Experimental Limit Strains Research Articles

Formability of SS304 stainless steel foil at elevated strain-rate

Necking and fracture are vital issues during the production of metallic bipolar plates. Therefore, evaluating the formability of thin metallic foil is a critical demand for the fabrication of metallic bipolar plates. Here, the static and dynamic formability of SS304 stainless steel foil with the thickness of 0.1 mm were investigated using traditional rigid-punch bulging and electromagnetically-impacted stamping methods, respectively. The strain rate of the traditional rigid-punch bulging experiment is about 10−3s−1, while the strain rate of the electromagnetically-impacted stamping experiment can reach 102s−1. The experimental limit strains at necking were determined by the position-dependent method, and the simulated limit strains at necking were identified by the time-dependent method. The fracture limit strains were determined by the reverse engineering method. The accuracy of the simulation was subsequently verified. The results show that the dynamic formability at necking and fracture is slightly higher than the static formability. The formability of SS304 stainless steel foil exhibits slight strain rate sensitivity. Furthermore, the fracture locus of the SS304 stainless steel foil was predicted by the Johnson-Cook fracture model.

A novel three-dimensional M-K model by integrating GTN model for accurately identifying limit strains of sheet metal

To accurately identify the limit strains and improve the prediction accuracy of forming limits for sheet metal, a novel three-dimensional M-K model by integrating GTN model is developed and named 3D M-K-GTN model. By introducing the through-thickness normal stress and friction stress, the original M-K model is extended for adapting to the three-dimensional stress state. Furthermore, the empirical failure criterion is replaced by integrating the GTN model, and thus the limit strain is identified when the void volume fraction within the groove accumulates to a critical value. Besides, the voids nucleation and growth expressions are also re-derived and modified by embedding the friction stress and normal stress. Finally, the comparison between predicted forming limit curves and experimental limit strains of AA6016-T4 sheet indicates that the 3D M-K-GTN model solves the significant overestimation of prediction results under large strain paths, and always provides a high prediction accuracy for each strain path given.

Forming Limit Analysis of Thin-Walled Extruded Aluminum Alloy Tubes under Nonlinear Loading Paths Using an Improved M-K Model

To meet the requirement of lighter weight and better performance in tube hydroforming, one of the most important tasks is to accurately predict the forming limit of thin-walled tubes under nonlinear loading paths. This work established the M-K+DF2012 model, a combination of the M-K model and the DF2012 ductile fracture criterion, for the forming limit prediction of thin-walled tubes under nonlinear loading paths. In this model, the failure of the groove is determined by the DF2012 criterion, and the corresponding strains in the uniform region are the limit strains. The limit strains of an AA6061 aluminum alloy tube under a set of linear loading paths and two typical nonlinear loading paths were tested. Parameter values of the M-K+DF2012 model for the tube were determined based on the experimental limit strains under linear loading paths, and the limit strains under the two nonlinear loading paths were predicted. Then the strain-based forming limit diagram (ε-FLD) and the polar effective plastic strain FLD (PEPS-FLD) of the tube under different pre-strains were predicted and discussed. The results show that the limit strains of the tube are obviously path-dependent, and the M-K+DF2012 model can reasonably capture the limit strains of the tube under both linear and nonlinear loading paths. The predicted ε-FLD shows a strong dependence on the pre-strain, while the predicted PEPS-FLD is weakly strain path-dependent and almost path-independent on the right-hand side for the AA6061 tube.

Localized necking of sheet metal under the biaxial stretching condition

To account for the localized necking of sheet metal under the biaxial stretching condition, a theoretical model of localized necking was proposed. To develop the model, it was assumed that the deformation of sheet metal under biaxial stretching becomes locally inhomogeneous after the onset of diffuse necking due to the pre-existing imperfections, and thereby the local elements of the sheet undergo the transition of loading path. Based on the assumed condition, the onset condition of localized necking was identified. The proposed model was combined with particular constitutive equations to provide its application cases, where Hill's theory of localized necking was adopted together to cover non-biaxial stretching paths. Material properties and the forming limit strains of the aluminum alloy (Al6014-T4) sheet were characterized and compared with the limit strains obtained from the proposed model. Theoretical limit strains produced by the original M−K model and the MMFC were also compared with those of the proposed model and the experiments. With the advanced constitutive model, the proposed model well captured the distribution of experimental limit strains of the Al alloy sheet under biaxial stretching. The sheet instability was identified in terms of the instantaneous N-value of the work hardening model.

Formability of AA7075 Sheet in Single Point Incremental Forming

This article presents formability analysis of aluminium alloy 7075 thin sheets in single point incremental forming (SPIF) through prediction of forming limit curve (FLC) and maximum formable wall angle. Deformation instability method based on tool-sheet contact and non-contact zones in incremental forming was used for the prediction of limit strains for plane strain and equi-biaxial stretching strain path. FLC of the material was also determined experimentally, after measuring limit strains for deformed sheet through groove test for the process. Further, maximum forming wall angle of the material was determined for deformed sheet in a square pyramid shape. The theoretical limit strains predicted by deformation instability approach were compared to the experimental values. Theoretically, calculated limit strains were observed to be higher for plane strain path but approximately close for equi-biaxial strain path compared to experimental limit strains. The maximum formable wall was found to be 55˚ for the material in the process.

Formability prediction of Ti6Al4V titanium alloy sheet deformed at room temperature and 600 °C

Formability predictions of Ti6Al4V titanium alloy sheets deformed at room temperature and 600 °C, using D-Bressan’s shear stress rupture criterion and the critical strain gradient macroscopic modelling are presented and discussed in relation to limit strain results obtained experimentally. Ti6Al4V Forming Limit Strain Curves were predicted and compared with experimental curves at 25 °C and 600 °C and strain rate 0.1 s−1. The analytical models were calibrated by means of tensile tests performed on samples cut at 0°, 45° and 90° to the rolling direction at different temperatures and strain rates to obtain the Lankford coefficients and material strain and strain rate hardening behavior. The applied critical shear stress rupture criterion showed to give a fairly good fit with experimental limit strains outcomes, proving that the shear stress rupture nature of specimens deformed at room and elevated temperatures were well reproduced, despite a not-null strain rate sensitivity coefficient at 600 °C. Fracture occurrence by fast shear stress mechanism through thickness direction was corroborated by experimental fractograph observations close to fracture surfaces. It was shown that predicted limiting major true strain of fracture by shear stress curve is governed by normal anisotropy, strain hardening exponent, pre-strain and normalized critical shear stress parameter, which depends on temperature and strain rate whereas the strain hardening exponent depends largely on temperature. In contrast, the critical strain gradient modelling for onset of localized necking showed poor correlation with the experimental limit strains. Best fit of the critical shear stress criterion with experimental limit strain curves was given by specimens deformed near plane strain or FLCo. Hence, a common feature of various strain-rate independent metals, annealed or cold rolled, is that the main fracture mechanism of thin sheet metals can be considered as fast shear stress through sheet thickness without a visible localized necking in biaxial stretching.

A numerical M-K approach for predicting the forming limits of material AA5754-O

In this paper, the forming limit curve (FLC) of AA5754-O was predicted numerically through simulating the M-K approach with the consideration of initial groove orientation and investigated experimentally through the biaxial tensile tests. Firstly, the uniaxial tensile test and the equi-biaxial tensile test were performed to determine the mechanical properties and the anisotropic coefficients of Yld2000-2d yield criterion. Secondly, the numerical M-K approach considering the initial groove orientation and Yld2000-2d yield function was simulated to study the effects of the initial groove orientation and the imperfection coefficient on the predicted limit major strain. Finally, the shape of the cruciform specimen thinned at the center region was optimized for reducing the shear stress, and the optimized cruciform specimen was stretched under different loading paths to determine the experimental limit strains. Through comparing the predicted limit strain at uniaxial tensile stress state and the experimental one, the imperfection coefficient was confirmed, and a good agreement between the numerical result and experimental data was presented. This work showed that experimentally determining the limit strains through biaxial tensile test was achievable, and the proposed numerical M-K approach was effective for predicting the limit strains.

Characterization of forming limits at fracture with an optimized cruciform specimen: Application to DP600 steel sheets

In order to identify experimental limit strains at fracture for metallic sheets under in-plane biaxial loadings, a specific specimen shape has to be defined. Ideally, the proposed geometry must lead to fracture at the specimen center whatever the strain path imposed by the experimental device. If such condition is ensured, the whole strain paths ranging from equi-biaxial to uniaxial could be experimentally investigated. Based on the literature review, four in-plane cross specimen shapes have been selected owing to strong potential to reach large strain and fracture in their central point. From finite element simulations, the behavior of these different shapes is evaluated. Based on these numerical results, a new shape is proposed and optimized for determining the forming limits at fracture of DP600 sheet metal with a thickness of 2mm. The forming limit strains at fracture are identified by a time-dependent method and the forming limit strains at necking are determined by a position-dependent method. The experimental forming limit strains at fracture of DP600 sheet metal are fitted by a forming line. Three ductile fracture criteria are then calibrated with experimental points. The Oyane criterion with two parameters gives the best prediction.

Prediction of limit strains in hot forming of aluminium alloy sheets

Theoretical analysis for the prediction of the limit strains of AA5083 aluminium alloy sheets deformed at room and elevated temperatures are presented and discussed in relation to experimental limit strains. The AA5083 forming limit strain curves, FLC, were predicted by employing D-Bressan and Marciniak–Kuczynski macroscopic concept models and were compared with the experimental FLC from Nakazima tests performed at room and high temperatures. In order to calibrate the models, tensile tests on specimens cut at 0°, 45° and 90° with respect to the rolling direction were carried out in a wide rage of temperatures and strain rates in order to obtain the coefficients of plastic anisotropy as well as material strain and strain rate hardening behaviour at different temperatures. The applied critical shear stress rupture criterion and strain gradient evolution models showed to give a satisfactory agreement with the forming limit strain curves of AA5083 aluminium sheet, proving the suitability of a novel concept of shear stress rupture and local necking evolution in sheet metals deformed at room and elevated temperatures. The correlation of M–K predicted FLC-N curve with the experimental points for room and high temperatures was also fairly good.

Experimental Evaluation and Prediction of Formability of Adhesive Bonded Steel Sheets at Different Adhesive Properties

Abstract The formability of adhesive bonded steel sheets is experimentally evaluated and predicted with the influence of carbon black (CB) nano powder filled adhesive. The epoxy adhesive properties are modified by filling CB nano powder at different wt. %. The tensile and in-plane plane-strain (IPPS) formability tests are carried out to evaluate the formability of adhesive bonded blanks. The true stress–strain behaviour of adhesive bonded blanks is evaluated from the experimental tests and predicted using a finite element (FE) model. The forming limit strains are evaluated during predictions by necking criteria, namely thickness gradient based necking criterion (TGNC) and effective strain-rate based necking criterion (ESRC), and validated with the experimental limit strains. The results show that the adhesive bonded blanks show improved elongation and limit strains of base materials constituting adhesive bonded blanks with increase in CB up to 2 wt. %. There is a reasonable difference in adhesive bonded sheets limit strains between predictions and experiments due to the absence of interface bonding between adhesive and base materials. In the tensile test, about 9.1 %–21.7 % variation in true major strain and about 10.3 %–13.4 % in true minor strain during TGNC predictions are noticed, while ESRC shows more variation than TGNC. In the IPPS forming test, about 8.3 %–12.4 % difference in true major strain and about 2.2 %–13.4 % difference in true minor strain are noticed during prediction by TGNC. The ESRC predictions are equally efficient as compared to TGNC predictions in this case. The TGNC shows better prediction of about 13.5 % in true major strain, and about 7.5 % in true minor strain as compared to ESRC at different adhesive properties in the tensile test. Similarly, a better prediction of about 1 % in true major strain and about 0.3 % in true minor strain in IPPS formability test is observed.

Forming Limit Analysis of DP600-800 Steels

Authors : Marcelo Costa Cardoso, Luciano Pessanha Moreira Abstract : In this work, the plastic behaviour of cold-rolled zinc coated dual-phase steel sheets DP600 and DP800 grades is firstly investigated with the help of uniaxial, hydraulic bulge and Forming Limit Curve (FLC) tests. The uniaxial tensile tests were performed in three angular orientations with respect to the rolling direction to evaluate the strain-hardening and plastic anisotropy. True stress-strain curves at large strains were determined from hydraulic bulge testing and fitted to a workhardening equation. The limit strains are defined at both localized necking and fracture conditions according to Nakajima’s hemispherical punch procedure. Also, an elasto-plastic localization model is proposed in order to predict strain and stress based forming limit curves. The investigated dual-phase sheets showed a good formability in the biaxial stretching and drawing FLC regions. For both DP600 and DP800 sheets, the corresponding numerical predictions overestimated and underestimated the experimental limit strains in the biaxial stretching and drawing FLC regions, respectively. This can be attributed to the restricted failure necking condition adopted in the numerical model, which is not suitable to describe the tensile and shear fracture mechanisms in advanced high strength steels under equibiaxial and biaxial stretching conditions.

Forming-limit prediction of perforated aluminium sheets with square holes

The forming-limit strains of perforated aluminium alloy (AA5052-O) sheets with square holes were theoretically and experimentally estimated for two types of hole arrangements: square and triangular patterns. The theoretical forming-limit curves were obtained by finite-element analyses on a unit module of the perforated sheets using two different approaches: the phenomenological theory and crystal plasticity theory. Hill’s quadratic anisotropic and von Mises yield functions were used for the phenomenological analysis, and the one-element-per-grain model was adopted for the crystal plasticity analysis. To determine the forming limits, two different types of plastic instability criteria were applied. The experimental forming-limit strains were also obtained through a Nakazima stretching test. The theoretical predictability of the forming-limit curves was assessed by comparing the theoretical and experimental results. The comparison demonstrated that (1) the plastic instability criterion based on the external force power predicted qualitatively the same forming-limit curves as the criterion based on the equivalent plastic strain of the ligament for both hole arrangement patterns and (2) although the shapes of the predicted forming-limit curves were in reasonable agreement with the experimental results, the level of the predicted limit strains was considerably higher than that of the experimental limit strains. Thus, it was found that neither of the plastic instability criteria previously proposed for perforated sheets is appropriate to characterise the formability of perforated aluminium sheets with square holes.

Prediction of formability of adhesive bonded steel sheets and experimental validation

The main aim of the present work is to predict the formability of adhesive bonded sheets and validate the same with experimental results at different adhesive properties. The tensile and in-plane plane-strain formability tests are carried out to predict the formability of adhesive bonded sheets. The forming limit strains are predicted using thickness gradient necking criterion (TGNC) and effective strain rate criterion (ESRC), and validated with the experimental limit strains. A simulation methodology has been analyzed thoroughly in the present work, and the prediction accuracies are compared and discussed.The results show that the adhesive bonded blanks show improved elongation and forming limit strains as compared to un-bonded base materials with increase in hardener/resin ratio of adhesive. The true stress–strain predictions are accurate as compared to experimental data. There is a moderate difference in adhesive bonded sheets limit strains between predictions and experiments. This may be due to the absence of interface bonding between adhesive and base materials during predictions. The necking criterion, TGNC, shows better prediction as compared to ESRC.

Effect of stress state on cavitation and hot forming limits of a coarse-grained Al5052 alloy

Effect of stress state on cavitation and deformation behaviour of superplastic or superplastic-like materials has less been investigated. A coarse-grained Al5052 alloy was deformed at its optimal temperature of 873 K under different biaxial stress states. A superplastic gas forming tester with die aspect ratios of 1, 0.75, 0.5 and 0.375 was used. It is observed that the amount of cavities increases with increasing strain level. More and larger cavities were observed at higher strain levels for all stress states. It is also found that an increase in stress ratio will slightly increase the cavity growth rate. An experimental forming limit curve of the alloy was constructed, and an analytical model based on M–K model and damage mechanics approach has been applied to predict limit strains of the alloy based on experimental cavitation data. It is found that the limit strain increases with increasing f 0 and decreases with increasing D B0/ D A0. The prediction is in reasonable agreement with the experimental limit strains.

Simulation of the effect of texture on limit strain in biaxially stretched steel sheet

Limit strains for biaxial stretching are predicted by the Marciniak and Kuczynski (M-K) method, suitably modified to take into account the textures present in sheet steels. The series expansion method is used for this purpose in the framework of the Taylor/Bishop and Hill theory. The effect on the limit strain of yield surface shape is allowed for by the use of an improvedP parameter. The experimental limit strains of an AKDQ steel are compared with the forming limit curves (FLCs) predicted on the assumption of two sets of slip systems with different critical resolved shear stresses (CRSSs). The limit strains in equibiaxial stretching with assumed groove orientations are also predicted for some idealized materials containing specific preferred orientations.

The use of a shear instability criterion to predict local necking in sheet metal deformation

A shear instability criterion can provide a consistent approach to the onset of local necking in sheet metal forming under biaxial stretching. The neck is anticipated to initiate in the direction of pure shear when the shear stress attains some critical value. The yield function proposed by Hill is employed and the material is assumed to display only normal anisotropy. Empirically it is found that the additional material parameter required by this yield function is simply related to R, the coefficient of normal anisotropy, for a number of materials. This allows the limit strain to be predicted in terms of three well established plastic properties, viz. work hardening coefficient, coefficient of normal anisotropy and initial pre-strain. The influence of these on the limit strain curve is analysed and the coefficient of work hardening shown to play the most important role. Data available in the literature are employed in a comparison of the present theory with that due to Marciniak. In general the predicted limit strains are in reasonable agreement with the trend of experimental results for a wide range of materials. In the case of isotropic materials with work hardening coefficients in the range 0·2-0·6 predictions from the present theory are almost identical with those from that presented by Stören and Rice. The theory presented here exhibits a good correlation with experimental limit strains for materials with high work hardening coefficients, of approx. 0·4 or more. Generally, for low work hardening materials, with coefficients of 0·25 or less, the shear instability theory tends to an underestimate of limit strains and a Marciniak type of analysis may be more appropriate. However, bearing in mind the scatter of the experimental data the present theory constitutes a safe lower bound on limit strains and, in addition, has the advantage of simplicity in the mathematical calculation required.

An experimental study of the in-plane stretching of sheet metal

Experimental results are presented of the limit strains for the in-plane stretching of steel, aluminium and brass sheets. The development of surface strains is studied in incremental tests and attention is drawn to “crazing” of the surface of sheet specimens and to “banding” in aluminium specimens. Despite the wide difference in the mechanical properties of the three materials the values for the limit strain are remarkably similar. For steel and aluminium the limit strains are greater than the predicted instability strains, but for brass the limit strains are considerably less than the predicted instability strains. The wide scatter in the experimental limit strains perhaps indicates that failure is largely influenced by random effects.