**1. Introduction**

[12] Filip R, Kubiak K, Ziaja W, Sieniawski J. The effect of microstructure on the mechani‐ cal properties of two-phase titanium alloys, Journal of Materials Processing Technol‐

[13] Sieniawski J, Grosman F, Filip R, Ziaja W. Microstructure factors in fatigue damage process of two-phase titanium alloys. Titanium '95 Science and Technology, P.A. Blenkinsop, W.J. Evans and H.M. Flower eds., The Institute of Materials, Birming‐

[14] Gil F. J, Manero J. M, Ginebra M. P, Planell J. A. The effect of cooling rate on the cy‐ clic deformation of -annealed Ti-6Al-4V. Materials Science and Engineering. (2003).

[15] Ziaja W, Sieniawski J, Kubiak K, Motyka M.: Fatigue and microstructure of two

phase titanium alloys. Inżynieria Materiałowa. (2001). 22(3):981-985.

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80 Titanium Alloys - Advances in Properties Control

ham. (1996). 1411-1418.

A349(1-2):150-155.

Recently, different industries faced the challenge of implementation of titanium alloys in order to produce components with different formability characteristics. Titanium alloy sheets are defined as hard-to-form materials regarding to their strength and formability characteristics. Consequently, in order to soundly manufacture a part made from the mentioned alloys, novel processes such as hydroforming, rubber pad forming and viscous pressure forming instead of conventional stamping or deep drawing are applied.

In sheet metal forming industries, FE simulations are commonly used for the process/tool design. Availability of suitable mechanical properties of the sheet material is important factor for obtaining accurate FE simulations results.

### **1.1. Biaxial bulge test**

The most commonly used method to investigate the flow stress curve is uniaxial tensile test in which true stress-true strain curve is expressed in uniaxial stress state. However, maximum plastic strains obtained in uniaxial loading condition is not sufficient for most sheet metal forming simulation processes which involve biaxial state of stress [1-5]. Hydraulic bulge test is a comparative test method in which biaxial stress-strain curve could be attained. In 1950, a key theoretical pillar for the hydraulic bulge test was established by Hill [6]. In his study, Hill assumed a circular profile for the deforming work piece which allowed for the introduction of a closed form expression for the thickness at the pole region [5].

The experimental bulge test method involves pumping hydraulic fluid [4, 7-10] or a viscous material as a pressure medium [2-3, 11] instead of a hydraulic fluid into the die cavity. Circular as well as elliptical dies can also be used to determine anisotropy coefficients of material in different directions with respect to rolling direction [12-15].

© 2013 Djavanroodi and Janbakhsh; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Djavanroodi and Janbakhsh; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### **1.2. Forming Limit Diagrams (FLD)**

As mentioned before, due to increased demand for light weight components in aerospace, automotive and marine industries, recently, titanium sheet alloys have gained ever more interests in production of structural parts. In order to better understand the cold formability of these alloys, their behavior in sheet metal forming operations must be determined both experimentally and theoretically. Sheet metal formability is often evaluated by forming limit diagram. The concept of FLD was first introduced by Keeler [16] and Goodwin [17]. Forming limit diagram provides the limiting strains a sheet metal can sustain whilst being formed. Laboratory testing has shown that the forming limit diagrams are influenced by several factors including strain hardening exponent and anisotropy coefficients [18-20], strain rate [21-23], temperature [24], grain size and microstructure [25-26], sheet thickness [27], strain path changes [28-29], and heat treatment [30].

for determination of the FLDs and for verification of the predicted FLDs resulted from

Formability Characterization of Titanium Alloy Sheets

http://dx.doi.org/10.5772/55889

83

Djavanroodi and Derogar [19] used the Hill-Swift model to predict the limit strains for titanium and aluminum sheets. They performed hydroforming deep drawing test in conjunction with a novel technique called "floating disc" to determine the FLDs experimentally. It was con‐ cluded from their work that as strain hardening exponent and anisotropic coefficients increase, the limit strains will also increase, and consequently, this allows the FLD to be shifted up. In this chapter, different analytical approaches as well as the experimental methods are applied to obtain the uniaxial and biaxial flow stress curves for Ti-6Al-4V sheet metal alloy. The hydraulic bulge test was carried out and findings were compared with the results obtained from the uniaxial tensile test. Circular-shaped die was used. Stepwise test with gridded specimens and continuous experiments were performed. For flow stress calculations, both the dome height and pressure were measured during the bulge tests. The effects of anisotropy and

On the other hand, a practical approach was implemented for experimental determination of FLD and several theoretical models for prediction of forming limit diagrams for 1.08mm thick Ti-6Al-4V titanium sheet alloy subjected to linear strain paths were applied. For the experi‐ mental approach, the following test pieces have been used to obtain different regions of FLD: circle specimens to simulate biaxial stretching region of FLD (positive range of minor strain); non-grooved tensile specimens (dog-bone shaped specimens) to simulate the uniaxial strain path and two distinctive grooved tensile specimens representing the strain path ranging from uniaxial tension to plane strain region of FLD. The onset of localized necking was distinguished by investigating the strain distribution profiles near the necking region. Furthermore to predict the theoretical FLDs, Swift model with Hill93 yield criteria [55] and M-K model with Hill93 and BBC2000 yield criteria [56] were used. Predicted FLDs were compared with the experi‐ mental data to evaluate the suitability of the approaches used. Moreover, considering the extensive application of *Autoform 4.4* software in sheet metal forming industries, several parts representing different strain paths were formed to evaluate the FLDs of the tested sheets numerically. The effects of process parameters as well as yield loci and material properties

Hydroforming bulge test is one of the most commonly used balanced biaxial tests in which a circular sheet metal fully clamped between two die surfaces is drawn within a die cavity by applying hydrostatic pressure on the inner surface of the sheet. The die cavity diameter (*dd*

any hydroforming bulge testing. Instantaneous variables of biaxial test are: bulge pressure (*p*), dome height (*hb*), bulge radius (*Rb*) and sheet thickness at the dome apex (*t*). The schematic

) and initial sheet thickness (*t0*) are constant parameters of

strain hardening on material formability were also investigated.

used in simulations were also discussed.

**2. Theoretical approaches**

**2.1. Hydroforming bulge test**

*=2Rd*), the upper die fillet radius (*Rf*

view of hydroforming bulge test is shown in Fig.1.

analytical models.

In recent years many experimental techniques have been developed to investigate the FLDs from different aspects [31-34]. These studies were based on elimination of frictional effects resulted from toolsets and materials, the uniformity of the blank surface and mechanical properties of sheet materials deduced from the conventional tensile testing.

The available tests for the determination of FLDs include: hydraulic bulge test [35], Keeler punch stretching test [36], Marciniak test [37], Nakazima test [38], Hasek test [39] and the biaxial tensile test using cruciform specimen [40] (in short cruciform testing device). From previous studies [36-39], it is widely acknowledged that friction remains an unknown factor yet to be effectively characterized and understood. Thus, the list of available tests is greatly reduced to only two options - hydraulic bulge test and cruciform testing device. Further analysis shows that due to simplicity of equipment and specimen (i.e. less costly), hydraulic bulge test is comparatively preferred [41].

On the other hand, several researchers have proposed a number of analytical models to predict FLD. Hill's localized instability criterion [42], combined with Swift's diffused instability criterion [43] was the first analytical approach to predict FLDs. It was shown that forming limit curves are influenced by material work hardening exponent and anisotropy coefficient. Xu and Wienmann [44] showed that for prediction of the FLD, the shape of the used yield surface had a direct influence on the limit strains. They used the Hill'93 criterion to study the effect of material properties on the FLDs. The M-K model [45] predicts the FLD based on the assumption of an initial defect in perpendicular direction with respect to loading direction. The assumption made for this non-homogeneity factor is subjective and hence, the forming limit diagram is directly influenced by it. This method was then developed considering the material properties [46-47].

Several researchers used the ductile fracture criteria for forming limit predictions in hydro‐ forming process [48], deep drawing process [49], bore-expanding [50] and biaxial stretching [51]. Fahrettin and Daeyong [52] and Kumar et al. [53] proposed the thickness variations and the thickness gradient criterion respectively. These criteria are limited because they require precise measurements of thickness. Bressan and Williams [54] used the method of shear instability to predict the FLDs. Consequently, experimental techniques are widely accepted for determination of the FLDs and for verification of the predicted FLDs resulted from analytical models.

Djavanroodi and Derogar [19] used the Hill-Swift model to predict the limit strains for titanium and aluminum sheets. They performed hydroforming deep drawing test in conjunction with a novel technique called "floating disc" to determine the FLDs experimentally. It was con‐ cluded from their work that as strain hardening exponent and anisotropic coefficients increase, the limit strains will also increase, and consequently, this allows the FLD to be shifted up.

In this chapter, different analytical approaches as well as the experimental methods are applied to obtain the uniaxial and biaxial flow stress curves for Ti-6Al-4V sheet metal alloy. The hydraulic bulge test was carried out and findings were compared with the results obtained from the uniaxial tensile test. Circular-shaped die was used. Stepwise test with gridded specimens and continuous experiments were performed. For flow stress calculations, both the dome height and pressure were measured during the bulge tests. The effects of anisotropy and strain hardening on material formability were also investigated.

On the other hand, a practical approach was implemented for experimental determination of FLD and several theoretical models for prediction of forming limit diagrams for 1.08mm thick Ti-6Al-4V titanium sheet alloy subjected to linear strain paths were applied. For the experi‐ mental approach, the following test pieces have been used to obtain different regions of FLD: circle specimens to simulate biaxial stretching region of FLD (positive range of minor strain); non-grooved tensile specimens (dog-bone shaped specimens) to simulate the uniaxial strain path and two distinctive grooved tensile specimens representing the strain path ranging from uniaxial tension to plane strain region of FLD. The onset of localized necking was distinguished by investigating the strain distribution profiles near the necking region. Furthermore to predict the theoretical FLDs, Swift model with Hill93 yield criteria [55] and M-K model with Hill93 and BBC2000 yield criteria [56] were used. Predicted FLDs were compared with the experi‐ mental data to evaluate the suitability of the approaches used. Moreover, considering the extensive application of *Autoform 4.4* software in sheet metal forming industries, several parts representing different strain paths were formed to evaluate the FLDs of the tested sheets numerically. The effects of process parameters as well as yield loci and material properties used in simulations were also discussed.
