Deformation behaviour of chromium sheets in mechanicaland laser bending

K.C. Chana,*, Y. Haradab, J. Lianga, F. Yoshidac

aDepartment of Manufacturing Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong KongbDepartment of Production Systems Engineering, Toyohashi University of Technology, Toyohashi, Japan

cDepartment of Mechanical Engineering, Hiroshima University, Higashi-Hiroshima, Japan

Received 4 June 2001

Abstract

Chromium is known to have limited room-temperature ductility but to exhibit apparent ductile-to-brittle transition behaviour at

temperatures ranging from 150 to 300 8C. In this paper, the deformation behaviour of a chromium sheet was investigated in roll-compression

and laser bending. Tensile tests and three-point bending tests were performed also to determine the basic mechanical properties of the

chromium sheet. The ductile-to-brittle transition temperature of the chromium determined by the tensile test was found to be 180 8C. While

the sheet could be bent to 908 at a temperature of 130 8C in three-point bending, it was possible to bend the sheet to the same bending angle

at a lower temperature (100 8C) in roll-compression bending, the presence of compressive stress in roll-compression bending being

considered to be the reason for the difference in the temperatures. A finite element stress analysis was also conducted to reveal the stress

distribution of the chromium sheet in roll-compression bending. Laser bending was demonstrated to be a possible process to deform

chromium sheets. A threshold laser power of 40 W is observed, below which bending is unlikely to occur. The bending angle was found

to increase with increasing laser power and number of irradiations, and decreasing scanning velocity. # 2002 Elsevier Science B.V.

All rights reserved.

Keywords: Chromium sheet; Ductile-to-brittle transition; Three-point bending; Laser-bending

1. Introduction

Chromium exhibits apparent ductile-to-brittle transition

behaviour at temperatures ranging from 150 to 300 8C.

Below this range, plastic deformation is virtually impossi-

ble. Even if plastic deformation of chromium can be accom-

plished at high temperatures, the induced tensile residual

stress will make the material of brittle nature at room

temperature. These are the main reasons why chromium

is rarely used as a bulk materials in industry, despite its high

corrosion and heat resistance. There have been research

efforts made to improve the mechanical properties and

workability of chromium [1–12]. It has been found that

the ductile-to-brittle transition temperature (DBTT) can be

lowered by: (i) using high purity chromium in which dis-

location locking is unlikely to occur [1–3]; (ii) deforming

the chromium at a low forming speed [4,5]; (iii) introducing

a small amount of plastic prestrain [1,5]; and (iv) applying

high hydrostatic pressure [6–9]. Ohmori et al. [10–12] have

recently reported that for some forming processes which

apply compressive stress such as rolling, upsetting and extru-

sion, chromium workpieces were successfully deformed

without any failure at a relatively low temperature.

The present paper reports the deformation behaviour of

chromium examined by two different techniques, namely

mechanical and laser bending. Laser bending is shown to be

particularly suitable for one-off or small batch production

and the shaping of hard and brittle materials, as no hard

tooling is required. In the process, repetitive irradiations of a

defocused laser beam are applied over the surface of metal

sheets [13,14]. Because of the development of a temperature

gradient across the sheet thickness, thermal stress is induced

and permanent deformation is produced. Chan and Liang

[15,16] have recently examined the deformation behaviour of

aluminium matrix based composites and Ti3Al-based inter-

metallic alloy. They have demonstrated that it is possible

to bend relatively brittle materials to large angle by laser

bending. For mechanical bending, roll-compression bending

is selected, in which a high roll-contact pressure is applied on

chromium sheets by using a roller-punch and a roller-die.

Journal of Materials Processing Technology 122 (2002) 272–277

* Corresponding author. Tel.: þ852-2766-4891; fax: þ852-2362-5267.

E-mail address: mfkcchan@polyu.edu.hk (K.C. Chan).

0924-0136/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 0 1 4 - 6

2. Experimental material and procedures

A chromium plate of 2.5 mm thickness produced by

powder metallurgy was investigated in the paper, its che-

mical composition being shown in Table 1.

Fig. 1 presents a schematic illustration of the experimental

set-up for roll-compression bending. The bending load is

servo-controlled. In the experiments, chromium sheets were

bent using a roller-punch and a rotating die in an oil bath at

temperatures ranging from 50 to 150 8C. In order to examine

the temperature dependence of the flow stress and ductility

of chromium, tensile tests were performed in vacuum at

various temperatures in an Instron testing machine with a

cross-head speed of 10 mm/min. Three-point bending tests

were also carried out in air in order to obtain the basic

bending properties of the chromium. A schematic diagram

of the three-point bending test is shown in Fig. 2.

For laser bending, samples of thickness of 0.5 mm and

dimensions of 10 mm � 20 mm were prepared by wire

electro-discharge machining. An 80 W YAG laser unit

operating in continuous wave (CW) mode was used in the

experiments to scan the specimens with laser powers of 48

and 68 W, scanning velocities ranging from 10 to 25 mm/s,

and the number of irradiations being from 10 to 50. No time

was allowed between two successive irradiations and the

laser was scanned back and forth along the same path in

multiple irradiations. An image processing system was used

to measure the bending angle to an accuracy of �0.58. No

graphic coating was applied and a defocused laser beam with

a diameter of 1.3 mm was used to avoid surface melting. The

experimental set-up is described in Ref. [14].

3. Results

3.1. Tensile and three-point bending tests

Fig. 3 shows the nominal stress vs. nominal strain curves

of chromium sheets tested at temperatures of 120, 150, 180

and 200 8C. It is found that chromium is relatively brittle at

temperatures of below 180 8C. The relationship between

fracture strain (defined as ef ¼ lnðA0=AfÞ, where A0 and Af

are cross-sectional areas of initial and fractured specimens,

respectively) and temperature under tensile tests is shown in

Fig. 4. The temperature dependence of the maximum (non-

dimensional) curvature k (t0/r, where t0 denotes the initial

thickness of the specimen and r the radius of the mid-plane

of the bent plate) obtained in three-point bending tests is

shown in Fig. 5. At temperatures of above 130 8C, the

specimens can be successfully bent up to an angle of 908,at which the curvature k is 0.35.

The ductile-to-brittle transition behaviour of chromium

can be explained by the concept of brittle fracture stress sfrac

Table 1

Chemical composition of the chromium specimens (wt.%)

C P S Fe H O N Cr

0.004 0.002 0.003 0.130 0.0004 0.006 0.008 Balance

Fig. 1. Schematic illustration of roll-compression bending (dimensions: mm).

Fig. 2. Schematic diagram of three-point bending (dimensions: mm).

K.C. Chan et al. / Journal of Materials Processing Technology 122 (2002) 272–277 273

[17], which states that for a tensile stress greater than sf, the

material fractures in a brittle manner. If plastic flow is

assumed to occur independently of brittle fracture at a flow

stress sflow, the fracture is brittle when sfrac is smaller than

sflow, and the fracture is ductile when sfrac is larger than

sflow. Using the experimental results of the tension test, sfrac

is determined as 310 MPa (true stress). Since sflow

decreases rapidly with temperature, and sfrac is almost

temperature independent, a sharp ductile-to-brittle transi-

tion occurs in chromium. It is interesting to note that

in three-point bending, chromium can be successfully bent

up to 908 at a temperature of 130 8C, which is much lower

than the DBTT of 180 8C determined by the tensile test. It

is considered that the difference in temperature is because

the strain achieved in bending is much smaller than that in

tensile test. Based on simple calculations, the maximum

surface strain of the sheet bent to 908 is 0.16. According to

Fig. 3, this amount of strain can be achieved in tensile test at

a temperature of 130 8C.

3.2. Roll-compression test

Fig. 6 shows the experimental results for roll-compression

bending. It has been demonstrated that it is possible to bend

chromium to a degree of 908 at a rather low temperature of

100 8C, which is smaller than the temperature of 130 8Cobtained in three-point bending. The presence of compres-

sive stress in the process is considered to be the reason for

the difference in temperature. It is also found that only under

a certain level of compressive load bending of chromium is

possible, and that the load is temperature-dependent.

Although compressive stress is beneficial in the forming

of chromium, a very large compressive load will result in

early stage fracture, as shown in Fig. 6. In order to under-

Fig. 3. Nominal-stress vs. nominal-strain curves in tension tests on chromium at various temperatures.

Fig. 4. Fracture strain ef vs. test temperature in tension tests on chromium.

274 K.C. Chan et al. / Journal of Materials Processing Technology 122 (2002) 272–277

stand this phenomenon, a finite element stress analysis

was conducted using the FE code ABAQUS [18]. The

plane-strain condition was assumed in the analysis. The

relationship between the effective stress and the effective

plastic strain was given by the equation:

s ¼ 125 þ 386e0:41 MPa

that was determined from the stress–strain curve obtained at

180 8C. Young’s modulus and Poisson’s ratio were assumed

as 250 GPa and 0.3, respectively. The calculated stress

distribution (longitudinal stress) in roll-compression bend-

ing under 10 kN compression is illustrated in Fig. 7, where a

large tensile stress of over 267 MPa is found in the vicinity

of the punch-contact area. This could be the reason for early

stage fracture of the specimen under a large punch load.

3.3. Laser bending

Fig. 8 shows the relationship between the laser bending

angle (a) and the number of irradiations (N). It has been

demonstrated that it is possible to bend chromium sheets

Fig. 5. Maximum non-dimensional curvature k vs. test temperature in three-point bending on chromium (k ¼ t0=r, where t0 is the initial thickness of the

specimen (2.5 mm) and r the minimum radius at middle surface of the specimen. Symbols (~) and (~) show the results for successfully bent and fractured

specimens, respectively).

Fig. 6. Maximum non-dimensional curvature k vs. compressive load in roll-compression bending at various temperatures (open symbols (&) and (*) and

filled symbols (&), (*) and (~) show the results for successfully bent and fractured specimens, respectively).

K.C. Chan et al. / Journal of Materials Processing Technology 122 (2002) 272–277 275

using multiple irradiations and low laser powers. The bend-

ing angle is found to increase linearly with increasing

number of irradiations. A similar phenomenon has been

observed with other materials [15,16]. Fig. 9 shows the a–N

curve of the chromium at a constant power of 68 W and at

laser scanning velocities of 10 and 20 mm/s. At a small

number of irradiations, the bending angles obtained at

the scanning velocity of 10 mm/s are significantly larger

than those for 20 mm/s. The difference is reduced when the

number of irradiations is increased. It is considered that the

effect of the scanning velocity is reduced when the number

of irradiations is large. The effect of scanning velocity on

bending angle is also illustrated in Fig. 10. It is found that the

bending angle decreases with an increase in the scanning

velocity. At a power of 48 W, the bending angle drops more

rapidly at high velocities, which is considered to be related

to the total laser energy applied to the sheet. Fig. 11 shows

the effect of the laser input power on the bending angle of

the chromium sheet at a number of irradiations of 30. A

threshold laser power of about 40 W is observed, below

which bending is unlikely to occur. The laser bending angle

increases with increasing laser power, but at high powers the

rate of change in bending angle becomes less. A temperature

gradient is formed across the sheet thickness in laser bending.

If the temperature gradient is too small because of inap-

propriate setting of the processing parameters, such as too

low an input power, no or small bending angles are observed.

Fig. 7. Distribution of longitudinal stress in roll-compression bending

under 10 kN compression.

Fig. 8. a–N curves at different laser powers.

Fig. 9. a–N curves at different laser scanning velocities.

Fig. 10. Influence of the laser scanning velocity on the bending angle.

276 K.C. Chan et al. / Journal of Materials Processing Technology 122 (2002) 272–277

Although, laser bending is shown to be feasible for

chromium sheet, it is worthwhile to examine the stress state

of the sheet during bending. In laser bending, thermal

expansion occurs at the upper surface of the sheet during

heating, which leads to an intermediate bending stage called

‘‘reverse bending’’. The reverse bending angle is related to

the amount of thermal expansion of the upper layer of the

sheet and a substantial compressive stress arises in this layer.

Being bent away, the bottom layer is also subjected to

compressive stress. During cooling, thermal contraction

occurs at the upper layer as there is heat lost by conduction.

The sheet will then be bent towards the laser beam, which is

called ‘‘positive bending’’. Since the amount of reverse

bending is much smaller than that of positive bending, an

overall positive bending angle is observed after cooling.

However, during positive bending, the stress at the heat

zone will change from compression to tension, which is

not beneficial for large deformation of chromium sheets.

As compared to roll-compression bending, laser bending

is considered to be a powerful and cost effective means to

deform chromium sheets at small strain or in the making

prototypes. Roll-compression bending is a more appropriate

process for large deformation or for making chromium

components, although it involves tooling cost and the pro-

cessing temperature is still around 100 8C. More research is

needed to improve this process so that it can deform

chromium sheets at an even lower processing temperature.

4. Conclusions

Chromium sheets are shown to be able to be deformed

by roll-compression and laser bending. In roll-compression

bending, the sheet can be bent to 908 without fracture at a

temperature of 100 8C. This temperature is significantly

lower than the ductile-to-brittle transition temperature

(180 8C) determined by the tensile test, and is also lower

than the minimum temperature at which the sheet can be

bent to the same bending angle in conventional three-point

bending. The presence of compressive stress in roll-com-

pression bending is considered to be advantageous in the

bending of chromium sheet. However, a finite element stress

analysis reveals that a very large compressive stress, which

will result in a large longitudinal tensile stress, is harmful to

the process and leads to early stage fracture. Laser bending is

also demonstrated to be able to deform chromium sheets

using multiple irradiations and low laser power. At a laser

power of 68 W, a maximum bending angle of 23.58 is

obtained at a scanning velocity of 10 mm/s, and at a number

of irradiation of 50. The laser bending angle is found to

increase with an increase in input power and in the number

of irradiations, and with a decrease in scanning velocity. It is

considered to be very worthwhile to further examine the

deformation behaviour of chromium sheet using a high

power laser which may enable the sheet to be deformed

to a large strain level with a lesser number of irradiations.

Acknowledgements

The work described in this paper was partly supported by

a grant from the Research Grant Council of the Hong Kong

Special Administration Region (Project No. PolyU 5166/

97E).

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K.C. Chan et al. / Journal of Materials Processing Technology 122 (2002) 272–277 277