure titanium at low and high temperatures: In-situ optical microscopy and digital image correlation

Heterogeneous deformation occurs between grains in polycrystalline α-titanium. Understanding the role of temperature in local deformation is essential for its applications in extreme environments such as cryo- or high-temperature, but the underlying mechanism still remains elusive. Here we report a study of grain-scale deformation behaviour in CP-Ti plate at the temperature range from −60 °C to 280 °C. The full-field strain measurements were conducted on the tensile samples loaded parallel (RD) and transverse (TD) to the rolling direction, using in-situ optical microscopy and digital image correlation (OM-DIC). The DIC local strain maps were coupled with scanning electron microscopy and electron backscatter diffraction analysis. The grain boundary sliding and slip transfer occurred depending on the geometric relationship (i.e., deformation compatibility) between adjacent grains at 20 °C, and a micro-crack was observed at the {101‾1} twist boundary. The strain was recovered in the grains in the RD sample favourable for slip, whilst more accumulated in the grains in TD sample unfavourable for slip at 280 °C. The plasticity of grains differs with decreasing temperature to −40 °C, resulting in the presence of soft/hard grain pairs. The strong strain localisation between the soft and hard grains led to the cracking along the GBs (RD) and cross the grains (TD). Interestingly, the cracking was significantly reduced with decreasing temperature to −60 °C due probably to the temperature dependence of the plasticity of grains. The strain-hardening behaviour of α-Ti polycrystals was significantly affected by the temperature and crystal orientation dependence of grain-scale deformation mechanism.

Spatiotemporal Patterns of Vegetation Evolution in a Deep Coal Mining Subsidence Area: A Remote Sensing Study of Liangbei, China

This study aims to provide a comprehensive analysis of the impacts of high-intensity coal mining on vegetation in Liangbei Town, a typical deep coal mining area in central of China. Using Landsat remote sensing data from 2000 to 2023, processed by the Google Earth Engine (GEE) platform, the study calculates the Normalized Difference Vegetation Index (NDVI). Temporal and spatial distribution patterns of vegetation were assessed using LandTrendr algorithm, Sen’s slope estimation, the Mann–Kendall test, the coefficient of variation, and the Hurst index. Vegetation growth dynamics were further analyzed through transfer matrix and intensity analysis frameworks. Driving factors influencing vegetation trends were evaluated using local climate data and surface deformation variables from SAR imagery. Temporal Dimension: From 2000 to 2023, the annual NDVI in Liangbei Township showed an upward trend with a growth rate of 0.0894 (10a)−1, peaking at 0.51 in 2020. Spatial Dimension: The NDVI distribution in Liangbei Township displayed a pattern of being lower in the center and higher around the edges, with values concentrated between 0.4 and 0.51, covering 50.34% of the total area. Trend of Change: Between 2000 and 2023, 83.28% of the area in Liangbei Township experienced significant improvement in the NDVI, with vegetation growth trends shifting primarily from slight to significant improvement, encompassing a total area of 10.98 km². This shift exhibited a marked tendency. Driving Factors: Deep mining in Liangbei Township is concentrated in the eastern part, with SAR imagery indicating a maximum surface subsidence of 0.26 m. As surface subsidence increases, the NDVI significantly decreases. The findings suggest that in the future, 91.13% of the vegetation in Liangbei Township will display an antipersistent change trend. The study offers critical insights into the interaction between mining activities and vegetation cover can serve as a reference for environmental evolution and management in similar mining areas.

Low-cycle fatigue behaviour of concrete-filled double skin steel tubular (CFDST) members for wind turbine towers

Wind energy has the advantages of being clean and renewable. Wind turbine towers endure horizontal cyclic loads that could influence the performance of entire structure. To clarify the low-cycle fatigue behaviour of concrete-filled double skin steel tubular (CFDST) members, a total of 16 specimens were experimented. The hollow, slenderness, and axial compression ratios are specifically designed to clarify the effects on performance under constant amplitude loading and hysteretic loading conditions. The typical failure modes under both loading conditions and the relationship between loop strain, loop bearing capacity, loop energy dissipation, cycle number, and various degradation indices were analysed. Studies indicate that the failure mode under low-cycle fatigue loading is mainly local deformation, which includes transverse fracture occurring at the region between the steel tube and ribbed stiffener, the crushing concrete. Fatigue specimens with different amplitudes exhibit varying shapes of hysteresis responses. Higher amplitudes could enhance damage and significantly reduce fatigue life. Increasing the hollow and axial compression ratios boosts the energy dissipation capacity, and decreasing the slenderness ratio enhances the lateral resistance. A 2 % constant amplitude preload intensifies the degradation of bearing capacity and energy dissipation under subsequent constant amplitude loading.

Contraction and expansion of a cylindrical cavity in an elastoplastic medium: A dislocation‐based approach

AbstractThe contraction or expansion of a cylindrical cavity in an elastoplastic medium is usually analyzed from a continuum based approach with a plasticity constitutive model. However, localized deformations, which are rooted in the post‐failure softening response of geomaterials, are observed in the form of spiral‐shaped fractures in laboratory tests. An alternative approach based on dislocation theory is introduced in this paper for modeling cavity contraction or expansion. In this model, several equally spaced spiral‐shaped shear fractures initiate and propagate away from the cavity within the linearly elastic medium. The Mohr‐Coulomb criterion and a dilatancy rule are imposed on the shear fractures to constrain the stresses and the displacement jumps. The direction of fracture propagation is determined by minimizing plastic dissipation. The displacement discontinuity method is used to discretize the shear and normal displacement jumps along the fracture and solve the problem numerically. The calculated crack path follows a logarithmic‐like spiral, similar to the slip lines predicted by plasticity theory. The relationship between the pressure and radial displacement at the cavity boundary converge towards the classical elastoplastic solution as the number of fracture branches increases.

A new finite element formulation for the lateral torsional buckling analyses of orthotropic FRP-externally bonded steel beams

Abstract The present study develops a new finite element (FE) formulation for the lateral torsional buckling (LTB) analyses of steel beams exteriorly bonded with orthotropic fiber-reinforced polymer (FRP) layers. The formulation considers shear deformations, partial material interaction, local and global warping deformations, and orthotropic FRP properties. The buckling responses of multispan FRP-bonded steel beams predicted by the present solutions are excellently validated against experiment and numerical solutions. As observed, the FRP strengthening is highly effective for the LTB resistance of steel beams. However, the LTB responses are strongly dependent on the orthotropic properties and strengthening lengths of FRP layers. The effects of shear deformations, span ratios, and loading conditions on the LTB responses are also quantified in the present study.

Microstructure, Mechanical, and Tribological Properties of Nb-Doped TiAl Alloys Fabricated via Laser Metal Deposition.

TiAl alloys possess excellent properties, such as low density, high specific strength, high elastic modulus, and high-temperature creep resistance, which allows their use to replace Ni-based superalloys in some high-temperature applications. In this work, the traditional TiAl alloy Ti-48Al-2Nb-2Cr (Ti4822) was alloyed with additional Nb and fabricated using laser metal deposition (LMD), and the impacts of this additional Nb on the microstructure and mechanical and tribological properties of the as-fabricated alloys were investigated. The resulting alloys mainly consisted of the γ phase, trace β0 and α2 phases. Nb was well distributed throughout the alloys, while Cr segregation resulted in the residual β0 phase. Increasing the amount of Nb content increased the amount of the γ phase and reduced the amount of the β0 phase. The alloy Ti4822-2Nb exhibited a room-temperature (RT) fracture strength under a tensile of 568 ± 7.8 MPa, which was nearly 100 MPa higher than that of the Ti4822-1Nb alloy. A further increase in Nb to an additional 4 at.% Nb had little effect on the fracture strength. Both the friction coefficient and the wear rate increased with the increasing Nb content. The wear mechanisms for all samples were abrasive wear with local plastic deformation and oxidative wear, resulting in the formation of metal oxide particles.

A coupled crystal inelasticity-phase field model for crack growth in polycrystalline nitinol microstructures

Abstract This paper introduces a comprehensive computational framework, comprising a finite deformation crystal inelasticity constitutive model and phase field model, for modeling crack growth in superelastic nitinol polycrystalline microstructures. The crystal inelasticity model represents crystal stretching and lattice rotation from elastic mechanisms, as well as local inelastic deformation due to austenite-martensite phase transformation. The phase field formulation decomposes the Helmholtz free energy density into stored elastic energy, phase transformation energy, and crack surface energy components. The elastic energy accounts for tension-compression asymmetry with the formation of the crack through a spectral decomposition. Kinetic Monte Carlo simulations generate equilibrium area fractions of different surface orientations, which serve as weights for the surface energy. An adaptive wavelet-enhanced hierarchical finite element (FE) model is introduced to alleviate high computational overhead in phase field crack simulations. Simulations with the coupled inelasticity phase field model are conducted under various loading conditions including Mode-I tension, a quasi-static Kalthoff experiment, and cyclic loading of polycrystalline microstructures. Crack propagation is effectively predicted by this model, providing valuable insights into the material mechanical behavior with growing cracks.

Probing local difference of martensite formation: a study on localized deformation modes in drawn 304H stainless steel wires

Probing local difference of martensite formation: a study on localized deformation modes in drawn 304H stainless steel wires

Hot Workability and Microstructure Evolution of Homogenized 2050 Al-Cu-Li Alloy during Hot Deformation.

For this article, hot compression tests were carried out on homogenized 2050 Al-Cu-Li alloys under different deformation temperatures and strain rates, and an Arrhenius-type constitutive model with strain compensation was established to accurately describe the alloy flow behavior. Furthermore, thermal processing maps were created and the deformation mechanisms in different working regions were revealed by microstructural characterization. The results showed that most of the deformed grains orientated toward <101>//CD (CD: compression direction) during the hot compression process, and, together with some dynamic recovery (DRV), dynamic recrystallization (DRX) occurred. The appearance of large-scale DRX grains at low temperatures rather than in high-temperature conditions is related to the particle-stimulated nucleation mechanism, due to the dynamic precipitation that occurs during the deformation process. The hot-working diagrams with a true strain of 0.8 indicated that the high strain-rate regions C (300 °C-400 °C, 0.1-1 s-1) and D (440 °C-500 °C, 0.1-1 s-1) are unfavorable for the processing of 2050 Al-Li alloys, owing to the flow instability caused by local deformation banding, microcracks, and micro-voids. The optimum processing region was considered to be 430 °C-500 °C and 0.1 s-1-0.001 s-1, with a dissipation efficiency of more than 30%, dominated by DRV and DRX; the DRX mechanisms are DDRX and CDRX.

Effect of Extrusion Ratio on Mechanical Behavior and Microstructure Evolution of 7003 Aluminum Alloy at High-Speed Impact.

The extrusion ratio (ER) is one of the most important factors affecting the service performance of aluminum profiles. In this study, the influence of ER on the mechanical behavior and microstructure evolution of 7003 aluminum alloy at high-speed impact with strain rates ranging from 700 s-1 to 1100 s-1 was investigated. The studied alloy with an ER of 56 formed coarse grain rings during the heat treatment. The microstructure of the alloys with ERs of 20 and 9 is relatively uniform. The results indicate that under high-speed impact, the mechanical response behavior of the 7003-T6 alloy with different ERs is different. For the alloy with an ER of 56, strain hardening is the main mechanism of plastic deformation. In contrast, a flow stress reduction occurs at middle deformation stage for the ones with ERs of 20 and 9 due to concentrated deformation, which is more significant in the alloy with an ER of 20. Under high-speed impact, the alloy with an ER of 56 undergoes uneven plastic deformation due to the presence of coarse grain rings. The deformation is mainly borne by the region of coarse grains near the edge, and the closer to the center, the smaller the deformation. The deformation of the alloys with ERs of 20 and 9 is relatively uniform, but exhibits localized concentrated deformation in the area near the edge. The significant plastic deformation within deformation band causes a local temperature rise, resulting in a slight decrease in flow stress after the peak. These results can provide reliable data support for the application of 7003 aluminum alloy in the vehicle body crash energy absorption structure.

Influence of processing parameters on the fracture behaviour of 316L SS printed by laser powder bed fusion

This study explored the relationship between process parameters and fracture behavior in 316L stainless steel printed by laser powder bed fusion. Fracture testing was conducted according to ASTM E1820 for single edge notch bending, and elastic mechanical properties were determined using ultrasonic surface wave analysis. Five test sets were considered in a vertical building configuration using five different volumetric energies belonging to conduction mode. The critical fracture toughness was calculated and discussed along with the plastic deformations at the crack tip. The study found that local plastic deformation for single edge notch bending was influenced by powder bed fusion process parameters. A correlation was observed between energy density, fracture toughness, and the dimensions of the fracture process zone. The R-curves showed different fracture behaviors depending on the energy density. The energy required to grow a crack was associated with larger plastic zones, resulting in fracture toughness values ranging from 43 (43 J mm−3) to 427 kJ/m2 (68 J mm−3). Results are discussed in terms of porosity and strain hardening capacity depending on the manufacturing conditions.

A B-spline based gradient-enhanced micropolar implicit material point method for large localized inelastic deformations

The quasi-brittle response of cohesive-frictional materials in numerical simulations is commonly represented by softening plasticity or continuum damage models, either individually or in combination. However, classical models, particularly when coupled with non-associated plasticity, often suffer from ill-posedness and a lack of objectivity in numerical simulations. Moreover, the performance of the finite element method significantly degrades in simulations involving finite strains when mesh distortion reaches excessive levels. This represents a challenge for modeling cohesive-frictional materials, given their tendency to experience strongly localized deformations, such as those occurring during shear band dominated failure. Hence, accurate modeling of the response of cohesive-frictional solids is a demanding task. To address these challenges, we present an extension of the material point method (MPM) for the unified gradient-enhanced micropolar continuum, aiming at the analysis of finite localized inelastic deformations in cohesive-frictional materials. The generalized gradient-enhanced micropolar continuum formulation is employed to tackle challenges related to localization and softening material behavior, while the MPM addresses issues arising from excessive deformations. The method utilizes a B-spline formulation for the rigid background mesh to mitigate the well-known cell crossing errors of the MPM. To demonstrate the performance of the method, 2D and 3D numerical studies on localized failure in sandstone in plane strain compression and triaxial extension tests are presented. A comparison with finite element results confirms the suitability of the formulation. Moreover, an efficient numerical implementation of the formulation is presented, and it is demonstrated that the additional MPM specific overhead is negligible.

Revisiting strain localization analysis for elastoplastic constitutive models in geomechanics

AbstractThe localization of deformations plays a crucial role in the failure of granular materials. Concerning classical continuum constitutive models, the localization of deformations is considered to be connected to the loss of ellipticity of the governing rate equilibrium equations, and entails mesh sensitivity in finite element simulations. While previous studies are often limited to strain localization analyses of individual tests, the focus of the present contribution lies on studying the localization properties in general constitutive states. For this purpose, a staggered optimization algorithm for determining the loss of ellipticity, considering both extreme values, minimum and maximum, of the determinant of the acoustic tensor, is proposed. Part of this algorithm representing a novel application of spherical Fibonacci lattices for discretizing the feasible domain of the associated optimization problem. In the presented localization study of the widely recognized modified Cam‐clay model, special attention is paid to determining the influence of the individual model parameters. Specifically, three factors favoring strain localization are found, namely (i) a low value of the ratio of the primary compression index and the recompression index, (ii) a large value of the critical state frictional constant, as well as (iii) a large value of Poisson's ratio. Moreover, a structural finite element study is performed, confirming the results of localization analyses at the constitutive level.

Shaping the crustal structure of the SW-Alpine Foreland: Insights from 3D Geological modeling

Reactivation processes play a significative role in the localization of deformation but still remain hard to establish at the lithospheric scale. In this work, we built a 3D structural model, which enables to bridge the gap between the main tectonic structures observed at the surface and the geometry of the major interfaces (the Mohorovičić-discontinuity (hereafter Moho) and top of the basement) inferred from geophysical data acquired in the external Western Alps and their foreland. The geometry of these tectonic structures is interpreted in relation to their geodynamic evolution. The main results of this study highlight: (1) a strong contribution of thick-skinned Pyrenean-Provence and Alpine tectonics, (2) a lithospheric rooting of Variscan shear zones and related faults, and (3) the regional-scale influence of these inherited structures on the post-Paleozoic strain localization in the study area. Our 3D model shows that the pattern of Variscan shear zones that were developed at the end of the Paleozoic involved the whole crust, as emphasized by the Moho offsets. These shear zones were reactivated and localized Meso-Cenozoic deformation. The Variscan deformation pattern controlled the geometry of extensional basins, the propagation of Pyrenean-Provence deformation, and finally the Alpine deformation at crustal scale. Our 3D model shows minor crustal thickening (ca. 40 km) located below the Pelvoux External Crystalline Massif, which probably resulted from both Pyrenean and Alpine tectonic phases. In contrast, the southern part of the Alpine front shows a thinned crust (ca. 18 km) resulting from extensional Meso-Cenozoic phases between the Cévennes margin and the Durance basin.

Discussion on the relationship between pathological changes of sciatic nerve and Sarm1 protein expression in rats with n-hexane poisoning

Objective: To explore the potential evidence of active peripheral nerve necrosis when n-hexane produces toxic effects on peripheral nerves. Methods: In May 2023, 36 SPF grade SD male rats with a body weight of 200-220 g were divided into 4 groups with 9 rats in each group and given normal saline and different doses of n-hexane (168, 675, 2 700 mg/kg) by gavage for 6 consecutive weeks (5 days/week). Three rats in each group were killed at the 2nd, 4th and 6th week, respectively. The spinal cord to sciatic nerve tissue was broken and the supernatant was extracted for SDS-PAGE protein isolation. The expression level of Sarm1 protein was analyzed with the β-Actin color strip of internal reference protein by Western blot. The expression of Sarm1 protein was analyzed by the gray ratio of the two. At the 6th week, the sciatic nerve sections of the each group were observed by light microscope and electron microscope. Results: The number of axons was obviously reduced by light microscopy. According to electron microscope, myelin lesions were mainly local disintegration, deformation, and different thickness. The deformation of axonal surface became smaller. The axons in the nerve bundle membrane showed degeneration and reduction. The gray ratio of Sarm1 protein and internal reference protein bands in each group had no significant change at the second week of exposure, and the ratio of SARM1 protein to internal reference protein bands was 1.47 in the high dose group at the fourth week, and 1.51 and 1.89 in the middle and high dose group at the sixth week, respectively. Conclusion: Waller's degeneration was observed in sciatic neuropathologic manifestations of n-hexane-poisoned rats, and the expression level of Sarm1 protein increased.

Experimental study of rock fracture behavior under direct tension using three-dimensional digital image correlation

Understanding the mechanical characteristics of rocks when subjected to direct tension is crucial for assessing the stability of rock formations. Within the scope of this research, a series of tests was conducted using Tage tuff to assess the deformation behavior and crack extension of rock under direct tension. The axial, lateral, and shear strain fields as well as crack propagation, localized deformation behavior, and failure mode of the rocks were analyzed using three-dimensional digital image correlation method. The results showed that the axial strain fields on the specimen surface were heterogeneous, with different locations and localization occurring in the pre-peak stage, which was similar to the evolution of shear strain, whereas the lateral strain only showed slight changes. The crack extension direction was inferred, indicating that both tensile and shear stress occurred in the tests. Furthermore, different stress–strain responses were observed for the inside and outside of the localized bands. Then, the surface patterns of specimen failure were scanned and analyzed to assess the failure mode and residual strength of the specimen under direct tensile stress. Finally, the results of direct tension, uniaxial compression, and Brazilian split tests for Tage tuff were compared, and the complete stress–strain curve of uniaxial tension (UT) was simulated using a nonlinear-variable-compliance constitutive equation. This study provides a deeper understanding into the damage behavior of rocks under direct tension.