Biaxial Tensile Tests Research Articles

Effect of cruciform specimen design on strain paths and fracture location in equi-biaxial tension

Abstract Hot stamping technologies require new methods for evaluating formability of sheet metal under various forming conditions. Biaxial tensile testing method using a cruciform specimen has been used for the applications, but a suitable cruciform specimen design has not yet been accepted. One of the challenges in designing a specimen for formability tests is to ensure proportional equi-biaxial strain paths arise at the location of fracture initiation. In this study, after reviewing existing cruciform specimen designs, three different geometries of cruciform specimen, named Type I, Type II and Type III, were proposed. Using numerical analysis and practical experiments, fracture initiation locations and corresponding strain paths in the specimens were investigated under equi-biaxial tension. Numerical simulations were performed to optimise the dimensions of Type I specimen to achieve a relatively high strain level near the centre point of the specimen. Based on the optimised dimensions, equi-biaxial tensile tests were carried out on cruciform specimens with different geometries, and strain paths at the fracture initiation locations were compared and analysed. It was found that in all cruciform specimens, equi-biaxial strain state appears only near the centre point. In the Type I and Type II specimens, fracture never initiates near the centre point, but at a location in the fillet transition zone where major strain is higher than that at the centre point. The Type III specimens have the ability to initiate fracture near the centre point, and to produce proportional strain paths with strain ratio β close to 1 in equi-biaxial tension, 0 in plane-strain tension, and -0.5 in uniaxial tension at the locations of fracture initiation. The research provides a cruciform specimen design, Type III, which has high potential to be used for evaluating formability for sheet metal.

New Investigations of Adhesives for Tear Repair of Canvas Paintings

ABSTRACT The thread-by-thread tear mending technique for canvas paintings represents an important field of research for the preservation of canvas paintings. This joining technology has been published and has become well established as a minimal invasive alternative for the treatment of local damage in the canvas, in contrast to the application of patches or the lining of paintings. Since then the technique has been further investigated, especially with regard to adhesive evaluation. For the first time, this paper presents the examination of five different test set-ups for the adhesive evaluation in an overall context: 1. uniaxial tensile tests on free adhesive films, 2. on mended yarns, 3. on fabric strips, 4. biaxial tensile tests, and 5. multiaxial burst pressure tests. The bonding was carried out on flax threads and canvas samples. For this purpose, single thread bonds were prepared within the specimens with a selection of different synthetic polymer dispersions and sturgeon glue modifications. Different bonding techniques were investigated, such as overlapping or butt joint mending, with and without bridging threads. The aim of the investigation was to understand the individual influencing factors in the various test series. Furthermore, the focus was on the development of a suitable test system for the evaluation of adhesives for the thread-by-thread tear mending treatment in textile painting supports. It can be stated that only the testing of several bonded threads in a fabric composite should be pursued as a long-term sensible test arrangement. This is in contrast to the previously very common set-up of testing mended single threads. Promising adhesives and adhesive modifications have been found for butt joints and overlap joints. The additional strengthening effect of bridging threads on butt joints has been proven and quantified.

Mechanical properties of UN-5100 envelope material for stratospheric airship

ABSTRACTStratospheric airships are promising aircraft, usually designed as a non-rigid airship. As an essential part of the non-rigid airship, the envelope plays a significant role in maintaining its shape and bearing the external force load. Generally, the envelope material of a flexible airship consists of plain-weave fabric, composed of warp and weft fibre yarn. At present, biaxial tensile experiments are the primary method used to study the stress–strain characteristics of such flexible airship materials. In this work, biaxial tensile testing of UN-5100 material was carried out. The strain on the material under unusual stress and the stress ratio were obtained using Digital Image Correlation (DIC) technology. Also, the stress–strain curve was corrected by polynomial fitting. The slope of the stress–strain curve at different points, the Membrane Structures Association of Japan (MSAJ) standard and the Radial Basis Function (RBF) model were compared to identify the stress–strain characteristics of the materials. Some conclusions on the mechanical properties of the flexible airship material can be drawn and will play a significant role in the design of such envelopes.

Biomechanical study on ascending aortic aneurysms associated with quadricuspid aortic valve

The quadricuspid aortic valve (QAV) is a rare anatomical situation and the biomechanical properties are not well known when it is associated with ascending aortic aneurysms (AsAA). The objective is to find out what is the biomechanical properties in such situation and to compare it with the existing data. In a sixty-three-years-old female (BMI 26,4) with hypertension disease, QAV, AsAA of 52 mm, an aortic valve and ascending aorta replacement were performed. The aortic wall sample was collected within 30 mins after replacement, partitioned related to medial, posterior, lateral, and anterior quadrants. The sample was cut in square size (15 mm × 15 mm, n = 13) with marking the circumferential and longitudinal directions. An average thickness was measured, using an electronic micrometer (Litematic VL-50, Mitutoyo®). The experiments were carried out by a biaxial tensile test machine (ElectroForce®). Each specimen was stretched at a rate of 10 mm/min until rupture. Maximum Elastic Modulus was calculated for each specimen. The CFD simulation was carried out by ANSYS® R1 2019, with the input of inlet measured in MRI sequence. The longitudinal direction of the aorta is stiffer than the circumferential direction except in the medial quadrant in both tissue types. The lateral quadrant of the aorta shows a higher stiffness (0.672 MPa), the double value of the medial quadrant (0.308 MPa). This result matches our previous study of AsAA on the bicuspid aortic valve. In the CFD simulation, it shows a higher velocity in the laterial quadrant of the acsending aorta near the aortic arch ( Fig. 1 ). In this study, the aortic biomechanical properties are similar regardless of quadricuspid or bicuspid aortic valve.

Multiscale modeling of cruciform dwell tests with the uncertainty-quantified parametrically homogenized constitutive model

This paper presents a novel multiscale approach for analyzing multi-axial stress-strain evolution in Ti-7Al cruciform specimens under dwell loading, through the use of an uncertainty-quantified, parametrically homogenized constitutive model (UQ-PHCM). The thermodynamically-consistent UQ-PHCM is built from rigorous upscaling of crystal plasticity FE models (CPFEM) using machine learning and uncertainty quantification. They explicitly incorporate microstructural information in the form of representative aggregated microstructural parameters (RAMPs). Uncertainty quantification accounts for uncertainty in model reduction, data sparsity and microstructural descriptors. This paper integrates advanced multiscale, multi-axial experiments with computational modeling at multiple scales to establish the UQ-PHCM as an effective tool for bridging the gap between laboratory specimen-scale experimental observations and micro-scale stresses and strains using CPFEM. The CPFEM is calibrated and validated by experimental data from surface strain measurements using digital image correlation (DIC) and grain-by-grain lattice strain measurements with in-situ far field high energy diffraction microscopy (ff-HEDM). A computational method is developed in CPFEM, to incorporate initial residual stresses consistent with measured lattice strains. The UQ-PHCM is validated with biaxial tensile dwell test results performed on the cruciform specimen with satisfactory prediction of gauge strain evolution in DIC measurements. Uncertainty in the strain field due to microstructural variability is also corroborated by the DIC measurements.

Thinning prediction of hole-expansion test for DP980 sheet based on a non-associated flow rule

The hole expansion process is widely used in automotive engineering to produce various car parts (e.g., lower arm, trailing arm, control arm, and chassis parts). A numerical study of the hole expansion test for the 3rd generation of advanced high-strength steel sheets is an attractive research topic because of the sheets’ high strength and low formability. This study presents a numerical prediction of the thinning behaviors observed in the hole expansion test for a DP980 sheet using finite element analysis. The experimental data of the tested material obtained from several standard testing methods, including uniaxial tensile, biaxial tensile, and hole expansion tests, are freely supported in the NUMISHEET 2018 conference Benchmark 01. Accordingly, several material models have been developed based on non-associated flow rule (NAFR) by using Hill’s quadratic, Yld2000-2d, and Yoshida polynomial functions to describe the yield and potential surfaces of the tested material. In addition, the Kim-Tuan hardening model is adopted to correctly represent the stress-strain relationship until large strains. Hence, a user-defined material subroutine (UMAT) is developed in Abaqus/Standard package to simulate hole expansion tests using these developed material models. The simulation results reveal that adopting the NAFR theory in the finite element analysis is an efficient method of simulating the hole expansion test. Additionally, the accuracy of the potential surface plays a crucial role in the thinning behavior prediction in the hole expansion simulation. The experimental data obtained from the plane-strain tension tests are recommended for use in calibrating the yield function parameters.

Evaluation of the deformability of a titanium alloy in isothermal forming

A method for assessing the deformability of metals and alloys under isothermal shaping based on biaxial tensile tests during membrane shaping has been developed and justified. The technical implementation of the method is completed.An installation for the forming of membranes by pressure of a gaseous medium – argon gas from a sheet material in isothermal conditions at hot plastic deformation temperatures was developed.The results of studies of sheet blanks from OT4-0 titanium alloy at temperature made it possible to establish the dependence of the limiting strain on the strain temperature in the range of 820-850 оC.It is shown that the results of the obtained ultimate strains can be used in the Normalized Cockcroft-Latham criterion for numerical calculations of plastic shaping in isothermal conditions.

Determination of the Properties of the Rubber Mounted Under the Agricultural Tractor Rollover Protective Structure Cabin Using a Hyperelastic Tensile Test and Finite Element Analysis

This study was carried out to determine the properties of materials used in the rubber mounted under the agricultural tractor rollover protective structure cabin. The natural rubber specimens were subjected to a hyperelastic uniaxial, biaxial, and planar tensile test, and a volumetric compression test for each of the four shore hardness types. The validity of the properties was assessed using ABAQUS, a commercial finite element analysis program. As a result of measuring the stress-strain curve with five repetitions of loading-unloading within each strain range, it was observed in all test results that the stress gradually eased from the initial level as the number of load iterations and strain intervals increased. The nominal tensile stress was shown in the order of uniaxial, planar, and biaxial tensile test. The nonlinear material models were similar to the tensile test results, and the Ogden 3rd model showed the best performance.

Conceptualisation of biaxial tensile test setup for sheet metal forming application using fuzzy analytical network process

ABSTRACT An accurate selection of a concept among all available alternatives is one of the critical and challenging task for the designers. The overall success of commercial products is largely dependent on accurate evaluation and selection of concepts. The present work is mainly focuses on the selection of appropriate concepts for biaxial tensile test setup on uniaxial tensile test machines for sheet metal forming applications. Since biaxial states of stresses are developed in a sheet metal forming process, therefore, uniaxial tensile test is inadequate to provide complete stress strain curves and formability parameters. A more feasible biaxial test setup concept will also help in understanding the behaviour of other anisotropic materials. The available methods for concept selection like Pugh Method, Analytical Hierarchy Process are not able to capture the ambiguity related to the human’s appraisal related to Multi Criteria Decision Making (MCDM). Analytical Network Process (ANP) does take into account the interdependencies of different attributes and key enablers. A hybrid approach to concept selection has been done using fuzzy logic using an analytical network process. Parameters for cost efficiency and usability effectiveness have been considered to zero down upon the best concept. The final judgement was made using weights derived from the FANP.

Mechanical characterization and identification of material parameters of porcine aortic valve leaflets

The ideal artificial heart valve does not exist yet. Understanding of mechanical and structural properties of natural tissues is necessary to improve the design of biomimetic aortic valve. Besides these properties are needed for the finite element modeling as input parameters. In this study we propose a new method combining biaxial tests and digital image correlation. These tests are carried out on porcine aortic valves. In this work, we use a modified version of the HGO (Holzapfel-Gasser-Ogden) model which is classically used for hyper-elastic and anisotropic soft tissues. This model can include fiber orientation. The identification of HGO model parameters can be determined using experimental data and two different protocols. One protocol is based on the identification of collagen fibers orientation as well as the mechanical parameters. The second one, is based on a complementary experiment to determine orientation (confocal laser scanning microscope). Both lead to determine different sets of material parameters. We show that the model is more likely to reproduce the actual mechanical behavior of the heart valves in the second case and that a minimum of three different loading conditions for the biaxial tensile tests is required to obtain a relevant set of parameters.

Mechanical and morphometric study of mitral valve chordae tendineae and related papillary muscle

The mitral valve (MV) apparatus is a complex mechanical structure including annulus, valve leaflets, papillary muscles (PMs) and connected chordae tendineae. Chordae anchor to the papillary muscles to help the valve open and close properly during one cardiac cycle. It is of paramount importance to understand the functional, mechanical, and microstructural properties of mitral valve chordae and connecting PMs. In particular, little is known about the biomechanical properties of the anterior and posterior papillary muscle and corresponding chords. In this work, we performed uniaxial and biaxial tensile tests on the anterolateral (APM) and posteromedial papillary muscle (PPM), and their respective corresponding chordae tendineae, chordaeAPM and chordaePPM, in porcine hearts. Histology was carried out to link the microstructure and macro-mechanical behavior of the chordae and PMs. Our results demonstrate that chordaePPM are less in number, but significantly longer and stiffer than chordaeAPM. These different biomechanical properties may be partially explained by the higher collagen core ratio and larger collagen fibril density of chordaePPM. No significant mechanical or microstructural differences were observed along the circumferential and longitudinal directions of APM and PPM samples. Data measured on chordae and PMs were further fitted with the Ogden and reduced Holzapfel - Ogden strain energy functions, respectively. This study presents the first comparative anatomical, mechanical, and structural dataset of porcine mitral valve chordae and related PMs. Results indicate that a PM based classification of chordae will need to be considered in the analysis of the MV function or planning a surgical treatment, which will also help developing more precise computational models of MV.

A novel spatio-temporal method for determining necking and fracture strains of sheet metals

Forming limit diagrams (FLDs) and fracture forming limit diagrams (FFLDs) have been widely used to evaluate formability of sheet metals. There are many existing methods for determining localised necking strain and fracture strain necessary to construct these diagrams, however, none has been widely accepted and applied to the range of available formability testing methods, e.g. Nakajima tests and biaxial tensile tests. In this study, a novel spatio-temporal method is proposed and developed for determining the localised necking strain and the fracture strain in deformed sheet metals. In the method, localised necking is assumed to appear at the beginning of an increasing difference between average thickness strain within two rectangular zones where localised necking occurs. The effects of dimensions of the two zones on determined localised necking strains were investigated using uniaxial tensile tests for three sheet metals: AA7075, boron steel and AA6082, and the optimal dimensions are recommended to ensure accurate determinations. In comparison with several widely used existing methods, it was concluded that the novel method has greater simplicity, stability and accuracy in determining the localised necking strains. The method was also successfully applied to determine the localised necking strain and the fracture strain for AA5754 in biaxial tensile tests and it was demonstrated to be unaffected by noise and the Portevin–Le Châtelier (PLC) effect.

Biaxial Testing Machine: Development and Evaluation

Biaxial mechanical testing gained increased importance for characterization of materials that present anisotropic behavior and/or different responses when subjected to tensile and compression loadings. In this work, a new biaxial testing machine was developed. The various systems and components were designed, manufactured, assembled, and assessed. Uniaxial tensile tests were performed to validate the device, showing results consistent with those obtained on a universal testing machine. Finally, biaxial tensile tests were also performed on polypropylene cruciform specimens. The results revealed high precision levels, thus showing the potential of this new machine.

Deep neural network approach to estimate biaxial stress-strain curves of sheet metals

To improve the accuracy of a sheet metal forming simulation, the constitutive model is calibrated using results from multiaxial material testing. However, multiaxial material testing is time-consuming and requires specialized equipment. This study proposes two different deep neural network (DNN) approaches, a two- and three-dimensional convolutional neural network (DNN-2D and DNN-3D), to efficiently estimate biaxial stress-strain curves of aluminum alloy sheets from a digital image representing the sample's crystallographic texture. DNN-2D is designed to estimate biaxial stress-strain curves from a digital image of {111} pole figure, while DNN-3D estimates the curves from a 3D image of the texture. The two DNNs were trained using synthetic texture datasets and the corresponding biaxial stress-strain curves obtained from crystal plasticity-based numerical biaxial tensile tests. The accuracy of the two trained DNNs was examined by comparing the results from that of the numerical biaxial tensile tests. It was observed that both the DNNs could estimate biaxial stress-strain curves with high accuracy. Though DNN-3D provides with a better estimation than DNN-2D, it displays lower computational efficiency. Thus, the two DNNs and their training procedures offer a new and efficient method to provide virtual data for material modeling.

Cruciform Specimen Machining Using EDM and a New Design Verification for Biaxial Testing

Cruciform flat specimen is mostly used to investigate experimentally the in-plane biaxial mechanical behavior of sheet metals. In this study, a modified cruciform specimen design is proposed and validated against the performance of current standard design. The existing standard cruciform specimen prepared through laser cutting for sheet metal can accurately provide biaxial stress–strain curve through biaxial tensile test by ensuring superior homogeneous stress and strain field in gauge section. However, preparation of such specimen using laser cut is cumbersome, expensive and prone to errors. The current standard cruciform specimen design features slotted arm of fixed length and width with specific gauge. Few other designs also feature reduced gauge section to localize failure. Both need high precision of laser cutting and machining to prepare specimens which can achieve biaxial stress–strain curve for more than 4% equivalent plastic strain level. The proposed specimen design features running slits in all four arms of specimen with uniform gauge section machined using electrical discharge machining (EDM) owing to higher accuracy and minimum heat-affected zone (HAZ). This technique also avoids machining effects with an understanding that proposed specimen design is to determine the yield behavior of material only. Also, specimen fabricated from as received sheets and without any thickness reduction in gauge area allows the user to keep full thickness in biaxial condition. The modified design qualifies the commonly accepted performance criteria for cruciform specimen, i.e., stress and strain distribution in the gauge section is found to be homogeneous and the biaxial stress–strain curve can be generated until 4% of equivalent plastic strain. The proposed specimen design is evaluated experimentally by conducting biaxial test at various stress ratios, and it is compared with alike experiments using standard specimen design. One automotive grade material, interstitial-Free high-strength (IFHS) steel sheet of thickness 0.70 mm is tested in this study to validate the specimen design.

Forming limit prediction using an integrated model for 7075 aluminum alloy sheets at an elevated temperature

A methodology for incorporating a ductile fracture criterion into an improved Marciniak–Kuczynski model, which extends the original works to include planar anisotropy using the Barlat89 yield criterion, is proposed to predict the forming limit diagram of AA7075. This is the most promising alloy to be introduced in the automotive industry, resulting in even greater weight reduction when compared with other alloys.Due to its poor formability at room temperature, this study is conducted at 480 °C, an elevated temperature adopted in a thermal multi-step process to form some complex parts. The integrated model is numerically solved using the Newton–Raphson method. Various ductile fracture criteria are estimated to identify the optimal theoretical model. The material constants are determined from uniaxial and equibiaxial tensile tests. To verify the model, a semispherical thickness reduction cruciform specimen is designed to achieve a fracture at the center. Further, thermal biaxial tensile testing technology, an in-plane and non-contact loading method, is adopted. Comparisons with the experimental results show that the integrated model with Oyane’s criterion achieves the optimal performance.

MECHANICAL CHARACTERIZATION OF SPINAL DURA USING A PD-CONTROLLED BIAXIAL TENSILE TESTER

In this study, we developed an equi-load biaxial tensile tester and applied it to a series of mechanical tests using specimens obtained from the porcine spinal dura mater. The dural sample exhibited a nonlinear and anisotropic behavior as it was more deformable in the longitudinal direction rather than in the circumferential direction at lower strains; i.e., mechanical response of the longitudinal direction was significantly compliant in the Toe region compared to that of the circumferential direction under 1:1 biaxial stretching. However, we have not observed a significant difference with respect to the resultant strain and Young’s modulus between the longitudinal and circumferential directions at higher strains or in the Linear region. Our results also indicated that the upper thoracic region (T1) was relatively compliant compared to the lumbar region (L), where the failure load was almost equal between them because the dural thickness of T1 was five-fold greater than that of L; i.e., spinal dura mater became stiffer and stronger at further distances from the brain. This shows structural effectiveness and may be preferable to mechanically protect the vulnerable spinal cord from externally applied impact loads.

Determination of Yield Surfaces in Accordance With ISO 16842 Using an Optimized Cruciform Test Specimen

Background: For the standard ISO 16842 cruciform test specimen, stresses obtained from the gauge area are far below the ultimate tensile strength due to high stress concentrations at the slit ends which lead to premature failure. Objective: To introduce a new cruciform specimen design which has been optimized with respect to the determination of yield surfaces. Methods: The proposed design differs from the ISO standard by an additional thinning of the gauge area and wider slits in the arms to avoid stress singularities. Compared to other cruciform test piece designs found in the literature, the stress distribution is still homogeneous and there is no need to reduce the size of the gauge area, thanks to the specimen’s well-balanced proportions. Results: Biaxial tensile tests have been conducted with aluminium 5754 alloy samples of different thicknesses. For the standard cruciform test piece, the maximum strain achieved at the gauge area is only 25% of the fracture strain. The optimized cruciform test piece can attain about 66% of the fracture strain before breaking. Conclusions: The optimized specimen design enables the measurement of yield surfaces at higher stress levels. In case of other materials such as elastomers, the slit length has be to adjusted accordingly.

An accurate determination method for constitutive model of anisotropic tubular materials with DIC-based controlled biaxial tensile test

The reliability of numerical simulation results vitally depends on the accurate determination of the constitutive model, which requires accurate and sufficient experimental data. To address the current limitations of the range and accuracy of the experimental data of tubular materials, a novel controlled biaxial tensile testing device was developed using digital image correlation (DIC) system as the deformation measuring tool. Using such a device, arbitrary biaxial tensile stress path can be accurately applied to tubular specimens, and the strain can be accurately and continuously measured over the whole deformation process. Firstly, the accurate experimental data of AA6061-O tubes were obtained through the controlled biaxial tensile tests. Then, using the experimental data, the constitutive model considering the evolution of anisotropic characteristics was calibrated based on the Yld2000-2d yield criterion. Finally, the accuracy of the calibrated constitutive model was verified in engineering practices by compiling the constitutive model into finite element software as a user material subroutine (VUMAT) for simulating tube hydro-bulging. Excellent agreements were achieved between experimentally-determined and predicted bulge height, bulge profile, and pole thickness of bulged tubes over the whole hydro-bulging process. It is demonstrated that the DIC-based controlled biaxial tensile test is effective to accurately calibrate the constitutive model of tubular materials, which can be used for both the research of plastic deformation behavior and practical application of hydroforming industry.

Gas permeability of CFRP cross-ply laminates with thin-ply barrier layers under cryogenic and biaxial loading conditions

Utilization of carbon fiber reinforced plastic (CFRP) composite materials in propellant tanks is expected to drastically reduce the structural weight of space vehicles. However, fuel leakage through the chain of matrix cracks caused by serious thermal residual stress is a considerable problem. To avoid fuel leakage, this study proposes leak barrier layers consisting of thin-ply prepregs. Biaxial tensile tests are performed for specimens with or without thin-ply barrier layers at cryogenic temperature, and the gas leakage properties of damaged CFRP cross-ply laminates are investigated. In addition, the formation of leakage paths at cryogenic temperature is simulated by the finite element method based on the experimental data. Finally, the experimental and numerical results demonstrate that thin-ply barrier layers increase the tolerance against damage and leakage.