Conditions Of Biaxial Tension Research Articles

Deformation characterization of multi-morphology composite cellular hyperelastic structure under biaxial tension: Analytic approaches for sensor applications

As a preliminary study to develop an effective stretchable sensor, we implemented multi-morphology cellular structures in the gauge area of a biaxial tensile specimen to obtain the desired biaxial mechanical behaviour. A numerical parametric study was conducted by considering the unit cell geometries, four biaxial tension conditions, and three groups of unit cells. The parametric study reveals that a multi-morphology composite cellular (M2C2) specimen with compliant unit cells near the centre and stiff unit cells along the border of the gauge area shows high linearity between the force and displacement relationships and high compliance. M2C2 specimens optimised using the Bayesian optimisation process share similar geometric patterns found in the parametric study and show enhancements in linearity and compliance up to 40.4 % and 65.6 %, respectively, compared with those of a conventional solid specimen.

A new analytical model for force prediction in incremental sheet forming

A new analytical model for forming force prediction in the whole process of incremental sheet forming (ISF) is presented in this work. The modelling of contact region, thickness distribution and strain components are carried out as the basis for the prediction of vertical and horizontal forces. The effect of local contact behaviour and material deformation, as well as the behaviours of global bending, changes of deformation mode and contact condition are taken into account in the modelling of ISF force history. The force prediction model at both plane strain and biaxial tension condition areas is developed based on the differences in contact region and thickness distribution between these two different deformation states. Validated by ISF tests for a truncated cone and pyramid part with varying drawing angles, the prediction of force history captures well the fluctuation of different force components due to the change of deformation conditions and provides an insight into the material deformation mechanisms and the direct correlation to forming force characteristics of the whole ISF process. In a practical case, the model is successfully applied to the force prediction in ISF-based cranial plate manufacture. The model is also validated by a series of ISF tests with accurate force predictions of both the peak and stabilised forces.

Forming limit of 6061 aluminum alloy tube at cryogenic temperatures

Cryogenic medium pressure forming has been proposed to fabricate aluminum alloy complex tubular components. It is urgently needed to evaluate and predict the cryogenic forming limit of aluminum alloy tubes for the novel process. Cryogenic bulging test using different length-diameter ratios was proposed to test the forming limit in the tension-tension zone. A modified M-K model was established to rapidly predict the cryogenic forming limit, based on the dynamic hardening with deformation. Theoretical analysis and fracture characterization were implemented to reveal the improvement mechanism of cryogenic forming limit from the macroscopic and microscopic perspectives, respectively. The forming limit of AA6061 tube at −196 °C is approximately double that at room temperature, especially in the tension-tension zone, which contributes significantly to the forming of complex features under biaxial tension. The cryogenic limiting deformation ability increases gradually as the strain state changes from plane strain to biaxial tension. Under the biaxial tension condition of λ=1.2, the limiting strain can reach 0.52 at −196 °C. The cryogenic forming limit can be successfully predicted by the modified M-K model with a prediction deviation of only 4.35% at −196 °C. The enhanced cryogenic hardening ability promotes the improvement of deformation uniformity and delays the occurrence of uncoordinated deformation. Ductile fracture is main fracture mechanism at cryogenic temperature. The significantly increased ductile fracture characteristics contribute to the improved cryogenic forming limit. This research can provide important guidance for the cryogenic forming of aluminum alloy tubular components.

Практическое использование результатов исследований технологических процессов формирования твердофазных соединений проволок в контролируемой газовой среде при создании листовых пористых сетчатых материалов с заданными свойствами

A specific feature of the structure-forming elements used for the manufacture of porous mesh materials is a high specific surface area and a complex configuration of wire meshes, which excludes the possibility of using wire cutting for welding. The research shows that cleaning in Freon-113 is an effective way to remove mineral oils, paraffins, fats and some other contaminants from the mesh surface, since this solvent is stable, non-flammable, non-explosive and does not interact with the workpiece material. In addition, improving the quality of mesh cleaning is achieved by superimposing ultrasonic vibrations in the range of 20...40 kHz. The study introduces flow layouts for the porous materials manufacture by pressure welding of wire meshes from steel 12Kh18N10T and titanium alloy VT2. Findings of the research show that welding envelopes of meshes made of steel I2XI8HI0T by rolling in evacuated makes it possible to obtain porous elements with sufficiently high mechanical and technological properties. It is possible to implement this process on any sheet rolling mill, which is its significant advantage. The paper gives the modes of welding by rolling and diffusion welding of meshes in the manufacture of porous materials. Within the study, we developed a mathematical model that makes it possible to predict the ultimate interlaminar strength for given values of technological parameters of the processes for manufacturing sheet blanks. It is proposed to control the interlayer strength by comparing the calculated data and the results of testing the samples for separation in accordance with the developed methodology. It is advisable to evaluate the control of strength, plasticity in the sheet plane and their anisotropy by comparing the calculated data and the results of testing specimens under conditions of biaxial tension, implemented during hydrostatic buckling through a round matrix.

Features of structural plywood operation in conditions of flat stress state

The aim of our research work was to study operation features of plywood structures in flat stress state, which takes place in conditions of real operation of sheet structural materials. The method of study the materials in such conditions was developed. It includes determination of optimal form of specimens and equipment, providing tests of structural plywood under various ratio of values and signs of loads, made in mutually perpendicular directions. The research results of plywood operation from larch timber in conditions of biaxial tension and the assessment of its strength criterion under biaxial tension are shown in the research paper. The values of destructive stresses under various ratio of tension stress, directed along the main axes of elastic anisotropy of the tested material, were obtained. The experimental research results testify to possibility of using the test results of plywood specimens in conditions of biaxial tension and show that addition of extra stress almost does not reduce the strength limit of structural plywood.

Determination of biaxial stress–strain curves for superplastic materials by means of bulge forming tests at constant stress

As the characterization of superplastic materials requires elevated temperatures and strain rate control, standard bulge testing procedure with optical measuring systems is not feasible for the determination of biaxial stress–strain curves. Standard superplastic bulge forming tests performed at constant pressure can be used for the identification of material constants or formability evaluation, but they are not applicable for accurate characterization of deformation behavior providing stress–strain curves at constant strain rates. The present paper is aimed to provide a technique for the direct characterization of stress–strain behavior of superplastic materials in conditions of biaxial tension. This technique is based on bulge forming testing with a closed-loop pressure control procedure allowing one to maintain the value of the effective stress at the dome pole at the predefined constant level. Thus, the variation of strain rate is reduced compared to the constant pressure testing. The results are evaluated using a double-step numerical procedure which provides the way to calculate the stress–strain curves, corresponding to constant referenced strain rates. The developed technique was used to characterize superplastic aluminum alloy Alnovi-U in conditions of biaxial tension at 500°C.

Weld orientation effects on the formability of tailor welded thin steel sheets

Abstract Tailored welded blanks (TWBs) technology can give the important possibilities to obtain components in the automobile industry. Friction stir welding (FSW) is a joining approach, which can adhere parts well with desired properties in weld zone. In this article, the main aim is investigation the effect of weld zone orientation on forming limit diagram (FLD) of the TWBs using experimental and finite element model. Three TWBs are produced FSW with three different orientations of weld zones including 0 0 , 45 0 and 90 0 against major stress direction. The microstructure of the weld zones is divided and then observed via metallography procedures. Tensile tests are carried out to determine the mechanical properties of TWB sections and duplicate the tests numerically to validate the formability results. The Nakazima stretch test is used to derive the limit strains for three different weld orientations (between rolling direction and welding path) and what can be seen is the changeable effect of these ordinations on varying strain paths. The best formability is for TWB with orientation weld 90 0 in tension mode while, results reveals that in Plane strain condition best formability is originated from TWB with weld orientation 0 0 . For biaxial tension condition e 2 = e 1 , changing the weld orientation has no effect on formability. The comparison between FEM and experimental tests reveals good agreement and high recommended FEM for this type of study.

Numerical simulation of hydraulic bulging using uniaxial and biaxial flow curves and different yield criteria

In sheet metal forming industry, finite element analysis has become a necessary step before actual production of the parts. It helps in the improvement of part quality as well reduces the effort applied in experimental trials. However, the success of finite element simulation mainly depends on the constitutive model used for defining the plastic deformation behaviour of the sheet material. Material characterization in biaxial stress state helps in selecting advanced constitutive models in numerical simulations. In this work, aluminium alloy AA5083 sheet material is characterized in uniaxial and biaxial tension conditions. Hydraulic bulge tests are performed to obtain the flow curves and material properties which are then used to find the coefficients in different yield criteria. These coefficients and the flow curves, fitted using different work hardening laws, are used in finite element simulation of the hydraulic bulge test and the results are validated by experiments.

First-principles study on the mechanical properties of M2CT2 (M = Ti, Zr, Hf; T = O, F, OH) MXenes

Two-dimensional (2D) transition metal carbides known as MXenes belong to a new branch of 2D material family, and their fundamental properties vary with their compositions and surface functionalizations. In this study, the structural and ideal mechanical properties of M2C-type MXenes and their functionalized M2CT2 MXenes (M = Ti, Zr, Hf; T = O, F, OH) were systematically examined via first-principles methods. The stress–strain curves of the MXenes under homogenous biaxial and uniaxial tension are identified, and the fundamental quantities (e.g., Young’s modulus, in-plane stiffness, and Poisson’s ratio) are addressed. With significantly higher strength and extended critical strains, the M2CO2 MXenes exhibit optimal flexibility when compared with that of M2C, M2CF2, and M2C(OH)2. Additionally, Hf2CT2 exhibits optimal tensile performance under uniaxial or biaxial tension when compared to that of Ti2CT2 and Zr2CT2. The Young’s modulus, in-plane stiffness, and Poisson’s ratio of MXenes with different surface functionalization increase in a sequence corresponding to OH < F < O. Furthermore, the effects of vacancy on the mechanical properties of MXenes are further explored and indicate that vacancy can significantly weaken the tensile properties of MXenes that are considered. Moreover, vacancy also results in a certain anisotropy of stress along armchair and zigzag directions even under the biaxial tension condition.

Friction influence on the AA6060 aluminium alloy formability

Using a finite element calculation code, this work analyses the influence of friction during a stamping test conducted on the AA6060 aluminium-based alloy. The study focuses on phenomena happening when the sheet necking appears. This condition, based on the Hill’s localized necking theory and the Swift’s diffuse necking theory, is dependent on the material hardening index. This work shows that the punch stroke at the necking condition point is maximum when the main strain measured on the sheet surface are unbalanced and close to a balanced biaxial tension condition.

Characterization of Stress-Strain Behavior of Superplastic Titanium Alloy by Free Bulging Tests with Pressure Jumps

The work is dedicated to determination of stress-strain behavior of Ti6Al4V alloy deformed in conditions of biaxial tension provided by free bulging testing. The dome height during each test was continuously measured and recorded using a magnetostrictive position transducer. All the tests were performed using stepped pressure regime with jump pressure changing between two values at evenly spaced time moments. This experimental technique provides the possibility to study strain rate sensitivity index variation during the test and subsequently construct strain and strain rate dependent material model. The output data of each test include the evolution of dome height, subsequent pressure regime and final thickness of the specimen at the dome pole. In the framework of this study the processing of such data in order to evaluate the material behavior is discussed. Inverse analysis with different material models was implemented as well as special direct technique allowing one to construct stress-strain curves based on the results of free bulging tests with pressure jumps. The obtained material model was verified by finite element simulation.

Material characterization and fracture prediction with advanced constitutive model and Polar EPS fracture diagram for AA 3104-H19

Material characterizations for plasticity and fracture have been conducted from uniaxial tensile tests, bi-axial bulge test, and disk compression test for a beverage can AA3104-H19 material. The results from the experimental tests are used to determine material coefficients for the Yld2004-18p model [1]. Finite element simulations are developed to evaluate the predicted earing profile. Excellent agreement with the experimental data for eight ears exhibited in AA3014-H19 is achieved using the Yld2004-18p constitutive model. Further mechanical tests are also conducted on the AA3104-H19 to generate fracture data under different stress triaxiality conditions. Tensile tests are performed on the samples with a central hole and notched specimens to achieve tensile and plane-strain conditions. A specially designed torsion test of a double bridge specimen is conducted to generate the points near pure shear conditions. The Nakajima test is also utilized to produce a bi-axial tension condition. The data from the experiments is used to generate the fracture locus in the principal strain space. Mapping from the principal strain space to Polar Effective Plastic Strain (PEPS) space is accomplished for a general yield function. Finite element modeling is used to validate the fracture diagram in the polar space. A hole expansion demonstrates the accuracy of the PEPS fracture theory for the direction for onset of failure.

Plastic anisotropy and failure in thin metal: Material characterization and fracture prediction with an advanced constitutive model and polar EPS (effective plastic strain) fracture diagram for AA 3014-H19

Material characterizations for plasticity and fracture have been conducted from uniaxial tensile tests, bi-axial bulge test, and disk compression test for a beverage can AA3104-H19 material. The results from the experimental tests are used to determine material coefficients for the Yld2004-18p model (Barlat et al., 2005). Finite element simulations are developed to evaluate the predicted earing profile. It is shown that the Yld2004-18p model is capable of accurately predicting the complex earing profile. Excellent agreement with the experimental data for eight ears exhibited in AA3014-H19 is achieved using the Yld2004-18p constitutive model. Further mechanical tests are also conducted on the AA3104-H19 to generate fracture data under different stress triaxiality conditions. Tensile tests are performed on the samples with a central hole and notched specimens to achieve tensile and plane-strain conditions. A specially designed torsion test of a double bridge specimen is conducted to generate the points near pure shear conditions. The Nakajima test is also utilized to produce a bi-axial tension condition. The data from the experiments is used to generate the fracture locus in the principal strain space. Mapping from the principal strain space to stress triaxiality space, principal stress space, and Polar Effective Plastic Strain (PEPS) space is accomplished for a general yield function. Finite element modeling is used to validate the fracture diagram in the polar space. A model of a hole expansion during cup drawing demonstrates the robustness of the PEPS fracture theory for a condition with a highly anisotropic material and accurately predicts the direction for onset of failure.

Characterization of OT4-1 Alloy by Multi-Dome Forming Test.

In this study, the rheological characteristics of a titanium alloy have been obtained by multi-dome bulging test. Free bulging process is an experimental technique that can be used to characterize material in conditions of biaxial tension during superplastic, as well as conventional, hot forming. The constitutive constants are calculated on a base of the information about the bulge geometry, applied pressure, and forming time. A multi-dome forming test allows one to reduce the number of the experiments required for the characterization, since every multi-dome test produces several domes of different size. In this study, a specific die for multi-dome test was used. The die has six holes with different radiuses of 20, 25, 30, 35, 40, and 45 mm. During a test, the specimen is clamped between blank holder and die holder, heated to a specific temperature, and formed by applying constant gas pressure. The experiments were conducted at different temperatures for OT4-1 titanium alloy. The constitutive constants were obtained by processing the experimental data using two different techniques and compared with tensile test results. In order to estimate the influence of friction on the experimental results and to verify obtained material characteristics, finite element (FE) simulation was performed. Finally, the results of FE simulation were compared with the experimental data. The results of the simulation show the advantage of material characterization based on multi dome tests and its interpretation by inverse analysis. The deviations produced by the effect of friction are more significant when the direct approach is applied instead of inverse analysis with a semi analytical model of the bulging process.

Применение обратного анализа для определения реологических констант материалов по результатам тестовых формовок круглых мембран

The paper is devoted to a problem of determining rheological characteristics of materials from the results of experiments on free forming of sheet blanks to a cylindrical matrix. This information on the material behavior is used in the design of gas forming processes for the production of parts for aerospace industry. Realization of such technologies requires to follow optimum technological regimes, in computer simulations of which one should adequately describe the properties of materials under consideration. A significant disadvantage of the classical experimental method of tensile testing of plate specimens is that an information taken from these tests is related to metal forming in the conditions of uniaxial tension that is not typical for gas forming processes. Experimental method of forming circular membranes considered here allows one to study the behavior of a material in the conditions of biaxial tension. Interpretation of the results is proposed to carry out by an inverse analysis utilizing a special semianalytical model for the solution of the direct task. The key role in this semianalytical model belongs to a dependence of the blank thickness at the dome pole on the dome height, which accounts for the strain rate sensitivity coefficient. This approach was applied for the processing of experimental results obtained by free forming of industrial aluminum alloys. The material characteristics obtained were compared to charecteristics determined by other methods for the same set of experimental data available in the literature. To estimate the efficiency of the method proposed, the characteristics obtained were verified by finite element simulations. For simulations, MSC Nastran software was used. The results of the simulations were found to be in good agreement with the experimental data not only with respect to the dome height but also to the blank thickness at the dome.

Investigation of stress-strain behavior of a sheet material using free bulging test

Abstract In this work, a new experimental-numerical technique is developed in order to investigate the constitutive behaviour of a sheet material in conditions of superplastic forming. The principal feature of this technique is that unlike classical tensile testing it allows one to obtain stress-strain curves for a material formed in biaxial tension conditions produced by free bulging process. These conditions are much closer to the ones that the material undergoes during the superplastic forming process. Consequently, they give more accurate information about the material behaviour than the ones coming from tensile tests data. The drawback is that the strain (and similarly its time derivative) cannot be directly measured and controlled during free bulging test but its value has to be derived from other macroscopic measurement. Towards this end, a blow forming machine was equipped with a position transducer for the measurement of the dome height during the test. In order to control the stress in the dome apex at a predetermined level the applied pressure was continuously adjusted to current dome height using a special algorithm. After the test, the dome height data were processed to obtain the evolution of stress, strain and strain rate at the dome apex as well as the stress strain curves for constant referenced strain rates. The tests were performed on superplastic aluminium alloy (ALNOVI-U) sheets of 1.35 mm initial thickness at 500 °C. Using the data from two tests with different strain rate paths the stress-strain curves and the strain rate sensitivity index evolution were calculated for two constant referenced strain rates. The obtained constitutive data were verified by finite element simulation of a blow forming.

Failure Investigation for QP Steel Sheets under uniaxial and Equal-Biaxial Tension Conditions

The Quenching and Partitioning (QP) steel sheet is new generation material to induce phase transformation for plasticity in forming vehicle parts. The phase transformation is strongly stress state dependent behavior in experiments, which should affect the failure timing and limit strain in forming processes. In this paper, Nakajima test with QP980 and DP1000 steel sheets under equal-biaxial loading condition is performed for failure behavior. X-ray diffraction (XRD) is adopted to obtain the volume fraction of retained austenite (fA). Digital Image Correlation (DIC) is used to record the surface strain field and its evolution during equal-biaxial tension deformation. The same level Dual Phase (DP) steel is also employed for the purpose of comparison. The results show that phase transformation in QP steel gives small impact on failure strain under equal biaxial tension condition which is contradicted with our understanding. It suggests that failure behavior under uniaxial tension of QP980 is strongly phase transformation dependent. But it shows almost independent under equal biaxial tension condition.

Room Temperature Shear Band Development in Highly Twinned Wrought Magnesium AZ31B Sheet

Failure mechanisms were studied in wrought AZ31B magnesium alloy after forming under different strain paths. Optical micrographs were used to observe the shear band formation and regions of high twin density in samples strained under uniaxial, biaxial, and plane strain conditions. Interrupted testing at 4 pct effective strain increments, until failure, was used to observe the evolution of the microstructure. The results showed that shear bands, with a high percentage of twinned grains, appeared early in the samples strained under biaxial or plane strain tension. These bands are similar to those seen in uniaxial tension specimens just prior to failure where the uniaxial tensile ductility was much greater than that observed for plane strain or biaxial tension conditions. A forming limit diagram for AZ31B, which was developed from the strain data, showed that plane strain and biaxial tension had very similar limit strains; this contrasts with materials like steel or aluminum alloys, which typically have greater ductility in biaxial tension compared to plane strain tension.

Mechanical relation for porous metal foams under complex loads of triaxial tension and compression

The mechanical relation of isotropic three-dimensional reticulated porous metal foams with stochastic pores is investigated under complex loads of triaxial tension and compression. From the simplified structural model, the mathematical relationship between three nominal main stresses and porosity has been derived for this class of porous materials at failure under the above-mentioned complex loads, covering three loading conditions of biaxial tension with monoaxial compression, of biaxial compression with monoaxial tension, and of triaxial compression. Through the relevant expression from the deduction, the criterion of strength design can be further obtained for these porous materials under these multiaxial complex loadings.

Elastic T-Stress Solutions of Embedded Elliptical Cracks Subjected to Uniaxial and Biaxial Loadings

Abstract The elastic T-stress has been found to be an important parameter in characterizing the near crack tip elastic-plastic stress states of 2-D and 3-D crack problems. In addition to the J-integral, the T-stress provides an effective two-parameter characterization of 2-D and 3-D elastic-plastic crack tip fields in a variety of crack configurations under small scale yielding conditions. Embedded elliptical crack in an infinite solid subjected to uniaxial or biaxial tension conditions represents an excellent model for many engineering components with embedded cracks. Although extensive analyses are available for stress intensity factors (SIFs) for embedded elliptical cracks, to date no analytical T-stress solutions are available. This paper presents the exact close form solutions for elastic T-stress of an embedded elliptical crack in an infinite body under remote uniaxial or biaxial tension. The foundation of the derivation is based on the potential method for three-dimensional elasticity. Solutions of stress components parallel to and perpendicular to the cracked plane are derived first. T-stress is then obtained from the asymptotic stress field near the crack front. Complete solutions of T-stress along the crack front are established. Further, three-dimensional finite element analyses are conducted to verify the derived solutions; excellent agreements are achieved. When combined with the corresponding K or J solutions, these T-stress solutions are suitable for the analysis of constraint effects for embedded elliptical shaped cracks in engineering components.