Plane Strain Tensile Test Research Articles

Development of a plane strain tensile test to characterize the formability of 5xxx and 6xxx aluminium alloys

Development of a plane strain tensile test to characterize the formability of 5xxx and 6xxx aluminium alloys

Prediction of strain distribution during the plane strain tensile test based on artificial neural networks

In this study, finite element method was used to study the effects of various notch geometries on the strain field distributions during the plane strain tensile test for cold-rolled steel (DC01). The artificial neural network approach (ANN) and the response surface methodology (RSM) were adopted to develop the mathematical prediction models applied in the optimization procedure. The strain state was expressed by self-defined metrics, namely, the Plane Strain State Index (PSSI) and the Homogeneity Index (HI) were predicted by changing the notch angle (X degree), notch width (d mm), and notch length (c mm). The Quadratic mathematical models obtained by the RSM, and ANN presented the evolution of PSSI, and HI based on (X, d, and c). The results show that the ANN method provides more precise results compared to those of the RSM approach.

A Deterministic Methodology to Calibrate Pressure-Independent Anisotropic Yield Criteria in Plane Strain Tension Using Finite-Element Analysis

The yield strength of materials under plane strain deformation is often not characterized experimentally due to difficulties that arise in interpreting the results of plane strain tensile tests. The strain and stress fields in the gauge region of these tests are inhomogeneous, making it challenging to extract the constitutive response from experimental measurements. Consequently, the plane strain yield stress is instead predicted using phenomenological plasticity models calibrated using uniaxial and biaxial tension data. To remove this uncertainty, a simple finite-element based inverse technique is proposed to determine the arc of the associated yield locus from uniaxial-to-plane strain tension using a constrained form of Vegter’s anisotropic yield criterion to analyze a notch tensile test. The inverse problem is formulated under associated deviatoric plasticity and constrained such that only a single parameter, the major principal yield stress under plane strain deformation, needs to be identified from the finite-element simulations. The methodology was applied to two different automotive steel grades, an ultra-high strength DP1180 and a DC04 mild steel. The predictive accuracy of the constitutive models was then evaluated using an alternate notch geometry that provides an intermediate stress state between uniaxial and plane strain tension. By performing notch tensile tests in three sheet orientations, three arcs of the yield surface were obtained and employed to calibrate the widely used Yld2000 yield function. The study shows that for DP1180, the normalized plane strain yield stress was in the range of 1.10 to 1.14 whereas for DDQ steel, the normalized plane strain yield stress was notably stronger, with values ranging from 1.22 to 1.27, depending on the orientation. The proposed methodology allows for a wealth of anisotropic plasticity data to be obtained from simple notch tests while ensuring the plane strain state is accurately characterized, since it governs localization and fracture in many forming operations.

Optimization of notched tensile test specimen under plane strain condition

In the current paper, specimen notch geometries during plane strain tensile test for cold-rolled steel DC01 is studied and optimized using Response Surface Methodology (RSM) and the desirability approach. The notch angle (X°), notch width (d), and notch length (c) were the main geometry parameters considered in this study. The effects of these parameters on the strain state were expressed by self-defined metrics, namely the Plane Strain State Index (PSSI) and the Homogeneity Index (HI) as well as those were analyzed by ANOVA analysis. The quadratic mathematical models obtained by the RSM presenting the evolution of the PSSI and the HI depending on (X°, d, and c) are presented. Optimization of the geometry parameters to achieve the optimal PSSI and better HI was carried out by a desirability function.

SIMULATION OF STRAIN DISTRIBUTIONS FOR PLANE STRAIN TENSILE TEST USING DC05 COLD ROLLED STEEL

Material prediction behavior in the sheet metal forming operations is one of the critical fields of this process, especially for the industry and sheet metal forming processes in more precisely. Knowing the material behavior is a must to ensure the accuracy during the prediction for the best final size and shape. In this work we made a numerical investigation using a finite element software ABAQUS, of a plane strain tensile test for a DC05 cold rolled steel with different specimen geometry, to investigate the effect of different geometries on the strain distributions.

Study the near plane strain tensile test specimen using finite element code ABAQUS

In the present work, optimization of near plane strain tensile test specimen for four types of cold-rolled steel DC01, DC04, DP600, and DP1000 are studied using finite element code ABAQUS. The sample width (A), notch radius (R), and material anisotropy (r-value) were the main parameters considered in this study. The effects of these parameters on the Plane Strain State Index (PSSI) and Homogeneity Index (HI) were analyzed and presented.

Predicting ductile fracture in ferrous materials during cylinder upsetting using an ellipsoidal void model

The ductile fracture in ferrous materials during cylinder upsetting was predicted using an ellipsoidal void model to show the validity of the proposed model. The simulation and experiment of cylinder upsetting were performed using five types of ferrous bars. Seven kinds of prestrains different in magnitude were introduced in the bars by drawing, and special attention was paid to the effect of the prestrain on ductile fracture during cylinder upsetting, which was scarcely paid attention to in earlier studies. A specimen for the plane-strain tensile test obtained from a bar was proposed to obtain a material constant on ductile fracture. Both in the simulation and in the experiment, with increasing the prestrain, the axial strain at fracture initiation monotonically increased, whereas the circumferential strain at fracture initiation monotonically decreased. The effect of the prestrain on the circumferential and axial strains at fracture initiation calculated using an ellipsoidal void model substantially agrees with that obtained experimentally, whereas the effect of the prestrain on the circumferential and axial strains at fracture initiation calculated using conventional ductile fracture criteria considerably differs from that obtained experimentally. Hence, the validity of the ellipsoidal void model was confirmed.

Evaluation of Prediction Accuracy for Anisotropic Yield Functions Using Cruciform Hole Expansion Test

To evaluate the prediction accuracy of the anisotropic yield function, we propose an original cruciform hole expansion test. Displacements on two axes were applied to the cruciform specimens with a hole in the center. The thickness strain in the region near the hole was compared to the simulation results. Because this forming test is free of friction and bending, it is an appropriate method to assess the anisotropic yield function without the influences of friction or the Bauschinger effect, or the need to consider the stress-strain curve in high-strain region. Hill1948, YLD2000-2D, and spline yield function which is an improved version of the Vegter model were selected, and 6000 series aluminum alloy sheets (A6116-T4) were used in this study. The parameter identification method of the spline yield function also proposed in this paper using the pseudo plane strain tensile test and optimization software. As a result, the spline yield function has better predictive accuracy than the conventional anisotropic yield functions Hill1948 and YLD2000-2D.

Process Optimization of Plane Strain Compression for 06Cr19Ni9NbN Steel Based on Processing Maps

Hot compression tests of 06Cr19Ni9NbN steel were conducted at strain rates of 0.005-5 s−1 and temperatures of 900-1200 °C on a Gleeble 1500 thermo-mechanical simulation tester. Based on the true stress-true strain data, processing maps of the steel were established. The influences of the temperature and strain rate on the processing map were analyzed in detail. The optimal process parameters for hot compression were determined to be in the temperature and strain rate ranges of 1000-1200 °C and 0.005-0.1 s−1, respectively. Plane strain compression experiments were conducted using the recommended process parameters. A temperature of 1200 °C and reduction ratio of 38% are the recommended compression parameters, yielding a grain size of 74 µm. The mechanical properties of the material after compression were obtained by tensile tests at room temperature. The mechanical properties were optimal at 1200 °C and a reduction ratio of 38%. The elongation, area reduction, yield strength, and tensile strength were 63.69%, 76.12%, 281 MPa, and 703 MPa, respectively. The results of the plane strain compression experiments and tensile tests were consistent with the processing map results, indicating that the processing maps were accurate for optimizing the compression process parameters.

Simplification of the Gurson model for large-scale plane stress problems

This paper discusses formulation of the constitutive model for ductile fracture prediction in large-scale metal structures that can be approximated using shell mechanics. One of the primary considerations is the issue of bridging the length scales between micromechanical phenomena governing ductile fracture (i.e. void nucleation, growth and coalescence), which occurs on the scale of several micrometers, and large scale industrial applications. A micromechanics-based shear-modified Gurson model is used as a reference for the proposed formulation. The model is simplified and implemented in generalized plane stress state, with only the most relevant phenomena considered. Bridging of the length scales is achieved through the calibration function that approximates exponential damage growth after the onset of localized neck that cannot be explicitly represented with shell elements. The resulting formulation is a phenomenological three invariant plasticity model with a scalar damage variable dependent on the volumetric plastic strain and deviatoric plastic work. The latter term is dependent on the Nahshon-Hutchinson omega function, which is based on a normalized Lode angle. The model is used to simulate a response of a hat-shaped high strength steel automotive component under three-point bending. Calibration of the model parameters is performed based on uniaxial and plane-strain tensile tests. Close correlation between experimental and analysis results are achieved validating the assumptions and proposed formulation.

An investigation of plastic behaviour in cold-rolled aluminium alloy AA2024-T3 using laser speckle imaging sensor

The mechanical anisotropy of aluminium alloy AA2024-T3 with strong cold-rolled crystallographic texture is investigated in this paper. A non-contact and non-destructive laser speckle imaging sensor is developed for surface strain measurement so that extensive mechanical tests can be readily performed without surface preparation on the specimens. Both Hill’s 48 and Yld2004-18p yield functions are accurately calibrated using the experimental results from uniaxial tensile, pure shear and plane-strain tensile tests. The constitutive models based on these yield functions were successfully implemented in a commercial finite element (FE) package Abaqus via user material subroutine UMAT. Simulations of single element tensile tests and pure shear tests were carried out to validate the accuracy of UMAT subroutine. The performance of these constitutive models was further evaluated with deep drawing experiments in which the predicted earing profiles were compared with those obtained from FE simulations. The results showed that the constitutive model based on Yld2004-18p yield function accurate representing the anisotropic behaviour of AA2024-T3. The predicted earing profiles coincide well with experimental measurements.

Numerical Verification of Simplified Identification Method of Yield Function Using Circumscribing Polygon of Yield Locus

A method for identifying the yield function using simple material tests is proposed. The identification accuracy of this method is verified by finite element analysis. In the proposed method, a polygon circumscribing the equal plastic work contour is defined through uniaxial tensile tests, hydraulic bulge test, and plane strain tensile tests. The parameters of the anisotropic yield function are identified as a smooth curve inscribed in the polygon. The virtual material tests of three material models, namely, mild steel, aluminium alloy, and pure titanium, are conducted by the finite element method. On the basis of the results, stress measurement error and yield surface identification error are discussed. When the material exhibits strong in-plane anisotropy, the measurement error of equi-biaxial stress in the hydraulic bulge test becomes large. When the initial gradient of work hardening is large, the stress value of the circumscribed line of the small plastic strain stage in the plane strain tensile test is estimated to be lower than that on the true yield surface. These errors affect the identification accuracy of the material parameters of the yield function quantitatively, but the difference between the identified locus and true yield locus is small. The proposed method is feasible as a simple identification method of the yield function.

Stakes and solutions for in-plane sheet-metal formability assessment

In body design, Finite Element Analysis becomes an unavoidable step in optimizing forming processes to ensure the feasibility of a specific designed shape. Different failure criteria exist but the Forming Limit Diagram remains the most used criterion. It can be built in a wide variety of forms but the most usual one is composed only of a Forming Limit Curve (FLC) which represents the onset of localized necking limit of sheet metal. FLC is determined experimentally by standardized Nakajima or Marciniak tests. However, both present lots of roadblocks in the accurate determination of product formability limits due to the use of counter-blanks, no linear strain paths and because they are not adapted for high ductility steels. Tensile tests were performed in the past to determine the left hand side of the FLCs. They were not included into the ISO 12004-2 standard because of technical reasons although they present lots of advantages (frictionless, no curvature effect and planar configuration). Now, thanks to the current advanced technologies and tools, these issues are overcome. In this paper, the advantages of tensile tests compared to Nakajima or Marciniak ones are briefly discussed. The design and conceptualization of specific jaws to perform plane strain tensile tests on AHSS are presented. A wide range of AHSS was characterized through plane strain tensile tests and results were compared to formability limits determined by the usual practice using Nakajima tests. Different evaluation strategies were used to determine the maximum formability: the position dependent method, the time dependent one and close to fracture.

Experimental study of Portevin–Le Châtelier bands on tensile and plane strain tensile tests

The aim of this article is to show that it is possible to create an experimental database to better model Portevin–Le Châtelier (PLC) phenomenon with two kinds of solicitation. Indeed, two kinds of specimen are tested: conventional tensile specimens and specimens designed for plane strain tensile test. In order to better understand this phenomenon and above all to put away any geometry effect, two materials are tested: one without PLC bands (AU4G) that is used as reference and AlMg3 which is well known for its PLC bands. The image correlation tool is used to analyse the creation and the spread of PLC bands. Characteristic parameters of the bands are then measured: width, angle, transported strain, strain rate, and velocity.The originality of this paper is first to show that PLC bands are present during plane strain tensile test and then to characterize the bands thanks to image correlation. These experimental databases could be very useful for those who develop models on PLC phenomenon.

Modelling of the post yield response of amorphous polymers under different stress states

In this contribution, an elasto-viscoplastic constitutive model based on the single mode EGP (Eindhoven Glassy Polymer) model is proposed to describe the deformation behaviour of solid polymers subjected to finite deformations under different stress states. The polymeric material examined in this work is a specific commercial grade of Bisphenol, a polycarbonate called Makrolon 2607, for which there were experimental results available in the open literature for: uniaxial compression, plane strain compression and tensile test on a dumbbell shape specimen. The material properties of the original model are determined and calibrated from a uniaxial compression-loading test. Then, several numerical examples under different stress states are presented to illustrate the limitations of the single mode EGP model. A more general elasto-viscoplastic model is proposed, which preserves the isotropy of the original model, using the lode angle parameter to distinguish shear-dominated stress states and capture the material post yield response. The numerical treatment of the model, including the state update procedure and also the consistent tangent operator, required for the finite implementation of the model within an implicit finite element scheme, is presented. A comprehensive set of numerical examples is employed to compare the predictions of the original and new models against experimental results and to investigate the effect of the proposed modifications. The numerical results show that the proposed model provides a closer agreement with experimental evidence and opens the possibility for computational simulations of amorphous polymers under different stress states.

The inverse parameter identification of Hill 48 yield criterion and its verification in press bending and roll forming process simulations

Yield criterion is an essential factor that affects the FEM simulation accuracy. In order to improve the simulation accuracy of bending processes including press bending and roll forming which are mainly under plane strain condition, an inverse parameter identification method to determine the parameters of Hill48 yield criterion in a convenient manner is presented. The plane strain tensile test is performed, and the orthogonal experiments based on FEM simulations are conducted. Then the parameters of Hill 48 yield criterion are obtained based on the load-displacement data of both the test and simulation results. Press bending and roll forming processes are selected to verify this parameter identification method. Final shapes of the experimental and numerical results are compared. It is shown that the numerical results based on Hill 48 yield criterion are better than those based on Mises yield criterion in terms of the final shapes, which indicates that the proposed method is reliable and can well reflect material behavior in real forming processes.

Assessment of Damage and Anisotropic Plasticity Models to Predict Ti-6Al-4V Behavior

The plastic behavior of the Ti-6Al-4V alloy includes several features as strength differential effect, anisotropy and yield strength sensitivity to temperature and strain rate. Monotonic tensions in the three orthogonal directions of the material are performed to identify the Hill '48 yield criterion. Monotonic compression and plane strain tensile tests are also included in the experimental campaign to identify the orthotropic yield criterion of CPB06. An assessment of the two models is done by comparing the yield loci and the experimental data points for different levels of plastic work. A first approach of the damage modelling of the Ti-6AL-4V alloy is investigated with an extended Gurson-Tvergaard-Needleman damage model based on Hill '48 yield criterion. Finite element simulations of the experiments are performed and numerical results allows checking force-displacement curves until rupture and local information like displacement and strain fields. The prediction ability of the Hill '48, CPB and extended Gurson models are assessed on simple shear and notched tensile tests until fracture.

Development of a Global Indicator to Assess Mechanical Tests

Full-field measurement methods have emerged in the last years and these methods are characterized by directly providing displacement and strain fields for all points over the specimen surface. Thus, the design of heterogeneous tests can be performed for material parameter identification purposes since the inhomogeneous strain fields can be measured. However, (i) no defined criterion yet exists for designing new heterogeneous tests, (ii) it is rather difficult to compare and rate different tests and (iii) a quantitative way to define the best test for material behavior characterization of sheet metals has yet to be proposed. Due to this, the goal of this work is the development of a global indicator able to assess mechanical tests. The proposed indicator quantifies the strain state range, the deformation heterogeneity and the strain level achieved in the test, based on a continuous evaluation of the strain field up to rupture. This global indicator was applied to rank some classical tests, such as uniaxial tensile, simple shear, plane strain and biaxial tensile tests. These tests were carried out numerically by reproducing the virtual behavior of DC04 mild steel. A constitutive model composed by the non-quadratic Yld2004-18p yield criterion combined with a mixed isotropic-kinematic hardening law and a macroscopic rupture criterion was used. The performance of the tests was compared with the indicator and a ranking was established. The results obtained show that biaxial tension is the test providing more information for the mechanical behavior characterization of the material. It was also verified that plane strain test presents a better performance than simple shear and uniaxial tensile tests.

Uniaxial near plane strain tensile tests applied to the determination of the FLC0 formabillity parameter

b An alternative procedure for the determination of the FLC 0 value, the limit strain value corresponding to the plane strain mode of the Forming Limit Curves (FLC), a critical parameter in the sheet formability analysis, is suggested and compared with conventional Nakazima simulation tests. The procedure was tested using two different materials: interstitial-free quality steel (IF) and a spheroidized SAE 1050 steel. The intrinsic tensile test, in a near plane strain state, was performed using a small number of samples, with dimensions suggested by the literature. The results were checked against Nakazima test results using the same materials. The plane strain test was reliable in determining consistent FLC 0 values and should be preferred since it is not affected by the geometric aspects and by friction, which do affect the Nakazima test. The reliability of the FLC 0 values obtained by near plane strain was also corroborated through comparison with literature data.

Simulation and experimental verification of flexible roll forming of steel sheets

Roll forming is a sheet metal forming process that has been used for decades. Usually roll-formed sections have a constant cross section. Flexible roll forming is a brand new forming process that produces parts with variable cross sections, in which the rollers translate back and forth in a direction that is perpendicular to the sheet feeding direction. Theoretical analysis gives an explanation of the plane strain state, compressive stresses, tensile stresses, and shear stresses in flexible roll forming. In order to analyze the mechanics and the deformation characteristics of flexible roll forming, the finite element method (FEM) model of a 17-step flexible roll forming process is established. The yield criterion used in the FEM simulation is Hill 48, and the parameters of which are solved with the yield stresses under different loading conditions and are firstly verified with a plane strain tensile test. The complicated roller paths are realized with data extracted from the computer-aided design (CAD) files with VC++ programs developed by the authors. We developed the first flexible roll forming prototype machine in China, with which the roll forming experiment of a side door beam is performed. Final shapes of the experimental and numerical results are compared. It is shown that the numerical results based on Hill 48 yield criterion that is solved with yield stresses agree well with the experimental results, which indicates that the simulation model can well reflect the real forming process. Detailed analysis of the distribution and history of plastic strain, longitudinal strain, shear strain, and thickness of both the constant cross section and the variable cross section is performed, which is of great help to understand this forming process.