Microstructure and Mechanical Properties in Progressively Drawn ...

Materials Transactions, Vol. 55, No. 1 (2014) pp. 93 to 98 Special Issue on Strength of Fine Grained Materials ® 60 Years of Hall­Petch ® © 2013 The Japan Institute of Metals and Materials

Microstructure and Mechanical Properties in Progressively Drawn Pearlitic Steel Jesús Toribio1,+, Beatriz González1 and Juan-Carlos Matos2 1

Department of Materials Engineering, University of Salamanca, E.P.S. Zamora, 49022, Zamora, Spain Department of Computing Engineering, University of Salamanca, E.P.S. Zamora, 49022, Zamora, Spain

2

This paper studies the relationship between the microstructural changes caused by the cold drawing process in pearlitic steel wires (axial orientation of the pearlitic lamellae together with decrease of the average interlamellar spacing) and the improvement of their mechanical properties. The strength is related to plastic strain by means of the Embury-Fisher equation, and also by a new Hall­Petch expression, where to calculate the distance between barriers against dislocational movement one must consider, apart from the average interlamellar spacing, the average orientation angle. A modelling of the evolution of pearlitic lamellae with cold drawing was made, assuming that initially all angles appear with the same probability, that lamellae change their geometry along the longitudinal section of the wire similarly to the specimens and that the projection of the average interlamellar spacing on the cross section of the wire is proportional to the specimen diameter. The results obtained with this modelling show a good correspondence with experimental data. [doi:10.2320/matertrans.MA201316] (Received August 8, 2013; Accepted September 20, 2013; Published November 15, 2013) Keywords: pearlitic steel wire, cold drawing, microstructural anisotropy, Hall­Petch equation

1.

Introduction

Cold drawing produces several changes in the pearlitic microstructure of eutectoid steels.1­7) The basic unit is the pearlite colony formed by ferrite and cementite lamellae parallel to each other and with an orientation different from that of the lamellae of neighbouring colonies. Cold drawing produces changes in the pearlite colony (first microstructural unit) in the form of increasing slenderising4) and progressive orientation parallel to the wire axis or drawing direction.5) In a finer microstructural scale, the lamellar pearlitic structure itself made up of ferrite and cementite is the following level of analysis (second microstructural unit), the key parameter being the pearlite interlamellar spacing. Cold drawing also produces changes in the lamellae in the form of increase of packing closeness associated with decrease of interlamellar spacing6) and orientation parallel to the main axis or cold drawing direction.7) During the earliest stages of drawing (small cumulative plastic strain) the orientation effect predominates while during the final stages of drawing (large cumulative plastic strain) both the slenderising of pearlitic colonies and the decrease of pearlite interlamellar spacing (with increase of packing closeness) predominate, cf.4­7) Yield strength increases with cold drawing due to the decrease of interlamellar spacing8­12) because blocking of dislocational movement is favoured at the ferrite/cementite inter-phase, while at the same time plastic anisotropy is favoured due to microstructural alignment in the material.13) In plain pearlitic steel (i.e., hot rolled material), the yield strength follows a Hall­Petch type relationship14,15) in relation to its pearlite interlamellar spacing,2,8,9) where the Hall­Petch parameter is independent of the cooling rate and thus on the interlamellar spacing, but strongly increases with the increment of carbon content.16) In the case of cold drawn pearlitic steel a Hall­Petch relationship cannot be fitted between the yield strength and the interlamellar spacing,17) due to the fact that the decrease of interlamellar spacing is accompanied by a progressive microstructural orientation.7) +

Corresponding author, E-mail: [email protected]

On the contrary, the Embury-Fisher equation1) relating the yield strength to the cumulative plastic strain produced by cold drawing has been successfully applied to pearlitic steels with different degrees of drawing.18) Previous paragraphs demonstrate that the basic materials science problem of the association between microstructural evolution and macroscopic properties is far from being fully understood in progressively drawn pearlitic steel. This paper tries to provide insight into this key item in materials science and engineering by analyzing (firstly) the microstructural evolution in pearlitic steel during cold drawing together with its relationship with the improvement of material strength, and formulating (secondly) a model of such a microstructural evolution on the basis of the physical distance between barriers to dislocation movement. 2.

Experimental Procedure

Material was pearlitic steel with the following chemical composition: 0.789% C, 0.681% Mn, 0.210% Si, 0.218% Cr and 0.061% V. It was supplied with different drawing degrees from the hot rolled bar (not cold drawn) to the commercial prestressing steel wire (heavily drawn). Materials were named with a letter “E” (indicating the chemical composition) and a number between 0 and 7 referring to the number of drawing steps undergone by each particular steel wire. The drawing degree can be characterised through the cumulative plastic strain ¾P as a function of the initial diameter of the wire before cold drawing D(0) to the instantaneous diameter D(i) of the wire at any drawing stage, ¾P ðiÞ ¼ 2 ln

Dð0Þ DðiÞ

ð1Þ

so that an increase of cumulative plastic strain is observed with the cold drawing process. Longitudinal samples from each drawing stage were cut (through an axial plane), mounted, grounded and polished until a mirror surface was obtained. After being etched with 4% Nital (mixture of 4 ml of nitric acid with 96 ml of ethanol)

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J. Toribio, B. González and J.-C. Matos

Fig. 1 Microstructure of steels.

to reveal microstructure, so the exposing time decreased while cold drawing increased, they were examined by scanning electron microscopy (SEM) with magnification factor up to ©6000. For each material, the area measured to obtain the average values of the microstructural parameters was about 4500 µm2. Standard tension tests were performed on cylindrical samples of about 30 cm length and different cross section area (associated with the drawing degree) in a universal testing machine. Two extensometers were placed to evaluate the strain as an average of two signals. Tests were performed under displacement control with a crosshead speed of 3 mm/min. 3.

Experimental Results

3.1 Microstructure of pearlitic steel Figure 1 shows the SEM micrographs revealing the microstructure of steels E0 to E7, as longitudinal sections

in which the horizontal side of the photograph is associated with the radial direction in the wire, whereas the vertical side of the photograph corresponds to the axial direction in the wire. Pearlite is formed by alternating ferrite and cementite lamellae, forming colonies (groups of neighbouring pearlitic lamellae parallel to each other). The pearlitic lamellae orientation can be evaluated by the angle ¢ calculated as the average of angles of the lamellae in the photographs of longitudinal sections (Fig. 1) and the axial (drawing) direction (Fig. 2), so an angle ¢ is accounted for every visible colony. Pearlite interlamellar spacing s0 is the distance from the centre of a ferrite lamella to the centre of the following within the same colony (Fig. 3). There are several methods to calculate the pearlite interlamellar spacing, such as the random linear intercept method19) and, its variation, the circular line method.20) The perpendicular line method8,20,21) can also be used, where the minimum pearlite interlamellar

Microstructure and Mechanical Properties in Progressively Drawn Pearlitic Steel

ez

Table 1 ðs0 Þ.

β

 and average interlamellar spacing Average orientation angle ð¢Þ

Steel

er

95

E0

E1

E2

E3

E4

E5

E6

E7

0.00

0.22

0.42

0.59

0.77

0.97

1.13

1.57

¾P ¢

46.9°

42.3°

35.9°

30.6°

27.9°

22.7°

19.4°

14.0°

s 0 (µm)

0.203

0.185

0.180

0.174

0.171

0.164

0.151

0.142

0.18

40°

0.15 30°

0.12

20°

0.09

10° 0° 0.0

0.2

β

0.06

s

0.03 0

0.4

0

Average Orientation Angle, β

Fig. 2 Orientation angle of pearlitic lamellae. er is the transverse direction and ez is the axial direction.

0.21

0.6

0.8

1.0

1.2

Cumulative Plastic Strain, ε

spacing is obtained by measuring the interlamellar distance in those colonies where the lamellae are orientated close to the perpendicular of the observing plane. Due to the described microstructural orientation, the use of the circular line method seems to be difficult. With regard to the perpendicular line method, a problem arises because the average interlamellar spacing does not necessarily have to match with the minimum,22) matter which gets worse with cold drawn steel2) due to the large strains undergone by the material. On the basis of previous reasoning, and considering that the material analyzing in the present paper has been progressively drawn, the procedure used for measuring the interlamellar spacing is an adaptation of the random linear intercept method, taking into account that pearlite lamellae are progressively oriented in axial direction when the steel is cold drawn. The evaluation of the average interlamellar spacing of pearlite s 0 is carried out on the longitudinal sections, where the cut plane is random, because the lamellae are only orientated on the axial direction. Perpendicular lines to the pearlitic lamellae were traced and were divided by the number of intercepted pearlitic lamellae, so the plane is random but not the line traced on it. The average value obtained was divided by a constant, square root of two, value obtained from comparing the proposed method and that of random linear intercept for hot rolled wire. The average angle and the average interlamellar spacing of pearlitic lamellae for the steel used are shown on Table 1 and Fig. 4, together with the cumulative plastic strain caused by the drawing process. While the degree of drawing increases, the pearlitic lamellae decrease their interlamellar spacing and, at the same time, they progressively align in the drawing direction.

1.4

0.00 1.6

P

 and average interlamellar spacing ðs0 Þ Fig. 4 Average orientation angle ð¢Þ of pearlitic lamellae as functions of plastic strain (¾P).

2.0

Stress, σ /GPa

Fig. 3 Interlamellar spacing of pearlitic lamellae.

Average Interlamellar Spacing, s /μm

50°

1.5

1.0 E7 E6 E5 E4

0.5

0.0 0.00

0.02

Fig. 5

E0

0.06

0.08

Stress­strain curves (tension tests).

Table 2 Steel

0.04 Strain, ε

E3 E2 E1 E0

E1

Mechanical properties. E2

E3

E4

E5

E6

E7

E (GPa)

202

187

189

192

194

199

201

209

·Y (GPa)

0.70

0.79

0.89

0.92

1.02

1.12

1.20

1.48

·max (GPa) 1.22

1.27

1.37

1.40

1.50

1.59

1.64

1.82

3.2 Mechanical properties From stress­strain curves (Fig. 5) obtained in standard tension tests (plots representing the true stress vs. the true, or logarithmic, strain), the mechanical parameters of each steel were obtained (Table 2): the Young’s modulus (E), almost constant during cold drawing (³200 GPa); the 0.2% offset yield strength (·Y) and the ultimate tensile strength UTS (·max), the two latter increasing with cold drawing as an obvious consequence of such a manufacturing technique.

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4.

J. Toribio, B. González and J.-C. Matos

Relationship between Microstructure and Mechanical Properties

For progressively drawn pearlitic steel, Embury and Fisher1) obtained an equation describing quantitatively the strength of the steel in axial direction ·R (obtained from the standard tension test) and the cumulative plastic strain through an exponential relationship as follows:

p  k ¾ ðiÞ · R ðiÞ ¼ · 0 þ exp ð2Þ 1=2 4 ð2rð0ÞÞ where ·0 is the apparent friction stress, k a material characteristic parameter and r(0) the initial distance between barriers to the dislocational movement. Figure 6 shows the Embury­Fisher fitting for the considered steels. The Embury­Fisher equation is a modification of the Hall­ Petch relationship,14,15) · R ðiÞ ¼ · 0 þ kðcrðiÞÞ1=2

ð3Þ

in which r(i) is the average distance between barriers after i drawing steps and c a constant. On the basis of the fact that the Embury­Fisher equation is valid for the pearlitic steel under consideration, the Hall­Petch relationship must also apply but taking into account, apart from the average interlamellar spacing, the average angle of the pearlite lamellae (both parameters evolve with cold drawing),

Strength, σR /GPa

2.0

1.5

 s 0 ðiÞ 1=2 ð4Þ  cos ¢ðiÞ In the approach used in the present work (based on the Embury-Fisher equation) the constant kA depends on chemical composition, the value remaining constant during the whole drawing process. This is fully consistent with the ideas presented in Ref. 18). In addition, the basic assumption of the present paper is that the projection of the average interlamellar spacing over the transverse section of the wire is proportional to the wire diameter (Fig. 7 left). The interlamellar spacing is reduced in accordance with the change in wire diameter up to a strain of 2.5.23) Figure 7 right, shows the new Hall­Petch relationship for the considered steels. · R ðiÞ ¼ · 0 þ k0

5.

Modelling of Microstructural Evolution with Cold Drawing

The changes caused in the pearlitic lamellae due to the drawing process have been modelled using two hypotheses. The first one, which allows calculating the average angle of the pearlitic lamellae, assumes that initially there are colonies with all possible angles, from 0 to 90°, and these colonies change geometry proportionally to the test specimen during the drawing process (Fig. 8). After i drawing steps, a generic pearlitic lamella (GPL) in the longitudinal section will change from having an initial radial projection d(0) to a final one d(i) and from having an initial axial projection l(0) to a final one l(i). Therefore, the following ratios appear between these dimensions associated with each lamella and the specimen geometry, dðiÞ DðiÞ ¼ dð0Þ Dð0Þ lðiÞ LðiÞ ¼ lð0Þ Lð0Þ

1.0

σ max

0.5

σY 0.0 1.0

1.1

1.2

1.3

1.4




1.5

exp (ε /4)

¢ðiÞ ¼ atan

Fig. 6 Embury-Fisher equation.

dðiÞ lðiÞ

β s0 er

Strength, σR /GPa

2.0

β

1.5

1.0

σ max

0.5

0.0 1.8

ð6Þ

In addition, the initial angle ¢(0) of the lamella turns into the angle ¢(i), after i drawing steps,

P

ez

ð5Þ

σY 2.0

2.2

2.4

Measured (s0/cosβ )

-1/2

2.6

2.8

-1/2

/(μm)

 1=2 . er is the transverse direction and ez is the axial Fig. 7 New Hall-Petch relationship between strength and measured ðs0 = cos ¢Þ direction.

ð7Þ

Microstructure and Mechanical Properties in Progressively Drawn Pearlitic Steel

d(0)

Average Orientation Angle, β

l(i)

er

i drawing steps

L(i)

l(0)

L(0)

50°

ez β(i)

e z β(0)

er d(i)

D(0) D(i)

30° 20° 10°

Experiments Modelling

Cumulative Plastic Strain, ε

 An average of this orientation angle, ¢ðiÞ, can be calculated considering the plastic strain, since it is assumed that initially all angles occur with the same probability, Z 90  ¼ 1 ¢ðiÞ atanððexpð¾P ðiÞÞÞ3=2 tan ¢ð0ÞÞd¢ð0Þ ð9Þ 90 0

0.18 0.15 0.12 0.09 0.06 Experiments Modelling

0.03 0.00 0.0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

Cumulative Plastic Strain, ε

1.6

P

Fig. 10 Average interlamellar spacing ðs0 Þ, experiments vs. modelling.

Strength, σ R /GPa

2.0

ð10Þ

The average interlamellar spacing s 0 ðiÞ, after i drawing steps, can be calculated from its initial value and the cumulative plastic strain, considering that the initial average angle of pearlitic lamellae is, approximately, 45°, pffiffiffi P  s 0 ðiÞ ¼ 2s 0 ð0Þ cos ¢ðiÞðexpð¾ ðiÞÞÞ1=2 ð11Þ The results for the average angle and the average interlamellar spacing of pearlitic lamellae, obtained by experiments and modelling, are shown on Figs. 9 and 10. It can be observed that the pearlitic lamellae experience a greater orientation on the first drawing steps, while the average interlamellar spacing shows a greater decrease on the last drawing steps6,7,24) for the studied strains (from ¾P = 0 to ¾P = 1.6). Finally, the new Hall­Petch relationship (modified as proposed in the present paper, cf. eq. (4)) is used to perform a fitting (Fig. 11) between the experimentally-measured mechanical properties (yield strength ·Y and ultimate tensile  1=2 (where the strength ·max) and the calculated ðs0 = cos ¢Þ average interlamellar spacing and orientation angle are microstructural parameters calculated by geometrical consid-

0.21

0

Average Interlamellar Spacing, s (μm)

ð8Þ

The second hypothesis comes from the Embury­Fisher equation. It is assumed that the blocking distance for dislocational movement (distance between ferrite/cementite inter-phases) varies proportionally to the wire diameter and, therefore, it has been considered that so does the average interlamellar spacing projection on the cross section. This is how the following ratio between the characteristic parameters of the pearlitic lamellae and the wire diameter is obtained,

P

 experiments vs. modelling. Fig. 9 Average orientation angle ð¢Þ,

Using eqs. (5) and (6) and the cumulative plastic strain value (1), characteristic parameter of the drawing process, the orientation angle ¢(i) turns out to be:

 DðiÞ s 0 ðiÞ= cos ¢ðiÞ ¼  Dð0Þ s 0 ð0Þ= cos ¢ð0Þ

40°

0° 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Fig. 8 Geometrical changes of the generic pearlitic lamella (GPL) during cold drawing (evaluated in longitudinal sections). D is the diameter of the wire (measured in radial/transverse direction er), L is the reference length of the wire (measured in axial/longitudinal direction ez), d is the radial projection of the GPL and l is the axial projection of the GPL.

¢ðiÞ ¼ atanððexpð¾P ðiÞÞÞ3=2 tan ¢ð0ÞÞ

97

1.5

1.0

σ max

0.5

σY 0.0 1.8

2.0

2.2

2.4

Calculated (s 0 /cosβ )

2.6

-1/2

2.8

-1/2

/(μm)

Fig. 11 New Hall­Petch relationship between strength and calculated  1=2 . ðs0 = cos ¢Þ

 1=2 ) erations). Figure 11 (strength vs. calculated ðs0 = cos ¢Þ shows a clear improvement of the regression coefficient with  1=2 ). respect to Fig. 7 (strength vs. measured ðs0 = cos ¢Þ 6.

Conclusions

Cold drawing produces microstructural orientation in pearlitic steel, so that pearlitic lamellae progressively orientate in the drawing (axial) direction, while its interlamellar spacing decreases during straining. This produces an improvement

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J. Toribio, B. González and J.-C. Matos

of mechanical properties such as the yield strength and ultimate tensile stress. Steel strength follows an Embury­ Fisher type relationship with plastic strain produced by cold drawing, and a Hall­Petch equation can also be fitted if the orientation angle of pearlite lamellae is taken into account, together with the variation of average interlamellar spacing. It is possible to model the geometrical changes induced on the pearlitic lamellae by the drawing process: (1) The variation of the pearlitic lamellae average angle is obtained assuming that in hot rolled wire all possible angles for pearlitic lamellae have the same probability to occur and that geometric changes for lamellae on the wire longitudinal section are proportional to those of the specimen. (2) The evolution of the pearlitic average interlamellar spacing is calculated considering that its projection on the cross section changes similarly to that of the wire diameter, based on the Embury­Fisher equation which assumes that this is what happens to the physical distance between barriers to dislocation movement. Acknowledgments The authors wish to acknowledge the financial support provided by the following Spanish Institutions: Ministry for Science and Technology (MICYT; Grant MAT2002-01831), Ministry for Education and Science (MEC; Grant BIA200508965), Ministry for Science and Innovation (MICINN; Grants BIA2008-06810 and BIA2011-27870); Junta de Castilla y León (JCyL; Grants SA067A05, SA111A07, and SA039A08); and the steel supplied by TREFILERÍAS QUIJANO (Cantabria, Spain).

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