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Hertzian contact of a rigid sphere and a highly deformable soft solid is investigated using integrated photoelasticity. The experiments are performed by pressing a styrene sphere of 15 mm diameter against a 44 x 44 x 47 mm$^3$ cuboid made of 5% wt. gelatin, inside a circular polariscope, and with a range of forces. The emerging light rays are processed by considering that the retardation of each ray carries the cumulative effect of traversing the contact-induced axisymmetric stress field. Then, assuming Hertzian theory is valid, the retardation is analytically calculated for each ray and compared to the experimental one. Furthermore, a finite element model of the process introduces the effect of finite displacements and strains. Beyond the qualitative comparison of the retardation fields, the experimental, theoretical, and numerical results are quantitatively compared in terms of the maximum equivalent stress, surface displacement, and contact radius dimensions. A favorable agreement is found at lower force levels, where the assumptions of Hertz theory hold, whereas deviations are observed at higher force levels. A major discovery of this work is that at the maximum equivalent stress location, all three components of principal stress can be determined experimentally, and show satisfactory agreement with theoretical and numerical ones in our measurement range. This provides valuable insight into Hertzian contact problems since the maximum equivalent stress controls the initiation of plastic deformation or failure. The measured displacement and contact radii also reasonably agree with the theoretical and numerical ones. Finally, the limitations that arise due to the linearization of this problem are explored.

Elastic waves are generated and propagate when a material undergoes plastic deformation and can be detected by acoustic emission (AE). In this work, AE measurements are obtained during a uniaxial tension (UT) test using a custom-made sensor employing piezoelectric crystals. The UT tests are performed on an MTS machine with two AE sensors clamped on each end of the specimen gage section. A low pass Butterworth filter is designed to attenuate the high frequency noise from the AE signals. Also, full-field strain measurements on the specimen surface are acquired using the 2-D digital image correlation (DIC) method. A typical result from a UT test reveals, as the plastic deformation increases, the AE signals from each sensor increase until they reach a maximum value followed by a drop of signal until the specimen fractures. It is found through interrogation of the DIC images that the maximum amplitude from the AE signals corresponds to the early onset of localized necking. The goal of this work is to implement the UT findings in an actual forming process (e.g., cup drawing) and monitor the event in real time using closed loop control to achieve improved formability.

The purpose of this research is to understand the effect of process parameters in multi-pass, mandrel-free, room-temperature tube-spinning, and in particular the role of axial feed-rate on the shape and thickness change when producing a hemisphere. This is tackled with a combination of experiments and analysis. The material of this study is heat-treated, commercially-pure aluminum (AA1070) tubes of 100 mm diameter. To produce the hemisphere, seven linear passes are selected. The spinning experiments are conducted for two tube thicknesses (2 mm and 3 mm) under three different axial feed-rates (2, 5, and 7.5 mm/rev.) and identical radial feed-rate (5 mm/pass). It is found that decreasing the axial feed-rate generates less spatial variation in the final thickness, while also making the process slower. During every experiment, the tube wrinkles axially. The experiments are interrupted after different spinning passes, and the shape and thickness are measured. Three different finite element models are described, using axisymmetric, shell and solid elements, respectively. Comparing them to the experiments shows that the computationally-efficient axisymmetric model gives reasonable shape and thickness predictions. The shell element model tends to overpredict the shape and thickness evolution during spinning, while being about 250 times slower. Finally, the solid element model provides good agreement with the experiments across the board, while being only 2 times slower than the shell element one. Hence it is recommended for industrial practice to use the axisymmetric model for preliminary process design (i.e., selection of toolpath and process parameters) and then to refine these selections with the solid element model.

Buckling of a column under pre-load restraint has been found to differ from the conventional bifurcation problems and thus requires better understanding. To this end, a simple model consisting of two collinear rigid bars connected by a rotational spring, resting on a smooth surface, loaded by an axial force and restrained by a constant force at the common joint is investigated. The energy method is adopted to establish the equilibrium and stability conditions. The post-buckling response of the simple system indicates that the load-restrained buckling problem is a snap-through problem. The minimum possible buckling force and the buckling force based on the Maxwell construction are found to increase with the restraining force, and can be approximated by power-law functions. It is further shown that an energy barrier exists for the snap-through to occur and the buckling force depends on the perturbation energy. Sensitivity of this system to initial geometric imperfections is also investigated, and an energy barrier is also found to exist for the buckling of systems with imperfection amplitudes smaller than a certain critical value. The characteristic imperfection amplitude depends on the restraining force and, interestingly, transforms the snap-through problem into an eigenvalue problem identical to the conventional one, i.e., the one without imperfection and restraining force.

This paper revisits proportional and non-proportional experiments performed earlier by the authors, with the aim to establish the fracture envelope of the material. The experiments involved inflation of thin-walled AA6260-T4 tubes under axial force and internal pressure. By controlling the force/pressure ratio during the experiments, proportional (i.e., radial) and non-proportional (i.e., corner) loading paths were generated. These experiments are reviewed here. Since fracture is of interest, a computationally-efficient finite element model with solid element discretization around the anticipated fracture location and shell elements in the rest of the tube is described. The Yld2000-2D and Yld2004-3D yield criteria are calibrated and implemented in the simulations. In concert with earlier findings, these criteria are found to offer significantly better agreement with the experiments than von Mises. In particular, the local normals to the yield locus show discrepancies under 3°, while 8°–12° are typical for von Mises. This has significant impact in the prediction of the induced strain paths. The fidelity of the modeling framework is established by comparing the predictions of average stress-strain responses, as well as post-mortem local surface strains, to experiments. Then, the finite element models are used to establish the fracture locus of the material, under proportional loading. The fracture strains are found to increase monotonically as the triaxiality approaches zero from above, i.e., no spike is found at triaxiality of 1/3. The fracture strains also increase at higher triaxialities. The presence of the radial stress shifts that spike from triaxiality of 2/3 (equibiaxial tension) to lower values. By superposing the non-proportional results, it is found that the fracture locus is path-dependent.

Continuous-bending-under-tension (CBT) has been conceived as a mechanical test or a forming process imparting cyclic bending during stretching of a metallic sheet or strip in order to increase its elongation to fracture (ETF) relative to simple tension (ST). In a recent work, over five times improved ETF by CBT over ST has been reported for a dual-phase (DP) steel DP 1180. This paper evaluates the behavior in CBT of three additional automotive advanced high strength steels (AHSS), DP 590, DP 780, and DP 980. In doing so, the process parameter space defined in terms of crosshead velocity applying the tensile force, and roller depth imposing the amount of bending to the specimen has been explored to maximize the ETF of these materials. The studied steel sheets had different thicknesses, in addition to intrinsically containing different fractions of ferrite and martensite phases. After establishing the optimal process parameters, significant improvements in ETF are achieved for all studied steels. Based on comprehensive data, it is found that lower martensitic content moderately improves ETF, while increasing of the sheet thickness rapidly deteriorates ETF, under CBT. The behavior in tension of sheets that were subjected to CBT processing under the established optimal process condition is investigated to determine enhancement in strength and any residual ductility of the materials. In addition to testing, a combination of electron microscopy along with electron-backscattered diffraction and neutron diffraction is employed in order to assess the initial microstructure, evolution of crystallographic texture, and fracture mechanisms for the studied steels. Texture evolution in CBT forms a more pronounced {011} fiber along the stretching direction than in ST, revealing that the deformation in CBT could extend to greater strain levels than those reached at the fracture location in ST. Fractured surfaces after CBT are found to consist of fine ductile dimples, while those after ST consist of coarser dimples and some content of brittle flat martensitic regions.

The use of abrasive waterjets (AWJ) to machine metal surfaces is prevalent through-out industry. AWJ requires the purchase and disposal of costly abrasive particles which increases manufacturing costs and environmental-footprint. This motivates the exploration for low-cost, eco-friendly alternatives. A novel method which utilizes a stream of high-speed water droplets (WD) travelling through a sub-atmospheric pressure environment to remove material without using abrasive grit is presented. In this paper, the efficacy of this new process is investigated and compared to AWJ and pure water jet (WJ) (i.e., without abrasive particles) by measuring the material removal rates (MRR) of each process on a hard-to-machine steel, DP 1180, for equivalent water-flow conditions. Trench profiles are created by traversing each of the jets across a metal sample, from which the MRR and trench profiles are obtained. The MRR results reveal that WD is significantly faster than WJ, but is subordinate compared to AWJ for MRR efficiency. This identifies a trade-off between manufacturing cost and time.

Flange wrinkling is often seen in deep-drawing process when the applied blankholding force is too small. This paper investigates the plastic wrinkling of the flange under a constant blankholding force. The strain and stress state in the flange are first established and a plastic wrinkling reduced-order model is then proposed using energy method. The reduced-order model is implemented to predict the flange wrinkling of AA1100-O sheet by incrementally updating the flange ratio and other material parameters along the drawing process. A finite element model is developed in ABAQUS/standard to verify the results from the reduced-order model. The predicted punch displacements and wave numbers at the onset of wrinkling agree well with the simulated results for different blankholding forces, which demonstrates the accuracy of the reduced-order model and its potential application in fast prediction of wrinkling in deep-drawing process.

Integrated photoelasticity is investigated for a soft material subjected to a three-dimensional stress state. In the experiment, a solid sphere is pressed against a gelatin gel (Young's modulus is about 4.2 kPa) that deforms up to 4.5 mm depending on the loading forces. The resulting photoelastic parameters (phase retardation, azimuthal angle, and stress-optic coefficient) in the gel are measured using a polarization camera. The measured retardation and azimuth are compared with the analytical prediction based on Hertzian contact theory. Remarkably, experimental and analytical results of the photoelastic parameters show a reasonable agreement not only in the retardation but also in the azimuth that is related to the direction of principal stresses and but rarely validated in previous studies, is essential for reconstructing three-dimensional stress fields in soft materials. The stress-optic coefficient of the gelatin gel used is 3.12$\times10^{-8}$ 1/Pa. Such findings proved that integrated photoelasticity is useful for measuring the three-dimensional stress field in soft materials, which is of importance in biomedical engineering and cell printing applications., Comment: 15 pages, 13 figures

The shear resistance of 3D printed periodic auxetic chiral mechanical metamaterial was quantified via a picture-frame apparatus. The experimental set-up allowed the accurate measurement of the effective shear modulus of the material. Also, a rigid-rod-rotational spring model shows that the effective shear modulus of the material is directly related to the chiral geometry and the rotational rigidity of the center joints and the corner joints in the chiral cell. To facilitate practical design, design guidelines were developed through an integrated analytical, numerical and experimental approach. The influences of the chiral geometry and the joint rigidity on the shear resistance of the periodic auxetic chiral mechanical metamaterial were quantified. The design guidelines were verified by systematic finite element (FE) simulations.

This paper reports a robust shape interpolation procedure for constructing a voxel-based model from a set of parallel 2D sections. The procedure is based on a morphing technique and is applicable to compact shapes of grains that appear in at least two consecutive sections. It relies on a set of images of the same resolution and containing the same sets of colors that correspond to different phases of the given volume. In addition to a simple demo example, we successfully apply the procedure to reconstruct the volumetric grain structure morphology of a thin Al-Mg oligocrystal specimen from two electron-back-scatter-diffraction scans of two parallel faces. For verification purposes the same physical specimen was machined down and two interior sections, parallel to the faces, were scanned. A good matching between reconstructed and actual grain structures at these two sections is observed. As a further illustration, the 3D shapes of several grains are extracted and shown. A demonstration of reconstruction from multiple sections using a dual-phase, martensite-ferrite representative volume element is also given. Finally, a quantitative analysis of false-positive results, as well as a way to decide the applicability of this method for grain reconstruction for a given material are described.

This paper presents an experimental setup for continuous-bending-under-tension (CBT) of thin strips and sheets, aimed at the investigation of the observed elongation-to-fracture (ETF) enhancements under such conditions. In particular, the kinematics of the process are described and correlated with the evolution of axial force measured during testing. The main results of the effect of process parameters, such as crosshead velocity and bending depth, on the ETF and the reduction of axial force are presented for the aluminum alloy AA6022-T4. The force vs. displacement response is not found to be a strong function of the crosshead velocity, which is explained by the near rate-independence of the material in the strain-rate range that occurs in CBT. Similarly, ETF does not show a clear dependence on the bending depth or the crosshead velocity. On the other hand, the axial force decreases linearly with the bending depth and slightly increases with the velocity. From the detailed analysis, the optimal parameters for enhancing ductility of AA6022-T4 under CBT are 1.2 mm/s for crosshead velocity and 2.0 for normalized bending depth. Under these conditions, a significant finding is that the strain level achieved throughout the CBT specimen is comparable to that in the necked region of a specimen tested to rupture in uniaxial tension.

The transient force exerted by a low-speed liquid droplet impinging onto a flat rigid surface is investigated experimentally. The measurements employ a high-sensitivity piezo-electric sensor, along with a high-speed camera, and cover four decades in droplet Reynolds number and greater than two decades in Weber number. Across these ranges, the peak of individual force profiles span from 3 mN to over 1300 mN. Once normalised, the force–time profiles support the existence of an inertially dominated self-similar regime. Within this regime, previous numerical and theoretical studies predict a $\sqrt{t}$ dependence of impact normal force during the initial pre-peak rise. While our measurements confirm this finding, they also indicate that, after the peak force the profiles exhibit an exponential decay. This long-time decay law suggests treatment of the momentum transport from the droplet using a lumped model. An observed linear dependence between the force and force decay rate supports this approach. The reason for the efficacy of treating this system via a lumped model apparently connects to the physics right at the surface that limit the rate of momentum transport from the droplet to the surface. This is explored by estimating the momentum transfer by solely using the deforming droplet shape, but under the condition of negligible momentum gradients within the droplet. The short- and long-time solutions are combined and the resulting model equation is shown to accurately cover the entire force–time profile.

The plastic anisotropy and ductile fracture behavior of an Al–Si–Mg die-cast alloy (AA365-T7, or Aural-2) is probed using a combination of experiments and analysis. The plastic anisotropy is assessed using uniaxial tension, plane-strain tension and disc compression experiments, which are then used to calibrate the Yld2004-3D anisotropic yield criterion. The fracture behavior is investigated using notched tension, central hole and shear specimens, with the latter employing a geometry that was custom-designed for this material. Digital image correlation is used to assess the full strain fields for these experiments. However, fracture is expected to initiate at the through-thickness mid-plane of the specimens and thus it cannot be measured directly from experiments. Instead, the stresses and strains at the onset of fracture are estimated using finite element modeling. The loading path and the resulting fracture locus were found to be sensitive to the yield criterion employed, which underscores the importance of an adequate modeling of plastic anisotropy in ductile fracture studies. Based on the finite element modeling, the fracture locus is represented with three common criteria (Oyane, Johnson–Cook and Hosford–Coulomb), as well as a newly proposed one as the linear combination of the first two. However, beyond that, it is still questionable if all of these experiments are probing the same fracture locus, since the predicted loading paths of notched tension specimens are highly evolving compared to those of central hole and shear ones.

The anisotropic plastic flow and ductile fracture of AA6013 aluminum sheet is investigated under quasistatic conditions. The plasticity of the material is probed through uniaxial tension, plane-strain tension and disk-compression experiments, from which the Yld2004-18p non-quadratic 3D anisotropic yield criterion and the combined Swift-Voce hardening model are calibrated. The ductile fracture is characterized with two notched-tension (different notch radii), one center-hole tension and one shear experiment. These experiments cover a wide range of stress triaxialities, while requiring only a universal testing machine to be conducted. Digital Image Correlation is used throughout the experiments to assess the surface strain fields. The predictions of three plasticity models, i.e., von-Mises and Yld2004-18p with constant and with evolving exponents and the corresponding Swift-Voce curves, are compared to the measured force–displacement curves and surface strain histories. These models are then used to probe the stresses, strains, stress triaxiality and Lode angle parameter throughout the loading to fracture. It was found that this hybrid experimental-numerical approach for the fracture strain determination is very sensitive to the constitutive model adopted. As an independent assessment, a microstructure-based estimation of the fracture strains is described. This verified that the von–Mises yield criterion for this AA6013 aluminum sheet provides erroneous estimates of the fracture strains. The most suitable constitutive model is the Yld2004-18p with evolving exponent. Based on these results, the fracture loci are represented by the Oyane, Johnson–Cook and Hosford–Coulomb models.

The plastic flow and anisotropy of a low-carbon steel (AISI 1018) across a range of strain-rates is probed using compression experiments. Material models are then calibrated from these results. The strain-rates examined were 10−3 /s, 1 /s and 3.5 × 103 /s. It was found that the strain-hardening behavior is similar between the 10−3 /s and 1 /s families of experiments, with the latter showing a higher flow stress, as expected. However, the 3.5 × 103 /s experiments show not only an even higher flow stress, but a different strain-hardening behavior as well: they exhibit almost perfect plasticity, due to deformation-induced thermal-softening at larger strains. Comparing experiments in 3 mutually perpendicular directions, some mild plastic anisotropy was discovered. The initial yield and plastic flow of the material in 2 of these directions is comparable, and higher than in the 3rd one. It was also found that the plastic anisotropy evolves differently between the three directions, and also non-linearly with the strain-rate. These results were used to calibrate 3 versions of the Johnson–Cook (J–C) material model (original and 2 modified). The J–C modifications involve strain-rate-dependent model coefficients and exponents, as well as modified functional dependencies of the flow stress on the strain-rate and yield the best agreement with the experiments across the 6 orders of magnitude variation of the strain-rate. Assuming symmetry in tension and compression, and pressure-independence of yield, the plastic anisotropy was represented using the Hill 1948 yield criterion and 2 versions of the Karafillis–Boyce (K–B) one. The calibrations were performed at 5 levels of reference true strain: 0.075, 0.1, 0.15, 0.2, 0.25. For the material and experiments in this work, the Hill criterion provides good representation of anisotropy in the stress space. To capture the evolving plastic anisotropy, the parameters of the Hill criterion were evolved with plastic strain. Despite this, the criterion failed to provide accurate descriptions of the shape of the deformed specimens. In contrast, the performance of the 2 versions of K–B is significantly better, which would justify the higher effort required for calibration.

Aluminum (Al) alloys play a critical role for the transportation applications where weight reduction is a key aspect; however, the poor formability at room temperature limits their application for complex components. An innovative methodology to overcome this limitation is based on subjecting the material to a local, short-term heat treatment before stamping, to obtain a tailored distribution of properties. In addition, Continuous-Bending-under-Tension uses the action of three rollers to remarkably increase the total elongation to failure. In the present work, the combination of the two approaches is investigated to improve the formability at room temperature of a strain-hardenable 5xxx Al alloy, AA5754-H32. Specimens were subjected to both CBT and pre-forming heat treatments, and force-displacement curves were compared to evaluate the formability improvements.

In this work, the plastic anisotropy of AA6022-T4 in hole-expansion is investigated focusing on prestraining effect, and its numerical solution is predicted by Homogeneous Anisotropic Hardening (HAH) model combined with an anisotropic yield function. For the prestraining, the material is subjected to a prestrain of 8% in uniaxial tension in the RD. Then, hole-expansion is conducted in a fully instrumented hydraulic press with a flat-headed punch. In both experiments, Digital Image Correlation (DIC) is used, to confirm the prevalence of uniaxial loading in the prestraining step and to measure thickness strain in the hole-expansion. The results show that the plastic anisotropy is manifested as a non-axisymmetric strain distribution around the hole. The prestraining, leading to non-proportional loading, changes the location of failure from ~45° to RD. The simulation shows the current version of HAH model is limited in capturing the thickness contours and the failure location.

This paper is concerned with the design of a new cruciform-like specimen to measure plastic flow under combined tension and shear loading conditions. An AA6013-T4 aluminum sheet is used as example material. The specimen design borrows from the “smiley” shear specimen, which is commonly used for the simple shear experiment, but has four arms, as a cruciform specimen: two arms are used to induce shearing, while the other two induce tension. The details of the geometry are determined by FEA to promote stress uniformity in the gage-section under combined loading conditions with the force ratio of 1 to 1. Parametric studies are conducted to determine the final design in terms of notch shape, gage-length, gage-width and offset of the notch. The dimensions of the final design are suggested with good uniformity in stress distribution along the gage-length.

In this paper, results for SS316 L microtube experiments under combined inflation and axial loading for single and multiloading segment deformation paths are presented along with a plasticity model to predict the associated stress and strain paths. The microtube inflation/tension machine, utilized for these experiments, creates biaxial stress states by applying axial tension or compression and internal pressure simultaneously. Two types of loading paths are considered in this paper, proportional (where a single loading path with a given axial:hoop stress ratio is followed) and corner (where an initial pure loading segment, i.e., axial or hoop, is followed by a secondary loading segment in the transverse direction, i.e., either hoop or axial, respectively). The experiments are designed to produce the same final strain state under different deformation paths, resulting in different final stress states. This difference in stress state can affect the material properties of the final part, which can be varied for the intended application, e.g., biomedical hardware, while maintaining the desired geometry. The experiments are replicated in a reasonable way by a material model that combines the Hill 1948 anisotropic yield function and the Hockett–Sherby hardening law. Discussion of the grain size effects during microforming impacting the ability to achieve consistent deformation path results is included.

The temperature-dependent work-hardening of AA6061-T6 aluminum alloy is investigated using a combined experimental-numerical approach. Uniaxial tension experiments are performed from room temperature to 500°C, and the force-displacement curves up to fracture are established. Both the yield strength and the work-hardening rate of the material decrease with increasing temperature. Despite the marked increase in the elongation-to-fracture, the uniform elongation remains limited, indicating the early appearance of diffuse necking in the elevated temperature tests. A simplified technique for identifying the work-hardening curves at elevated temperatures and beyond the limit of uniform deformation in uniaxial tension is proposed. The technique uses an isothermal, rate-dependent, finite element (FE) model of the experiments. The post-necking hardening curve is represented by a hybrid Swift/Voce hardening law combined with a form of Johnson-Cook strain-rate dependence. To identify the material model parameters at each temperature, an objective function that correlates the experimental and FE-predicted force-displacement curves is constructed and minimized. These model parameters are then fit with Fourier series across the temperature range considered here, providing smooth functions suitable for subsequent implementation in FE analyses of forming and structural problems. As an illustration, it is shown that a FE model utilizing these material parameters reproduces the full-field features of the elevated temperature experiments very well.

Manufacturers invested in a diverse array of industries, ranging from automotive to biomedical, are seeking methods to improve material processing in an effort to decrease costs and increase efficiency. Many parts produced by these suppliers require forming operations during their fabrication. Forming processes are innately complex and involve a multitude of parameters affecting the final part in several ways. Examples of these parameters include temperature, strain rate, deformation path, and friction. These parameters influence the final part geometry, strength, surface finish, etc. Previous studies have shown that varying the deformation path during forming can lead to increased formability. However, a fundamental understanding of how to control these paths to optimize the process has yet to be determined. Adding to the complexity, as the forming process is scaled down for micromanufacturing, additional parameters, such as grain size and microstructure transformations, must be considered. In this paper, an analytical model is proposed to calculate strain-paths with one or two loading segments and their associated stress-paths. The model is created for investigations of stainless steel 316L using a microtube inflation/tension testing machine. This machine allows for the implementation of two-segment strain-paths through biaxial loading consisting of applied force and internal pressure. The model can be adjusted, based on the desired forming process or available equipment, to output the appropriate parameters for implementation, such as force, displacement, and pressure.

The plasticity and formability of a commercially-pure aluminum sheet (AA1100-O) is assessed by experiments and analyses. Plastic anisotropy of this material is characterized by uniaxial and plane-strain tension along with disk compression experiments, and is found to be non-negligible (e.g., the r-values vary between 0.445 and 1.18). On the other hand, the strain-rate sensitivity of the material is negligible at quasistatic rates. These results are used to calibrate constitutive models, i.e., the Yld2000-2d anisotropic yield criterion as the plastic potential and the Voce isotropic hardening law. Marciniak-type experiments on a fully-instrumented hydraulic press are performed to determine the Forming Limit Curve of this material. Stereo-type Digital Image Correlation is used, which confirms the proportional strain paths induced during stretching. From these experiments, limit strains, i.e., the onset of necking, are determined by the method proposed by ISO, as well as two methods based on the second derivative. To identify the exact instant of necking, a criterion based on a statistical analysis of the noise that the strain signals have during uniform deformation versus the systematic deviations that necking induces is proposed. Finite element simulation for the Marciniak-type experiment is conducted and the results show good agreement with the experiment.

The surface-normal impingement of a liquid jet emanating from a nozzle is of use in numerous technological applications (e.g., surface cleaning, waterjet cutting, and needle-free injection). Upon impact, the (Rayleigh) jet is characterized as either a steady-state (time-invariant) jet, a wavy jet, or a droplet train. The present study experimentally investigates the force imparted by these three distinctly different processes for identical nozzle flow conditions (i.e., velocity and jet diameter). Force models are developed based on Rayleigh jet theory, and they are shown to compare well with the measurements. The force induced by the wavy jet is sinusoidal, oscillating about the steady-state force, while the droplet train force is discrete with periods of zero induced force. Due to conservation of momentum, the peak force experienced by the droplet train is significantly higher than that of the steady stream. This identifies the droplet train as the dominant process to obtain higher peak forces than the continuous stream counterparts during impact with a surface. This can then be used as a means to increase the performance of applications such as waterjet cutting and surface cleaning.

A new nano-graphite water-based lubricant, named DN, is presented in this paper. This new lubricant is contrasted with a water-based micro-graphite lubricant, named D1, and a traditional graphite lubricant which has been used in actual forming, named D0. The comparison is done by means of two different friction test methods to assess the friction coefficients and the lubrication effects at warm forming temperatures. Also, a typical automobile steering flange part is chosen for warm extrusion. Both numerical simulation tests and actual forming tests are conducted in order to study the actual friction and lubrication effects of the three test lubricants. Then, the practical applications of the lubricants are studied through the SEM observation of the surface morphology of the formed parts. The test results show that the friction coefficient of the new water-based nano-graphite lubricant is 20% lower than the ordinary lubricant D0, and the friction and lubrication effects are better than that of the micro-graphite lubricant D1. It also shows the excellent lubrication performance during the warm extrusion processing of the test flange part.

The strength differential effect (SDE), i.e., the difference between the flow stress of uniaxial tension and compression, of a dual-phase steel sheet with a tensile strength of 980 MPa (DP980) was measured using an in-plane uniaxial tension–compression test apparatus for sheet metals. The SDE data were obtained for a logarithmic total strain range of 0 ≤ | e | ≤ 0.086 in both the rolling (RD) and transverse (TD) directions of the test material. It was observed that the magnitude of the compressive flow stress, σ C , was consistently higher than that of the tensile flow stress, σ T , for a strain range of | e | > 0.009 in both the RD and TD; the amount of SDE, defined as σ C − σ T / σ T × 100 (%), at | e | = 0.086 was 5.2% in the RD and 6.2% in the TD. Moreover, in order to validate the SDE, a novel test apparatus for obtaining the pure bending moment M versus curvature κ (i.e., M − κ ) diagram was designed and manufactured. The obtained M − κ curves were consistent with those based on the elastoplastic numerical analysis considering the SDE. Thus, the SDE of the test material is experimentally validated using the pure bending test.

The elastic anisotropy of 5 cold-rolled steel sheets typical of automotive applications is probed experimentally and the results are represented using orthotropic elasticity. The steels have an increasing volume fraction of martensite, ranging from zero to over 90%. This leads to different strength and ductility for each of the 5 steels, with the strongest being 5.8 times so over the weakest, but only 0.11 times as ductile. The elastic properties measured are the Young's modulus and Poisson's ratio at 15° increments from the rolling direction of the sheets. These properties are measured by uniaxial tension and pure-bending experiments, respectively, instrumented with electrical-resistance strain-gages. The recorded responses are repeatable and, well within the limit of elastic deformations, linear. Both properties are found to have orientational dependence. The variation of the Young's modulus is the opposite of that of Poisson's ratio. In addition, the dual-phase (ferritic-martensitic) steels exhibit the opposite trends than the single-phase (purely ferritic) one. These experiments are then compared to the results of orthotropic elasticity. Under plane-stress, this material model depends on 4 material parameters. This simple model represents all of the experiments very well, indicating that the elastic anisotropy stems from the rolling-induced microstructure and, for the dual-phase steels, the presence of the second, reinforcing phase. Furthermore, the model allows the quantification of extension-shear coupling when these orthotropic materials are loaded off-axis to the material orientations. This coupling was found to be limited, so that the off-axis tension tests are indeed close to the uniaxial stress state. One of the material parameters needed is the in-plane shear modulus, which poses challenges in its determination for the present thin sheets. Despite the mild anisotropy found in these materials, assuming the isotropic value for the shear modulus deteriorates the predictions significantly. This work demonstrates that single- and dual-phase steels indeed behave elastically as orthotropic materials, as expected on theoretical grounds based on their pre-processing by rolling. The results of this work can be used to introduce elastic anisotropy in sheet metal forming simulations intending to predict springback, with only a limited number of experiments needed for calibrating the model for a given material.

The response of the dual-phase steel DP 590 under continuous loading and unloading from a biaxial stress state is examined using a combination of experiments and analysis. The experiments utilize cruciform specimens of a custom geometry that develop quite uniform strain fields in the test-section and allow the development of large strains (>12%, depending on the loading path). Experiments along 9 radial stress paths in the first quadrant of the plane-stress space were performed. The first part of each unloading and reloading follows the prediction of orthotropic elasticity using the initial elastic properties. A second linear slope is observed, before the responses become fully non-linear. The non-linear strain recovery is measured to be about 1/5 of the linearly elastic strain for this material. Furthermore, the chord modulus reduces exponentially to a value of ∼90% of the initial. The biaxial cruciform experiments are also used to determine contours of constant plastic work and to calibrate the Yld2000-2D anisotropic yield function. A combined isotropic/kinematic hardening model with a simple exponential-decay shrinkage of the yield surface is adopted. The non-linear unloading response is represented by a 4-term Chaboche non-linear kinematic hardening model using the Ziegler back-stress evolution rule. Plasticity during unloading is assumed to occur as soon as deviation from proportionality is detected. The 4 terms are necessary for capturing both the second linear slope after (re-) yielding and the work-hardening stagnation observed in the experiments. The agreement between experiments and predictions for the induced strain paths is very good. The predictions of the non-linear strain recovery are good overall, and are independent of the yield surface adopted. In summary, it is proposed to capture the biaxial unloading behavior using a constitutive model that includes an anisotropic yield function suitable for predicting the induced strain paths, and a non-linear kinematic hardening rule suitable for predicting the tension–compression behavior of the material at hand.

In this study, an electromagnetic forming process using a uniform pressure actuator is investigated through electro-magnetic-mechanically coupled numerical simulations; a simplified analytical model to predict the forming pressure and shell theory for mechanical deformation; and experimental results, which include Photon Doppler Velocimetry to measure the deformation. Velocity and the final deformed part shape are compared between the numerical, analytical, and experimental methods and reasonably good agreement is demonstrated. However, accurate comparison is affected by the energy level used with the numerical simulations matching better for the lower energy case due to less material draw-in and the analytical model providing more precise results for the higher energy case.

Buckling of structures under lateral load restraint has been found to differ from the conventional bifurcation problems and cannot be handled with conventional analysis. Towards a better understanding of this type of unconventional buckling problems, this work investigates the upheaval buckling of an elastica resting on a smooth surface and restrained by a lateral constant force. Analytical solutions for the Mode-1 and Mode-2 post-buckling responses and configurations of the elastica are established. Stability of the post-buckling configurations under force-control are investigated via the energy method. An energy barrier is found to exist and the buckling load depends on the restraining force and perturbation energy. The imperfection sensitivity of the system is different from the conventional buckling ones, and a characteristic imperfection is found to exist that can transform a snap-through instability into a bifurcation buckling. As a first attempt to address the problem of flange wrinkling under a constant blank-holding force during the cup-drawing process, the fundamental solutions are extended to study the wrinkling of a shrinking elastic annulus under a constant lateral restraining force. The post-wrinkling responses are established and an energy barrier is found to exist for each wrinkling mode. A characteristic imperfection is also found to exist for each mode, which eliminates the energy barrier and enables bifurcation wrinkling. The linear relationship between the critical restraining force that prevents the wrinkling of the elastic annulus and the imperfection amplitude is established, which is also verified by numerical simulations. This study contributes to a better understanding of load-restrained buckling problems and is expected to shed light on the elastoplastic buckling of plates and shells under lateral load restraints in general, and on the wrinkling of a thin sheet during cup-drawing in particular.

The kinetics of Portevin-Le Chatelier (PLC) bands in the hole-expansion of a circular hole using a flat-headed punch are investigated for a solid-solution heat-treated AA7075 aluminum sheet. This experiment is performed under quasi-static strain-rate and at room temperature. The full strain field in the hole periphery during the entire deformation is measured by a stereo-type digital image correlation system. The observations of PLC band activity are based on the thickness strain-rate field. Each individual PLC band appears aligning along the radial direction, spanning diverse stress states, and propagates along the circumferential direction during the life time from nucleation to dissipation. Furthermore, the nucleation sites of all the PLC bands are recorded during the experiment, which shows that the nucleation frequency of a PLC band is influenced by the plastic anisotropy, and that it increases proportionally to the level of thickness strain.

Influence of tempers on the hole-expansion formability of an AA7075 aluminum sheet is investigated for -T6 (as-received) and -W tempers (super saturated by the solution heat treatment followed by water quenching). The hole is prepared by end-milling, to limit the effects of hole preparation on the results and instead highlight the effects of material behavior. A flat-headed punch is used to expand the hole, and digital image correlation captures the strain fields throughout the experiment. The results present that the hole can expand by 70 % more in -W compared to -T6 temper with the lower forming force. In contrast, thickness strain distribution around the hole shows a similar pattern in both tempers except the observation of Portevin-Le Chatelier (PLC) effect in -W temper, which causing the inhomogeneous deformation. In parallel, the numerical simulation of the hole-expansion is performed using a user material subroutine implemented for the elasto-plastic material behavior, including plastic anisotropy, of both tempers. The predictions on the thickness strain variation and average level show good agreement with the experiment for -T6 temper, but less so for -W temper. This is shown to be the effect of PLC bands on the deformation: the material in -T6 temper is mainly governed by plastic anisotropy, but -W temper shows combined effect of plastic anisotropy and PLC bands. Nevertheless, the reasonable predictions of both tempers verify that the numerical framework established in this study can be used for preliminary, computationally-efficient virtual process design with a practical purpose, despite omitting the explicit physics of the PLC effect.

A method for identifying the material hardening curves past the limit of necking in uniaxial tension and across a range of strain-rates and temperatures in a fully-coupled way is proposed. Experiments on microtubes of 304 L stainless steel, which is a rate- and temperature-dependent material, were performed using a custom isothermal testing setup. Digital Image Correlation and Infrared Thermography provided full-field measurements of the strain and temperature during testing. The identification procedure uses a finite element (FE) model of the experiments and the problem is cast as one of mathematical optimization. The corresponding objective function has input parameters that control the post-necking shape of the hardening curves and a scalar output that represents the proximity between the FE predictions of the force-average axial strain response and the experimental data. Since the objective function in not available in closed form and is expensive to evaluate, an efficient optimization procedure that requires a limited number of function evaluations is proposed. The method proposed here is then applied to identifying the post-necking hardening response under different assumptions, starting from a single material curve with no rate and temperature effects included, to a family of curves with both rate and temperature considered in a coupled way. To validate the family of hardening curves identified for 304 L stainless steel, a fully-coupled FE model is used to simulate a conventional tension test. This model is shown to be able to reproduce this experiment, including the strain and temperature fields which develop during testing.

The anisotropic plastic flow and ductile fracture of Al-Si-Mg die-cast aluminum alloy (trade name, Aural2) is investigated using a combination of experiments and analysis. The material is in the form of a 2 mm thick sheet and was received in the –T7 temper. The plasticity of the material is probed using uniaxial tension and plane-strain tension experiments at 3 angles to the material direction, and disc-compression experiments. Good repeatability is obtained in every case. These experiments are used to calibrate the Yld2004-18p anisotropic yield function. This function is flexible enough so that very good fitting of the experiments is obtained. The ductile fracture of the alloy is then probed using notched-tension (with 6 mm and 20 mm notch radii) and central-hole experiments. Each of these specimens is designed so that it provides a different stress triaxiality in the region of rupture, while still requiring only a universal testing machine. Digital Image Correlation is used throughout the experimental work to assess the surface strain fields. However, since the sheet is relatively thick, rupture did not necessarily initiate at the surface. For this reason, fully-3D finite element simulations, using the Yld2004-18p yield function and 3 post-necking hardening models (Swift, Voce and combined) are performed. The surface strains predicted by the simulations depend strongly on the material model adopted. Hence the predicted fracture strains reported here underscore the fact that the plasticity of the material needs to be carefully established before any fracture study is undertaken.

The tension-compression asymmetry (TCA) of a dual phase steel sheet with a tensile strength of 980 MPa is measured using an in-plane uniaxial tension-compression testing apparatus. The TCA data within a logarithmic strain range of 0≤| e |≤ 0.086 are observed both in the rolling and transverse directions of the test material. Moreover, a novel testing apparatus for measuring a pure bending moment-curvature (M-K) diagram is designed and manufactured. The measured M-K curves are consistent with those calculated taking into account the TCA of the stress-strain curve both in the rolling and transverse directions.

Continuous-bending-under-tension (CBT) is a stabilized tension test, whereby a strip is bent around three reciprocating rollers while being loaded remotely with an axial force. This subjects the strip to plastic bending while under tension, and has the beneficial effect of suppressing the instability that, in a conventional tension test, leads to localization of deformation and rupture. CBT experiments were performed on strips extracted from cold-rolled, automotive-grade AA6022-T4 sheet using a custom CBT testing machine. The CBT experiments revealed that the remote axial force necessary to plastically deform the materials was lower than the yield force under uniaxial tension, due to the synergy between tension and plastic bending. Furthermore, the force-displacement curves exhibited a saw-tooth like pattern, which can be explained from the kinematics of the process. A parametric investigation identified the combination of bending depth, crosshead velocity and roller velocity that yielded the maximum elongation-to-fracture. However, the experiments also revealed that the elongation-to-fracture was different between the rolling and transverse directions of the sheet, and significantly more than the uniaxial testing would indicate. The CBT experiments were then simulated using the non-linear finite element code Abaqus. Solid, linear, full-integration elements were used in the simulations, which replicated only half of the strip width, due to the symmetries present. The key for successful simulations is the use of an appropriate material model. Cyclic tension-compression tests on the AA6022-T4 were performed, and the results were captured accurately by a combined isotropic/non-linear kinematic hardening model, using a simple, exponentially-decaying, expansion of the yield surface and a 4-term Chaboche model, respectively. The force-displacement response from the simulations matched the experimental results well. In the future, the simulations will be used to probe the stress and strain development during each CBT cycle, to improve the understanding of the stabilization of deformation that the CBT loading mode provides.

Impacting water droplets are capable of eroding steam turbine blades, high speed aircraft and even serve as a machining operation. In this latter process, high velocity (∼100m/s) water droplets impact a solid surface under conditions in which the ambient air pressure is sub-atmospheric. The physics of this erosion mechanism is not completely understood. To begin to unravel these physics, we present results pertaining to the effects of ambient air pressure on the impact force of low velocity (1m/s) droplets. It is well known that droplet splash is suppressed when the ambient air pressure is reduced. The effects on the associated impact force are, however, unknown. In this article we examine the impact force of 3.5 mm diameter, low velocity droplets in a reduced pressure environment. A 38x38x50 cm vacuum chamber fitted with a unidirectional piezoelectric force sensor to measure the transient force of impacting droplets. Preliminary results in atmospheric air pressure reveal that the impulse of the droplets depends linearly on impact velocity while the average impact force depends quadratically on impact velocity. The results under reduced pressures are compared and discussed relative to the underlying physics.