•Plasticity and fracture experiments are performed on AA6013.•The Yld2004-18p yield criterion is calibrated, including an evolving exponent.•The fracture strains are determined by a hybrid ...experimental-numerical approach.•The fracture strains are also estimated based on grain distortion and rotation.•Oyane, Johnson–Cook and Hosford–Coulomb fracture models are calibrated.
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.
•Plasticity and fracture of heat treated aluminum sheet is characterized.•New cruciform specimen is proposed that has proportional loading paths to fracture.•Fracture locus is determined by hybrid ...experimental-numerical method.•Plasticity modeling is critical for the fracture locus; Yld2004-18p criterion is used.
The ductile fracture of an AA6111 aluminum sheet after a thermal cycle typical of auto-body paint-baking is investigated with the hybrid experimental-numerical method. The plastic flow of the material is examined by uniaxial tension, plane-strain tension, disk-compression and notched-tension experiments, that are used to calibrate the Yld2004-18p anisotropic yield criterion and the combined Swift-Voce hardening model. Then, the fracture behavior under equibiaxial and plane-strain tension, as well as uniaxial tension and shear, is characterized using a specially-developed cruciform specimen, along with center-hole and shear specimens, respectively. The cruciform fracture specimen proposed here contains two shallow hemispherical depressions (dimples) in the test-section, to initiate fracture. For the fracture characterization, special emphasis is put on specimen design, so that the stress states developed at the neighborhood of the fracture initiation point remain proportional throughout the loading history. In all experiments, the surface strain fields are measured by a stereo-type digital image correlation system. This information is used to validate finite element simulations of the fracture experiments. It is found that the Yld2004-18p model provides a better agreement with experiments than von Mises does, which underscores the sensitivity of the hybrid method to the plasticity models adopted. Once validated, these simulations are used to obtain the fracture loci in terms of two stress-state metrics, i.e., the stress triaxiality and Lode angle parameter.
The plastic behavior of commercially-pure titanium (CP-Ti) is assessed using a combination of experiments and analysis. A total of 23 (with three repetitions each) experiments were performed on a ...hot-rolled CP-Ti plate of 12.7 mm thickness. The experiments performed are uniaxial tension and uniaxial compression in-plane at 15° angles to the rolling direction (RD), and in the normal direction (ND), as well as plane-strain tension (PST) at 15° angles to the RD of the plate. The uniaxial tension and compression tests involve standard specimen geometries, except for the one in the ND, which required the creation of a custom, miniature tensile specimen. The PST specimen is a custom geometry to impose a constraint in the transverse direction, giving rise to the plane-strain condition. A procedure using finite element analysis is described to determine the axial stress in a PST test. The experiments reveal the deformation-induced anisotropy and tension-compression asymmetry of CP-Ti. The material strength is found to increase going from RD to transverse direction (TD) to ND. The experiments are then used to calibrate four constitutive models of increasing complexity: von Mises, Hill '48, KYL '12 and CPB '06. The calibrated models along with the experimental information are shown using three alternative approaches: biaxial tension-compression plane, Haigh-Westergaard or π-plane, and the one recently introduced by (Korkolis et al., 2017) that allows representation of stress states where the full stress tensor is active. Furthermore, the test results from off-axis experiments, not used in the calibration, are used to examine the performance of each model. The best performance in predicting the experiments was exhibited by the KYL '12 and CPB '06 models. It is expected that this improved understanding and representation of the plastic behavior of CP-Ti can lead to improved material models and numerical simulations of manufacturing and service.
•Mechanical tests are performed on CP-Ti at multiple angles to the material axes.•The material strength increases going from RD to TD to ND.•Some compression orientations exhibit transition from twinning to slip.•The von Mises, Hill 1948, KYL ′12 and CPB ′06 models are calibrated.•The 4 model predictions are compared with the experiments.
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 prediction of earing during cup-drawing of the anisotropic aluminum alloy Al-6022-T4 is studied through a combination of experiments and analysis. At first, the anisotropy of the material is ...established experimentally, using uniaxial and plane-strain tension, as well as disk compression experiments. The material is seen to possess mild anisotropy, which however evolves with deformation. Two plastic potentials, Yld89 and Yld2000-2D are then calibrated to that data. The latter potential is flexible enough to represent the experimental plastic work contours almost exactly. Subsequently, the cup-drawing experiments are detailed, including descriptions of the equipment and tooling, measurements during forming as well as measurements of thickness and earing in the drawn-cups. Three analytical models for predicting the maximum drawing force are compared to the experiments. The cups exhibit maximum thinning around the punch-radius, as well as four ears. The ears are oriented along the RD and TD directions, with the TD ears being higher than the RD ones. A simple analytical model is seen to closely capture these results. The experiments are then simulated with shell finite elements in DYNAFORM, which uses the explicit solver of LS-DYNA. The simulations permitted the inverse determination of the friction between the blank and the tooling. The thickness and earing profile predictions from the numerical model are in good agreement with the experiments.
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•Fracture locus of a thin-walled tube under axial force and internal pressure is probed.•Fracture parameters are determined by a hybrid experimental-numerical approach.•The Yld2000-2D ...and Yl2004-3D yield criteria are adopted in a compound solid-shell finite element model.•Proportional loading paths are used to determine the fracture locus.•Non-proportional loading paths are used to establish the path dependence of the fracture locus.
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.
•Plasticity and fracture characteristics of microscale tubes with 2.38 mm diameter and 0.15 mm thickness are comprehensively examined under 15 different near-proportional stress paths.•The results ...show significantly higher fracture anisotropy than plastic anisotropy.•Anisotropic flow is modeled numerically by the Yld2004-3D yield function.•The DF2016 criterion is extended into an anisotropic form by coupling it with the Yld91 yield function to capture the fracture anisotropy.
The anisotropic ductile fracture behavior of a stainless steel is investigated using a combination of experiments and analysis. The material is SS-304L, an austenitic, low-carbon stainless steel, received in the form of tubes of 2.38 mm dia. and 0.15 mm thickness. The tubes are inflated under volume control in a custom apparatus. At the same time, the axial force on the tubes is kept proportional to the pressure induced by the inflation. This leads to quasi-proportional stress paths in the meridional-hoop engineering stress space. A total of 15 discrete paths are successfully tested. Stereo-type Digital Image Correlation is used to measure the strains. In every case, the tubes develop a series of instabilities before bursting. The failure is oriented along the meridional or the hoop direction of the tube, depending on which stress is greater. A mild plastic anisotropy is detected in these experiments. Hence these results are then used for calibrating the anisotropic yield criterion Yld2004-3D. This is introduced in a finite element model of the experiments, which includes a thickness imperfection designed to capture the two failure orientations observed in the experiments. The numerical model using the Yld2004-3D criterion reproduces the experiments well, e.g., it captures the experimental stress-strain and induced strain paths better than von Mises. It is then used to probe the conditions at the onset of fracture (hybrid method). It is found that most paths lead to essentially proportional loading during deformation. A significant anisotropy in the fracture behavior is detected, with the meridional-stress-dominated paths being able to develop much higher strains than the hoop-dominated ones. These results are then captured by the DF2016 ductile fracture criterion, modified to use the anisotropic yield criterion Yld91. The proposed criterion is flexible enough to represent the fracture anisotropy very well, without being unnecessarily complex. The fracture forming limit curve (i.e., the fracture envelope in strain space) predicted by the DF2016/Yld91 model is also found to be very close to the experiments. The results and findings of this work help establish a framework to reliably design components and processes when significant fracture anisotropy is expected.
Abstract The ductile fracture behaviours of two tubular specimens, a AA6260-T4 macrotube (60 mm diameter and 2 mm thickness), and a SS-304L microtube (2.38 mm diameter and 0.15 mm thickness) under ...non-proportional loading condition are studied using a combined experimental-numerical approach. The experiments are conducted by loading the tubes under axial force and internal pressure along various non-proportional (i.e., corner) paths until failure by controlling the force/pressure ratio. The plastic behaviours of the tubes are characterized using the non-quadratic anisotropic yield criteria Yld2000-2D and Yld2004-3D. The material models are employed in the finite element (FE) simulation of the tube experiments using Abaqus/Standard (implicit). The FE models, which include thickness imperfection to capture the failure modes observed in the experiments, are then used to probe the fracture parameters inside the tube wall where fracture is likely to initiate. It is observed that the fracture strains from the non-proportional loading results are noticeably different when introduced to the proportional fracture strains, revealing the path-dependence fracture behaviour in tubular specimens.
There is extensive evidence in the literature that plastic deformation of metals is associated with an increase in Acoustic Emission (AE) activity. Thus, AE measurement techniques have the potential ...to monitor a forming process in real time and provide a signal for feedback control, to exploit optimum formability. In this work, custom-made AE sensors employing piezoelectric crystals are implemented to measure the emitted acoustic signal during uniaxial tension and cup drawing tests of an AA6013-T4 aluminum sheet (1.5 mm thick). The uniaxial tension tests are conducted with two AE sensors clamped to each end of the specimen gage section, along with full-field surface strain measurement using Digital Image Correlation (DIC) techniques. The AE signals along with the interrogation of the DIC images reveal that the maximum AE amplitude corresponds to the onset of diffuse necking, i.e., when the strain field starts to become spatially inhomogeneous. Interestingly, this onset occurs before the maximum force is attained. Comparing these observations to a model of dislocation activity supports the notion that dislocation is the main driver of AE activity. With these findings, AE measurements are performed in a cup drawing process where a custom-made Marciniak-type punch incorporates three AE sensors. These sensors are used to triangulate and determine the location of necking and eminent fracture based on the time difference of arriving signals to each sensor. The results from the cup drawing tests show that AE signals can identify the onset of necking and accurately predict the location of necking and fracture.
The study aims to present the results of paper compression under an axial load. Different heights of samples subjected to compression were taken into account. The main goal of the analysis was to ...determine experimentally the maximum compression load. In addition, numerical models based on the finite element method (FEM) were validated to refer to empirical results. The performed numerical simulations were founded on Green-Lagrangian nonlinear equations for large displacements and strains. The progressive failure of the compressed orthotropic material after exceeding maximum stresses was based on Hill's anisotropy theory. Nonlinear calculations were conducted by using a typical Newton-Raphson algorithm for achieving a sequence convergence. The accuracy of the developed model was confirmed experimentally in compression tests. The technique of analysing the shape of the compressed paper sample on the basis of images recorded during the measurement was used. The obtained test results are directly applicable in practice, especially in the calculation of the mechanical properties of corrugated cardboard and in determining the load capacity of cardboard packaging. Knowing the maximum compressive stress that packaging paper can withstand allows packaging to be properly designed and its strength assessed in the context of the transport and storage of goods.
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