Novel Technique for Static and Dynamic Shear Testing of Ti6Al4V Sheet

Few shear test techniques exist that cover the range of strain rates from static to dynamic. In this work, a novel specimen geometry is presented that can be used for the characterisation of the shear behaviour of sheet metals over a wide range of strain rates using traditional tensile test devices. The main objectives during the development of the shear specimen have been 1) obtaining a homogeneous stress state with low stress triaxiality in the zone of the specimen subjected to shear and 2) appropriateness for dynamic testing. Additionally, avoiding premature specimen failure due to edge effects was aimed at. Most dimensional and practical constraints arose from the dynamic test in which the specimen is loaded by mechanical waves in a split Hopkinson tensile bar device. Design of the specimen geometry is based on finite element simulations using ABAQUS/Explicit. The behaviour of the specimen is compared with the more commonly used simple shear specimen with clamped grips. Advantages of the new technique are shown. The technique is applied to Ti6Al4V sheet. During the high strain rate experiments high speed photography and digital image correlation are used to obtain the local shear strain in the specimen. Comparison of experimental and numerical results shows good correspondence.     

A New Experimental Technique for the Multi-axial Testing of Advanced High Strength Steel Sheets

This paper deals with the development of a new experimental technique for the multi-axial testing of flat sheets and its application to advanced high strength steels. In close analogy with the traditional tension-torsion test for bulk materials, the sheet material is subject to combined tension and shear loading. Using a custom-made dual actuator hydraulic testing machine, combinations of normal and tangential loading are applied to the boundaries of a flat sheet metal specimen. The specimen shape is optimized to provide uniform stress and strain fields within its gage section. Finite element simulations are carried out to verify the approximate formulas for the shear and normal stress components at the specimen center. The corresponding strain fields are determined from digital image correlation. Two test series are performed on a TRIP-assisted steel sheet. The experimental results demonstrate that this new experimental technique can be used to investigate the large deformation behavior of advanced high strength steel sheets. The evolution of the yield surface of the TRIP700 steel is determined for both radial and non-proportional loading paths.     

Adiabatic shear localization in the dynamic punch test,part II: numerical simulations

The behavior of 1018 steel, 6061-T6 aluminum, and titanium 6%Al–4%V alloy during the dynamic punch test is investigated using the finite element method. Specifically, the possibility and effects of adiabatic shear localization and its role in burr formation are examined, and comparisons to experimental tests in the first part of this two part study are made. A maximum stress criterion involving strain and strain rate hardening and thermal softening is used to determine the occurrence of shear localization in the simulations. It is observed that adiabatic shear localization occurs in the simulations of the titanium alloy. This material exhibits narrow regions of concentrated shear strain during the deformation, and the shear localization criterion is satisfied in these regions. The strain is more widely distributed in the other two metals, and the same criterion is not satisfied. In the calculations of the shear localization criterion it is seen that strain rate hardening has a significant effect when compared to strain hardening and thermal softening. Also, contact between specimen and punch is lost around the center of the punch during operation. This loss of contact is important as it leads to higher stress concentrations at the punch corner and dishing of the blank.     

Comparison of Test Specimens for Characterizing the Dynamic Properties of Rubber

Dynamic material properties inferred via experiment can be strongly influenced by the choice of test specimen geometry unless care is taken to ensure that mechanical fields (stress, strain, etc.) within the specimen adequately reflect the ideal homogeneous deformation state. In this work, finite element models of simple shear, cylindrical compression, simple tension, and bi-conical shear test specimens were analyzed in order to quantify the relative conformity of each specimen to its corresponding ideal. Three metrics of conformity were evaluated, based respectively on the distributions of stress, strain, and strain energy density. The results show that a simple shear specimen provides superior conformity. Other factors involved in the selection of test specimen geometry are also discussed. Such factors include relative linearity and symmetry of measured stress–strain data, grip slip, and heat build up.     

A study of localisation in dual-phase high-strength steels under dynamic loading using digital image correlation and FE analysis

Tensile tests were conducted on dual-phase high-strength steel in a Split-Hopkinson Tension Bar at a strain-rate in the range of 150–600/s and in a servo-hydraulic testing machine at a strain-rate between 10^?3 and 10⁰/s. A novel specimen design was utilized for the Hopkinson bar tests of this sheet material. Digital image correlation was used together with high-speed photography to study strain localisation in the tensile specimens at high rates of strain. By using digital image correlation, it is possible to obtain in-plane displacement and strain fields during non-uniform deformation of the gauge section, and accordingly the strains associated with diffuse and localised necking may be determined. The full-field measurements in high strain-rate tests reveal that strain localisation started even before the maximum load was attained in the specimen. An elasto-viscoplastic constitutive model is used to predict the observed stress–strain behaviour and strain localisation for the dual-phase steel. Numerical simulations of dynamic tensile tests were performed using the non-linear explicit FE code LS-DYNA. Simulations were done with shell (plane stress) and brick elements. Good correlation between experiments and numerical predictions was achieved, in terms of engineering stress–strain behaviour, deformed geometry and strain fields. However, mesh density plays a role in the localisation of deformation in numerical simulations, particularly for the shell element analysis.     

Nonlinear shear behavior and interlaminar shear strength of unidirectional polymer matrix composites: A numerical study

Detailed finite element implementation is presented for a recently developed technique (He et al., 2012) to characterize nonlinear shear stress–strain response and interlaminar shear strength based on short-beam shear test of unidirectional polymeric composites. The material characterization couples iterative three-dimensional finite element modeling for stress calculation with digital image correlation for strain evaluation. Extensive numerical experiments were conducted to examine the dependence of the measured shear behavior on specimen and test configurations. The numerical results demonstrate that consistent results can be achieved for specimens with various span-to-thickness ratios, supporting the accurate material properties for the carbon/epoxy composite under study.     

Numerical validation of the shear compression specimen. Part I: Quasi-static large strain testing

The shear compression specimen (SCS), which is used for large strain testing, is thoroughly investigated numerically using three-dimensional elastoplastic finite element simulations. In this first part of the study we address quasi-static loading. A bi-linear material model is assumed. We investigate the effect of geometrical parameters, such as gage height and root radius, on the stress and strain distribution and concentration. The analyses show that the stresses and strains are reasonably uniform on a typical gage mid-section, and their average values reflect accurately the prescribed material model. We derive accurate correlations between the averaged von Mises stress and strain and the applied experimental load and displacement. These relations depend on the specimen geometry and the material properties. Numerical results are compared to experimental data, and an excellent agreement is observed. This study confirms the potential of the SCS for large strain testing of material.     

Effects of texture on shear band formation in plane strain tension/compression and bending

In this study, effects of typical texture components observed in rolled aluminum alloy sheets on shear band formation in plane strain tension/compression and bending are systematically studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic–viscoplastic continuum slip constitutive relation. First, a simple model analysis in which the shear band is assumed to occur in a weaker thin slice of material is performed. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. Second, the shear band development in plane strain tension/compression is analyzed by the finite element method. Predictability of the finite element analysis is compared to that of the simple model analysis. Third, shear band developments in plane strain pure bending of a sheet specimen with the typical textures are studied. Regions near the surfaces in a bent sheet specimen are approximately subjected to plane strain tension or compression. From this viewpoint, the bendability of a sheet specimen may be evaluated, using the knowledge regarding shear band formation in plane strain tension/compression. To confirm this and to encompass overall deformation of a bent sheet specimen, including shear bands, finite element analyses of plane strain pure bending are carried out, and the predicted shear band formation in bent specimens is compared to that in the tension/compression problem. Finally, the present results are compared to previous related studies, and the efficiency of the present method for materials design in future is discussed.     

A coupled temperature and strain rate dependent yield function for dynamic deformations of bcc metals

A coupled temperature and strain rate microstructure physically based yield function is proposed in this work. It is incorporated along with the Clausius–Duhem inequality and an appropriate free energy definition in a general thermodynamic framework for deriving a three-dimensional kinematical model for thermo-viscoplastic deformations of body centered cubic (bcc) metals. The evolution equations are expressed in terms of the material time derivatives of the elastic strain, accumulated plastic strain (isotropic hardening), and the back stress conjugate tensor (kinematic hardening). The viscoplastic multipliers are obtained using both the Consistency and Perzyna viscoplasticity models. The athermal yield function is employed instead of the static yield function in the case of the Perzyna viscoplasticity model. It is found that the static strain rate value, at which the material shows rate-independent behavior, varies with the material deformation temperature. Computational aspects of the proposed model are addressed through the finite element implementation with an implicit stress integration algorithm. Finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program ABAQUS/Explicit [ABAQUS, 2003. User Manual, Version 6.3. Habbitt, Karlsson and Sorensen Inc., Providence, RI] via the user material subroutine coded as VUMAT. Numerical implementation for a simple compression problem meshed with one element is used to validate the proposed model implementation with applications to tantalum, niobium, and vanadium at low and high strain rates and temperatures. The analysis of a tensile shear banding is also investigated to show the effectiveness and the performance of the proposed framework in describing the strain localizations at high velocity impact. Results show mesh independency as a result of the viscoplastic regularization used in the proposed formulation.     

On neck propagation in amorphous glassy polymers under plane strain tension

Unlike metals, necking in polymers under tension does not lead to further localization of deformation, but to propagation of the neck along the specimen. Finite element analysis is used to numerically study necking and neck propagation in amorphous glassy polymers under plane strain tension during large strain plastic flow. The constitutive model used in the analyses features strain-rate, pressure, and temperature dependent yield, softening immediately after yield and subsequent orientational hardening with further plastic deformation. The latter is associated with distortion of the underlying molecular network structure of the material, and is modelled here by adopting a recently proposed network theory developed for rubber elasticity. Previous studies of necking instabilities have almost invariably employed idealized prismatic specimens; here, we explicitly account for the unavoidable grip sections of test specimens. The effects of initial imperfections, strain softening, orientation hardening, strain-rate as well as of specimen geometry and boundary conditions are discussed. The physical mechanisms for necking and neck propagation, in terms of our constitutive model, are discussed on the basis of a detailed parameter study.     

Anisotropic Hardening of Sheet Metals at Elevated Temperature: Tension-Compressions Test Development and Validation

New test equipment has been developed to measure the in-plane cyclic behavior of sheet metals at elevated temperatures. The tester has clamping dies with adjustable side force to prevent the sheet specimens from buckling during compressive loading. In addition to the room temperature experiment, cartridge type heaters are inserted in the clamping dies so that the specimen can be heated up to 400 °C during the cyclic tests. For the strain measurement, a non-contact type laser extensometer is used. In order to validate the newly developed test device, the tension-compression (and compression-tension) tests under pre-strains and various temperatures have been performed. As model materials, the aluminum alloy sheet which exhibits a large Bauschinger effect and the magnesium alloy sheet which exhibits different amounts of asymmetry under cyclic loading are used. The developed device can be well-suited to measure the cyclic material behavior, especially the anisotropic and asymmetric hardening of light-weight materials.     

Fracture characteristics of a cold-rolled dual-phase steel

In this study, the fracture characteristics of a cold-rolled, low-strength, high-hardening steel sheet (Docol 600DL) under quasi-static loading conditions are established using five different test set-ups. In all the tests, the sheet material is initially in plane-stress states. Optical field measurements with digital image correlation were used to determine the strain fields to fracture, to calibrate the material model for the sheet material and to validate the finite element models of the tests. Based on the field measurements, a novel method for experimental determination of the stress triaxiality and the Lode parameter is presented for isotropic materials and plane-stress states. These parameters were also obtained from finite element simulations. Comparisons show that the two methods give approximately the same average values of the stress triaxiality and the Lode parameter up to fracture. The sheet material displays only moderate variation in ductility as a function of the stress triaxiality and the Lode parameter within the investigated range of these parameters. The most critical through-thickness position in the specimens was found to be in the centre where the strains and the stress triaxiality are highest.     

Effective simulation of flexible lateral boundaries in two- and three-dimensional DEM simulations

Discrete element method （DEM） models to simulate laboratory element tests play an important role in advancing our understanding of the mechanics of granular material response, including bonded or cemented, particulate materials. Comparisons of the macro-scale response observed in a real physical test and a ＂virtual＂ DEM-simulated test can calibrate or validate DEM models. The detailed, particle scale information provided in the DEM simulation can then be used to develop our understanding of the material behaviour. It is important to accurately model the physical test boundary conditions in these DEM simulations. This paper specifically considers triaxial tests as these tests are commonly used in soil mechanics. In a triaxial test, the test specimen of granular material is enclosed within a flexible latex membrane that allows the material to deform freely during testing, while maintaining a specified stress condition. Triaxial tests can only be realistically simulated in 3D DEM codes, however analogue, 2D, biaxial DEM simulations are also often considered as it is easier to visualize particle interactions in two dimensions. This paper describes algorithms to simulate the lateral boundary conditions imposed by the latex membrane used in physical triaxial tests in both 2D and 3D DEM simulations. The importance of carefully considering the lateral boundary conditions in DEM simulations is illustrated by considering a 2D biaxial test on a specimen of frictional unbonded disks and a 3D triaxial test on a bonded （cemented） specimen of spheres. The comparisons indicate that the lateral boundary conditions have a more significant influence on the local, particle-scale response in comparison with the overall macro-scale observations.     

Comparison of the work-hardening of metallic sheets using tensile and shear strain paths

This work deals with the characterization of the kinematic work-hardening of a bake-hardening steel. A shear test device has been designed and its use for the characterization of the work-hardening of sheet metals is described. Two main results are presented. Firstly, a local strain measurement, based on the following of three dots drawn on the gauge area, gives the evolution of the strain tensor eigenvalues during the test. It is shown, by comparing the theoretical kinematics of simple shear with a slightly perturbated one, that the strain state is close to the ideal one in the center of the gauge area. Secondly, reversal of the shear direction is performed after several prestrain and the evolution of the kinematic work-hardening with the equivalent plastic strain has been identified using an anisotropic elasto-viscoplastic model of Hill 1948 type. Isotropic and kinematic contributions of the work-hardening are also calculated from loading–unloading tensile tests and are compared to those obtained from the simple shear tests. The results show a discrepancy between both identification for the isotropic and the kinematic hardening. However, they are in agreement concerning the evolution of the global work-hardening.     

A tension split Hopkinson bar for investigating the dynamic behavior of sheet metals

The dynamic response of sheet metals at high strain rate is investigated with a tensile split Hopkinson bar test using plate type specimens. The tension split Hopkinson bar inevitably causes some errors in the strain at grips with the plate type specimens, since the grip and specimens disturb the one-dimensional wave propagation in bars. To validate the experiment, the level of error induced from the grips is estimated by comparing the waves acquired from experiments with the Pochhammer-Chree solution. The optimum geometry of the specimen is determined to minimize the loading equilibrium error. High strain rate tensile tests are then performed with auto-body sheet metals in order to construct their appropriate constitutive models for use in crash-worthiness evaluation.     

Continuous, large strain, tension/compression testing of sheet material

Modeling sheet metal forming operations requires understanding of the plastic behavior of sheet alloys along non-proportional strain paths. Measurement of hardening under reversed uniaxial loading is of particular interest because of its simplicity of interpretation and its application to material elements drawn over a die radius. However, the compressive strain range attainable with conventional tests of this type is severely limited by buckling. A new method has been developed and optimized employing a simple device, a special specimen geometry, and corrections for friction and off-axis loading. Continuous strain reversal tests have been carried out to compressive strains greater than 0.20 following the guidelines provided for optimizing the test. The breadth of application of the technique has been demonstrated by preliminary tests to reveal the nature of the Bauschinger effect, room-temperature creep, and anelasticity after strain reversals in commercial sheet alloys.     

Effective simulation of flexible lateral boundaries in two-and three-dimensional DEM simulations

Discrete element method (DEM) models to simulate laboratory element tests play an important role in advancing our understanding of the mechanics of granular material response, including bonded or cemented, particulate materials.Comparisons of the macro-scale response observed in a real physical test and a "virtual" DEM-simulated test can calibrate or validate DEM models.The detailed, particle scale information provided in the DEM simulation can then be used to develop our understanding of the material behaviour.It is important to accurately model the physical test boundary conditions in these DEM simulations.This paper specifically considers triaxial tests as these tests are commonly used in soil mechanics.In a triaxial test,the test specimen of granular material is enclosed within a flexible latex membrane that allows the material to deform freely during testing, while maintaining a specified stress condition. Triaxial tests can only be realistically simulated in 3D DEM codes, however analogue,2D, biaxial DEM simulations are also often considered as it is easier to visualize particle interactions in two dimensions. This paper describes algorithms to simulate the lateral boundary conditions imposed by the latex membrane used in physical triaxial tests in both 2D and 3D DEM simulations.The importance of carefully considering the lateral boundary conditions in DEM simulations is illustrated by considering a 2D biaxial test on a specimen of frictional unbonded disks and a 3D triaxial test on a bonded (cemented) specimen of spheres. The comparisons indicate that the lateral boundary conditions have a more significant influence on the local,particle-scale response in comparison with the overall macro-scale observations.     

Quasi-Static and Dynamic Large Strain Shear-Tension Testing

A new shear specimen is designed, evaluated and tested quasi-statically and dynamically. The specimen consists of a long cylinder having a horizontal gauge section created by two diametrically opposed semi-circular slots machined parallel to the longitudinal axis. This geometry imposes a rather uniform stress state, close to pure shear in the gauge section. Quasi-static and dynamic tension-shear tests up to a strain rate of 10⁴ 1/s were carried out on 1020 cold-drawn steel specimens. The obtained stress–strain curves and ductility were validated numerically. The new specimen can be used to study the shear mechanical characteristics of a material using tensile testing.     

A plane stress anisotropic plastic flow theory for orthotropic sheet metals

A phenomenological theory is presented for describing the anisotropic plastic flow of orthotropic polycrystalline aluminum sheet metals under plane stress. The theory uses a stress exponent, a rate-dependent effective flow strength function, and five anisotropic material functions to specify a flow potential, an associated flow rule of plastic strain rates, a flow rule of plastic spin, and an evolution law of isotropic hardening of a sheet metal. Each of the five anisotropic material functions may be represented by a truncated Fourier series based on the orthotropic symmetry of the sheet metal and their Fourier coefficients can be determined using experimental data obtained from uniaxial tension and equal biaxial tension tests. Depending on the number of uniaxial tension tests conducted, three models with various degrees of planar anisotropy are constructed based on the proposed plasticity theory for power-law strain hardening sheet metals. These models are applied successfully to describe the anisotropic plastic flow behavior of 10 commercial aluminum alloy sheet metals reported in the literature.     

Measurement of the Dynamic Bulk and Shear Response of Soft Human Tissues

Traditionally, Kolsky bars are used to study the dynamic response of hard materials in uniaxial compression, tension or torsion. We present modifications to the technique that allow loading of a soft tissue specimen in (a) hydrostatic compression and (b) simple shear. The first modification is designed to determine the pressure vs. volume behavior of each material, and thence to extract a measure of the dynamic compressibility or equivalently of the bulk modulus. The second modification is designed to develop the shear stress versus shear strain behavior for a near-simple shear experiment. The critically important questions of the proper acquisition of human tissue samples and protocols for appropriate experimentation have also been addressed. The experimental techniques and the results are discussed in detail and the results compared to finite element simulations. We present examples of the dynamic response of typical tissue simulants as well as human liver and stomach tissues.