Forming Limit Strains Research Articles

Texture-based forming limit prediction for Mg sheet alloys ZE10 and AZ31

A viscoplastic self-consistent crystal plasticity model was employed to study the formability of two magnesium sheet alloys, i.e., AZ31 and ZE10 at 200 °C. The flow stress-strain curves obtained by uniaxial tension tests at various strain rates and the crystallographic texture obtained from X-ray diffraction were used to calibrate the model. The crystal plasticity model was incorporated with the Marciniak–Kuczyński model in order to address the forming limits of the magnesium sheets. A good agreement of the model predictions with the experimental data obtained by Nakajima tests was achieved. The model was further studied to quantify the effects of the sample orientation with respect to laboratory axes, the amount of pre-strain applied to the sheet prior to forming, and the initial crystallographic texture. The resulting forming limit diagrams demonstrate the optimal choice of sample orientation and crystallographic texture that can lead to a significant improvement in forming limit strains.

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.

Investigation of the forming limit strains at fracture of AA5086 sheets using an in-plane biaxial tensile test

An in-plane biaxial tensile test with a dedicated cruciform specimen is performed to determine the forming limit strains at fracture for aluminium alloy 5086. A method based on the evolution of strain in the central area of the specimen and the observation of the macroscopic image of specimen surface is proposed to identify the onset of fracture and the forming limit strains at this moment. The forming limit strains at fracture are determined under different strain paths provided by the two independent axes of the experimental device. Finite element simulations are performed to determine and compare numerical forming limit strains with three ductile fracture criteria (Cockroft and Latham, Brozzo and Ayada). The critical damage values of the criteria are determined by the experimental results under different strain paths.

Elevated temperature forming limit strain diagrams of automotive alloys Al6014-T4 and DP600: A case study

The press formability of the automotive materials such as aluminum alloys, magnesium alloys and steels is influenced by forming temperatures. While adjusting the temperature level of die, punch and binder, the lightweight materials can successfully be formed, especially for complex automotive body parts. The objective of this case study is to determine the forming limit curves of Al6014 and DP600 alloy sheet at elevated temperatures in specific range of 200 °C and 250 °C suitable for press operation in long-run production cycles. The focus is set on Al6014 and DP600 as these two materials are widely used in automotive panels due to their high strength and lightweight and improved resistance to corrosion. DP600 is sometimes preheated before forming to avoid cracks. Thus, it is essential to study the effect of preheating temperature on the formability. Experiments were conducted at forming temperatures of 200 °C and 250 °C and at low punch speed. The measurement of train distribution was carried out online using digital image correlation with the optical deformation measurement system GOM Aramis. Both Al6014 and DP600 alloys were found to have good drawability and stretchability. It was found that for Al6014, the forming limit curve level increases with temperature. On the contrary, DP600 showed slight decrease in the level of forming limit curve as temperature was increased. Warm formability for these alloys was further characterized through part depth and percentage thinning measurements.

Prediction and Experimental Validation of Forming Limit Curve of a Quenched and Partitioned Steel

Forming limit curve (FLC) is an effective tool to evaluate the formability of sheet metals. An accurate FLC prediction for a sheet metal is beneficial to its engineering application. A quenched and partitioned steel, known as QP980, is one of the 3rd generation advanced high strength steels and is composed of martensite, ferrite and a considerable amount of retained austenite (RA). Martensite transformation from RA induced by deformation, namely, transformation induced plasticity (TRIP), promotes the capability of work hardening and consequently formability. Nakazima tests were carried out to obtain the experimental forming limit strains with the aid of digital image correlation techniques. Scanning electron microscopy (SEM) was employed to examine the fracture morphologies of Nakazima specimens of the QP980 steel. The observed dimple pattern indicated that tensile stress was the predominant factor which led to failure of QP980 specimens. Therefore, maximum tensile stress criterion (MTSC) was adopted as the forming limit criterion. To predict the FLC of QP980 steel, Von-Mises yield criterion and power hardening law were adopted according to the tested mechanical properties of QP980 steel. Results were compared with those derived from other three representative instability theories, e. g. Hill criterion, Storen-Rice vertex theory and Bressan-Williams model, which shows that the MTSC based FLC is in better agreement with the experimental results.

Forming limit prediction using a self-consistent crystal plasticity framework: a case study for body-centered cubic materials

A rate-dependent self-consistent crystal plasticity model was incorporated with the Marciniak–Kuczyński model in order to study the effects of anisotropy on the forming limits of BCC materials. The computational speed of the model was improved by a factor of 24 when running the simulations for several strain paths in parallel. This speed-up enabled a comprehensive investigation of the forming limits of various BCC textures, such as , , , and fibers and a uniform (random) texture. These simulations demonstrate that the crystallographic texture has significant (both positive and negative) effects on the resulting forming limit diagrams. For example, the fiber texture, which is often sought through thermo-mechanical processing due to a high r-value, had the highest forming limit in the balanced biaxial strain path but the lowest forming limit under the plane strain path among the textures under consideration. A systematic investigation based on the results produced by the current model, referred to as ‘VPSC-FLD’, suggests that the r-value does not serve as a good measure of forming limit strain. However, model predictions show a degree of correlation between the r-value and the forming limit stress.

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.

Experimental Analysis of Forming Limits and Thickness Strains of DP600-800 Steels

In this work, the plastic behavior of cold-rolled zinc coated dual-phase steel sheets DP600 and DP800 grades is firstly investigated by means of uniaxial tensile and Forming Limit Curve (FLC) testing. The uniaxial tensile tests were carried out at 0o, 45o and 90o angular orientations with respect to the rolling direction to evaluate the mechanical properties and the plastic anisotropy Lankford r-values. The forming limit strains are defined according to Nakajima’s procedure. Thickness measurements of tested Nakajima’s samples cut perpendicular to the fracture allowed to identify a rapid decrease of the strain, which governs the plastic instability that preceded the fracture in the drawing region of the FLC. Optical metallographic and scanning electron microscopy techniques helped to characterize and distinguish the orientation of rotated grains and flat fractured surface (ductile shear failure in blank specimens close to plane-strain tension) from no grain rotations and rough fractured surface (ductile tensile fracture in blank geometries in the biaxial stretching domain).

Prediction of Burst Pressure in Multistage Tube Hydroforming of Aerospace Alloys.

Bursting, an irreversible failure in tube hydroforming (THF), results mainly from the local plastic instabilities that occur when the biaxial stresses imparted during the process exceed the forming limit strains of the material. To predict the burst pressure, Oyan's and Brozzo's decoupled ductile fracture criteria (DFC) were implemented as user material models in a dynamic nonlinear commercial 3D finite-element (FE) software, ls-dyna. THF of a round to V-shape was selected as a generic representative of an aerospace component for the FE simulations and experimental trials. To validate the simulation results, THF experiments up to bursting were carried out using Inconel 718 (IN 718) tubes with a thickness of 0.9 mm to measure the internal pressures during the process. When comparing the experimental and simulation results, the burst pressure predicated based on Oyane's decoupled damage criterion was found to agree better with the measured data for IN 718 than Brozzo's fracture criterion.

Modelling of Forming Limit Strains of AA5083 Aluminium Sheets at Room and High Temperatures

Present work analyses mathematical modelling to predict the onset of localized necking and rupture by shear in industrial processes of sheet metal forming of aluminium alloy 5083 such as biaxial stretching and deep drawing. Whereas the AA5083 sheet formability at room temperature is moderate, it increases significantly at high temperature. The Forming Limit Curve, FLC, which is an essential material parameter necessary to numerical simulations by FEM, of AA 5083 sheet was assessed experimentally by tensile and Nakajima testing performed at room and 400°C temperatures. Tensile test specimens at 0o, 45o and 90o to the direction of rolling (RD) and Nakazima type specimens at 0o RD of aluminium AA5083 were fabricated. Simple tensile tests at room and 400°C temperatures were performed to obtain the coefficients of plastic anisotropy and material strain and strain rate hardening behavior at different temperatures. Nakazima biaxial tests at room and high temperature, employing spherical punch were carried out to plot the limit strains in the negative and positive quadrant of the Map of Principal Surface Limit Strains, MPLS, of aluminium AA5083 sheet. The “Forming Map of Principal Surface Limit Strains”, MPLS, shows the experimental FLC which is the plot of principal true strains in the sheet metal surface (ε1,ε2), occurring at critical points obtained in laboratory formability tests or in the fabrication process of parts. Two types of undesirable rupture mechanisms can occur in sheet metal forming products: localized necking and rupture by induced shear stress. Therefore, two kinds of limit strain curves can be plotted in the forming map: the local necking limit curve FLC-N and the shear stress rupture limit curve FLC-S. Localized necking is theoretically anticipated to occur by two mathematical models: Marciniak-Kuczynski modelling, hereafter M-K approach, and D-Bressan modeling. Prediction of limit strains are presented and compared with the experimental FLC. The shear stress rupture criterion modeling by Bressan and Williams and M-K models are employed to predict the forming limit strain curves of AA5083 aluminium sheet at room and 400°C temperatures. As a result of analysis, a new concept of ductile rupture by shear stress and local necking are proposed. M-K model has good agreement with both D-Bressan models.

Fracture behaviour of aluminium alloy sheet under roller hemming process

Roller hemming is a tendency for hemming flexibility. While for aluminium alloy sheets, fracture happens easily. According to comparison of flat surface straight line flanging and limit strain under necking theory, the failure mode of aluminium alloy sheet under roller hemming is ductile fracture, with the aid of analysis of cross-section of the fracture location. Then ductile fracture criterion critical parameter is determined by simulation and experiments of uniaxial tensile test. Consequently, forming limit strain curve at fracture could be calculated from the assumptions including stress–strain curve, plane-stress condition, linear strain path, Deformation Theory of Constitutive Equation, Cockcroft–Latham fracture criterion, etc. Finally, the feasibility of ductile fracture criterion and bending effect on roller hemming process are analysed.

Characterization of Tensile Properties, Limiting Strains, and Deep Drawing Behavior of AA5754-H22 Sheet at Elevated Temperature

Automotive industries are very much interested in characterization of formability improvement of aluminum alloys at elevated temperatures before designing tools, heating systems, and processing sequences for fabrication of auto-body panels by warm forming technology. In this study, tensile tests of AA5754-H22 aluminum alloy were carried out at five different temperatures and three different strain rates to investigate the deformation behavior correlating with Cowper-Symonds constitutive equation. Laboratory scale warm forming facilities were designed and fabricated to perform limiting dome height and deep drawing tests to evaluate forming limit strains and drawability of sheet metal at different tool temperatures. The forming limit strain and dome height improved significantly when both the die and punch were heated to 200 °C. Remarkable improvement in deep drawn cup depth was observed when die and punch temperatures were maintained at 200 and 30 °C, respectively, producing a non-isothermal temperature gradient of approximately 93 °C across the blank from flange to center. The forming behavior at different isothermal and non-isothermal conditions were predicted successfully using a thermo-mechanical FE model incorporating temperature-dependent properties in Barlat-89 yield criterion coupled with Cowper-Symonds hardening model, and the thinning/failure location in deformed cups were validated implementing the experimental limiting strains as damage model.

Numerical approach to the evaluation of forming limit curves for zircaloy-4 sheet

Abstract

시간의존법에 의한 금속판재 성형한계변형률의 결정

Abstract The forming limit diagram (FLD) is the most commonly used tool for evaluating of sheet metal formability in the manufacturing field as well as the finite element analysis (FEA)-based design process. Determination of the forming limits is considerably influenced by testing/measuring machines, techniques and conditions. These influences may cause a large scatter in FLD from laboratory to laboratory. Scatter is especially true when the ‘position-dependent method’, as is specified in most national and international standards, is used. In the current study a new ‘time-dependent method’ is proposed, which is to determine the forming limit strains more accurately and reasonably when producing a FLD from experimental data. This method is based on continual strain measurement during the test. The results are compared to those from the existing standardized methods. Key Words : Time-dependent Method, ISO 12004-2, Forming Limit Strain, Forming Limit Diagram, Nakajima Test

Effect of Bending Strain in Forming Limit Strain and Stress of IN-718 Sheet Metal

The forming limit diagram (ε-FLD) was estimated by deforming IN-718 sheet metal in different strain paths using a sub-size limiting dome height test set-up. The bending strains induced due to the use of smaller punch were estimated in all the strain paths, and the corrected ε-FLD was evaluated. The mathematical models such as Hill localized necking, Swift diffuse necking and Storen-Rice bifurcation theories were implemented to predict the limiting strains. In-order to avoid the path dependency of the ε-FLD during multi-stage forming process, stress based forming limit diagram (σ-FLD) was estimated using von-Mises and Hill-48 anisotropy plasticity theory with incorporation of Hollomon power hardening law. It was found that the bending strain influenced the limiting strains and stresses in the forming limit diagram. However, IN-718 material has encouraging formability in stretch forming process. The plot of the equivalent strains versus triaxiality indicated increasing limiting strain of the material in tension-tension mode.

Experimental detection of forming limit strains on samples with multiple local necks

Sheet metal formability is traditionally described by the forming limit curve (FLC). Experimental FLCs are obtained by performing formability tests and determining failure strains. The strains are usually measured either by etching a grid on the sheet surface or by digital image correlation (DIC). Ductile metal sheets fail primarily by local necking which introduces a severe strain gradient in the failure region. This makes accurate detection of the failure strains challenging. An international standard (ISO12004-2:2008) was introduced in 2008 to unify the procedure of FLC detection; prior to this large discrepancies were observed between the results reported by different laboratories. The main limitation of the standard method for detection of forming limits is that its application is limited to cases where a single local neck is formed in the metal sheet prior to fracture. In the case of multiple local necks, the samples are simply discarded. Furthermore, the standard method does not include any guidelines to distinguish the failure by local necking and direct failure by fracture. One of the advantages of DIC over the traditional etched-grid technique is that the former allows us to obtain not only the strain distribution but also its history. This allows for alternative methods for detection of forming limit strains. This paper introduces a DIC-based method which was specially developed to handle the case of multiple local necks and to distinguish failure by local necking from direct fracture automatically. The method is not confined to a single test type and can be used in combination with different formability tests as long as DIC is used to measure strains.

Predicting the tensile behaviour of adhesively bonded sheets using equivalent geometrical heterogeneities

In the present work, the formability of adhesively bonded sandwichsteel sheets is predicted during tensile tests, with the help of equivalent geometrical heterogeneities in the base sheets, without incorporating adhesive layer and properties during modelling simulations. This will help us mainly to overcome the difficulties while incorporating adhesion/adhesive properties during formability simulation and prediction. The limit strains during the tensile test are predicted and validated with experiments. The effect of hardener to resin (H/R) ratios of adhesive on the forming limit strains has been predicted with a set of thickness heterogeneity factor ‘f’ and size (w) of the defect, located in the base material. In other words, a relationship between defect morphology (f, w) and adhesive properties has been evaluated. For example, in the case of rectangular-infinite groove of width, w = 0.5 mm, the limit strains of DDQ steel evaluated during tensile tests at f = 0.912, f = 0.9137, f = 0.924, f = 0.927, and f = 0.95 are equivalent to the H/R ratios of 0.6:1, 0.7:1, 0.8:1, 0.9:1, and 1:1 of adhesive, respectively. The limit strains are predicted in the same manner with a square hole and finite square defect in the base material. It is suggested that the overall forming (tensile) behaviour of adhesively bonded blanks (ABB) can be predicted with the help of a thickness heterogeneity factor (or similar geometrical heterogeneities) that is equivalent to all the geometrical and structural heterogeneities in the whole bonded sheets.

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.

Effect of Equivalent Stress-Strain Relation and Differential Hardening on Accuracy of Forming Limit Analyses

Multiaxial tube expansion tests (MTETs) were performed to measure the multiaxial plastic deformation behavior of a cold rolled interstitial-free (IF) steel sheet for a range of strain from initial yield to fracture. The testing machine is capable of applying arbitrary principal stress or strain paths to tubular specimens using an electrical, closed-loop servo-control system for an axial force and an internal pressure. Tubular specimens with an inner diameter of 44.6 mm were fabricated from a cold rolled IF steel sheet with a thickness of 0.7 mm by roller bending and laser welding. Many linear stress paths in the first quadrant of stress space were applied to the tubular specimens to measure the forming limit strains and forming limit stresses of the as-received sheet sample, in addition to the contours of plastic work and the directions of the plastic strain rates. It was found that the shapes of the measured work contours changed with increasing plastic work. The observed differential hardening behavior was approximated by changing the material parameters and the exponent of the Yld2000-2d yield function (Barlat et al, 2003) as functions of the reference plastic strain. The hydraulic bulge tests were also conducted to measure the forming limit strain and forming limit stress for equibiaxial tension and to determine the equivalent stress-equivalent plastic strain relation for a larger strain range. The forming limit curve and forming limit stress curve were calculated using the Marciniak-Kuczyński-type approach. The calculated results were in fair agreement with the measurement.

Optical Measurement of Forming Limit and Formability of Cu/Al Clad Metals

A digital image deformation measurement and analysis control system (XJTUDIC 8.0) was employed to measure the forming limit strain for Cu/Al clad metals produced via explosive welding technique. A contrast test between the digital image correlation (DIC) method and the conventional grid method was also implemented using the SPCC sheet metal forming limit test. The effect of heat treatment and contact status on forming limit was discussed based on the forming limit strain of Cu/Al clad metals. The interfacial and fracture structures were analyzed using scanning electron microscopy. The fracture site was predicted by finite element method. Results demonstrate that the forming limit curve of Cu/Al clad metals through DIC is more likely to reflect the formability of SPCC accurately. The forming limit of the clad with Al in the inner layer is higher than that of the clad with Cu in the inner layer. The formability of the annealed clads is superior to that of the non-annealed clads. The local interface failure induces the microcracks in Cu/Al clad metals during the forming process, which could be the main failure mode. With the finite element method, the fracture location of Cu/Al clad metals caused by uniaxial tensile during the forming limit test using DIC method is predicted accurately.