Stress Triaxiality Research Articles

A high-rate, impact-driven biaxial fragmentation experiment for ductile materials

The experimental investigation of high strain rate fragmentation has generally been limited to one of two cases: analytically powerful but simple one-dimensional loading configurations, or complicated multiaxial experiments more closely approximating use applications. The former, exemplified by Mott-style ring fragmentation, promotes simple and confident analysis—forming the backbone of the field and revealing the basic nature of dynamic fragmentation in solids—but ignores some critical mechanisms in order to achieve that simplicity. The latter, while informing applications of interest such as ballistic impact, may provide limited insight and is often difficult to access diagnostically. This work presents an attempt to help bridge the gap between 1D ring expansion and 3D fragmentation experiments in the form of impact driven, high-strain-rate biaxial tensile fragmentation experiments. The impact target system consists of a thin specimen plate and a thick polymer impact buffer. The latter serves as a fluid-like medium allowing momentum transfer between an impacting projectile and a rapidly growing near-hemispherical bulge in the specimen plate. The deformation of the specimen and fragmentation pattern are observed using ultra-high-speed optical imaging as well as flash x-ray imaging, and individual fragments are recovered and characterized post-mortem. Using this method, the fragmentation behavior of 6061-T6 Aluminum is investigated at tensile strain rates exceeding 105s−1 and at higher stress triaxiality than that commonly achieved.

Experimental and numerical analysis of injection-induced permeability changes in pre-existing fractures

This paper presents a combined laboratory and numerical investigation on the injection-induced permeability changes in pre-existing fractures. The analyses conducted were primarily based on the results of an innovative laboratory experiment designed to replicate the key mechanisms that occur during hydraulic stimulation of naturally fractured rocks and/or faulted zones. The experiment involved pressure-controlled fluid injection into a laboratory-scale pre-existing fracture within a granite block, which was subjected to true triaxial stress conditions. Rough and smooth fractures are investigated, and the results are discussed. Based on the experimental results, two contributing mechanisms were considered to describe the pressure-driven permeability changes in pre-existing fractures: (1) elastic opening/closure leading to a reversible permeability change, and (2) fracture sliding in shear mode, causing dilation and hence an irreversible permeability increase. With these assumptions, an aperture-dependent permeability function was adopted to couple the hydraulic flow with the mechanical deformations along the fracture. Subsequently, a 3D coupled hydro-mechanical model was developed to replicate fluid-injection tests conducted at various conditions, including different stress conditions and fracture surface roughness. The employed modeling framework effectively captured the experimental observations. Our results indicate that the maximum permeability increases twofold.

Influences of stress triaxiality and forming parameters on microstructural evolution and fracture mechanisms in a Ni–Cr–Mo-based superalloy

Hot tensile features in a Ni–Cr–Mo-based superalloy with different notched types are explored. Changes of microstructure and fracture mechanisms with stress triaxiality and tensile parameters are elucidated. Results manifest that the maximum load for the Ni–Cr–Mo-based superalloy in hot tensile ascends with increasing stress triaxiality. The development/interaction of dislocation clusters and subgrains is sensibly boosted, while the dynamic recrystallization (DRX) formation/coarsening behaviors is suppressed with ascending stress triaxiality or strain rate. Nevertheless, the intense generation/development in substructure and DRX grains appear at higher tensile temperature. The primary fracture mode is the ductile facture closely associated with dimples formation/coalescence and the progression of serpentine gliding. The primary fracture mechanism of Ni–Cr–Mo-based superalloy is the shear fracture characterized by the microporous polymerization. The coalescence/growing up in dimples becomes weaken with reducing stress triaxiality. Additionally, the dominant texture components are the E, F and Copper textures for the Ni–Cr–Mo-based superalloy with notched type in high-temperature tensile. With increasing stress triaxiality, the S texture sensibly increases.

Experimental study on strengthening the magneto-mechanical coupling effect of X80 steel by weak magnetic excitation

Abstract Current magnetic stress detection techniques are significantly impacted by external noise signals. The magnetic stress detection technology under excitation magnetic fields is proposed to weaken the external noise signals on the detection results. In this study, the uniaxial tensile magnetic signal testing system with the excitation magnetic field was built. The enhancement of the weak magnetic excitation on magnetic signals has been quantitatively analyzed and the concept of optimal weak excitation magnetic field has been proposed. The response law between triaxial magnetic induction intensity and stress under the excitation magnetic field is determined. The results indicate that the weak excitation magnetic field significantly enhances the magnetic induction signal intensity, more importantly, the linearity of the magnetic signal and stress response is also enhanced. Furthermore, the optimal excitation magnetic field under uniaxial stress states is 600 A/m, and the corresponding stress-magnetic change rate is 0.002 Oe/MPa. This study provides a theoretical basis for the long-distance detection of pipelines under weak magnetic excitation. The long-distance magnetic stress detection results of pipelines will become more accurate with the weak magnetic excitation which has a good engineering significance.

Deformation and failure behavior of 2024-T42 sheet under impact loading

The deformation and failure behavior of 2024-T42 aluminum alloy sheet was investigated through a combined experimental-numerical method. Nine types of specimens were designed to cover a wide range of stress triaxialities and strain rates. Quasi-static and dynamic tests were carried out by electronic testing machine and split Hopkinson tensile bar respectively, and digital image correlation (DIC) method was introduced to measure the deformation. The phenomenological damage model GISSMO (generalized incremental stress state dependent damage model) and Johnson-Cook model were adopted to simulate all of the above tests and the load-displacement curves through numerical simulation were derived. An optimization method was developed to obtain all the model parameters by matching the load-displacement curves from simulation with those from tests by LS-OPT. Finally, drop weight tests and tensile tests of the central-hole plate were conducted. The applicability and accuracy of the damage models were verified by comparing the simulation results with the experiments, which indicates that GISSMO model predicts better the tests than the Johnson-Cook failure model.

Multi-angle property analysis and stress–strain curve prediction of cementitious sand gravel based on triaxial test

In order to further promote the application of cementitious sand gravel (CSG), the mechanical properties and variation rules of CSG material under triaxial test were studied. Considering the influence of fly ash content, water-binder ratio, sand rate and lateral confining pressure, 81 cylinder specimens were designed and made for conventional triaxial test, and the influence laws of stress–strain curve, failure pattern, elastic modulus, energy dissipation and damage evolution of specimens were analyzed. The results showed that the peak of stress–strain curve increased with the increase of confining pressure, and the peak stress, peak strain and energy dissipation all increased significantly, but the damage variable D decreased with the increase of confining pressure. Under triaxial compression, the specimen was basically sheared failure from the bonding surface, and the aggregate generally did not break. Sand rate had a significant effect on the peak stress of CSG, and decreased with the increase of sand rate. Under the conditions of the same cement content, fly ash content and confining pressure, the optimal water-binder ratio 1.2 existed when the sand rate was 0.2 and 0.3. After analyzing and processing the stress–strain curve of triaxial test, a Cuckoo Search-eXtreme Gradient Boosting (CS-XGBoost) curve prediction model was established, and the model was evaluated by evaluation indexes R2, RMSE and MAE. The average R2 of the XGBoost model based on initial parameters under 18 different output features was 0.8573, and the average R2 of the CS-XGBoost model was 0.9516, an increase of 10.10%. Moreover, the prediction curve was highly consistent with the test curve, indicating that the CS algorithm had significant advantages. The CS-XGBoost model could accurately predict the triaxial stress–strain curve of CSG.

Investigation on fracture resistance behaviour of dissimilar metal weld joint of modified 9Cr–1Mo steel and AISI 316LN SS

Fracture behavior of dissimilar metal weld joint consisting of mod. 9Cr–1Mo steel, AISI 316LN stainless steel, Inconel 82 butter layer and Inconel 182 weld has been investigated through experiments and FE simulations. The metallographic studies on weld joint and its interfaces have been carried out to determine the influence of microstructure on tensile and fracture properties. Tensile properties of different weld regions viz., weld metal, butter layer and HAZ have been evaluated using sub-size specimens. Fracture resistance behavior of weld joint has been studied through testing of compact type specimens with initial cracks machined at different locations. The plastic η factors for estimation of J-R curve have been obtained using FE analysis for crack in different regions viz., weld metal, butter layer and HAZ. Crack in weld metal exhibits lower fracture resistance as compared to butter layer and HAZ. Further, the constraint acting on crack and its susceptibility for deviation have been discussed in terms of stress triaxiality ahead of crack tip.

Measurement of strengths and fracture initiation strains of weld metal and HAZ in steel joints using miniature coupons

This paper investigates the strengths (fy, fu) and fracture initiation strains (εf) of the weld and heat affected zone (HAZ) of welded joints. Miniature coupons were extracted and tested using a custom-built jig. The weld metal was generally isotropic with the highest and lowest εf in the longitudinal and transverse directions, respectively. The HAZ had higher fy and fu than the base metal but smaller εf in the transverse direction under low stress triaxiality, indicating possible fracture through the weld and HAZ when loaded transversely. The strengths of the weld metal and HAZ can be approximated to within 7%-10% using empirical hardness-strength correlation functions.

A strain components-based Mohr–Coulomb fracture criterion for proportional loading

Ductile fracture criteria are crucial in the application of elastoplastic materials like advanced high-strength steels, particularly due to their tendency to fail without significant localized necking. It is aimed to figure out the unified mechanism for ductile fracture and accurately describe it with phenomenological criteria. In this study, the effect of the stress triaxiality and the Lode parameter is analyzed mathematically. The maximum shear strain and the normal strain to fracture are emphasized in the proposed strain components-based Mohr–Coulomb fracture criterion particularly designed for plane stress states, and it is assumed that fracture occurs when the combination of the maximum shear strain and the normal strain reaches the critical value. It is then extended to describe fracture with the equivalent plastic strain and the normal strain to fracture. The experimental fracture data of AA 2024-T351 and the additively manufactured Ti-6Al-4V titanium alloy are used to verify the proposed models. A fracture forming limit diagram comprising forming limit curves calibrated from stress states under different stress triaxialities is proposed based on the proposed fracture criteria for plane stress states. This study shows that a strong correlation between the maximum shear strain and the normal strain to fracture has been observed, and it can be described piecewise-linearly. Besides, the orientation of the fracture surface under both tension (including plane strain tension) and compression (including plane strain compression) can be qualitatively explained by the Mohr’s strain circles. The results provide a new insight into the intrinsic deformation and fracture mechanism of materials that fail without severe localized necking.

Transverse failure prediction of unidirectional carbon fiber reinforced polymer composites subjected to uniaxial and biaxial loading by stress-triaxiality-dependent computational micromechanics

Accurate characterizing the mechanical behavior of the component materials is crucial for failure predicting of unidirectional carbon fiber reinforced polymer (UD CFRP) composites. A stress-triaxiality-dependent micromechanics model is developed for the transverse failure prediction of the composites in this study, in which the stress triaxiality is innovatively adopted to define the plastic hardening behavior of the matrix material. Therefore, diverse hardening behaviors generated by heterostructures, accurate confirmation of biaxial failure, as well as hardening behavior evolution caused by stress status changes during loading process can be considered. The accuracy performance of the micromechanics model is provided by comparing the predicted results (stress–strain curves, RVE profiles and failure points) with existing experimental data and failure envelopes of failure criterion. The comparison results show that the micromechanics model can accurately capture the failure phenomenon and failure evolution mechanism of the composite under uniaxial and biaxial loadings.

Mechanisms of void nucleation on neat and Glass Syntactic PolyPropylene using in situ synchrotron radiation tomography

The mechanisms of void nucleation of a hollow glass syntactic foam during tensile loading were studied in depth. Flat-notched geometries, cut-out from neat and Glass Syntactic PolyPropylene (GSPP), were investigated by in situ microtomography. Notched specimens with two notch root radii, 4 mm and 0.15 mm named respectively N4 and N0.15, to set initial triaxial stress state in the minimum cross section, were observed. Tomographic data sets, with a resolution of 1.3μm, from stepwise tensile loading, at the SOLEIL synchrotron radiation facilities, were retrieved from the notched zone. In addition, they allowed gathering both the width and thickness evolution in the minimum cross section, and the notch opening displacement during the tests.In line with literature, neat PolyPropylene (PP) showed crazes concentration at the specimen core in N4 specimen, whereas, in N0.15 specimen, they were located at the notch root. In isolated Hollow Glass Microspheres (HGM), mechanisms of crazing and debonding were correspondingly highlighted in the PP matrix and at the poles of HGM. Finally, in GSPP, decohesion follows the same trend as in neat PP, i.e. at the specimen core and near the notch, respectively in N4 and in N0.15 geometry. Scenarios of void nucleation and propagation were outlined. The initiation of the brittle crack in the GSPP is mainly due to the matrix-HGM decohesion followed by the coalescence of near neighbouring caps.

Effect of true triaxial principal stress unloading rate on strain energy density of sandstone

Deep rock are often in a true triaxial stress state. Studying the impacts of varying unloading speeds on their strain energy (SE) density is highly significant for predicting rock stability. Through true triaxial unloading principal stress experiments and true triaxial stress equilibrium unloading experiments on sandstone, this paper proposes a method to compute the SE density in a true triaxial compressive unloading principal stress test. This method aims to analyze the SE variation in rocks under the action of true triaxial unloading principal stresses. Acoustic emission is used to verify the correctness of the SE density calculation method in this paper. This study found that: (1) Unloading in one principal stress direction causes the SE density to rise in the other principal stress directions. This rise in SE, depending on its reversibility, can be categorized into elastic and dissipated SE. (2)When unloading principal stresses, the released elastic SE density in the unloading direction is influence by the stress path and rate. (3) The higher the unloading speed will leads to greater increases in the input SE density, elastic SE density, and dissipative SE density in the other principal stress directions. (4) The dissipated SE generated under true triaxial compression by unloading the principal stress is positively correlated with the damage to the rock; with an increase in unloading rate, there is a corresponding increase in the formation of cracks after unloading. (5) Utilizing the stress balance unloading test, we propose a calculation method for SE density in true triaxial unloading principal stress tests.

Effects of intergranular deformation incompatibility on stress state and fracture initiation at grain boundary: Experiments and crystal plasticity simulations

The heterogeneous deformation of polycrystalline metals inherently originates from the intergranular deformation incompatibility. This paper proposes physical parameters related to the crystal orientations, the Schmid factor of the most activated slip system, and the misorientation angle to characterize the deformation incompatibility between the adjacent grain couple. A comprehensive multiscale investigation is conducted to reveal the mechanism from intergranular deformation incompatibility to fracture initiation at grain boundaries. At the specimen scale, experimental and numerical uniaxial tensile tests are performed on smooth and pre-notched dog-bone specimens to achieve different loading paths on the materials. The heterogeneous fields of stress triaxiality explains the heterogeneous size of the dimples observed in fractography. At the grain scale, electron backscatter diffraction analysis is conducted to characterize the microstructural properties around the nucleated voids within the materials. Voids are captured at the grain boundaries with directions parallel to the loading direction and intergranular deformation incompatibility is characterized using the proposed parameters. Simulations on the plastic deformation of realistic microstructures are performed to clarify the phenomenon. The results reveal that the fluctuation in stress triaxiality at grain boundaries is ascribed to intergranular deformation incompatibility, leading to fracture initiation at these sites. The relationships between the proposed physical parameters of intergranular deformation incompatibility and fluctuation in stress triaxiality are summarized in all circumstances. Finally, the ductile damage at the grain scale is predicted by the Rice–Tracey model, and the results show that the effects of microstructures on heterogeneous plastic deformation and stress state can be well considered.

A microcrack-based anisotropic damage model for concrete under mechanical loading and calcium leaching

In underground construction, concrete is always subjected to triaxial stress and calcium ion leaching, which results in anisotropic damage to concrete and reduce the durability of the structure. To capture the anisotropic damage properties of concrete subjected to mechanical-chemical coupling effects and predict the durability of underground concrete structure accurately, a microcrack-based anisotropic damage model is proposed. The mechanical damage, reflecting the density and direction of the microcracks caused by mechanical loading, is defined by a second-order tensor. The degree of chemical damage is defined by the amount of solid calcium phase lost in the concrete. Considering oriented microcrack and the influence of chemical damage on fracture toughness, the anisotropic mechanical damage evolution law of microcrack was established by linear fracture mechanics. A phenomenological chemical model governed by a diffusion law considering the variation of diffusion coefficient with stress induced microcracks is defined to describe the calcium dissolution process. The simulation results are in good agreement with the experimental results. Compared with the traditional elastoplastic damage model, the maximum creep error is only 0.114 ‰.

Constitutive and numerical modelling for timber-metal connections under large deformations

Computational modelling of complex timber-metal connections undergoing large deformations is crucial for the design of safe and robust multi-storey timber structures. Accurate simulation through large deformations requires constitutive models that suitably capture the full post-elastic behaviour of materials. Post-elastic behaviour of timber is particularly challenging to model due to strong anisotropy and material non-linearity in the post-elastic regime. Efficient simulation of complex connections requires advanced numerical modelling techniques to expedite explicit solution in the finite element domain. In this study, a suitable constitutive model for ductile metal components through large deformations, including consideration of stress localisation and triaxiality post-necking, is described. Some existing constitutive models for timber are discussed, and new constitutive models capturing both ductile and brittle failure modes are presented. A new formulation of the Hoffmann yield criterion with isotropic hardening for explicit solution is presented, and new VUMAT user subroutines for explicit solution in ABAQUS for Hoffmann, Sandhaas, Gharib, Hill-Gharib and Hoffmann-Gharib models are developed and made available for the benefit of other researchers. A benchmarked numerical model incorporating advanced modelling techniques to improve computational efficiency without compromising accuracy is presented for a complex timber, aluminium and steel dowelled beam-column connection tested shear and moment dominated testing. The simulation results compare favourably with experimental results in the literature, demonstrating that the proposed constitutive models and numerical modelling techniques provide realistic predictions of behaviour, including failure mode, and thus have the potential to support the design of complex timber-metal connections through large deformations under quasi-static and dynamic loading.

A true triaxial experiment investigation of the mechanical and deformation failure behaviors of flawed granite after exposure to high-temperature treatment

Understanding the mechanical and deformation failure behaviors of heated flawed granite under true triaxial stresses is of great significance for evaluating the wellbore stability in developing hot dry rock resources. In this study, true triaxial experiments are conducted on flawed granite specimens of a varying flaw overlapping length lfo with and without high temperature (HT) treatment, with the emphases on the crack development under true triaxial stresses and its correlations with the strength, plastic anisotropy and failure forecast. Investigations demonstrate that HT, σ2 (intermediate principal stress) and lfo, significantly affect the mechanical properties of flawed granite. Due to strong 3D confinement, the loop crack, the secondary transverse crack and the far-field crack are frequently induced in flawed granite, unlike experiments of uniaxial, biaxial and conventional triaxial compression. When increasing lfo, the rock bridge undergoes the stress amplification which tendentiously drives the internal crack coalescence and typically causes a reduced strength. The PSIRs (Plastic Strain Increments Ratios) analysis, first extended to the true-triaxial experimental data, reveals that the 3D stress-induced extensional/shear fracturing from the flaw tips in σ2-direction is the mechanism of the plastic anisotropy generated. Besides, an attempt to anticipate the failure time in the framework of the time‐reversed Omori’s law suggests a poor predictability by using the acoustic emission but a higher-quality forecast (being more precise and less biased) by using the dissipated energy.

Influence of Platen Stiffness on the Contact Stress Distribution in the Standardized Uniaxial Compression Test

Uniaxial compressive strength is an essential mechanical parameter to adequately characterize any given material. Numerous standards have been developed to guarantee reliable testing execution, as well as the repeatability of results. In this sense, not only the geometric dimensions and tolerances of both the platen and the specimen have been prescribed, but also the testing parameters, such as the load application speed. However, all these recommendations are based on the assumption that the stresses are uniformly distributed across the contact interface between the platen and the specimen. Nevertheless, this is major elastic simplification that allows for obtaining a handy and useful formula to determine the compressive strength, but this strongly deviates the theoretical foundations from the actual experimental reality. Experimental and numerical research to determine the influence of relative stiffness between the specimen and the platen on the stress distribution generated during the execution of the uniaxial compressive test is performed. The results prove that the stresses are not uniformly distributed across the contact when the platen material is significantly stiffer or softer (less stiff) than that of the tested specimen, and additionally, an undesired triaxial stress field is induced inside the specimen. For these reasons, the use of platens with a similar stiffness to that of the specimen is strongly recommended, as it allows for the uniform distribution of the compressive contact stresses and minimizes the influence of the triaxial stress field.

Artificial neural network enhanced plasticity modeling and ductile fracture characterization of grade-1 commercial pure titanium

This study primarily aims to develop a robust modeling approach to capture the complex material behavior of CP-Ti, appeared by high anisotropy, differential hardening due to anisotropy evolution, and flow behavior sensitive to strain rate and temperature, using artificial neural networks (ANNs). Plasticity is characterized by uniaxial tension and in-plane biaxial tension tests at temperatures of 0 °C and 20 °C with strain rates of 0.001 /s and 0.01 /s, and the results are used to calibrate the non-quadratic anisotropic Yld2000–3d yield function with respect to the plastic work. In order to predict the intricate plastic deformation with the temperature and strain rate effects, two distinct ANN models are developed; one to capture the strain hardening behavior and the other to predict the anisotropic parameters in the chosen yield function. The developed ANN models predict an unseen dataset well, which is intermediate testing conditions at a temperature of 10 °C and strain rate of 0.005 /s. The ANN models, being computationally stable and adhering to conventional constitutive equations, are implemented into a user material subroutine for the ductile fracture characterization of CP-Ti sheet using the hybrid experimental-numerical analysis. The favorable agreement between experimental data and numerical predictions, particularly using the ANN models with evolving anisotropic material parameters for the Yld2000–3d yield function, underscores the significance of the differential hardening effect on the ductile fracture behavior and highlights the capabilities of ANN models to capture the complex plastic behavior of CP-Ti. The key parameters including stress triaxiality, Lode angle parameter, and equivalent plastic strain at the fracture location are extracted from the simulations, enabling the calibration of ductile fracture models, namely Johnson-Cook, Hosford-Coulomb, and Lou-2014, and construction of fracture envelopes.

Preparing bulk nanocrystalline Cu–Al alloys via rotary swaging

Although nanocrystalline (NC) metals and alloys have been studied for nearly 40 years, their preparation is limited to the laboratory as large-scale; low-cost commercial production remains a challenge. In this study, high-strength bulk NC Cu–Al alloys were prepared from coarse-grained Cu–Al alloy rods via rotary swaging. Rotary swaging is characterized by the low cost and infinite length of the processed samples; therefore, it can advance the industrial application of bulk NC alloys. Core–shell-structured Cu–Al alloy rods with a hard NC core (diameter of 2.2 mm) wrapped in a soft ultrafine-grained (UFG) shell with a thickness of 1.75 mm were prepared using a rotary swage. Tensile tests revealed that the hard NC Cu–Al alloy core exhibited an ultimate tensile strength of 1034 MPa, which surpassed current strength records. Microstructural characterization showed that the hard NC core was composed of NC fiber grains with widths of 45 nm and lengths of 190 nm. The edge of the rod contained numerous low-angle grain boundaries and shear bands, which provided it with a lower strength and higher elongation than those of the center. During swaging, strong (200) and (111) fiber textures perpendicular to the cross-section were produced during the early stages of deformation. In the latter deformation stages, the polar densities of the (200) and (111) textures weakened, and some complex textures were formed along with high-angle grain boundaries. The grain refinement mechanisms were dominated by multiple deformation twinning, stacking faults, and dislocation slips. Finite elemental analysis showed that triaxial compressive stress and a high strain rate were applied to grain refinement. In addition, the softer shell protects the harder core during deformation, preventing fracture. This study verified an effective preparation technique for bulk NC materials via rotary swaging because it is a simple process with low cost and broad industrial prospects.

Mechanical mechanism of specimen size effect on impact toughness of Al 6061: Experiment and simulation

Impact toughness has a strong size effect, which restricts the accurate evaluation of material toughness and safety of structural design. However, our understanding of the internal mechanical mechanism that influences the size effect remains incomplete. To fill this gap, this paper adopts the method of combining experiment, theory, and simulation. From the point of view of the dependence of plastic and fracture behavior of material on stress state, the internal mechanical mechanism of the size effect of impact toughness (αk) was studied. Firstly, the Charpy impact tests of different sizes were carried out on Al 6061. αk was divided into cracking initiation toughness (αini) and cracking growth toughness (αgro). The variation of αini and αgro with specimen size was analyzed. Then, through a series of tests, the influence of stress state on the plastic and fracture behavior of Al 6061 was studied. To simulate the whole process of the Charpy impact test, an uncoupled 3D fracture model was proposed. Subsequently, a stress state dependent yield function, modified Voce hardening law, and the proposed fracture model were used to simulate the Charpy impact tests. The predicted results were in good agreement with the tests. Finally, the internal mechanical mechanisms of the size effects of αini and αgro were analyzed. The results show that: (1) The αini and αgro have significant size effects, and there are significant differences between them. (2) The internal mechanical mechanism of the size effect of αini was revealed; that is, the dependence of the plastic behavior of the material on the stress state is the internal root cause of the dependence of αini on the specimen size. (3) The internal mechanical mechanism of the size effect of αgro was revealed; that is, the dependence of the plastic behavior of the material on the stress state and the fracture behavior of the material under ultra-high stress triaxiality is the internal fundamental reason affecting the size effect of αgro. (4) This study reveals the internal complex and intimate relationships between plastic behavior, fracture behavior, toughness behavior, stress state, and the size effect, providing a valuable reference for accurate and comprehensive understanding, evaluation, and selection of metal materials.