A novel method to evaluate the high strain rate formability of sheet metals under impact hydroforming

Journal Pre-proof A novel method to evaluate the high strain rate formability of sheet metals under impact hydroforming Da-Yong Chen, Yong Xu, Shi-Hong Zhang, Yan Ma, Ali Abd El-Aty, Dorel Banabic, Artur I. Pokrovsky, Alina A. Bakinovskaya

PII:

S0924-0136(19)30526-6

DOI:

https://doi.org/10.1016/j.jmatprotec.2019.116553

Reference:

PROTEC 116553

To appear in:

Journal of Materials Processing Tech.

Received Date:

10 April 2019

Revised Date:

11 November 2019

Accepted Date:

8 December 2019

Please cite this article as: Chen D-Yong, Xu Y, Zhang S-Hong, Ma Y, El-Aty AA, Banabic D, Pokrovsky AI, Bakinovskaya AA, A novel method to evaluate the high strain rate formability of sheet metals under impact hydroforming, Journal of Materials Processing Tech. (2019), doi: https://doi.org/10.1016/j.jmatprotec.2019.116553

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

A novel method to evaluate the high strain rate formability of sheet metals under impact hydroforming Da-Yong Chen a,b,1 , Yong Xu a, , Shi-Hong Zhang a, *, Yan Ma a, Ali Abd El-Aty a, Dorel Banabic c, Artur I. Pokrovsky d, Alina A. Bakinovskaya d a

b

Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China

School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China

d

Technical University of Cluj-Napoca, Cluj-Napoca 400641, Romania

ro of

c

Physical-Technical Institute, National Academy of Sciences of Belarus, Minsk 220141, Belarus

-p

* Corresponding author. Email: [email protected] (S.H. Zhang). 1 These authors contributed equally to this work.

Abstract:

re

In this study, a novel method was proposed to evaluate high strain rate (HSR) formability of Al-Cu-Mg 2B06-O sheets by impact hydroforming (IHF). IHF was suitable to manufacture hard-

lP

to-form sheets, since it combined the advantages of flexible liquid and impact impulse loading. Both 2D and 3D HSR formability curves were established to describe the relationship between impact energy, drawing height ratio (DHR) and deep drawing ratio (DDR). Moreover, the novel evaluation method was realized by finite element (FE) modeling using Fluid-Structure Interaction (FSI)

na

algorithm. FSI modeling was used to deal with the interaction of structure solid and flexible fluid. This evaluation means of FE modeling characterized with guiding production practice, saving evaluation costs, improving efficiency compared with corresponding experiments. The results

ur

obtained from FE modeling were in a remarkable agreement with those obtained from IHF experiments in the aspects of part shape, failure feature, thickness distribution. FE modeling showed that the limit deep drawing ratio (LDDR) and limit drawing height ratio (LDHR) were 1.99 and 1.04,

Jo

respectively when the blank was completely deep drawn to the cavity of the die in one step only. FE modelling is proved to be reliable and efficient to estimate high strain rate formability of low formability metal sheets. Keywords: Impact hydroforming, High strain rate formability, Al-Cu-Mg 2B06-O sheet, Finite element, Fluid-Structure Interaction algorithm.

1. Introduction

Jo

ur

na

lP

re

-p

ro of

The requirement of weight reduction in automotive, aircrafts, and aerospace applications promotes the utilization of lightweight material such as aluminum alloys (Choi et al., 2007). Nevertheless, the deformation of Al alloys at the room temperature is quite difficult especially for high strength aluminum alloys belong to 2xxx series (Abd El-Aty et al., 2018). Hydroforming is an attractive forming technology to form some complex-shaped components which are used in different fields. For example, micro-forming for tube component has been utilized for decades by means of hydroforming with consideration of size effect. Both numerical and experimental investigations are conducted in order to explore the influence of size effects on the material and friction behavior, as well as the feasibility restraint of forming tools (Cao et al., 2004) and (Hartl., 2019). Component size is one aspect and the forming speed is another significant one for hydroforming. In recent years, high-speed forming (HSF) was considered as a significant forming technology for manufacturing of complex-shaped, thin-walled components of Al alloys at room temperature (Abd El-Aty et al., 2019). Impact hydroforming (IHF) is one of high strain rate forming technologies which can be used to improve the formability of low ductility metal sheets (Kosing et al., 1998). At the early of 1968, IHF was proposed by Bruno et al. (1968) as Pneumo-mechanical forming. IHF can effectively combine the advantages of flexible liquid and impact impulse (Ma et al., 2018). Thus, it can be defined as a flexible forming technology because the liquid serves as a kind of selfadapting medium for both stress and strain (Yang et al., 2018). IHF is a suitable forming technology for small structure filling in a very short procedure (Lang et al., 2013). IHF has the merit of better safety when it is compared with the traditional explosive forming methods which possess a huge limitation in their usage (Zhang et al., 1994). Meanwhile, it is more economical and practical to form complex and large-size parts compared with the electromagnetic forming (Li et al., 2019) and laser shock processing for the restriction of power (Montross et al., 2002). IHF possesses several advantages over the conventional forming technologies such as reducing the procedures required in manufacturing (Zhang et al., 2004), enhancing the formability (Balanethiram et al., 1994), suppressing the wrinkling and springback (Abd El-Aty et al., 2018). A novelstyle IHF press is designed and manufactured based on the study of Ma et al. (2018), in the contrast to the machine with explosive source (Homber et al., 2013). The range of impact speed is 10~80 m/s and the impact energy can reach to 200kJ (Ma et al., 2018). Recently, Tekkaya et al. (2015) propose a new metal forming technology which not only focuses on shaping but also decides the product properties which emphasizes the significance of the formability. However, so far there is no applicable and efficient assessment method to evaluate the formability of metal sheets under IHF. Early in 1960s, Marciniak et al. (1967) has already focused on the formability by means of investigating limit strains of stretch-forming sheet based on anisotropic plasticity theory. The formability of the metallic materials is significant to be estimated

lP

re

-p

ro of

and utilized for process design of the HSF. Banabic et al. (2013) has developed a novel and effective method for obtaining the forming limit curves (FLC) based on the hydraulic bulging of two layers sheets which can cover the whole strain range. However, the IHF characterized both deep drawing and bulging which cannot be accurately described only by the FLC. Moreover, HSR formability of metal sheets by the IHF process is not as easy as the Hopkinson testing which is good at reflecting the proprieties of uniaxial tension (Li et al., 2009). Azaryan et al. (2016) establish an assessment method to evaluate the HSR formability of metal sheets under deep drawing. Nevertheless, the detailed parameters are difficult to be represented only by the experimentation because of the limit of the observe space and the short forming cycle, and plentiful experiments are required to establish the formability curve. On the other hand, the two-dimensional FLC cannot provide the information of drawing height only based on the experimentation. Thus, FE modeling is a reasonable and effective tool to estimate the formability of metallic sheets under hydroforming (Xu et al., 2016). In this study, FE method was innovatively proposed to investigate the impact energy and the DHR instead of extensive experiments such as the method of Azaryan et al. (2016). FE modeling based on the Fluid-Structure Interaction (FSI) was employed to deal with the coupling of liquid and solid (Khodko et al., 2015) by using the outstanding explicit-solving software LS-DYNA (LS-DYNA, 2007). FE modeling was established based on J-C constitutive model (Dey et al., 2007) and HSR mechanical properties of AA2B06-O that were investigated by Lang et al. (2009). HSR formability of AA2B06-O was investigated to explicit the relationship between the forming energies, the DHRs and the DDRs. Both 3D and 2D formability curves were quantificationally established based on the impact energies and DHRs. Finally, the corresponding experiments were conducted to compare with FE analysis.

2. Procedure of establishing high strain rate formability curve

Jo

ur

na

2.1 Principle of IHF process The basic principle of IHF is depicted in Fig. 1. The projectile is accelerated by the compressed air or other energy source and then it impacts the liquid; thereafter the liquid is activated and moved to the blank with high velocity and high pressure, and the energy is transferred to the blank. Afterwards, the initial blank is formed to be the final workpiece with designed size and structure by the shock wave of liquid in about several hundred microseconds. The technology is characterized with instantaneous high pressure, loading time of 100~500μs, pressure up to 500~1000MPa.

Fig.1 Principle of impact hydroforming (before, and after forming)

Jo

ur

na

lP

re

-p

ro of

2.2 Fluid Structure Interaction (FSI) Algorithm Fluid Structure Interaction (FSI) was employed to deal with the coupling interaction between the projectile and the liquid. FSI modeling of the IHF was accomplished by LS-DYNA FE code using the keyword for coupling called “CONSTRAINED_LARGRANGE_IN_SOLID” which was good at explicit solution. Namely, solid-liquid-solid interaction was realized in the whole IHF process. The liquid was assumed as the compressible substance based on the Gruneisen Equation of State according to the coupling theory (LS-DYNA, 2007). The fluid was defined as the master part while the projectile and the blank were treated as slave parts. The keyword of “CONTACT_FORMING_ONE_WAY_SURFACE_TO_SURFACE” in LS-DYNA FE code was employed to deal with the contact problem between tools and blank. The corresponding static coefficient of friction was selected as 0.05 for current simulation to ensure enough material feeding. Furthermore, the penalty factor and leakage control were elaborately considered and selected to estimate the interacting stiffness of the system and restrain the leak by utilizing the proper magnitude of additional coupling force (LS-DYNA, 2007). According to the investigation of Woo et al. (2018), the ALE algorithm was employed to treat the large deformation process with the obvious movement of the blank. In order to make a successful modeling, the following assumptions were assumed: (1) The forming tools were treated as rigid body because almost no deformation happened (material model *MAT_RIGID) and the mesh dimension would not affect the convergence. (2) The influence of air was ignored and the space was regarded as vacuum (void) that could reduce the computational costs obviously. 2.3 Characterization of the sheet specimens and the material property The material used in this study is rolled Al-Cu-Mg 2B06-O sheets which is the purified version of AA2A06. The chemical compositions of as-received AA2B06-O sheet is presented in Table 1. The temperature and humidity during experimentation are 20 ℃ and 20 %, respectively. The mechanical properties of AA2B06-O sheets are σT (tensile strength)=189 MPa, σY (yield strength) =58.2Mpa, δ (elongation)=15%. Table 1 Chemical compositions of AA2B06-O alloy (%)

Elements

Cu

Mg

Mn

Fe

Zn

Si

Ti

Be

Al

Fraction

3.58

1.76

0.56

0.16

0.015

0.063

0.012

0.0017

Basis, 93.85

The thickness of AA2B06-O blanks is 1.2 mm in this investigation. The DDR (𝐷𝑟𝑎𝑡𝑖𝑜 ) is defined according to the ratio of initial blank diameter and equivalent punch diameter (die diameter subtracts wall thickness) according to Leu et al. (1997) as introduced in Eq. 1. Furthermore, the DHR (𝐷ℎ𝑟𝑎𝑡𝑖𝑜 ) is defined as ratio of drawing depth and equivalent punch diameter in order to describe the deformation amount of the deep drawing at certain DDR as written in Eq. 2. 𝐷𝑟𝑎𝑡𝑖𝑜 = 𝐷

(1)

𝑑 −2×𝑡

𝐻

(2)

𝐷𝑑 −2×𝑡

ro of

𝐷ℎ𝑟𝑎𝑡𝑖𝑜 =

𝐷0

where, 𝐷0 , 𝐷𝑑 represent the initial diameter of blank and diameter of drawing die, respectively. 𝑡 is the wall thickness of the deformed part, and 𝐻 is the bulging height. The details of the specimens used in the simulation and experiment are depicted in Table 2.

-p

Table 2 Setting of blank diameter and the DDRs

51.2

54.7

Deep drawing ratio

1.42

1.51

57.8

63.9

70.5

77.0

83.6

1.60

1.77

1.95

2.13

2.31

lP

Diameter /mm

re

Blanks

Jo

ur

na

2.4 Dynamic material constitutive equation Johnson-Cook (J-C) model was first proposed by Johnson and Cook in 1985 (Johnson et al., 1985). J-C constitutive model is acceptable to be used for HSR deformation because it clearly describes the relations between stresses and strains under large deformation and high strain rates. In the J-C model, the strain hardening, strain rate hardening, and thermal softening are assumed to be independent phenomena and can be separated from each other. Thus, the unknown parameters, are easily calculated by fitting the stress-strain curve at different strain rates. In this study, the strain rate was limited to 1500 s-1 whose adiabatic heat could be neglected (Wang et al., 2013). Nevertheless, two strain rates beyond 1500/s were used to validate the constitutive model. The increasing in temperature under different strain rates were calculated for AA 2B06-O sheets. And it was noticed that the temperature was increased in the range of 10~20 ℃ when the strain rates were not more than 2000/s, as it was illustrated in Table 3. Thus, the effect of thermal softening was neglected in current study, which led to simplify (J-C) model to Eq. 3. σ(𝜀, 𝜀̇) = 𝑓1 (𝜀)𝑓2 (𝜀̇) = (𝐴 + 𝐵𝜀 𝑛 )(1 + 𝐶ln𝜀̇∗ ) (3) where 𝜎 is the equivalent stress, 𝜀 is the equivalent plastic strain, 𝜀̇ is the strain rate, 𝜀̇0 is the reference strain rate, A is the yield stress under reference deformation

conditions (MPa), B is strain hardening coefficient (MPa), C is strain rate strengthening 𝜀̇

coefficient, 𝜀̇∗ stands for the non-dimensional strain rate and 𝜀̇ ∗ = 𝜀̇ . In this study, the 0

reference strain rate was selected as 10-1 s-1 for AA2B06-O sheets. Table 3 Increase of temperature with strain rates Strain rates /s

1141

1888

4047

Increase of temperature /℃

11.8

19.4

47.7

lP

re

-p

ro of

Furthermore, the dog bone specimen was made for the mechanical property testing with parallel length of 4mm, in order to obtain the stress-strain curves of AA2B06-O sheets under quasi-static and dynamic strain rates. The specimen was stretched by tensile testing machine (INSTRON 55822) along to the rolling direction of blank for quasi-static forming under reference strain rate. As for high strain rate, Hopkinson split tensile bar was employed to form the specimen whose diameter of incident bar is 20mm. (1) Calculation of 𝑩 and 𝒏 Initially, when 𝜀̇=𝜀̇0 , Eq. 3 was reduced to: σ = 𝐴 + 𝐵𝜀 𝑛 (4) -1 -1 by substituting the stress-strain data under 10 s to the Eq. 4, and choosing A as 58.2 MPa, B and n were obtained by nonlinear fitting as 272.59 MPa and 0.52767, respectively. (2) Calculation of C The parameter C was treated as constant when the strain rate was increased in the investigation. By using the stress-strain data at strain rate of 4047 s-1, C was obtained by employing non-linear fitting as 0.02911. The parameters of J-C model of AA2B06O sheets were summarized in Table 4. Table 4 Parameters of J-C model of AA2B06-O -T8 sheet Items

B

n

C

58.2

272.6

0.52767

0.02911

na

Value

A

Jo

ur

As depicted in Fig. 2, the final fitting curve under strain rate of 4047 s-1 was obtained according to Eq. 3. Meanwhile, other two strain rates were used to validate the fitting effectiveness with the condition of 1141 s-1 and 1888 s-1. As depicted in Fig. 2, the flow stress curve fluctuated slightly when the strain increased gradually. Moreover, the true stress slightly increased when the strain rate was increased from 1141 s-1 to 4047 s-1, while the strain increased obviously with the increasing of strain rate. It was proved that the plastic strain was greatly increased when the strain rate enhanced compared with the quasi-static tensile testing. In addition, the fitting curves coincided well with the experimental results which illustrated it was suitable to be adopted in FE modelling.

Fig. 2 The stress-strain curve of simplified J-C constitutive material model

ur

na

lP

re

-p

ro of

The simplified J-C material model with damage (numbered 99 in LS-DYNA) was selected to describe the crack of the blank (LS-DYNA, 2007). The failure strain was set as 0.3 according to the crack strain of the material during IHF. The elements would be deleted from the part when rupture was found at integration points until the threshold strain was reached. 2.5 Geometrical models and meshing As shown in Fig. 3, the forming tools mainly include the upper die, fixing ring, lower die, centering plate, locating ring, and die set. The diameter of the lower die cavity is 38.5mm and the fillet of the lower die is 5 mm. Only the projectile, liquid, upper die, lower die and blank are substantially useful for FE modeling according to the contact relationship and the process principle.

Fig. 3 Geometrical models of the tools

Jo

In order to simplify the model, the liquid was treated as cylinder with a diameter of 48.5mm. Furthermore, the lower surface of the upper die and the inner surface of the lower die cavity were selected as the forming dies as shown in Fig. 4. The eight-node hexahedron elements were employed for the FSI model with the parts of projectile, liquid and blank. Moreover, for the upper and lower die, the four-node quadrilateral shell element was selected to reduce the calculation time. By using the 3D model, a remarkable accuracy was obtained while the calculation time was relatively increased in the same time. Because the elements size affected the calculation efficiency and precision of the simulation, a proper element size was selected to prevent the penetration. Firstly, a mesh

size of 2 mm was used, however the penetration occurred. Thereafter the mesh size of 1.2 mm and 0.6 mm were employed in order to address the aforementioned issue. Mesh size of 1.2mm was finally used considering both efficiency and precision. The element size of 1.2mm×1.2mm was necessary for the forming medium (water), as well as the projectile and the blank. The blank was discretized to three layers of solid element with the vertical size of 0.4mm. The upper and lower die were treated as the rigid bodies (*MAT_RIGID in LS-Dyna keywords) because they possessed a higher strength than the blank. Therefore, relative coarse shell element of 1mm was employed without affecting the integration process but could reduce the computational time. For the projectile, “MAT_POWER_LAW_PLASTICITY” was used as the constitutive equation in LS-Dyna software, and its function was as follows: 𝑛

(5)

ro of

𝜎𝑦 = 𝑘𝜀 𝑛 = 𝑘(𝜀𝑦𝑝 + 𝜀̅𝑝 )

na

lP

re

-p

where, 𝜀𝑦𝑝 is the elastic strain to yield and 𝜀̅𝑝 is the effective plastic strain (logarithmic). Furthermore, k and n are the strength coefficient and the hardening exponent, respectively. k and n were used as 1426 MPa and 0.52, respectively in current FE modelling. For the initial yield stress, a high value was adopted to prevent the improper deformation of projectile. The main purpose of using this constitutive equation was providing the real mass by means of solid elements.

Fig. 4 Model simplification and meshing

Jo

ur

2.6 Equation of state The material model of MAT_NULL was employed to calculate the forming liquid because this kind of material model did not have shear stiffness, and yield strength only performed in a liquid-like mode (Boyd et al., 2000). The null material was endowed with the detailed parameters including the sound velocity in the liquid, Gruneisen gamma. According to the Gruneisen equation of state, the pressure of the compressed material is expressed as (LS-DYNA, 2007): 𝑃=

𝛾 𝑎 𝜌0 𝐶 2 𝜇[1+(1− 0 )𝜇− 𝜇 2 ]

2 2 2 𝜇2 𝜇3 [1−(𝑆1 −1)𝜇−𝑆2 −𝑆3 ] 2 𝜇+1 (𝜇+1)

+ (𝛾0 + 𝑎𝜇)𝐸

The pressure for the expanded materials is introduced as: 𝑃 = 𝜌0 𝐶 2 𝜇 + (𝛾0 + 𝑎𝜇)𝐸 The compression is presented in the form of the relative density as:

(6)

(7)

𝜌

𝜇 =𝜌 −1

(8)

0

where C stands for the sound speed in water at room temperature, 𝜌0 is the initial density of water, 𝛾0 represents the Gruneisen gamma and a is the first order volume correction for 𝛾0, E stands for the internal energy per volume. 𝑢𝑠 stands for the shock wave velocity and 𝑢𝑝 is fluid particle velocity, shock wave and fluid particle velocity are illustrated as follows according to Shin et al., (1998): 𝑢𝑠 −𝑐 𝑢𝑠

𝑢

2

𝑢

𝑢

3

= 𝑆1 (𝑢 𝑠 ) + 𝑆2 (𝑢 𝑠 ) + 𝑆1 (𝑢 𝑠 ) 𝑝

𝑝

(9)

𝑝

ro of

in which 𝑢𝑠 stands for the shock wave velocity and 𝑢𝑝 is the fluid particle velocity, and 𝑆1, 𝑆2 , 𝑆3 are the slope coefficients for the curve 𝑢𝑠 − 𝑢𝑝 . The corresponding parameters are from Khodko et al., (2015) which are listed in Table 5. Table 5 Parameters in equation of state Items Value

𝐶 1484 m/s

𝜌0 3

3

1.0 × 10 kg/m

𝑆1

𝑆2

𝑆3

𝛾0

𝑎

𝐸

1.979

0

0

0.11

0

0

Jo

ur

na

lP

re

-p

2.7 Experimental procedures The experiments were conducted using the IHF press which had the maximum impact energy of 200 kJ. This means that the press possesses enough energy for the current experiments with impact speed range of 4 to 30 m/s (Ma et al., 2018). As depicted in Fig. 5, the IHF press is consisted of four zones: power zone, acceleration zone, forming zone and control zone. During the experimentation, a cylindrical projectile with the diameter of 300 mm (which equaled to the diameter of the working chamber) was used to provide enough precision when it flew with the high speed. The ratio of the liquid mass in the working chamber to the mass of the projectile was defined as α = 𝑚𝑤 ⁄𝑚ℎ = 0.061.

Fig. 5 Novel impact hydroforming press

The round blank was placed on the lower die and it was located inside the centering

ur

na

lP

re

-p

ro of

plate which had equal thickness with the blank. The upper die was fixed on the master cylinder of the press by the fixing ring. The locating ring was used to guide the upper die to the right position along to the axial direction. After the upper die contacted the blank and the centering plate with the suitable clamping pressure, the liquid was accelerated by the high-speed projectile. Then the blank was formed by the liquid (water) with the high energy in the manner of shock wave. The initial impact energy (impact energy per unit area) was determined mainly by the speed and the mass of the projectile. The impact energy per unit area was used in this study to assure that the validity of the evaluation method for the other size sheets. The velocity sensor was set in the lateral wall of the chamber whose position was near to the upper surface of the liquid to exactly detect the finial velocity of the accelerated projectile. Once the experiment started, the energy of the first specimen with DDR of 1.4 was selected based on the trial and error method. The specimen would not be completely deep drawn into the cavity of the die if the impact energy was not enough. After that, the impact energy was increased step by step (with a very small increment) until the specimen was completely deep drawn into die cavity. Meanwhile, the corresponding speed value of projectile was recorded and the other two experiments were repeated on the same speed. If three experiments coincided well with each other (the relative error was in 8%) from the aspect of velocity, the average of velocity was chosen as the velocity under the current DDR. Otherwise, subsequent experiments would be conducted until the three experimental results coincided well. The velocity value under other DDRs was obtained according to the previous procedure. The uncomplete and complete deep drawing areas were distinguished according to the fitting the data of the complete deep drawing under different DDRs. The cracks would happen on the specimens before they were completely deep drawn into the die cavity if the DDR was large enough. Finally, the minimum value of velocity could be obtained for the specimen just has defect of crack with small increase of energy step by step. Another two groups of the experiments were conducted with the increase of the DDR according to the previous assumption. Finally, the uncomplete and crack areas were distinguished by fitting the critical crack data that obtained previously. Finally, the LDDR was selected as the DDR at the interjection of complete and crack fitting curves.

3. Results and discussion

Jo

In this section, the main FE modeling results of IHF process and high strain rate formability curve are presented and compared with the experimental results. 3.1 The validation of FE modeling A series of blanks with different DDRs were formed by FE modelling with different impact energies according to the forming states of the parts. The forming states included incomplete deep drawing, complete deep drawing and cracking. The forming parts are depicted in Fig. 6 (a). As shown in this figure, the circular specimens were deep drawn in different levels under different impact energies and DDRs. If the DDRs were less than 1.77, the blanks could be completely drawn into the die cavity without any defects once the forming energy was enough. The blank with the DDR of 1.95

-p

ro of

could be completely drawn if the suitable energy was selected, however, it also had the possibility to be fractured if the energy was too high. The blanks could not completely draw if the DDRs were 2.13 and 2.31, respectively. Moreover, crack with three to four segments was occurred on the dome central area of the blanks if the impact energy was high. The deformed parts from experimentation are shown in Fig. 6 (b). Three to four cracks occurred in the dome area of the part which were in the line with the results obtained from FE modeling when the DDRs were more than 2.02. It was noticed that the large value of effective plastic strain was located on the dome and the round corner of lateral wall and flange which was the potential failure zone. All the results obtained from FE modelling are in remarkable agreements with those achieved from experimentation in the aspects of part shape and failure feature.

re

Fig. 6 Parts feature of (a) FE modeling, (b) experiment for AA2B06-O

Thinning ratio /%

Jo

ur

na

lP

3.2 Wall thickness distribution The wall thickness was measured based on the 83.6mm diameter blank when it was deep drawn to the largest depth. Forty-two measuring points were adopted along the arc length of the part. For the actual formed part, the thickness was measured by micrometer gauge along the longitudinal section of this part. The distribution of the thinning ratio is presented in Fig. 7. The deformed part was mainly composed of flange area ( I ), round corner ( II ), near bottom area ( III-B ) and bottom ( III-A ). The wall thickness of the flange area was increased because of the compressive stress from circumferential direction. The largest thinning ratio was 20.89 % in the central of the bottom area. 5.0 2.5 0.0 -2.5 -5.0 -7.5 -10.0 -12.5 -15.0 -17.5 -20.0 -22.5 -25.0

Flange Area I

II

I

II

Round Corner

III-B I II

Near Bottom

II I

III

III 0

5

10

Bottom Area Experiment FSI-FEM

III-A 15

20

25

30

35

Number of measurement points

40

Fig. 7 Wall thickness distribution and comparison between FE simulation and experiment

In current study, the correlation coefficient (R) which introduced in Eq. 10 (Huang et al., 2017) was utilized to reveal the linear relationship between the results of the wall thickness obtained from FE modelling and those achieved from experimentation. If the value of R was closed to 1 the simulated results coincided well with the experimental results. As depicted in Fig. 8, it was noticed that the R value was 0.98483 and the largest difference existed at the near bottom area III-B. In the areas of flange and bottom, the R value was very close to 1 which verify the reliability of the FE modeling. 𝑅=

𝑖 𝑖 ̅ ̅ ∑𝑖=𝑁 𝑖=1 (𝑇𝐸𝑋𝑃 −𝑇𝐸𝑋𝑃 )(𝑇𝐹𝐸𝑀 −𝑇𝐹𝐸𝑀 ) 2

√∑𝑖=𝑁(𝑇 𝑖 −𝑇̅𝐸𝑋𝑃 ) ∑𝑖=𝑁(𝑇 𝑖 −𝑇 ̅ 𝐹𝐸𝑀 ) 𝑖=1 𝐸𝑋𝑃 𝑖=1 𝐹𝐸𝑀

(10)

2

re

-p

ro of

𝑖 𝑖 where, 𝑇𝐸𝑋𝑃 and 𝑇̅𝐸𝑋𝑃 are the current and average thickness of experiment, 𝑇𝐹𝐸𝑀 and 𝑇̅𝐹𝐸𝑀 are the current and average thickness obtained from FE modeling, N is the whole number of measuring points. Furthermore, the root mean square error (RMSE) (Xiao et al., 2018) and the average absolute relative error (AARE) (Huang et al., 2017) were also calculated to quantify the predictability of the wall thickness as the unbiased parameters. According to Eq. 11 and Eq. 12, the values of RMSE, and AARE were 0.017 % and 1.22 %, respectively. The FE results agreed well with the experimental results. Finally, NMBE was defined as normalized mean bias error and the calculated value of -2.01% illustrated that FE modeling made a little underprediction compared with the real forming process (Li et al., 2013). 1

lP

𝑖 𝑖 𝑅𝑀𝑆𝐸 = √𝑁 ∑𝑖=𝑁 𝑖=1 (𝑇𝐸𝑋𝑃 − 𝑇𝐹𝐸𝑀 ) 1

𝐴𝐴𝑅𝐸 = 𝑁 ∑𝑖=𝑁 𝑖=1 |

Jo

𝑖 𝑇𝐸𝑋𝑃

(11)

| × 100%

1 𝑖=𝑁 𝑖 𝑖 ∑ (𝑇 ) −𝑇𝐹𝐸𝑀 𝑁 𝑖=1 𝐸𝑋𝑃 1 𝑖=𝑁 𝑖 ∑ 𝑇 𝑁 𝑖=1 𝐸𝑋𝑃

(12)

× 100%

(13)

5

R=0.98483 0 RMSE=0.01730 AARE=1.22424% NMBE=-0.20138% -5

ur

Thinning ratio of simulation /%

na

𝑁𝑀𝐵𝐸 =

𝑖 𝑖 𝑇𝐸𝑋𝑃 −𝑇𝐹𝐸𝑀

2

-10

III-A

-15

Bottom Area

III-B Near Bottom

I II

-20 -25 -25

Flange Area

Round Corner -20

-15

-10

-5

0

5

Thinning ratio of experiment /% Fig. 8 Correlation of wall thickness between simulation and experiment when the initial diameter of blank is 83.6mm

The thinning ratio of other specimens was also calculated under the condition of

complete deep drawing and uncomplete deep drawing but with largest height before crack. It was illustrated in Fig. 9, which showed the comparison of thinning ratio between FE simulation and experiment under different DDRs. As illustrated in Fig. 9, the FSI-FE results coincided with the ones of experiment. However, the results from simulation fluctuated when initial blanks were too small as shown in Fig. 9 (a) and (b). This maybe because the forming procedure was unstable when the part was deformed under high strain rates but without enough restriction acting on flange area. The correlation coefficient (R) increased with the increase of the initial diameter of blanks. The validity of the FSI simulation was confirmed especially when the blank with the flange was formed under IHF. The NMBE value changed in the range of 0.01~0.47 which illustrated FE modeling made a little overprediction compared with the experiment.

5

FSI simulation Experiment

0

0

10

20

30

40

Number of measurement points R=0.95261 RMSE=0.01501 AARE=1.00543 NMBE=0.01173 FSI simulation Experiment

0

-5

-10

0

10

na

5

20

30

40

5

FSI simulation Experiment

0

-5

-10

0

15 10

(d)

5 0

0

-20 -25

50

-20

0

10

20

30

FSI simulation Experiment 40 50 60

Number of measurement points

R=0.97400 RMSE=0.02633 AARE=2.00559 NMBE=0.09576

0

FSI simulation Experiment 10 20

30

40

50

Number of measurement points 15

R=0.99034 RMSE=0.02997 AARE=2.48337 NMBE=0.24486

(e)

40

-15

-10

-30

30

-10

R=0.98475 RMSE=0.02948 AARE=2.12627 NMBE=0.41851

10

Thinning ratio /%

Jo Thinning ratio /%

10

20

-5

Number of measurement points

20

10

Number of measurement points

lP

(c)

ur

Thinning ratio /%

10

R=0.91172 RMSE=0.01960 AARE=1.42722 NMBE=0.46623

re

-5

(b)

-p

10

Thinning ratio /%

R=0.94632 RMSE=0.01365 AARE=0.97961 NMBE=0.25270

ro of

10

(a)

Thinning ratio /%

Thinning ratio /%

15

5 0 -5 -10 -15 -20 -25 -30 -35

FSI simulation Experiment

(f) 0

10

20

30

40

50

60

Number of measurement points

70

Fig. 9 Comparison of thinning ratio between FE simulation and experiment under different DDRs; (a) DDR=1.42, (b) DDR=1.51, (c) DDR=1.60, (d) DDR=1.77, (e) DDR=1.95, (f) DDR=2.13

re

-p

ro of

3.3 High strain rate formability curve A three-dimensional (3D) formability curve was established by describing the relationship between impact energy, DHR and DDR by both simulation and experiment. As shown in Fig. 10 (a), both the impact energy and the LDHR increased when the DDR was not more than 1.95. However, both would decrease once the DDR surpassed a certain value. The 3D formability curve is drawn in Fig.10 (b) using the same method as aforementioned discuss by means of experimentation. As shown in Fig. 9, both impact energy and DHR changed with the variation of the DDRs. Moreover, the experiments and the simulation had the same trend in the aspect of curve shape.

Fig. 10 The three-dimensional formability curve from (a) FE simulation and (b) experimentation

Jo

ur

na

lP

HSR formability curve is depicted in Fig. 11 which mainly presents the relationship between the impact energy and the DDR. As shown in this figure, the HSR formability curves were the boundaries of three areas: (1) incomplete deep drawing area (Area I), (2) complete deep drawing area (with no flange as Area II), and (3) crack area (Area III). The formability curve was fitted according to the incomplete, complete and crack experimental results. The LDDR of 1.99 represented ultimate value under the condition that the sheet could be totally drawn into the cavity without flange. It was obtained from the intersection of complete drawing and crack curve. The value of 1.99 was more than 1.92 which was the LDDR of the conventional drawing under very low velocity for AA2B06-O sheets. This proved that IHF could improve the formability of AA2B06-O sheets slightly in current condition of the projectile velocity and mass. This phenomenon was studied systematically by Marciniak et al. (1973) who revealed the strain-rate sensitivity of the material. The limit strain would be increased if proper strain rate was employed. And the shape of forming limit curve would be changed even adopting a very low value of exponent m (represented the influence of strain rate on mechanical property). The impact energy was about 2207.2kJ/m2 if the blank reached to the LDDR. It was also concluded that the sheet had a very widely allowable energy span for the small DDR. However, the span became narrow once the DDR was close to the limit value from left side. This meant that the blank could not be completely drawn

under low energy, however, the cracks would happen once the energy increased slightly. Furthermore, the blank was going to damage directly from the state of incomplete drawing if the energy was slightly increased when the DDR was more than 1.99. Similarly, the 2D dynamic formability curve was established using the experimental results as depicted in Fig.11. The 2D dynamic formability curve was also divided into three different zones by fitting the complete drawing and crack curves. The LDDR of 2.02 was obtained from the intersect of two forming curves. This value was larger than 1.99 which was acquired from the FE modeling. On the other hand, the impact energy of each curves was lower than the one of FE simulation, such as it was 1902.3kJ/m2 when the LDDR was achieved. If the impact energy per unit area is defined as 𝐸𝑖𝑚𝑝𝑎𝑐𝑡 , the following HSR formability curve would be obtained from the simulation:

ro of (14)

lP

re

-p

𝐸𝑖𝑚𝑝𝑎𝑐𝑡

−18807.21 + 38792.44 ∗ 𝐷𝑟𝑎𝑡𝑖𝑜 − 27104.02 ∗ 𝐷𝑟𝑎𝑡𝑖𝑜 2 = {+6488.88 ∗ 𝐷𝑟𝑎𝑡𝑖𝑜 3 , 𝑤ℎ𝑒𝑛 𝐷𝑟𝑎𝑡𝑖𝑜 ≤ 1.99 800.47 + 8.35𝑒7 ∗ 0.00402𝐷𝑟𝑎𝑡𝑖𝑜 , 𝑤ℎ𝑒𝑛 𝐷𝑟𝑎𝑡𝑖𝑜 ≥ 1.99

Fig. 11 HSR formability curves from FE modeling and experiment

Jo

ur

na

The LDHR was very useful to predict the permissible drawing height to effectively avoid the fracture when the DDR exceeded the limit value. The DHR would increase with the impact energy in condition of certain DDR. And the DHR would no more change if the specimen was completely drawn into the cavity. The largest value of DHR for each DDR was used to fit the drawing height ratio as illustrated in Fig. 12. As depicted in Fig. 12, the DHR changed linearly with the DDR before reaching the LDDR, however it decreased exponentially once the value surpassed 1.99. The LDHR reached to 1.04 (the height was 37.5 mm) when the initial blank with diameter of 72.9 mm was completely drawn. The DHR curve is depicted according to the points of corresponding part with the variation of DDRs. As shown in Fig. 12, the curve obtained from the experimental results had the same trend with those obtained from FE simulations in the form of linear and exponential change. The LDHR was 0.95 (the limited drawing height was 34.3 mm) when the blank with diameter of 71.8mm was completely deep drawn. Meanwhile, the value of 0.95 was smaller than the value of 1.04 from FE modelling. The DHR sharply

reduced firstly, and then the DHR reduction was lower after the DDR surpassed the threshold value. The equations of the two curves are: 𝑤ℎ𝑒𝑛 𝐷𝑟𝑎𝑡𝑖𝑜 ≤ 1.99 𝑤ℎ𝑒𝑛 𝐷𝑟𝑎𝑡𝑖𝑜 ≥ 1.99

(15)

ro of

−1.67 + 1.36 ∗ 𝐷𝑟𝑎𝑡𝑖𝑜 , 𝐷ℎ𝑟𝑎𝑡𝑖𝑜 = { 0.55 + 2.15𝐸12 ∗ (4.27𝐸 − 7)𝐷𝑟𝑎𝑡𝑖𝑜 ,

Fig.12 DHR vs DDR from FE simulation and experiment

Jo

ur

na

lP

re

-p

For the LDDR and the DHR, the difference between numerical and experimental results was the influence of the dynamic liquid on the upper die. For experimentation, the dynamic liquid could flow into the gap between the upper die and blank in a short time which would suddenly change the blank holder force. This contributed to selfadaption flow of the material which decreased the impact energy compared with simulation. Nevertheless, for simulation, so far it was difficult to establish the model to consider the influence of the liquid on the holding force and material feeding. Thus, the simulation overestimated the impact energy and drawing height which caused a smaller estimation on the LDDR in the same time. The example for the quantitative designing of IHF process was illustrated using formability curve including the DHR and the DDR. Firstly, the blank (the DDR was less than 2.02) could be deep drawn into the die cavity without the flange area in one step of IHF. However, the blank did not have the possibility to be completely deep drawn into the die cavity if the DDR was larger than 2.02. In this condition, the DHR played a significant role in the process design. This meant that the limit drawing height would not be more than the diameter of the die cavity (because the DHR for AA 2B06O was about 1). Moreover, the DHR sharply decreased with the exponential trend once the DDR was larger than the limit value. In another words, the limit drawing height distinctly declined when the blank possessed more flange area which restrained the material feeding. When the DDR was large enough, the DHR would slowly decrease because the blank behaved pure bulging in the local area without enough material feeding. 3.4 Analysis on dynamic forming procedure by FE modelling In this study, the FE modelling presents many detailed information which cannot be obtained from experimentation during very short forming procedure. For instance, the variation of the drawing depth can be presented dynamically for 83.6 mm blank.

lP

re

-p

ro of

The time interval was chosen as 60μs to output the profile of the deep drawing part. The curve described the variation of deep drawing depth vs x coordinate, as it was depicted in Fig. 13. As presented in the figure, the blank experienced a forming process with variational speed. Furthermore, it was noticed that the high pressure acted on the fringe area (second central area) of the blank in the beginning. This made almost a flat bottom as it was seen from the local enlarged detail. Then the high pressure mainly focused on the central area which made the flat bottom be sunken and gradually brought the round shape cup into the cavity. As depicted in Fig. 13, the increase rate of depth for the second central area was smaller than the central area after the flat bottom stage which gave rise to the early crack in the central area of the blank. It was also concluded that the increase rate of depth experienced three stages: two stages with trend of increasing-decreasing and for the third stage, it increased until the forming end. This vividly reflected the whole forming procedure proceeded with the intermittent manner because of the shock wave from the dynamic liquid. The maximum of the depth was 20.37mm before the crack happened in the central area of the blank.

Fig. 13 Dynamic forming procedure for 83.6mm blank

na

4. Conclusions

Jo

ur

In the current study, a novel method was proposed to evaluate the HSR formability of AA2B06-O sheet under IHF process with FE modelling. Corresponding experimentation was accomplished to verify the validity of FE simulation. The conclusions could be drawn as follows: (1) Formability curves established by experimentation coincided with the FE simulation from the aspects of wall thickness, part feature, impact energy and DHR. The value of R was 0.98483 which meant that the simulation results were in good agreements with the experimental ones. (2) Both 2D and 3D formability curves were established based on the fitting data of impact energy and DHR. HSR formability curves showed that the LDDR for AA2B06-O was 1.99 and the LDHR was 1.04 when the impact energy was 2207.2 kJ/m2 and the blank was completely deep drawn into the cavity of the die. For experimentation, the LDDR of 2.02 was 1.5 % larger than FE simulation. The LDHR of 0.95 was 8.7 % smaller than the numerical value. The effect of dynamic liquid on

na

Author contribution

lP

re

-p

ro of

the blank holder force caused the difference of DHR between experimentation and FE modelling. The drawing height increased when the larger blank was deep drawn because influence of holding force would be more obvious. Hence, the DHR from simulation was larger than the one from experimentation in these cases. (3) The forming diagram was divided into three different areas by the formability curve: incomplete, complete deep drawing and crack. In the current condition, the impact energy increased with the DDRs when they were smaller than the LDDR in a manner of polynomial variation trend. However, it decreased exponentially when the DDRs were larger than the limit one. When the DDR was close to the limit value from left side, the impact energy should be strictly controlled to prevent the defect of the crack because this area possessed only a trigonal and narrow range between the complete deep drawing and failure. In addition, the blank did not have any possibility to be completely deep drawn into the die cavity if the DDR was larger than the limit value. This illustrated that the forming energy in this area should be strictly controlled too. For the DHR, it increased linearly and decreased exponentially with the DDR before and after the limit value. When the DDR was larger than limit value, the blank should be designed and formed according to the limit of the drawing height. Meanwhile, the impact energy should also be dominated precisely to prevent the defect of the crack for the component with the flange. (4) In the current experimental condition, the LDDR of 2.02 was larger than the value of 1.92 in conventional deep drawing with the rigid punch. The LDDR had the possibility to be further improved if the whole level of the strain rate was enhanced to the range of 3000/s~5000/s according to the mechanical testing. In future study, the formability under different level of strain rates will be evaluated in order to achieve a systematic assessment on formability.

Jo

ur

Author 1: Da-Yong Chen √ Conceived and designed the study □ □ Collected the data □ Contributed data or analysis tools √ Performed the experiments □ √ Performed the analysis □ □ Revised the analysis √ Wrote the paper □ √ Proofed reading □ Author 2: Yong Xu √ Conceived and designed the study □ □ Collected the data □ Contributed data or analysis tools

□ √ □ √ □ □ √ □

Performed the experiments Performed the analysis Revised the analysis Wrote the paper Proofed reading

-p re

lP

Author 4: Yan Ma □ Conceived and designed the study □ Collected the data √ Contributed data or analysis tools □ √ Performed the experiments □ √ Performed the analysis □ □ Revised the analysis □ Wrote the paper □ Proofed reading

ro of

Author 3: Shi-Hong Zhang √ Conceived and designed the study □ □ Collected the data □ Contributed data or analysis tools □ Performed the experiments □ Performed the analysis √ Revised the analysis □ □ Wrote the paper □ Proofed reading

Jo

ur

na

Author 5: Ali Abd El-Aty □ Conceived and designed the study □ Collected the data √ Contributed data or analysis tools □ □ Performed the experiments □ Performed the analysis □ Revised the analysis □ Wrote the paper √ Proofed reading □ Author 6: Dorel Banabic □ Conceived and designed the study □ Collected the data □ Contributed data or analysis tools □ Performed the experiments □ Performed the analysis

□ Revised the analysis √ □ Wrote the paper □ Proofed reading

-p re

na

Declaration on interest

lP

Author 8: Alina A. Bakinovskaya □ Conceived and designed the study □ Collected the data □ Contributed data or analysis tools □ Performed the experiments □ Performed the analysis □ Revised the analysis □ Wrote the paper √ Proofed reading □

ro of

Author 7: Artur I. Pokrovsky □ Conceived and designed the study √ Collected the data □ □ Contributed data or analysis tools □ Performed the experiments □ Performed the analysis □ Revised the analysis □ Wrote the paper □ Proofed reading

The authors hereby declare that no competing financial interests or personal

Jo

ur

relationships that could have appeared to influence the work reported in this paper.

Acknowledgements This project is supported by National Natural Science Foundation of China (No. 51875548), Natural Science Foundation of Liaoning Province of China (Grand No. 20180550851), Shenyang Science and Technology Program (17-32-6-00), Research Project of State Key Laboratory of Mechanical System and Vibration (MSV201708). The author would like to particularly appreciate Prof. Karl Brian Nielsen from Alborg University of Denmark for his unselfish support on FE modeling.

References Abd El-Aty, A., Xu, Y., Guo, X.Z, Zhang, S.H., Ma, Y., Chen, D.Y., 2018. Strengthening mechanisms, deformation behavior, and anisotropic mechanical properties of Al-Li alloys: A review. Journal of Advanced Research 10, 49-67. Abd El-Aty, A., Xu, Y., Ha, S., Zhang, S.H., 2018. Computational homogenization of tensile deformation behaviors of a third generation Al-Li alloy 2060-T8 using crystal plasticity finite element method. Materials Science and Engineering: A 731, 583-594. Abd El-Aty, A., Xu, Y., Zhang, S.H., Ha, S., Ma, Y., Chen, D.Y., 2019. Impact of high strain rate deformation on the mechanical behavior, fracture mechanisms and anisotropic response of 2060 Al-Cu-Li alloy, Journal of Advanced Research 18, 19-37. Azaryan, N.S., Shirkov, G.D., Zhurauski, A.Y., Petrakovski, V.S., Batouritski, M.A., 2016. Manufacture of superconducting niobium cavity parts by hydropercussion punching. Physics

ro of

of Particles and Nuclei Letters 13(2), 218-223.

Balanethiram, V.S., Hu, X.Y., Altynova, M., Daehn, G.S., 1994. Hyperplasticity: Enhanced formability at high rates. Journal of Materials Processing Technology 45(1-4), 595-600.

Banabic, D., Lazarescu, L., Paraianu, L., Ciobanu, I., Nicodim, I., Comsa, D.S., 2013. Development

of a new procedure for the experimental determination of the Forming Limit Curves. CIRP

-p

Annals-Manufacturing Technology 62(1), 255-258.

Boyd, R., Royles, R., El-Deeb, K.M.M., 2000. Simulation and validation of UNDEX phenomena relating to axisymmetric structures. In: Proceedings of sixth international LS-DYNA users

re

conference.

Bruno E.J., 1968. High-Velocity Forming of Metals. American Society of Tool and Manufacturing Engineers, Dearborn, Michigan.

lP

Choi, H., Koç, M., Ni, J., 2007. A study on the analytical modeling for warm hydro-mechanical deep drawing of lightweight materials. International Journal of Machine Tools and Manufacture 47, 1752-1766

Cao, J., Krishnan, N., Wang, Z., Lu, H., Liu, W. K., Swanson, A., 2004. Microforming: experimental

na

investigation of the extrusion process for micropins and its numerical simulation using RKEM. Journal of Manufacturing Science and Engineering, Transactions of the ASME 126(4), 642652.

ur

Dey, S., Børvik, T., Hopperstad, O.S., Langseth, M., 2007. On the influence of constitutive relation in projectile impact of steel plates. International Journal of Impact Engineering 34(3), 464-486. Hartl, C., 2019. Review on Advances in Metal Micro-Tube Forming. Metals 9(5), 542-567.

Jo

Homber, G.W., Djakow, E., AKST, O., Гомберг, В., Дьяков, Е., Акст, О., 2013. Investigation of a pneumo-mechanical high speed forming process with respect to the forming of complex sheet and tube components. Journal of Mechanical Engineering NTUU 67(1), 180-185.

Huang, C.Q., Deng, J., Wang, S.X., Liu, L.L., 2017. A physical-based constitutive model to describe the strain-hardening and dynamic recovery behaviors of 5754 aluminum alloy. Materials Science and Engineering: A 699, 106-113. Johnson, G.R., Cook, W.H., 1985. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Engineering Fracture Mechanics 21, 31-48. Khodko, O., Zaytsev, V., Sukaylo, V., Verezub, N., Scicluna, S., 2015. Experimental and numerical

investigation of processes that occur during high velocity hydroforming technologies: An example of tubular blank free bulging during hydrodynamic forming. Journal of Manufacturing Processes 20, 304-313. Kosing, O.E., Skews, B.W., 1998. AN Investigation of high-speed forming of circular plates in a liquid shock tube. International Journal of Impact Engineering 21(9), 801-816. Lang, L.H., Wang, S.H., Yang, C.L., 2013. Investigation on the innovative impact hydroforming technology. AIP Conference Proceedings 1532(1), 791-798. Lang, L.H., Li, T., An, D.Y., Chi, C.L., Nielsen, K.B., Danckert, J., 2009. Investigation into hydromechanical deep drawing of aluminum alloy-Complicated components in aircraft manufacturing. Materials Science and Engineering: A 499(1-2), 320-324. Leu, D.K., 1997. Prediction of the limiting drawing ratio and the maximum drawing load in cupdrawing. International Journal of Machine Tools and Manufacture 37(2), 201-213.

ro of

Li, C.F., Liu, D.H., Yu, H.P., Ji, Z.B., 2009. Research on formability of 5052 aluminum alloy sheet

in a quasi-static-dynamic tensile process. International Journal of Machine Tools and Manufacture 49, 117-124.

Li, H.W., Yan, S.L., Zhan, M., Zhang, X., 2019. Eddy current induced dynamic deformation

behaviors of aluminum alloy during EMF: Modeling and quantitative characterization. Journal

-p

of Materials Processing Technology 263, 423-439.

Li, H.Y., Wang, X.F., Duan, J.Y., Liu, J.J., 2013. A modified Johnson Cook model for elevated temperature flow behavior of T24 steel. Materials Science and Engineering: A 577, 138-146. Technology Corporation (LSTC).

re

LS-DYNA, 2007. Keyword user’s manual, version 971, Livermore, CA: Livermore Soft-ware Ma, Y., Xu, Y., Zhang, S.H., Banabic, D., Abd El-Aty, A., Chen, D.Y., Cheng, M., Song, H.W,

lP

Pokrovsky, A.I., Chen, G.Q., 2018. Investigation on formability enhancement of 5A06 aluminium sheet by impact hydroforming. CIRP Annals-Manufacturing Technology 67, 281284.

Marciniak, Z., Kuczyński, K., 1967. Limit strains in the processes of stretch-forming sheet metal.

na

International Journal of Mechanical Sciences 9(9), 609-620. Marciniak, Z., Kuczyński, K., Pokora, T., 1973. Influence of the plastic properties of a material on the forming limit diagram for sheet metal in tension. International Journal of Mechanical

ur

Sciences 15(10), 789-800.

Montross, C.S., Wei, T., Ye, L., Clark, G., Mai, Y.W., 2002. Laser shock processing and its effects on microstructure and properties of metal alloys: A review. International Journal of Fatigue

Jo

24(10), 1021-1036.

Shin, Y. S., Lee, M., Lam, K. Y., Yeo, K. S., 1998. Modeling mitigation effects of watershield on shock waves. Shock & Vibration 5(4), 225-34.

Tekkaya, A.E., Allwood, J.M., Bariani, P.F., Bruschi, S., Cao, J., Gramlich, S., Groche, P., Hirt, G., Ishikawa, T., Löbbe, C., Lueg-Althoff, J., Merklein, M., Misiolek, W.Z., Pietrzyk, M., Shivpuri, R., Yanagimoto, J., 2015. Metal forming beyond shaping: Predicting and setting product properties. CIRP Annals-Manufacturing Technology 64(2), 629-653. Wang, X., Du, D.Z., Zhang, H., Shen, Z.B., Liu, H.X., Zhou, J.Z, Liu, H., Hu, Y., Gu, C.X., 2013. Investigation of microscale laser dynamic flexible forming process-Simulation and

experiments. International Journal of Machine Tools and Manufacture 67, 8-17. Woo, M.A., Song, W.J., Kang, B.S., Kim, J., 2018. Evaluation of formability enhancement of aluminum alloy sheet in electrohydraulic forming process with free-bulge die. International Journal of Advanced Manufacturing Technology 101(1-4), 1085-1093. Xiao, W.C., Wang, B.Y., Wu, Y., Yang, X.M., 2018. Constitutive modeling of flow behavior and microstructure evolution of AA7075 in hot tensile deformation. Materials Science and Engineering: A 712, 704-713. Xu, Y., Ma, Y., Zhang, S.H., Chen, D.Y., Zhang, X.S., Li, J.M., Zhao, C.J., 2016. Numerical and experimental study on large deformation of thin-walled tube through hydroforging process. International Journal of Advanced Manufacturing Technology 87, 1885-1890. Yang, D.Y., Bambach, M., Cao, J., Duflou, J.R., Groche, P., Kuboki, T., Sterzing, A., Tekkaya, A.E., Lee, C.W., 2018. Flexibility in metal forming. CIRP Annals-Manufacturing Technology 67(2),

ro of

743-765.

Zhang, R., Zhang, T.S., 1994. Non-die explosive forming of spherical pressure vessels. Journal of Materials Processing Technology 41(3), 341-347.

Zhang, S.H., Wang, Z.R., Xu, Y., Wang, Z.T., Zhou, L.X., 2004. Recent developments in sheet

Jo

ur

na

lP

re

-p

hydroforming technology. Journal of Materials Processing Technology 151, 237-241.