Cruciform Samples Research Articles

Effect of continuous and discontinuous non-proportional loadings on formability of DX54 sheet material

Both continuous and discontinuous non-proportional loadings occur in multi-stage automotive stamping processes. Discontinuous loading is widely studied, but due to requiring sophisticated experimental procedures, continuous loading has been studied less. This study explores the impact of continuous loading on DX54 steel utilising an innovative experimental setup that enabled cruciform samples to undergo uniaxial to biaxial strain path change continuously without unloading. A similar two-stage discontinuous loading from uniaxial to biaxial with unloading in between was generated in DX54 to understand the differences in macro-strain, micro-strain, microstructure, and micro-texture evolution between the continuous and the discontinuous loadings. The stress state of the material during continuous loading was different to that during discontinuous loading. In this study, the occurrence of ‘pseudo-localisation’ was observed during continuous loading, and the observed rotation of high-strain bands differed between continuous and discontinuous loading. The discontinuous loading induced a higher strain, hardening rate, and increased elongation compared to the continuous loading. These results suggest the potential for higher formability during the discontinuous loading compared to the continuous loading.

Dynamic biaxial loading of vascular smooth muscle cell seeded tissue equivalents

An intricate reciprocal relationship exists between adherent synthetic cells and their extracellular matrix (ECM). These cells deposit, organize, and degrade the ECM, which in turn influences cell phenotype via responses that include sensitivity to changes in the mechanical state that arises from changes in external loading. Collagen-based tissue equivalents are commonly used as simple but revealing model systems to study cell–matrix interactions. Nevertheless, few quantitative studies report changes in the forces that the cells establish and maintain in such gels under dynamic loading. Moreover, most prior studies have been limited to uniaxial experiments despite many soft tissues, including arteries, experiencing multiaxial loading in vivo. To begin to close this gap, we use a custom biaxial bioreactor to subject collagen gels seeded with primary aortic smooth muscle cells to different biaxial loading conditions. These conditions include cyclic loading with different amplitudes as well as different mechanical constraints at the boundaries of a cruciform sample. Irrespective of loading amplitude and boundary condition, similar mean steady-state biaxial forces emerged across all tests. Additionally, stiffness-force relationships assessed via intermittent equibiaxial force–extension tests showed remarkable similarity for ranges of forces to which the cells adapted during periods of cyclic loading. Taken together, these findings are consistent with a load-mediated homeostatic response by vascular smooth muscle cells.

Biaxial Tensile Testing of Cruciform Samples to Determine the Impact of Pre-Strain on the Forming Limit Diagram of Aluminum Alloy 5052 through Finite Element Simulation

The present work focuses on the effect of pre-strain on the forming limit curves (FLCs) of aluminium alloy 5052 sheet of 2.5 mm thickness using cruciform samples. To identify the effect of pre-strain on the FLC, the finite element simulations are performed on cruciform samples. The cruciform samples are deformed to a small level of pre-strain in different strain paths. Thereafter, the further deformation under the various strain paths to measure the effect of pre-strain on the forming limits are carried out. Pre-strain in uniaxial, plane strain and biaxial loading conditions are considered in this work. For each case, i.e., uniaxial, plane strain and biaxial conditions two pre-strain conditions are considered. The cruciform samples are carefully thinned in the central region to promote development of large plastic strains there and eventually to neck and fail. The output obtained through simulations are presented in terms of forming limit curves for various strain paths.

Residual stress effects on short crack propagation behavior in friction stir welded 7075-T6 aluminum alloy panel under biaxial loading: An experimental and numerical study

The effects of residual stress on short crack propagation behavior of friction stir welded (FSWed) 7075-T6 aluminum alloy panel was investigated under biaxial loading. The biaxial fatigue tests were carried out on three kinds of cruciform samples, including base material (BM) cruciform sample and FSWed cruciform sample with crack perpendicular or parallel to the weld. Scanning electron microscope (SEM) fractography was conducted to identify and relate fracture surface features to governing fatigue damage mechanisms. Finite element method combined with stress intensity factor (SIF) analysis was used to simulate the biaxial fatigue propagation. In a comparison of the crack path in BM and FSWed cruciform samples, experimental and numerical results showed that residual stress can change the nominal biaxiality ratio, leading to crack path changes in FSWed cruciform sample with crack parallel to the weld, and the curved fatigue crack front formed on the fracture surface due to the non-uniform distribution of the residual stress through the thickness. The fatigue damage mechanisms are different depending upon the biaxiality ratio as well as the weld direction.

Steel Cruciform Sample with Nitrided Arms Achieves Higher Plastic Strain in the Gauge Region

This paper describes a novel solution to increase plastic strain in the gauge region of a cruciform sample during a forming limit test. A nitriding procedure was used to increase the strength of the arms of the specimen and at the same time enabled higher plastic deformation in the centre of the sample. DC 5 steel sheets were cut in bone-shape samples and subjected to the nitriding procedure. Uniaxial tensile tests were done to obtain the properties of both the raw and thermo-chemically treated material. Two shapes of the gauge region, partially protected against diffusion of nitrogen, were modelled with the use of Abaqus software and a numerical analysis of biaxial tensile tests were conducted. Based on the obtained numerical analysis results DC 5 steel cruciform samples were nitrided while keeping the same gauge region geometries and subsequently subjected to a biaxial tensile test. The obtained results prove the positive influence of the nitriding procedure on increasing the strength of the cruciform sample arms and at the same time the plastic strain in the centre of the sample. The test bench analysis showed almost six times higher plastic deformation, as compared to the raw specimen, however special attention should be paid to the nitriding process parameters and the shape of the protected gauge region.

Anti-buckling device for biaxial testing with cruciform specimens

The use of an anti-buckling device is proposed to avoid the appearance of undesired instabilities during biaxial testing with cruciform specimens in which the compressive loads are applied directly on the arms of the sample by means of compression plates. The device consists on a cross-shaped accessory that restricts out-of-plane displacements and a L-shaped support that forces the alignment of the fixture, the specimen and the testing machine. In addition, recommendations about the test methodology and the conditioning of the cruciform sample are given. For this purpose, analytical and numerical studies are developed to design the experiments and to describe both the global buckling of the cruciform specimen and the local instability of the central region subjected to biaxial loading. The risk of instability in the arms of the sample is reduced under tension-compression and compression-compression loading cases whenever the device is used, ensuring that the results are not affected by premature buckling of the specimen and favoring the appearance of appropriate failure modes.

Analysis of the Cruciform Sample Shapes for Bi-Axial Tensile Tests Based on the Geometries Currently Presented in the Literature

Analysis of the Cruciform Sample Shapes for Bi-Axial Tensile Tests Based on the Geometries Currently Presented in the Literature

Comparison of the shear behavior in graphite-epoxy composites evaluated by means of biaxial test and off-axis tension test

Abstract Characterization of shear behavior in composite materials remains a not fully solved problem. In the last fifty years, many different approaches have been proposed to solve this problem (rail shear, thin-walled tube torsion, off-axis tensile, ±45° tensile, Arcan, Iosipescu, asymmetric four-point bend, plate twist, v-notched rail shear, off-axis flexural, and shear frame), although none of these approaches have achieved an unquestionable solution. For this reason, proposals of alternative methods and comparison between different experimental techniques are of interest. In the present work, the use of cruciform samples with the fiber oriented at 45° with respect to the load directions, and subjected to tension-compression (creating a pure shear stress state at the central part of the samples), is studied. The experimental results of the cruciform samples have been compared with the off-axis tests (with the fiber at 10°) for the same material (AS4/8552), finding a good agreement between the shear experimental curves, especially at the initial part of the curve, where the shear modulus is calculated. Nevertheless, the shear strength value obtained by means of the cruciform specimen has shown to be significantly lower than that obtained using the off-axis test. A Finite Element numerical model of the cruciform specimen has been developed to analyze the stress field of the samples. Numerical results have shown that there is a central area of the cruciform specimens where a pure and uniform shear stress state is developed, which is suitable for the evaluation of the shear constitutive law of the material. It has been observed that there is a (σ 22) stress concentration in the transition between the straight and curved parts of the boundary geometry of the samples, which explain some premature failures of the samples. This premature failure could be avoided with tabs extended up to the beginning of the central part of the sample.

In-situ study of strain and texture evolution during continuous strain path change

Automotive stamping is a multi-stage process where a sheet material is drawn in first stage and then redrawn, flanged and pierced in subsequent stages. In the first draw stage, continuous strain path change is induced in the material while a discontinuous strain path change occurs when the material is processed in the subsequent stages of a multi-stage stamping operation. The strain path transition can potentially alter the forming limit of the material. Previous research has investigated the effect of the discontinuous mode of strain path change by loading the sample in one strain path, unloading it, then reloading it in a second path. Thus, discontinuous strain path change was obtained. In this work, the effect of continuous strain path change was investigated with a novel experimental design that allowed cruciform samples to change strain path continuously without unloading. The work was carried out in two stages. In the first stage, the design of the cruciform sample was verified with finite element modelling to ensure the occurrence of continuous strain path change and this was validated experimentally using DX54 material by capturing full-field strain measurements data using digital image correlation technique. The size of the experimental apparatus permitted it to be placed inside a scanning electron microscope chamber. In the second stage, the validated test method was used to evaluate microstructural changes during the deformation including full-field strain and texture evolution. The micro-strain evolution showed rotation of strain bands while the texture evolution conveyed grain rotation during continuous strain path change.

Neutron Diffraction and Diffraction Contrast Imaging for Mapping the TRIP Effect under Load Path Change.

The transformation induced plasticity (TRIP) effect is investigated during a load path change using a cruciform sample. The transformation properties are followed by in-situ neutron diffraction derived from the central area of the cruciform sample. Additionally, the spatial distribution of the TRIP effect triggered by stress concentrations is visualized using neutron Bragg edge imaging including, e.g., weak positions of the cruciform geometry. The results demonstrate that neutron diffraction contrast imaging offers the possibility to capture the TRIP effect in objects with complex geometries under complex stress states.

Двухосные испытания металлических образцов на испытательных машинах с одной осью нагружения

The necessity of experimental studies to assess the growth rate of fatigue cracks under biaxial loading is substantiated. An overview of testing machines for biaxial testing of metal samples, devices and fixtures used to ensure biaxial loading is made. An original device for distributing the vertical force of the testing machine along two axes of a cruciform sample is described

Strengthening of cruciform sample arms for large strains during biaxial stretching

Material-forming abilities are crucial for the optimisation of sheet metal-forming processes. Among the many methods used for the evaluation of forming limits, those based on cruciform samples are very promising, mostly because of their frictionless character and access to a pure two-dimensional stress area. In contrary to punch or tubular test samples, they allow in-situ strain measurements on both sides of the gauge region. Nevertheless, they have some disadvantages. Namely, the arms of the sample crack at the gauge region before reaching the deformation limit. This reduces the mechanical insights that can be gained from a single specimen. The paper describes the development of cruciform specimens in which large strains can be achieved during bi-axial tensile testing. The experiments focus on the application of initial deformation on the cruciform sample arms prior to the test. Strain-induced hardening of the sample arms is shown to increase the maximum achievable strain within the gauge section. This allows the stress strain response of a given material to be characterised following large plastic deformation. The samples used in the bi-axial tensile tests each had one particular pre-deformed shape in the corners, whose degree of pre-deformation differed between them. The results demonstrate the increased strain characterisation capabilities, which can be determined from the addition of initial plastic deformation. Increased cold working was found to increase the maximum plastic deformation, and the associated data collection, which could be achieved within the test area. Selecting the correct degree of pre-deformation in the support region made it possible to increase the strain in the gauge section of the sample from ∼1% to about ∼11% without the need to build up the arms or reduce the thickness of the test area.

Microstructure evolution of stainless steel subjected to biaxial load path changes: In-situ neutron diffraction and multi-scale modeling

The lattice strain and intensity evolution obtained from in-situ neutron diffraction experiments of 316L cruciform samples subjected to 45° and 90° load path changes are presented and predicted using the multi-scale modeling approach proposed in Upadhyay et al., IJP 108 (2018) 144-168. At the macroscale, the multi-scale approach uses the implementation of the viscoplastic self-consistent polycrystalline model as a user-material into ABAQUS finite element framework to predict the non-linearly coupled gauge stresses of the cruciform geometry. The predicted gauge stresses are then used to drive the elasto-viscoplastic fast Fourier transform polycrystalline model to predict the lattice strain and intensity evolutions. Both models use the same dislocation density based hardening law suitable for load path changes. The predicted lattice strain and intensity evolutions match well with the experimental measurements for all reflections studied. The simulation results are analyzed in detail to understand the role of elastic anisotropy, plastic slip, grain neighborhood interactions and cruciform geometry on the microstructural evolution during biaxial load path changes.

In situ tension-tension strain path changes of cold-rolled Mg AZ31B

The mechanical behavior of cold-rolled Mg AZ31B is studied during in-plane multiaxial loading and tension-tension strain path changes performed on cruciform samples using in situ neutron diffraction and EBSD. The results are compared with uniaxial tension loading of dogbone-shaped samples measured with in situ neutron diffraction and acoustic emission. The activity of slip and twinning mechanisms and the active twin variants are discussed for the different strain paths. It is shown that initial strains of 4–5% cause a strengthened yield stress during reload for strain path change angles of 90 and 135°. The strengthening is primarily due to dislocation accumulation during the initial load impeding dislocation motion during the reload. The twinning observed during the prestrain activates complex multivariant secondary twinning which may also contribute to the strengthening in the reload.

Mechanical response of stainless steel subjected to biaxial load path changes: Cruciform experiments and multi-scale modeling

We propose a multi-scale modeling approach that can simulate the microstructural and mechanical behavior of metal/alloy parts with complex geometries subjected to multi-axial load path changes. The model is used to understand the biaxial load path change behavior of 316L stainless steel cruciform samples. At the macroscale, a finite element approach is used to simulate the cruciform geometry and numerically predict the gauge stresses, which are difficult to obtain analytically. At each material point in the finite element mesh, the anisotropic viscoplastic self-consistent model is used to simulate the role of texture evolution on the mechanical response. At the single crystal level, a dislocation density based hardening law that appropriately captures the role of multi-axial load path changes on slip activity is used. The combined approach is experimentally validated using cruciform samples subjected to uniaxial load and unload followed by different biaxial reloads in the angular range [27°,90°]. Polycrystalline yield surfaces before and after load path changes are generated using the full-field elasto-viscoplastic fast Fourier transform model to study the influence of the deformation history and reloading direction on the mechanical response, including the Bauschinger effect, of these cruciform samples. Results reveal that the Bauschinger effect is strongly dependent on the first loading direction and strain, intergranular and macroscopic residual stresses after first load, and the reloading angle. The microstructural origins of the mechanical response are discussed.

On the identification of an effective cross section for a cruciform specimen

AbstractBiaxial tensile testing of sheet metals is becoming increasingly popular for sheet metal forming. Determining equivalent stresses in biaxial tensile specimens is more complicated than in conventional uniaxial tensile specimens. In the present study, we compare four different approaches to calculate effective stresses during biaxial tensile loading of a cruciform specimen: (a) partial unloading method, where stresses are determined based on force–strain curves; (b) identification with uniaxial tensile testing; (c) an analysis of equivalent biaxial tests; and (d) numerical simulations. Considering experimental results for an AA1050 aluminium alloy and for a low‐carbon steel DC06, we show that, for the cruciform sample studied here, two methods do not yield physically reasonable results: The uniaxial approach does not properly take into account the effect of transverse loading, and the equivalent biaxial approach exhibits uncertainties in strain measurement data. The most comprehensible approach is the numerical method, because it also yields detailed information about the local stress and strain states. The numerical results are in excellent agreement with the partial unloading method in terms of the initial flow stress and of effective stress–strain curves for strains up to 0.02, with both methods predicting a similar effective cross section of 18.0 mm2 for the considered specimen.

Formability analysis of sheet metals by cruciform testing

Cruciform biaxial tests are increasingly becoming popular for testing the formability of sheet metals as they achieve frictionless, in-plane, multi-axial stress states with a single sample geometry. However, premature fracture of the samples during testing prevents large strain deformation necessary for the formability analysis. In this work, we introduce a miniature cruciform sample design (few mm test region) and a test setup to achieve centre fracture and large uniform strains. With its excellent surface finish and optimized geometry, the sample deforms with diagonal strain bands intersecting at the test region. These bands prevent local necking and concentrate the strains at the sample centre. Imaging and strain analysis during testing confirm the uniform strain distributions and the centre fracture are possible for various strain paths ranging from plane-strain to equibiaxial tension. Moreover, the sample deforms without deviating from the predetermined strain ratio at all test conditions, allowing formability analysis under large strains. We demonstrate these features of the cruciform test for three sample materials: Aluminium 6061-T6 alloy, DC-04 steel and Magnesium AZ31 alloy, and investigate their formability at both the millimetre scale and the microstructure scale.

Stresses and Strains in Cruciform Samples Deformed in Tension

The stress and strain relationship in the gauge region of six cruciform geometries is studied: the ISO standard geometry with slits in arms, two geometries with thinned gauge areas, two geometries with thinned gauge areas and slits in arms, and one modified ISO standard geometry with slits in arms and a thinned gauge area. For all the geometries, finite element simulations are performed under uniaxial loading to compare the plastic strain, the von Mises stress distribution and the in-plane stress evolution. Results show that less plastic strain can be achieved in the gauge of the two ISO standard geometries. For the remaining cruciform geometries, a strong non-linear coupling between applied forces in arms and gauge stresses is generated. The evolution of this non-linear coupling depends on the geometry type, applied biaxial load ratio and the elastic-plastic properties of the material. Geometry selection criteria are proposed to reduce this non-linear coupling.

Failure analysis of plain woven glass/epoxy laminates: Comparison of off-axis and biaxial tension loadings

An experimental study was focused on investigation of the failure properties of plain woven glass/epoxy composites under off-axis and biaxial tension loading conditions. Four fibre orientations (0°, 15°, 30° and 45° with respect to the load direction) were considered for off-axis tests and two biaxial load ratios for biaxial tests to study failure characteristics and mechanism. Four classical polynomial failure criteria - Tsai-Hill, Hoffman, Tsai-Wu and Yeh-Stratton - were analysed comparatively to predict off-axis and biaxial failure strength of the composites. For failure prediction of the plain woven composites under multiaxial tension loads, the Tsai-Wu criterion was modified by introducing an interaction coefficient F12 obtained from 45° off-axis or biaxial tension tests and the Yeh-Stratton criterion was modified with the interaction coefficient B12 = 0 or obtained from the biaxial tension test. The former criterion was found to have higher accuracy. Finally, according to macroscopic and microscopic studies, the failed specimens showed mostly distinct failure with a specific fracture orientation, mainly exhibiting fibre or fabric tensile fracture mode and a combination of matrix cracking and delamination, both in off-axis and cruciform samples.

Adam Creuziger Shares New Insights into Cruciform Sample Design

Adam Creuziger Shares New Insights into Cruciform Sample Design