Tension Stress States Research Articles

Development of the Views of Yu.N. Rabotnov on Strength Criteria of Composites

Besides the well-known fundamental works of Yu.N. Rabotnov in the field of hereditary elasticity and creep theory, one of the aspects of his scientific activity was the mechanics of composite materials and, in particular, a new class of strength criteria for structurally anisotropic composites proposed by him. The main feature of Yuri Rabotnov’s approach was not an attempt to construct a uniform smooth limiting surface in the stress-space, but taking into account real fracture mechanisms, which, as a rule, are directional in nature. Now such approaches become crucial in calculation algorithms modeling the fracture process with taking into account the degradation of elastic and strength properties, but in the period of the first Yu.N. Rabotnov’s papers they were pioneering and caused certain discussions. Development and application of some of Rabotnov’s proposed types of strength criteria for fiber-reinforced composites in tension, compression and complex stress state are discussed in this anniversary paper.

Modeling of distortional hardening including plane strain tension and pure shear for a TWIP steel

This paper focuses on calibrating and modeling of distortional hardening behaviours in twinning induced plasticity steels. True stress-strain curves for uniaxial tension, plane strain tension, and pure shear specimens are inversely identified from corresponding load-displacement curves. The study reveals that accurately predicting the hardening behaviours of TWIP980 steel under plane strain tension and pure shear stress states is challenging with an isotropic hardening model, and a negative hydrostatic effect for TWIP980 is observed through shear testing. A novel distortional hardening model is proposed to simultaneously accommodate the three stress states on the contours of plastic work. Coefficients of the distortional hardening model are calibrated at discrete levels of plastic work and then interpolated to describe the distortion of the initial yield surface. The model is then expanded to consider the true stress-strain curves under uniaxial tension along 0, 45 and 90-degree directions, as well as under the plane strain tension along the 0-degree direction simultaneously. This expansion explicitly incorporates the three true stress-strain curves under uniaxial tension, with the curve of plane strain tension captured by an evolutionary exponent related to plastic work. The developed distortional hardening models demonstrate reasonable reproduction of load-displacement curves for TWIP980 steel under uniaxial tension, plane strain tension, and pure shear stress states.

Ultrasonic Non-Destructive Detection Method for Residual Stress in Rotary Forging Aluminum Alloy Plates.

Aluminum alloy plates are widely used to manufacture large-scale integral structure parts in the field of aerospace. During the forming and processing of aluminum alloy plates, different degrees of residual stress are inevitably produced. Fast and accurate detection of residual stress is very essential to ensuring the quality of these plates. In this work, the longitudinal critically refracted (LCR) wave detection method based on a one-transmitter and double-receiver (OTDR) transducer and the finite element simulation were employed to obtain the residual stress. Aluminum alloy plates with different deformation amounts were fabricated by rotary forging to obtain different residual stress states. Results reveal that the plate formed by rotary forging is in a stress state of central tension and edge compression. As the deformation increases from 20% to 60%, the peak residual tensile stress increases from 156 MPa to 262 MPa, and there is no significant difference in the peak compressive stress. When the deformation reaches 60%, the difference in the residual stresses at different depths is less than 13%, which indicates that the plastic deformation zone basically penetrates the entire longitudinal cross-section of the plate. The maximum deviation between measurement and FE is 61 MPa, which means the experimental data are in good agreement with the FE results.

Anisotropic Hardening and Plastic Evolution Characterization on the Pressure-Coupled Drucker Yield Function of ZK61M Magnesium Alloy.

This paper studies the plastic behavior of the ZK61M magnesium alloy through a combination method of experiments and theoretical models. Based on a dog-bone specimen under different loading directions, mechanical tests under uniaxial tension were carried out, and the hardening behavior was characterized by the Swift-Voce hardening law. The von Mises yield function and the pressure-coupled Drucker yield function were used to predict the load-displacement curves of the ZK61M magnesium alloy under various conditions, respectively, where the material parameters were calibrated by using inverse engineering. The experimental results show that the hardening behavior of the ZK61M magnesium alloy has obvious anisotropy, but the effect of the stress state is more important on the strain hardening behavior of the alloy. Compared with the von Mises yield function, the pressure-coupled Drucker yield function is more accurate when characterizing the plastic behavior and strain hardening in different stress states of shear, uniaxial tension, and plane strain tension for the ZK61M alloy.

Petrophysical Analyses of Rock Construction Materials from a Roman Rural Settlement in Podšilo Bay on Rab Island (North-East Adriatic, Croatia).

This article presents the results of petrophysical analyses of limestones and sandstones used for the construction of the wall structures of a Roman rural settlement located in Podšilo Bay on Rab Island (Croatia). An on-site analysis of the walls indicated the use of different lithotypes, which is an uncommon case in the area. So far, no petrophysical properties of the applied materials have been tested, and their provenance has not been specified. The aim of this research was to determine their usability as construction materials in an attempt to determine the possible reasons behind the usage of multiple lithotypes and their suitability as building materials. The following procedure was used to address these issues: (1) determination of the petrographic characteristics of the rocks, (2) performance of tests to characterise the mechanical properties in a complex stress state of uniaxial tension followed by uniaxial and triaxial compression, and, finally, (3) determination of the internal structure of the rocks using methods based on X-ray imaging. Multi-proxy characteristics of the materials including numerous observations and methods were performed: optical microscopy used to characterise rock petrography and mineralogy, scanning electron microscopy (SEM) coupled with EDS, as well as grinding tests; furthermore, mechanical properties were determined on cylindrical samples in accordance with European standards. X-ray microtomography using the XμCT method enabled microscopic observations and determination of the orientation of discontinuities and the rock structure. The performed analyses allowed us to distinguish three lithological types of sandstone and two types of limestone among the examined stone blocks. Stone blocks of fine- and medium-grained sandstone with carbonate binders, as well as sparitic limestone and mudstone with calcite veins, were used to build the studied structures. The analysed blocks showed traces of partial edge processing. Despite the defects in the material structure identified using XμCT, all the types of rock were characterised by high or very high strength. High values of longitudinal wave velocity confirmed the good quality of the material. These results contribute to a better understanding of the construction process and the related technological choices, and they provide the first dataset which can be used for the reconstruction of the building's original appearance in the future.

The strength of the Brazilian fracture test

Since its introduction in the 1940s until present times, the so-called Brazilian test has been embraced by practitioners worldwide as a method of choice to indirectly measure the tensile strength of concrete, rocks, and other materials with a large compressive strength relative to their tensile strength. This is because of the ease that the test affords in both the preparation of the specimen (a circular disk) and the application of the loads (two platens compressing the specimen between them). Yet, this practical advantage has to be tempered by the fact that the observations from a Brazilian test — being an indirect experiment in the sense that it involves not uniform uniaxial tension but non-uniform triaxial stress states throughout the specimen — have to be appropriately interpreted to be useful. The main objective of this paper is to carry out a complete quantitative analysis of where and when fracture nucleates and propagates in a Brazilian test and thereby establish how to appropriately interpret its results. We do so by deploying the phase-field fracture theory of Kumar et al. (2020), which has been recently established as a complete theory of fracture capable of accurately describing the nucleation and propagation of cracks in linear elastic brittle materials under arbitrary quasistatic loading conditions. The last section of this paper puts forth a new protocol to deduce the tensile strength of a material from a Brazilian test that improves on the current ISRM and ASTM standards.

Biaxial Tensile Mechanical Properties of HTPB Solid Propellant

The purpose of this work is to study the effects of different loading rate ratios and loading speeds on the biaxial tension of hydroxyl-terminated polybutadiene (HTPB) solid propellant. A proper kind of biaxial tensile specimen with which the stresses in its central part can be obtained with the loads acted on each loading direction is designed and used in the study, and the strains in its central parts are obtained with the digital image correlation (DIC) method. The stress and strain relationship at each direction can be obtained by experiments. The uniaxial stress vs. strain curves and the biaxial stress vs. strain curves were obtained, and it was found that the loading speed remarkably influenced the biaxial tensile behaviors of HTPB propellant. The Mises equivalent stress and strain could be used to describe the biaxial tension stress and strain state, and the exponential constitutive model obtained in the study could be used to predict the stress vs. strain curve under different test conditions.

Inhibiting plastic tensile instability of non-symmetric thin-walled shell component via increasing regional metal inflow based on heterogeneous pressure-carrying medium

Heterogeneous pressure-carrying medium was employed to establish a differentiated pressure field on sheet metal in flexible die forming process in this work, which aimed at matching the non-symmetric shape of target component and improving metal inflow to avoid local tensile instability. Specifically, metal inflow corresponding to the differentiated pressure field was analytically evaluated. Forming of a typical non-symmetric shell component was experimentally and numerically studied based on the proposed method. Compared with forming processes based on the uniform pressure, difference of metal inflow in two sides of the non-symmetric component increased from 2.16 mm to 3.36 mm and metal inflow in critical region increased by 11.9% when differentiated pressure field (taking heterogeneous elastomer #4–3 for example) was employed. The resultant maximum thinning ratio decreased by 4.2% and the uniformity of shell thickness increased by 16.9%. With the decrease of Shore hardness of elastomer in the formed region, stress path in the ready-to-form region transferred towards the bi-axial tension stress state, i.e., stress ratio (α) increased. And, stress triaxiality (η) in characteristic regions were regulated appropriately, which decreased the risk of tensile instability. It was attributed to the decreased normal pressure and frictional resistance at sheet/elastomer interface in the formed region.

Constitutive modeling of non-ideal isotropic materials based on a novel theoretical framework

If a plastic constitutive relation is used to simulate a metal forming process, the main concern should be its ability to predict the plastic strain parameters. At present, constitutive modelling basically relies on the properties of stress parameters, and emphasizes on how to improve the prediction accuracy of initial yield and subsequent hardening stresses. Although, corresponding to the anisotropic materials, the experimental data of plastic strain ratios are also used, the experimental plastic strains data obtained from all related experiments, in addition to the one as the equivalent plastic strain, are not employed at all. The lack of the most important experimental data in the constitutive model will inevitably weaken its ability to predict the plastic strain parameters which will determine the final shape of formed parts.To make a constructed constitutive relation that can fully reflect the experimental characteristics of materials, a new theoretical framework of constitutive model is proposed, and the application of experimental plastic strain data can be achieved with the introduction of a plastic strain-increment function. To illustrate the importance of the application of plastic strain-increment function to improve the predictive accuracy of plastic strain-increments, a new constitutive model is constructed and combined with a large amount of experimental data to verify it. Experimental verifications were carried out by some sheet metals with different anisotropic properties under uniaxial and equi-biaxial tension stress states, and also deal with multiple sets of experimental data obtained under complex tension-tension and tension-compression stress states. Discussions also include the results predicted by the models constructed based on the classical theory. Calculation examples show, the stronger the anisotropic properties of material, the greater the prediction deviation of plastic strains generated by the classical-theory-based models. Moreover, such prediction deviations will gradually increase with the accumulation of predicted plastic strain-increments. Predictive ability of the new constitutive relation is completely unimpacted by the increased degree of anisotropic features of materials. Predicted results are in good agreement with all experimental data.

Plasticity, ductile fracture and ballistic impact behavior of Ti-6Al-4V Alloy

The strength and fracture behavior of a metal are crucial to its response in impact events. In the present paper, a hybrid experimental-numerical study was conducted to characterize the plasticity and ductile fracture behavior of Ti-6Al-4V alloy. To this end, ten types of specimens were utilized to cover a range of stress states from uniaxial tension to high stress triaxiality, shear, plane strain as well as elevated temperatures and strain rates. Especially, a slightly modified in-plane shear specimen suggested by Roth and Mohr was proposed and adopted to prevent premature fracture initiation from the free boundaries at a tension stress state. Aside from a Split Hopkinson Pressure Bar (SHPB) system, a high-speed servo-hydraulic testing machine was applied to conduct high-rate tests. A Modified Johnson-Cook (MJC) plasticity model and an extended Xue–Wierzbicki (XW) fracture criterion with strain rate and temperature effects were used and calibrated using a combined experimental-numerical approach. It was found that the fracture strain of the metal is sensitive to both the stress triaxiality and the deviatoric state parameter, and reduced ductility is reached at increasing stress triaxialities and a plane strain as well as shear stress states. The yield strength increases with increasing strain rate and decreasing temperature. An enhanced ductility is achieved at elevated temperatures and lower strain rates, except for at the highest strain rate of 750 /s, at which a higher ductility is observed compared with that at slightly lower strain rates. Ballistic impact tests on 4 mm thick Ti-6Al-4V alloy targets were conducted using 5.95 mm diameter blunt rigid projectiles in an impact velocity range of 167.9 – 321.6 m/s. Parallel finite element simulations were performed for the ballistic tests and the validity of the calibrated material models was confirmed by comparing the predicted ballistic resistance and failure pattern of the target with the experimental ones. In addition, it was found that a finite element prediction on the ballistic resistance of the Ti-6Al-4V alloy targets struck by blunt projectiles is highly mesh size sensitive and a converged solution was obtained by using a mesh size of 20 μm.

Numerical analysis of interface damage in ballastless track on simply supported bridge due to thermal and vehicle dynamic load

The stiffness, mass and damping matrix of 17 degree of freedom (DOF) vehicle model are derived on the basis of Lagrange equation. The bilinear discrete cohesive zone model (DCZM) is utilized to simulate the bonding performance of the interface between the track slab and the CA mortar layer. The ballastless track-bridge element model is proposed by the direct stiffness method, and the vehicle-ballastless track-simply supported bridge vertical-longitudinal coupled model with consideration of interface damage is established. In addition, based on the ballastless track-bridge element model, the ballastless track continuous welded rail (CWR) model on multi-span simply supported bridge is proposed. The ballastless track CWR model is employed to obtain the initial longitudinal relative displacement of track slab-CA mortar layer interface under bridge thermal load. The displacement response of ballastless track-bridge structure is taken as the initial displacement field of vehicle-track-bridge coupled dynamic model. The vehicle-track-bridge coupled model is adopted to obtain the interface damage of ballastless track under the action of bridge thermal load and vehicle dynamic load. Then, the effects of bridge temperature and longitudinal stiffness of the DCZM on the longitudinal relative displacement of ballastless track-bridge structure are investigated in detail. The mechanism and distribution law of interface damage of ballastless track under different running speeds, CA mortar layer gap length and DCZM parameters are discussed. The conclusions obtained in this paper could provide a technical guide for the formulation of maintenance standards for interface damage of ballastless track on simply supported bridge. Then, some parametric studies are presented based on the model in this paper. The analysis indicates that the longitudinal relative displacement of the track slab-CA mortar layer becomes large at both ends and small in the middle within the range of a simply supported bridge. When there is CA mortar layer void, the ballastless track interface is in the stress state of tension + shear mixed mode. The recommended threshold of void length of CA mortar layer is 0.65 m. More attention shall be paid to the construction quality of interface between the track slab and the CA mortar layer.

Seismic response analysis of long-span continuous girder bridge considering fluctuating friction of bearing

Under the combined action of horizontal and vertical earthquakes, separation-pounding of bridge beam ends and bearings occurs, which adversely affects the overall mechanical behaviour of any bridge. Based on D'Alembert's principle, this study proposes a theoretical analysis method to verify the separation of bridge beam ends and bearings, which is substantiated by the measured data. A three-span continuous steel-box-girder bridge was selected as the research object, and finite element models (FEMs) using the bilinear bearing and friction bearing models were established. The numerical models were verified by comparing the simulation results with the theoretical calculations. A comparative study on the seismic response of continuous girder bridges with different bearing models was conducted, and it was found that the friction bearing model is better for simulating the whiplash effect of long-span continuous girder bridges. The results indicate that the peak pounding force generated by the separation of the beam end and bearing is 1.74 times the weight of the beam end. Moreover, the whiplash effect causes the tension and compression stress states of the side span of the main beam to reverse and drastically reduce the compressive stress of the middle span by 70%. Finally, it is recommended that the friction bearing model which is able to realistically simulate the seismic response of the bridge more accurately be used to simulate bearings with large axial force fluctuations.

Investigation of deformation mechanics and forming limit of thin-walled metallic bipolar plates

The present study is conducted on forming of the metallic bipolar plates made of 316 stainless steel sheet with a parallel serpentine flow field. The plastic deformation of straight and curved microchannels, forming limit criteria, and deformation mechanics during the process are investigated partially to present a reliable model for estimating fracture initiation. For this purpose, experimental stamping tests are employed to fabricate metallic bipolar plates and the process is simulated by finite element software. The validity of simulation results is examined by comparing thickness distribution and force-displacement curves reflecting 4.76% and 3.85% error rates, respectively. According to experimental observations, fracture starts at a channel depth of 0.610 mm. Hence, for determining the forming limit and predicting the fracture during the process, the deformation mechanic is studied at different points of the microchannels. Results of stress states analysis indicate that the stress state of plane-strain tension up to biaxial tension governs this process. Despite the presence of different loading paths during the process, the critical element in each channel is deformed under plane-strain tension. Therefore, a fracture model is developed based on thinning percentage and equivalent strain to predict the instability of metallic bipolar plates. According to the results, both the equivalent strain and thinning percentage criteria with critical limits of 0.56 and 33.45%, respectively, are considered as an allowable range of plastic deformation during the conventional stamping process of bipolar plates. Results indicate that maximum thinning in all directions is lower than 33.45% by using the modified stamping process.

Machine Learning for Predicting Fracture Strain in Sheet Metal Forming

Machine learning models are built to predict the strain values for which edge cracking occurs in hole expansion tests. The samples from this test play the role of sheet metal components to be manufactured, in which edge cracking often occurs associated with a uniaxial tension stress state at the critical edges of components. For the construction of the models, a dataset was obtained experimentally for rolled ferritic carbon steel sheets of different qualities and thicknesses. Two types of tests were performed: tensile and hole expansion tests. In the tensile test, the yield stress, the tensile strength, the strain at maximum load and the elongation after fracture were determined in the rolling and transverse directions. In the hole expansion test, the strain for which edge cracking occurs, was determined. It is intended that the models can predict the strain at fracture in this test, based on the knowledge of the tensile test data. The machine learning algorithms used were Multilayer Perceptron, Gaussian Processes, Support Vector Regression and Random Forest. The traditional polynomial regression that fits a 2nd order polynomial function was also used for comparison. It is shown that machine learning-based predictive models outperform the traditional polynomial regression method; in particular, Gaussian Processes and Support Vector Regression were found to be the best machine learning algorithms that enable the most robust predictive models.

Crystal Plasticity Modeling of Al Alloy under Linear and Non-Linear Loading

The crystal plasticity (CP) model is widely used in many applications to link microstructure and mechanical properties. There are varying CP constitutive laws with phenomenological or physical-based formulation to cover a large range of loading conditions. In order to predict the deformation behavior of an Al alloy during the sheet metal forming process with either linear or non-linear strain path, both phenomenological and physical-based CP constitutive laws have been chosen, and the prediction performance of both models is compared. For the linear loading condition, the uniaxial tensile tests are performed on the smooth-dog-bone (SDB) specimens along rolling and transverse directions (RD/TD). The non-linear strain path is achieved by the Marciniak testing followed by uniaxial tension. In the first stage, the Marciniak testing is performed under the stress states of RD-uniaxial, plane strain, and biaxial tension. After being loaded to a certain strain level, mini-SDB specimens are cut along RD and TD from the uniform deformation region and reloaded under RD-uniaxial tension. The digital image correlation (DIC) technique is employed to measure the strain during testing. The electron backscatter diffraction (EBSD) technique is used to characterize the initial microstructure as well as the microstructure evolution of the specimens after the first stage loading in the non-linear strain path. A phenomenological power law and a dislocation-density-based hardening law have been employed in this study. The parameters are calibrated based on the flow curve of the RD uniaxial tension. The model performance is validated by stress–strain response under all the rest loading conditions including the non-linear loading path.

Analysis of damage and fracture behavior in ductile metal sheets undergoing compression and shear preloading

The present paper comprises the experimental and numerical analysis of damage and fracture behavior of ductile metals under non-proportional loading with compression and shear preloading. For this purpose, biaxial experiments with the H-specimen using a pneumatic downholder for compression loading followed by failure under a tension stress state and corresponding numerical simulations are performed and analyzed. A thermodynamically consistent anisotropic continuum model is presented. It takes the effects of micromechanical damage mechanisms on the macro scale behavior as a motivation for a phenomenological description of damage behavior as a function of stress state. The experimental findings are compared with the results of tests with proportional load paths and corresponding numerical simulations. Thereto, strain fields of the critical areas of the specimens are analyzed by means of digital image correlation (DIC) technique. Compression and shear preloading can lead to significantly reduced ductility of the material with initiation of failure processes in the small damage strain range. Evolution of numerically predicted plastic and damage equivalent strains illustrates their stress state dependence. The numerical results are also confirmed by images of fracture surfaces taken by scanning electron microscopy (SEM). This experimental-numerical methodology is therefore an efficient tool to develop and validate general modeling approaches, and it is characterized by almost arbitrarily definable load paths with changes in stress states occurring in forming processes.

Numerical Simulation Experimental Study of the Deformation and Failure of Granite with Multiaxial Tension

A numerical simulation method is proposed to study the deformation and failure rule of granite with multi-directional tensile stress, based on the importance of the rock tension. This investigation took into consideration the fact that the current experimental equipment cannot complete multi-directional tension experiments for rock. The deformation and failure rule of the granite material model with biaxial and triaxial tensile stress are studied using the numerical simulation software CASRock. The results show that in a biaxial tensile stress state, the tensile strength of granite decreases with the increase in the confining pressure, but the influence of the compression confining pressure on the strength reduction is greater than the tensile confining pressure. The number of cracks generated during failure decreases with the increase in the compressive confining pressure, and the inclination angle of the failure surface increases with the increase in the compressive confining pressure. In the three-direction tension stress state, the tensile strength of granite decreases slightly with the increase in the compressive confining pressure. However, when the compressive confining pressure in one direction is close to the uniaxial tensile strength, the tensile strength of granite will decrease quickly, and the failure result is similar to that of the uniaxial tensile failure.

Upset bulging as a preforming operation for hot metal gas forming of 22MnB5 tubes

Hot Metal Gas Forming (HMGF) is a coupled process of gas forming and quenching of tubes. This process allows to obtain complex and accurate geometry due to the elimination of springback and high mechanical properties due to the formation of martensite, as a result, the weight of the parts can be reduced. HMGF is widely used in the aerospace and automotive industries to make critical parts from high hardenability steels such as 22MnB5. A typical hot stamped component has 1000 MPa yield stress and 1500 MPa ultimate tensile strength. The main challenge of HMGF process is a significant material thinning and cracking due to the biaxial tension stress state. The paper proposes a preforming method for increasing the forming limits of HMGF by the cold upset bulging of tubes by means of the additional volume of material in the deformation zone. This method allows to obtain one or several waves in the cross section of the tube, which helps to increase the minimum workpiece wall thickness after the forming process by more than 40% and to reduce a probability of the crack formation.

Effects of strain path and girth weld heterogeneity on strain limits of X70 pipeline

Geological disasters frequently cause pipeline failure. Therefore, the strain limits of pipelines under various strain paths should be carefully considered to provide the critical strain, particularly for girth welds. The iterative method was used to determine local accurate constitutive relations for the three typical zones of X70 girth weld: base material (BM), heat affected zone (HAZ), and welding metal (WM). By combing accurate constitutive equations of local deformation with a modified elliptical fracture criterion. The prediction strain limits were then verified using a hybrid experimental-numerical method with four geometries (uniaxial tension, tension with notch, flat-groove tension, and pure shear specimens) and three zones (BM, HAZ, and WM). The microstructure and fractography of BM, HAZ, and WM zones were analyzed to investigate the difference in strain limits under different strain paths. The results demonstrate that in tension stress states, the strain limits of WM for under-matched girth welds are the weakest, while the tension-compression asymmetry for WM is the greatest. As a result, when a pipeline is under tension, the girth weld is prioritized for protection. On the other side, the pipeline itself focuses on protection in compression to avoid buckling. Furthermore, the ferrite content is mostly responsible for the contribution of strain limits for these zones. The lower strain limit of WM in the tensile state is attributable to the inclusions in the welding process.

An anisotropic constitutive model for forming of aluminum tubes under both biaxial tension and pure shear stress states

In forming of complex thin-walled tubular parts, such as tube hydroforming with axial feeding, both biaxial tension and one axial tension & one axial compression (around the pure shear stress state) deformations are involved. The deformations under both biaxial tension and pure shear stress conditions cannot be accurately modeled and described with the symmetrical constitutive models based on the tensile properties. It is due to the fact that the anisotropic yielding and plastic flow behaviors of tubes are not well articulated over the entire range of stress states. To address this issue, an enhanced constitutive model was proposed based on the Yld2000–2d model (Barlat et al., 2003). The enhanced model improves the applicability of the Yld2000–2d by introducing an additional term, which can flexibly describe the change of the curvature of yield locus around the pure shear stress state. The yielding and plastic flow characteristics of the tubes under both biaxial tension and pure shear stress conditions can be well considered by the enhanced model and the model convexity can be strictly guaranteed. Moreover, the predictability of the proposed model for the deformation behaviors under these states was analyzed and compared with the quoted anisotropic constitutive models. The accuracy and efficiency were also verified and corroborated with the forming of AA6061-O tubes. It showed that the enhanced constitutive model can accurately predict the experimental yield loci and the plastic flow directions of the AA6061-O tube under both biaxial tension and pure shear stress deformations. The in-depth comparisons with the three benchmarked models and experiments were also conducted in terms of the predicted profile and wall thickness distribution of tube hydroforming, in such a way to further validate the enhanced model in terms of the efficiently and accurately modeling of the forming of complex tubes.