In-plane Biaxial Tension Research Articles

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.

Mechanical Behavior of Lithium-Ion Battery Separators under Uniaxial and Biaxial Loading Conditions.

The mechanical integrity of two commercially available lithium-ion battery separators was investigated under uniaxial and biaxial loading conditions. Two dry-processed microporous films with polypropylene (PP)/polyethylene (PE)/polypropylene (PP) compositions were studied: Celgard H2010 Trilayer and Celgard Q20S1HX Ceramic-Coated Trilayer. The uniaxial tests were carried out along the machine direction (MD), transverse direction (TD), and diagonal direction (DD). In order to generate a state of in-plane biaxial tension, a pneumatic bulge test setup was prioritized over the commonly performed punch test in an attempt to eliminate the effects of contact friction. The biaxial flow stress-strain behavior of the membranes was deduced via the Panknin-Kruglov method coupled with a 3D Digital Image Correlation (DIC) technique. The findings demonstrate a high degree of in-plane anisotropy in both membranes. The ceramic coating was found to negatively affect the mechanical performance of the trilayer microporous separator, compromising its strength and stretchability, while preserving its failure mode. Derived from experimentally calibrated constitutive models, a finite element model was developed using the explicit solver OpenRadioss. The numerical model was capable of predicting the biaxial deformation of the semicrystalline membranes up until failure, showing a fairly good correlation with the experimental observations.

Comparison of anisotropic yield functions and calibrations for accurate thickness prediction in hole expansion test

The hole expansion test is an appropriate evaluation method for assessing the formability of automotive parts, where fracture prediction using simulated localized thickness is crucial. However, the accurate thickness prediction in the hole expansion test remains challenging. In this study, the selection of yield functions and calibration strategies were investigated to accurately predict the thickness of advanced high-strength steel subjected to the hole expansion test. An accurate description of the material anisotropy is important for thickness prediction because of the generation of various multiaxial stress states. To describe plastic anisotropy, a series of uniaxial tension, bulge, and in-plane biaxial tension tests were conducted on DP980 steel. Because conventional biaxial tension tests for DP980 steel showed a small strain range owing to its low ductility, a new laser-welding-reinforced biaxial tension test was developed to investigate the anisotropy of the plane strain at large strains. Differences in the ratio of the plastic strain rates were observed between the conventional and new tests. Finally, a hole expansion test and corresponding finite element simulations were conducted with different yield functions and calibrations for the Yld2000-2d yield function. The thickness strain profiles along the hole circumference and 3 mm inward were measured and predicted using simulations. In conclusion, both the yield stress and the ratio of plastic strain rates in the plane strain state were equally important for accurate thickness prediction during the DP980 hole expansion test. Furthermore, the crack location was inconsistent with the thinnest region in the experiment, which might be because of the shear fracture anisotropy encountered in DP980 steel.

Ductile fracture of 2024 aluminum under unequal biaxial in-plane tension and out-of-plane compression

The ductile fracture of 2024 aluminum loaded under unequal in-plane biaxial tension and out-of-plane compression is investigated. This stress state is induced in materials during ballistic impacts. A novel experimental design is presented which utilizes an elliptical shaped punch to induce unequal amounts of tension along the in-plane axes of a thin specimen plate. An annealed copper backing plate placed behind the specimen induces out-of-plane compression. Fracture is observed directly with Digital Image Correlation during continuous loading of unbacked specimens. Interrupted testing and acoustic emissions are used to determine the instant of fracture in tests where a backing plate is used. Numerical simulations are performed using an assumed plasticity model, and the model is validated by matching the simulated force-displacement response and strain with the experiments. The equivalent plastic fracture strain is determined for various stress states that correspond to averaged triaxiality values ranging from 0.14 to 0.61 and averaged Lode parameter values ranging from −0.72 to −0.29.

Plastic anisotropy evolution of SS316L and modeling for novel cruciform specimen

In this paper, the evolution of the plastic anisotropy of stainless steel 316L samples is investigated under proportional loading paths using a customized cruciform specimen. The determination of a novel cruciform specimen by a design of experiments approach integrated with finite element simulations is described. The mechanical properties of the material are characterized under uniaxial tension applied in every 15° from the rolling direction and equibiaxial tension from hydraulic bulge experiments. The results reveal that the plastic anisotropy shown in stress and strain significantly evolves with respect to the plastic work. Based on the experiments, the material behavior is modeled using a non-quadratic anisotropic yield function, Yld2004–18p, with parameters modeled as a function of the equivalent plastic strain, assuming plastic work equivalence, and with constant parameters for comparison. The Hockett-Sherby model is also used for the strain hardening behavior to extrapolate the results to higher strain values. The models are implemented into a user material subroutine for finite element simulations. To validate the model, in-plane biaxial tension experiments are performed, using a customized specimen, to achieve greater deformation than previous designs by introducing double-sided pockets for thickness reduction and notches in the corner areas. The results are compared with finite element simulations implemented with the plasticity models.

First principles study of magnetic transition of strain induced monolayer NbSi<sub>2</sub>N<sub>4</sub>

The effective control of two-dimensional material magnetism is a frontier research field. In this work, the influences of in-plane biaxial tension strain on the electronic structure, magnetic properties, and Curie temperature of monolayer NbSi<sub>2</sub>N<sub>4</sub> are investigated by first-principles calculations based on density functional theory and Monte Carlo simulations in the frame of the Heisenberg model. We demonstrate that the monolayer NbSi<sub>2</sub>N<sub>4</sub> has favorable dynamic and thermal stability through the phonon spectral calculations and ab initio molecular dynamics simulations. It is found that the intrinsic monolayer NbSi<sub>2</sub>N<sub>4</sub> is a non-magnetic metal, which can be transformed into a ferromagnetic metal by 1.5% tensile strain. The electronic structure analysis of monolayer NbSi<sub>2</sub>N<sub>4</sub> shows that the ferromagnetism induced by tensile strain is caused by traveling electrons. There is a half-full band at the monolayer NbSi<sub>2</sub>N<sub>4</sub> Fermi level, which is mainly contributed by the dz<sup>2</sup> orbital of the Nb atom. When there is no additional strain, the band is spin-degenerate. Tensile strain can make this band more localized, which leads to Stoner instability, resulting in the ferromagnetic ordering of monolayer NbSi<sub>2</sub>N<sub>4</sub> traveling electrons. The stability of the ferromagnetic coupling is enhanced with the increase of the strain degree. The calculation results of the magnetic anisotropy energy show that the strain can make the direction of the easy magnetization axis of the monolayer NbSi<sub>2</sub>N<sub>4</sub> reverse from the vertical direction to the in-plane, and then back to the vertical direction. Furthermore, the strain can significantly increase the Curie temperature of monolayer NbSi<sub>2</sub>N<sub>4</sub>. The Curie temperature of monolayer NbSi<sub>2</sub>N<sub>4</sub> is 18 K at 2% strain and 87.5 K at 6% strain, which is 386% higher than that at 2% strain. Strain engineering can effectively control the magnetic ground state and Curie temperature of single-layer NbSi<sub>2</sub>N<sub>4</sub>. The research results are expected to promote the development of <i>MA</i><sub>2</sub><i>Z</i><sub>4</sub> materials in the field of mechanical sensing device design and low-temperature magnetic refrigeration.

Deformation characteristics and formability of a tricot-stitched carbon fiber unidirectional non-crimp fabric

Deformation characteristics and formability of a heavy-tow unidirectional non-crimp fabric (UD-NCF) was studied. The fabric response under in-plane shear and biaxial tension loading (experienced during forming operations) was first investigated. Local deformations captured by measuring tensile/compressive strains in the stitching segments traversing the carbon fiber tows was correlated to the fabric three-stage macroscopic response during shear tests. Biaxial tension tests were performed at room and elevated temperatures with different displacement ratios to mimic typical preforming processes. Variations in biaxial displacement ratio revealed the interdependency of the fabric orthogonal tensile deformation modes, while temperature did not influence the response. Next, single layer hemispherical and flat punch draping experiments were performed to monitor defects (wrinkling) and capture strain contours, which correlated with in-plane shear and biaxial tension deformations. The results yield an improved understanding of the complex multiscale deformation modes for the heavy-tow UD-NCF and represent important data sets for constitutive models.

Effect of interfacial stiffness on the stretchability of metal/elastomer bilayers under in-plane biaxial tension

Flexible electronic devices are often subjected to large and repeated deformation, so that their functional components such as metal interconnects need to sustain strains up to tens of percent, which is far beyond the intrinsic deformability of metal materials (~1%). To meet the stringent requirements of flexible electronics, metal/elastomer bilayers, a stretchable structure that consists of a metal film adhered to a stretchable elastomer substrate, have been developed to improve the stretch capability of metal interconnects. Previous studies have predicted that the metal/elastomer bilayers are much more stretchable than freestanding metal films. However, these investigations usually assume perfect bonding between the metal and elastomer layers. In this work, the effect of the metal/elastomer interface with a finite interfacial stiffness on the stretchability of bilayer structures is analyzed. The results show that the assumption of perfect interface (with infinite interfacial stiffness) may lead to an overestimation of the stretchability of bilayer structures. It is also demonstrated that increased adhesion between the metal and elastomer layers can enhance the stretchability of the metal layer.

Design and development of a miniaturized multiaxial test setup for in situ x-ray diffraction experiments.

In this work, a novel stand-alone multi-axial loading test setup was developed to test miniature samples under uniaxial tension, uniaxial compression, in-plane biaxial tension, and biaxial compression stress states. Good agreement in stress-strain responses was observed between the uniaxial experiments carried out using the miniature sample geometry in the custom-built setup and the uniaxial standard geometry in a universal testing machine. With regard to biaxial experiments, the full-field strain captured using digital image correlation for the biaxial specimens revealed strain homogeneity in the central gage section of the sample. Furthermore, the in situ capability of the setup was demonstrated by integrating it with a commercial laboratory x-ray diffractometer, and good agreement was found between the calculated stress values from the load sensor and the stress obtained using x-ray diffraction.

Forming limits of magnesium alloy AZ31B sheet at elevated temperatures

Magnesium alloy sheets usually has to be processed by warm forming, and change of strain path and evolution of microstructure can significantly influence their warm formability. Forming limit test for an AZ31B alloy sheet under strain path changes was configured and implemented, and the effects of strain paths and microstructure evolution on the forming limit diagram are investigated. The sheet was pre-strained under in-plane uniaxial, plane strain and biaxial tension loading paths at 150 °C, 200 °C and 300 °C, followed by hemispherical punch stretching experiments at the three temperatures using specimens extracted from the pre-strained samples. A crystal plasticity model that incorporates dynamic recrystallization (DRX) and annealing recovery was combined with the Marciniak-Kuczyński (M-K) approach to calculate the FLDs. The evolution of dislocation density during annealing in the pre-strained FLD test at 200 °C was evaluated, through which the predictions of pre-strained FLDs were considerably improved. The present work provides experimental as well as crystal plasticity based methods for evaluating warm formability of magnesium alloys influenced by temperature, pre-straining, DRX and recovery.

Transversely isotropic elastic properties of multi-walled boron nitride nanotubes under a thermal environment

The temperature-dependent transversely isotropic elastic properties of multi-walled boron nitride nanotubes (MWBNNTs) were determined using molecular dynamics simulations with a three-body Tersoff potential force field. These elastic properties were calculated by applying the four different loading conditions on MWBNNTs: uniaxial tension, torsional moment, in-plane biaxial tension and in-plane shear. The effect of chirality, number of layers and aspect ratio (AR) were taken into consideration. The results reveal that the elastic constants of MWBNNTs decrease as their number of layers increase. The elastic moduli of MWBNNTs do not depend on the AR, but are a function of chirality. Furthermore, the effect of temperature on the transversely isotropic elastic constants of MWBNNTs was studied. Higher temperature considerably affects the mechanical properties of MWBNNTs. For instance, the reduction in the values of axial Young’s, longitudinal shear, plane-strain bulk and in-plane shear moduli of MWBNNTs was found to be by approximately 10% due to the increase in temperature. The results reveal that the mechanical properties and failure behavior of MWBNNTs significantly depend on the number of layers, chirality and temperature. The finding of this work can be utilized for engineering MWBNNT-based advanced nanocomposite structures for specific application under thermal environment.

Effect of Stone–Wales defects on the mechanical behavior of boron nitride nanotubes

The transversely isotropic response of pristine as well as defective boron nitride nanotubes (BNNTs) containing Stone–Wales (SW) defects was comprehensively studied via molecular dynamic simulations with a three-body Tersoff force field. The elastic properties and the failure behavior of BNNTs were studied under the transversely isotropic loading conditions, namely uniaxial tension, twisting moment, in-plane shear and in-plane biaxial tension. The effect of chirality, diameter and SW defect density was taken into consideration. The failure mechanism of BNNTs under each loading condition was explained in detail. Our study reveals that the elastic moduli of zigzag BNNTs are higher than for armchair tubes and decrease as the diameter of the tube increases. The effect of SW defects is found to be higher on the elastic properties of smaller diameter BNNTs than for larger diameter tubes, regardless of chirality. The higher defect density reduces the axial Young’s modulus, shear, plane strain bulk and in-plane shear moduli by 11%, 18%, 9% and 7%, respectively. The SW defects affect the (1) longitudinal shear moduli of BNNTs more profoundly irrespective of chirality and (2) the mechanical behavior of zigzag BNNTs stronger compared to armchair ones. It is also found that the mechanical properties of BNNTs are functions of chirality and diameter, especially for small diameter tubes.

Ductile fracture under in-plane biaxial tension and out-of-plane compression

A new experiment for determining the equivalent plastic strain at fracture of a ductile material subjected to loading under a state of stress of in-plane biaxial tension and out-of-plane compression is introduced. In this experiment a small diameter spherical punch is pushed into a thin specimen plate that is backed up by another plate made of a different material. Upon loading, the material element at the back surface of the specimen along the center line of the punch that is in contact with the backing plate deforms under a state of stress of in-plane biaxial tension and out-of-plane compression and eventually fractures. A combined experimental–numerical approach is used to determine the state of stress throughout the test and the final strain at the fracture point. The experiment is simulated using an assumed plasticity model, and the results are validated by comparing the simulated and measured quantities (force and displacement of the punch and strain at the back surface of the specimen). The results from the experiment provide data needed for the construction of a surface of plastic strain to fracture as a function of triaxiality and Lode parameter. In testing specimens made of 2024 aluminum and a backing plate made of annealed copper, the equivalent plastic strain to fracture is determined for Lode parameter of about −1 and several values of triaxiality.

Effects of phase difference and stress ratio on biaxial tension–tension fatigue crack propagation behavior of rolled ZK60 magnesium alloy

The effects of phase difference and stress ratio on in-plane biaxial tension–tension fatigue crack propagation behavior of rolled ZK60 magnesium alloy were explored in this study. The initial crack propagation angle φ was computed and compared via finite element and analytical methods. The biaxial fatigue crack propagation rate and fractographic analysis were also investigated to identify reasonable fracture parameters and crack propagation mechanisms, respectively. Results show that the initial crack propagation angle could be accurately computed by the finite element method. The energy release rate range ΔG considers the effects of modes I (KⅠ) and II (KⅡ) stress intensity factors. Thus, ΔG is a reasonable fracture parameter for describing the fatigue crack growth rates with phase differences. ΔKeff and ΔG could uniformly describe the biaxial fatigue crack growth rate of ZK60 magnesium alloy under different stress ratios. Furthermore, the crack growth mechanism of ZK60 magnesium alloy is identical under different stress ratios and varies under phase difference.

Material characterization of high strength sound-deadening sheets and its application on a square cup drawing simulation

In this study, the mechanical properties of a high strength sound-deadening sheet (SDS) in the stretch deformation mode was characterized, and it successfully apply to the formability prediction of the square cup drawing tests. The high strength SDS was fabricated with dual phase (DP) 590 steel sheets as outer skins and polymeric adhesive layer as a core by a roll bonding process. Uniaxial and biaxial mechanical characteristics were evaluated by the uniaxial tension tests and the in-plane biaxial tension tests, respectively, while the forming limit was investigated by the punched dome tests. Then, based on the experimental data, the mechanical properties of SDS was characterized, viz., hardening curve, yield function and forming limit curve. Square cup drawing was carried out using the SDS, and its deformation and failure behaviour were successfully predicted via the finite element simulation performed by inputting characterized mechanical properties.

Characterization of the Mechanical Properties of a High-Strength Laminated Vibration Damping Steel Sheet and Their Application to Formability Prediction

In this study, the mechanical properties of a high-strength laminated vibration damping steel sheet (LVDSS) with stretch-dominated deformation behavior were characterized and successfully applied to formability prediction. The high-strength LVDSS was fabricated with dual-phase 590 steel sheets as outer skins and polymeric adhesive layer as a core via roll bonding. The uniaxial and biaxial mechanical behaviors were evaluated by performing uniaxial tension and in-plane biaxial tension tests, respectively, while the forming limit was investigated by conducting punched dome tests. Then, based on the experimental data, the mechanical properties of the LVDSS were characterized, viz., the hardening curve, yield function, and forming limit curve. As an example of LVDSS application, a square cup drawing test was conducted and a dashboard prototype was fabricated using an LVDSS, and the deformation and failure behaviors were successfully predicted via a finite element simulation performed by inputting the characterized mechanical properties.

Effect of atom vacancies on elastic and electronic properties of transversely isotropic boron nitride nanotubes: A comprehensive computational study

Molecular dynamics (MD) simulations were carried out with a three-body Tersoff potential force field to predict the transversely isotropic elastic properties of pristine and defected BNNTs. This is accomplished by imposing uniaxial tension, twisting moment, in-plane shear and in-plane biaxial tension to the BNNTs. Effects of various factors such as chirality and diameter of BNNTs, vacancy concentration, and distribution of vacancy pores along the length and circumference of BNNTs were critically examined. Our study reveals that the elastic coefficients of BNNTs decrease as their diameter increase, except axial Young’s modulus. Young’s modulus of BNNT increases with the diameter and reaches its maximum value when the tube diameter is ∼14 Å and then it starts decreasing. We also found that the axial Young’s modulus of a BNNT increases as its aspect ratio increases and stabilizes at a particular value of aspect ratio (L/D ∼ 15). The vacancies greatly affect the elastic properties of BNNTs; for instance, the vacancy concentration of 2% in (10, 10) BNNT reduce its axial Young’s, shear, plane strain bulk and in-plane shear moduli by 14%, 25%, 14% and 18%, respectively. Furthermore, we studied the electronic properties of pristine and defective BNNTs under four transversely isotropic loading conditions using the strain effective method. The results reveal that the electronic properties of BNNTs can be altered via different routes: loadings conditions, diameter and vacancy concentration. Our fundamental study highlights the critical role played by vacancy defected BNNTs in determining their elastic and electronic properties as they are vastly being used in multifarious applications such as nano-electronic devices and reinforcements in multifunctional nanocomposites.

Transversely isotropic elastic properties of carbon nanotubes containing vacancy defects using MD

Molecular dynamics simulations with Adaptive Intermolecular Reactive Empirical Bond Order force fields were conducted to determine the transversely isotropic elastic properties of carbon nanotubes (CNTs) containing vacancies. This is achieved by imposing axial extension, twist, in-plane biaxial tension, and in-plane shear to the defective CNTs. The effects of vacancy concentrations, their position, and the diameter of armchair CNTs were taken into consideration. Current results reveal that vacancy defects affect (i) the axial Young’s and shear moduli of smaller-diameter CNTs more than the larger ones and decrease by 8 and 16% for 1 and 2% vacancy concentrations, respectively; (ii) the plane strain bulk and the in-plane shear moduli of the larger-diameter CNTs more profoundly, reduced by 33 and 45% for 1 and 2% vacancy concentrations, respectively; and (iii) the plane strain bulk and in-plane shear moduli among all the elastic coefficients. It is also revealed that the position of vacancies along the length of CNTs is the main influencing factor which governs the change in the properties of CNTs, especially for vacancy concentration of 1%. The current fundamental study highlights the important role played by vacancy defected CNTs in determining their mechanical behaviors as reinforcements in multifunctional nanocomposites.

Deformation-induced anisotropy of uniaxially prestrained steel sheets

This article investigates the macroscopic behavior of uniaxially pre-strained large-scale DP780 and CHSP45R sheet specimens. A novel grip system was designed for the pre-straining of the large tensile specimens. After this first loading, the uniformly strained gauge-section of the large-scale specimen was machined to smaller standard specimens. After pre-strain, further uniaxial tension tests at 45° and 90° from the pre-tensile direction, compression test and in-plane biaxial tension tests at 1:1, 2:1 and 1:2 force ratios were conducted. The flow curves and the instantaneous r-values of the pre-strained steel in the aforementioned uniaxial loading directions were compared with their monotonic response. In addition, the pre-strained compression test was incorporated to the π-plane at several incremental offset strains.The yield function- and isotropic hardening-based homogeneous anisotropic hardening (HAH) model (Barlat et al., 2014) was selected to predict the material response after non-linear strain path change. The Swift law characterized the isotropic hardening, while the Yld2000-2d anisotropic yield function (Barlat et al., 2003a) represented the yield locus. All the coefficients of the distortional plasticity model were manually determined and validated with an optimization algorithm. The HAH-predictions of the pre-strained flow curves and yield loci at several offset strains were in reasonable agreement with the experimental data, while the instantaneous r-value evolution was qualitatively well captured.

Influence of material modeling on earing prediction in cup drawing of AA3104 aluminum alloy sheet

In-plane biaxial tension and combined tension-compression tests are carried out for AA3104 aluminum alloy sheets. Linear stress paths are applied to cruciform specimens to measure the contours of plastic work in the stress space and the directions of plastic strain rates at each stress path. Coefficients α1- α8 and exponent M of the Yld2000-2d yield function are determined to minimize the mean square error of the analytical yield locus from a measured work contour. The values of the weighting coefficients in the evaluation of the error are varied to check the effect of a specific stress state on the earing behavior. The effects of the combinations of the weighting coefficients on the accuracy of earing prediction in the cup drawing process are discussed.