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FIERF/FIA FINAL REPORT: Ultra-Fine Grain Processing of

Steel Billet – Phase I - Effect of Initial Microstructure on the Microstructural Evolution and Tensile Properties of 4140 Steel

Thomas Kozmel, Ryan Cassel, and Sammy Tin

Illinois Institute of Technology 10 W 32nd St.

Chicago, IL 60616 tin@iit.edu

Phone: 1-312-567-3780 Fax: 1-312-567-7230

April 27th, 2015

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Abstract:

4140, a high strength steel, was heat treated from its initial pearlitic and ferritic

microstructure to produce three discretely different microstructures: pearlitic and ferritic,

bainitic, and martensitic microstructures. These microstructures were then warm rolled at

temperatures between 866 K (593 °C) and 977 K (704 °C) to produce varying levels of

dynamically recrystallized microstructures. Once a height reduction of 80% had been reached,

samples were machined into dog-bone tensile samples. Tensile tests revealed yield strengths

between 600 and 1160 MPa, which were shown to be a function of the processing parameters.

Electron backscatter diffraction (EBSD) was used to analyze the deformed microstructures.

Constitutive analytical-empirical models were developed such that the yield stress of the material

could be directly predicted from the initial microstructure and its processing parameters.

Keywords: Steel; EBSD; Microstructure formation mechanism; Mechanical properties testing;

Modeling

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1. Introduction:

4140 is an alloy steel can be processed and heat treated to readily obtain yield stresses as

high as 1650 MPa while still retaining good ductility. Its properties make it suitable for

applications where high strength and good toughness are required, but where the service

conditions only expose the material to relatively low to moderate temperatures. The carbon

content of 4140 gives it excellent hardenability and wear resistance. Overall, the properties of

this steel make it suitable for use in connecting rods, crankshafts, industrial tooling, high

pressure tubing, and other applications [1]. Although 4140 steel exhibits a well-balanced

combination of properties, the structural properties of this alloy may potentially be further

enhanced, however, by taking advantage of recent developments in grain size refinement

technologies [2-3]. For structural materials, ultra-fine grain (<100 nm) processing has been

shown to enhance both strength and toughness simultaneously. Compared to other common

strengthening mechanisms, such as work hardening [4], strengthening via grain refinement

typically does not accompany a corresponding reduction in ductility. Various studies have shown

that a variety of severe plastic deformation (SPD) techniques can be utilized to form physically

large bulk structures with homogeneous ultra-fine grained microstructures. Commonly used SPD

techniques include equal channel angular pressing (ECAP) [5-7], high pressure torsion (HPT) [8-

9], accumulative roll bonding [10], accumulative angular drawing [11], multi-axial forging

(MAF) [12-15], and even conventional rolling [16-17]. Grain refinement and the formation of

sub-micron grain sizes has been shown to be achievable by all of these methods provided that

sufficiently high plastic strains are achieved [18-19]. In addition to plastic strain, the deformation

temperature is also a key factor, as it controls both the recrystallization and grain growth

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kinetics. Recent studies have shown that warm rolling of steel at temperatures below those

typically used in conventional hot rolling can be used to induce the formation of sub-micron

grains via recrystallization and restrict their subsequent growth [16-17].

Typically, deformation temperatures used for thermal – mechanical processing of steels

are selected such that they are well above the corresponding austenitizing temperature (AC3).

Under these temperature conditions, the microstructure of the material consists of a single FCC

phase and both recrystallization and grain growth occur rapidly as the thermal energy provided to

the system enhances the kinetics of the system. As a result, forming and retaining

microstructures comprised of sub-micron grains during thermo-mechanical deformation becomes

challenging. For most commercial steel alloys, the recrystallization and grain growth behavior

under these conditions have been well characterized [20-22]. When compared to thermal –

mechanical deformation of steels below the austenitizing temperature, where the microstructure

predominaetely consists of ferrite and carbides, the transformation kinetics are greatly reduced

and recrystallization and grain growth are retarded [23]. However, in order to induce grain

refinement during deformation at these temperatures, comparatively higher levels of plastic

strain are required due to the higher stacking fault energy associated with the BCC crystal

structure of the ferrite. The higher stacking fault energies prevent dislocations induced during

deformation from dissociating into stacking faults that restrict dislocation climb and contributes

to enhanced dislocation mobility that makes BCC metals more likely to accommodate

deformation by recovery [24-25]. Hence, significantly higher overall levels of plastic strain are

required in order to induce continuous dynamic recrystallization (CDRX) when deforming steels

below their respective austenitizing temperature [26-29]. It should also be noted that the presence

of carbides within the ferritic structure may also effect the recrystallization and grain growth

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kinetics as finely distributed carbides, serve to pin both dislocations and mobile grain

boundaries.

Throughout many alloy systems during the initial stages of continuous dynamic

recrystallization, the plastic strain induces the formation of cells that are bounded by dense

dislocation walls (DDWs). The interior of these cells contain relatively few dislocations and

their size is dependent on the kinetics and mobility of the dislocations. These cells or “subgrain”

structures form as the material attempts to rearrange the accumulated dislocations into

configurations that possess the lowest total energy. As these structures form, the initial relative

misorientation between adjacent dislocation walls is typically less than 1 degree. However, as the

plastic strain levels increase, the dense dislocation walls begin to evolve and the misorientations

within the sub-grain boundaries gradually increase such that they may eventually rotate to form

high angle boundaries and become continuously dynamically recrystallized. The mechanisms

associated with dynamic recrystallization may be iterative as dislocation walls and tangles may

continue to form within the newly formed grains with continued straining and serve to further

refine the system [26, 30-32].

Several recent studies have correlated the effects of initial microstructure with the

resulting microstructure of a given set of processing parameters. For example, with respect to

4140 steel, it was found that quenching and tempering a martensitic structure resulted in a finer

grain size than quenching and tempering an equivalent bainitic microstructure. However, upon

warm rolling at 773 K (500 °C), the initially bainitic microstructure exhibited a higher degree of

grain refinement than that of the martensite [33]. Effects of initial microstructure have also been

observed in Ti-6Al-4V [34], where the starting grain structure and morphology affected the

surface finish and flow behavior during ECAP. Hence, it is apparent that the starting

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microstructure may have a significant impact the formation of ultra-fine grained and sub-micron

grain structures, particularly in steel alloys where the microstructures may be comprised of

ferrite, bainite or martensite. For this reason, the objective of the current study was to quantify

and elucidate the effects of initial microstructure in 4140 steel on its recrystallization kinetics

during warm rolling at sub-AC1 temperatures.

2. Experimental:

Billet bar stock of 4140 steel was cut into nine 10.16 cm long sections with a cross

section of 2.286 cm in width by 0.94 cm in height. The initial microstructure was confirmed via

scanning electron microscopy (SEM) to be predominantly pearlitic, Figure 1a and 2a. Nominal

composition values for the 4140 steel used in this investigation is listed in Table I.

Table I: Nominal Elemental Composition for 4140 Steel, by % wt. Cr Mn C Si Mo S P Fe 0.80-1.10%

0.75-1.00%

0.38-0.43%

0.15-0.30%

0.15-0.25%

0.040% 0.035% Bal.

In order to form the distinct starting microstructures, the 4140 material was austenitized at 800

which corresponded to 15 K (15 °C) above the austenitizing temperature (AC3) and cooled at

different rates. Thermocouples were spot welded to the ends of the bars to monitor their

temperature during the heat treatment process. The bars reached the target temperature in

approximately 25 minutes, and were held at this temperature for an additional 20 minutes to

ensure a uniformly austenitized microstructure. Martensitic structures were formed by water

quench to room temperature at a cooling rates of ~30 K/s (30 °C/s).

Bainitic microstructures were formed by removing the bars from the furnace and placing them on

323 K (50 °C) at a rate of

approximately 0.83 K/s (0.83 °C/s).

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Each of the three different initial microstructures was warm rolled to 33%, 50%, 67%,

and 80% height reductions at the temperatures of 866 K, 922 K, and 977 K (593 °C, 649 °C, and

704 °C). Bars were individually isothermally heat treated to the target rolling temperature for

approximately 20 minutes to ensure a uniform internal temperature. The bars were then rolled to

the designated height reduction while being placed back into the furnace for 10 minutes after

every 2 rolling passes to retain the target rolling temperature. [roller speed and strain rate] The

rolling height reductions ranged from 0.076 cm down to 0.0076 cm per pass as deformation

progressed and the height of the samples decreased. After each bar was rolled to the appropriate

height reduction, it was immediately water quenched. Specimens were excised from each of the

samples for detailed microstructural characterization.

Bars in their heat treated state, and those samples that were rolled to various height

reductions were prepared for characterization using standard metallographic techniques and a

finishing polish using a 0.06 micron colloidal silica suspension. Samples were characterized and

quantitatively analyzed using electron backscatter diffraction (EBSD) in a JEOL-5900LV SEM

equipped with an Oxford Instruments Nordlys-HKL EBSD detector. For all samples, the rolling

direction was analyzed at all height reductions less than 80%. Samples reduced by 80% in height

were analyzed along the normal direction. Measurements were made to ensure that the center of

the cross section on the rolled-direction face was being characterized on each sample for

comparative purposes. 80% height reduced samples were likewise analyzed in the center of the

bar along the normal direction. EBSD scans were conducted by searching for both BCC and FCC

iron with the settings of 7 bands detection, 67 reflectors for the BCC iron, and 56 reflectors for

the FCC iron. Post processing was conducted within the Oxford HKL Channel 5 – Tango

software program. Conservative noise reduction and extrapolation was performed prior to the

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quantitative analysis of the inverse pole figure (IPF) maps. Grain boundaries were defined as

boundaries exhibiting greater than 15 degree critical misorientation with respect to their

neighbors. Average grain sizes were determined by the mean circle equivalent diameter. For a

grain to be considered recrystallized, size and shape requirements would need to be met,

depending on the initial microstructure.

Flat, dog-bone tensile samples were machined from the final 80% height reduction of

each rolled bar. Two tensile samples were obtained from each bar. Dimensions of the tensile

samples were 0.635 cm in width by approximately 0.188 cm in thickness. Gage sections were

2.54 cm long, and samples were tested in tension at a rate of 0.127 cm/min using an Instron

tension test machine with a 200 kN (45000 lbf) load cell. Tensile force and elongation were

recorded for each bar until failure. These data were used to construct stress-strain curves for each

bar, from which yield strength, ultimate tensile strength, elastic modulus, and percent ductility

were calculated. Because two samples were tested for each bar, these values were found by

averaging the two data sets.

3. Results:

3.1 Microstructural Characterization:

To obtain three different initial microstructures, sample bars with a mixed pearlitic and

ferritic microstructure were heat treated to obtain fully martensitic and fully bainitic

microstructures, Figure 1. Each of the starting microstructures was carefully characterized using

both optical and electron microscopy and evaluated using EBSD. For the pearlitic and ferritic

microstructure, the average grain size was 10.7 microns, Figures 1a. It was determined through

both optical microscopy and SEM that the phase fraction of pearlite was approximately 75%,

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Figure 2a. K/s, the microstructure of 4140 was

found to completely transform into martensite, Figure 1b. The average lath size measured via

EBSD was 2.4 microns and the average grain size was observed to range between 5-10 microns,

Figure 2b. A predominately bainitic microstructure was formed after cooling the 4140 samples at

a cooling rate of 0.83K/s, Figure 1c. A mixture of both upper and lower bainite was observed

within the microstructure, Figure 2c, and the area fraction of bainite grains within the

microstructure was nominally at least 85%. The remaining regions of the microstructure were

comprised of martensite and ferrite. In this instance, the average grain size was determined to be

3.4 microns.

Figure 1: Starting microstructures prior to warm rolling: a) the as received pearlitic and ferritic microstructure, b) the martensitic microstructure obtained through annealing and quenching, and c) the mixed bainite microstructure obtained through annealing and air quenching on a brass plate.

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Figure 2: SEM images verifying the phase components for the a) pearlitic microstructure, b) martensitic microstructure, and c) bainitic microstructure.

After warm rolling to reduce the height of all samples by ~33%, intragranular lattice

rotations and the formation of subgrain structures was observed in all samples. For example, in

the initially pearlitic and ferritic sample rolled at 866 K (593 °C), Figure 3, the local variations in

color within the grains indicate that subgrain formation was occurring. Recrystallized grains

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were also observed, which possess a reduced grain size relative to the rest of the microstructure.

With a warm rolling strain rate of X and a process that utilizes multiple rolling passes of the

deformed structures, both dynamic, meta-dynamic recrystallization mechanisms are likely

responsible for the refinement of the grain structure [ref]. When characterizing the as-deformed

microstructures, distinguishing between these recrystallization mechanisms is challenging and

beyond to scope of the present investigation. As a result, for the purposes of this investigation,

all of grain refinement was considered to occur dynamically.

Figure 3: Initially pearlitic and ferritic sample reduced by 33% in height via rolling at 866 K (593 °C), exhibiting a partially recrystallized structure. To best compare the effects of temperature and initial microstructure on the

recrystallization response of the 4140 steel, the samples warm rolled to 50% height reductions

for all temperatures and initial microstructures were selected, Figure 4. These observations

clearly show that the size of the recrystallized grains typically increased with increasing

temperature. For instance, following refinement of the pearlitic microstructure, the mean

recrystallized grain size was 0.8 microns at 866 K (593 °C), Figure 4a, which increased to 0.9

microns at 922 K (649 °C), Figure 4b, and finally to 1.0 microns at 977 K (704 °C), Figure 4c. In

the samples with the martensitic starting microstructure, the average recrystallized grain size

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increased from just under 0.6 microns, Figure 4d, to just over 0.6 microns, Figure 4e, and finally

to 0.7 microns, Figure 4f, at 866 K, 922 K, and 977 K (593 °C, 649 °C, and 704 °C) respectively.

Finally, the initially bainitic samples showed an increase in dynamically recrystallized grain size

from 0.7 microns, Figure 4g, to 0.9 microns, Figure 4h, and remaining at 0.9 microns, Figure 4i,

as the temperature increased from 866 K, to 922 K, and to 977 K (593 °C, to 649 °C, and to 704

°C) respectively. Effects of initial microstructure were also evident, as the initial microstructure

which appeared to generate the smallest dynamically recrystallized grains at a given temperature

was martensite, and the largest dynamically recrystallized grains were generated by the initially

pearlitic samples. In addition, differences in fraction of dynamic recrystallization were observed

between different starting microstructures. For instance, the pearlitic samples exhibited the

lowest fraction of dynamic recrystallization following warm rolling to a 50% height reduction,

Figure 4a-c, with values varying only slightly with temperature from 14%, to 10%, and to 5% as

the temperature increased from 866 K, to 922 K, and finally to 977 K (593 °C, 649 °C, and 704

°C). However, the martensite samples, Figure 4d-f, exhibited the largest fraction of dynamic

recrystallization at this height reduction. These values ranged from 78% at 866 K (593 °C), to

76% at 922 K (649 °C), and finally to 65% at 977 K (704 °C). Finally, the bainitic samples warm

rolled to 50% height reduction, Figure 4g-i, were observed to exhibit dynamically recrystallized

area fractions of 63%, 44%, and 30% at 866 K, 922 K, and 977 K (593 °C, 649 °C, and 704 °C)

respectively. Although the general trend at this height reduction indicated that samples rolled at

lower temperatures exhibited a larger area fraction of dynamically recrystallized grains, this

trend was least pronounced in the samples with the pearlitic starting microstructures. However,

this trend held for all instances in the initially martensitic samples. It also should be noted that

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the bainitic samples behaved differently at higher strain levels, where the difference between

rolling temperatures was not significant.

Figure 4: Comparison of and dynamic recrystallization and dynamically recrystallized grain size trends as a function of rolling temperature and initial microstructure. Pearlitic samples rolled at a) 866 K (593 °C), b) 922 K (649 °C), and c) 977 K (704 °C). Martensitic samples rolled at d) 866 K (593 °C), e) 922 K (649 °C), and f) 977 K (704 °C). Bainitic samples rolled at g) 866 K (593 °C), h) 922 K (649 °C), and i) 977 K (704 °C). Following warm rolling, some of the samples exhibited significant grain refinement as

the microstructures were found to completely or nearly completely dynamically recrystallize

(>75% area fraction recrystallization). These samples included the initially bainitic samples

rolled at 977 K (704 °C) to height reductions of 67% and 80%, and the martensitic samples

rolled at 866 K (593 °C) and 922 K (649 °C) to height reductions of 67% and 80%. Figure 5

shows the microstructure of an initially bainitic sample rolled at 977K (704 °C) to a height

reduction of 67%. This microstructure exhibited full dynamic recrystallization with a mean grain

size of 0.6 microns. These grains were observed to be nominally equiaxed with little difference

in size.

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Figure 5: The initially bainitic microstructure warm rolled at 977 K (704 °C) such that its height was reduced by 67%. The processed microstructure shown exhibited full dynamic recrystallization. 3.2 Tensile Results:

Two tensile specimens were machined from samples warm rolled to a height reduction of

80%, and loaded in tension until failure at room temperature. Values for key data points such as

the yield strength and elongation to failure were averaged between the two samples and reported

as such. As expected, the yield stress for all samples decreased as a function of rolling

temperature. For example, the initially pearlitic microstructure exhibited a yield stress of 1090

MPa after being rolled to 80% height reduction at 866 K (593 °C), which was reduced to 869

MPa as the rolling temperature was increased to 922 K (649 °C), and finally to 627 MPa at the

rolling temperature of 977 K (704 °C), Figure 6a. In Figure 6b, the initially martensitic

microstructure had yield strengths of 1160 MPa, 894 MPa, and 651 MPa for the corresponding

rolling temperatures of 866 K, 922 K, and 977 K (593 °C, 649 °C, and 704 °C) respectively.

Finally, Figure 6c shows the stress-strain curves for the initially bainitic microstructure rolled to

80% height reduction with respective yield strengths of 1087 MPa, 828 MPa, and 613 MPa at the

rolling temperatures of 866 K, 922 K, and 977 K (593 °C, 649 °C, and 704 °C). In addition,

ductility was also observed to increase in both the initially pearlitic and bainitic tensile samples.

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The initially bainitic sample warm rolled at 977 K (704 °C) had the best ductility of all samples,

reaching 11.7% strain. However, it was observed that the initially martensitic microstructures

experienced a decrease in ductility as the rolling temperature increased. These samples typically

had the least ductility. For example, the initially martensitic microstructure rolled at 977 K (704

°C) only withstood elongation to 1.0% strain, which was the lowest value recorded.

Figure 6: Tensile stress strain curves and results for samples rolled to 80% height reduction with: a) the initially pearlitic microstructure, b) the initially martensitic microstructure, and c) the initially bainitic microstructure.

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3.3 Development of a Microstructural Process Model:

Based on the observed microstructural changes collected during this investigation,

constitutive relationships were developed to describe the microstructural evolution of the

materials as a function of the initial microstructure and the processing parameters. This set of

expressions considers the effects of temperature, effective strain, and the starting microstructure

before rolling.

In order to best relate the rolling process to the microstructural evolution of the material,

the various height reduction steps were quantified in terms of their effective strain on the

material, Equation 1.

𝜀𝜀 = 𝜀𝜀 + 𝜀𝜀 + 𝜀𝜀/

(1)

In Equation 1, 𝜀𝜀 is the effective strain, and 𝜀𝜀 , 𝜀𝜀 , and 𝜀𝜀 are the respective strains in each

direction of the rolled bar, calculated from the change in dimensions of the bar as it was

processed. The strain based on the change in dimension in each respective direction was

calculated by Equation 2, where 𝜀𝜀 is the strain, DL is the change in length for the respective

direction, and L0 is the original length of that dimension prior to processing.

𝜀𝜀 = ∆ (2)

Typically, the fraction of dynamic recrystallization, 𝑋𝑋 , occurring at a specific effective

strain and temperature is described by an Avrami relation, Equation 3:

𝑋𝑋 = 1− 𝑒𝑒𝑒𝑒𝑒𝑒 −ln  (𝛼𝛼 ) .

. .

.

(3)

Where the effective strain required to initialize dynamic recrystallization is assumed to be the

effective strain required for 5% dynamic recrystallization, 𝜀𝜀 . , and is defined as:

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𝜀𝜀 . = 𝐴𝐴 𝑇𝑇 (4)

Where T is the rolling temperature in degrees Celsius, and A1, k1 are constants. Additionally, the

effective strain required for 50% dynamic recrystallization is defined by:

𝜀𝜀 . = 𝐴𝐴 𝑇𝑇 (5)

Where T is the rolling temperature in degrees Celsius, and A2, k2 are constants. The remaining

terms in Equation 3, a1, and n, are constants.

The size of the dynamically recrystallized grains, 𝐷𝐷 , in microns, may be described by

a decaying exponential function, Equation 6:

𝐷𝐷 = 𝐵𝐵exp   (6)

Where b1 is a constant, T is the rolling temperature and the lead term B can be described by:

𝐵𝐵 = 𝐴𝐴 𝑇𝑇 (7)

Where A3, k3 are constants, and T is the rolling temperature.

Once the constants from Equations 4 and 5 are determined, the parameters from Equation

3 can be back calculated from the data. Likewise, the constants from Equation 6 can be

determined from the data after Equation 7 is developed. Equations 4, 5, and 7 are used to

calibrate the initialization point, inflection point, and y-intercept within the data, respectively,

and to ensure that the proper variation with respect to temperature is achieved. The fully solved

equations for each respective starting microstructure are shown as follows:

Initially Pearlitic and Ferritic Microstructure:

𝑋𝑋 = 1− 𝑒𝑒𝑒𝑒𝑒𝑒 −𝑙𝑙𝑙𝑙  (1.834) .

. .

. . (8)

𝜀𝜀 . = 2.358 ∗ 10 𝑇𝑇 . (9)

𝜀𝜀 . = 0.6464 𝑇𝑇 . (10)

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𝐷𝐷 = 𝐵𝐵exp   . (11)

𝐵𝐵 = 9.196 ∗ 10 𝑇𝑇 . (12)

Initially Bainitic Microstructure:

𝑋𝑋 = 1− 𝑒𝑒𝑒𝑒𝑒𝑒 −ln  (2.088) .

. .

. . (13)

𝜀𝜀 . = 8.353 ∗ 10 𝑇𝑇 . (14)

𝜀𝜀 . = 9.995 ∗ 10 𝑇𝑇 . (15)

𝐷𝐷 = 𝐵𝐵exp   . (16)

𝐵𝐵 = 5.448 ∗ 10 𝑇𝑇 . (17)

Initially Martensitic Microstructure:

𝑋𝑋 = 1− 𝑒𝑒𝑒𝑒𝑒𝑒 −ln  (2.019) .

. .

. . (18)

𝜀𝜀 . = 8.079 ∗ 10 𝑇𝑇 . (19)

𝜀𝜀 . = 9.031 ∗ 10 𝑇𝑇 . (20)

𝐷𝐷 = 𝐵𝐵exp   . (21)

𝐵𝐵 = 2.138 ∗ 10 𝑇𝑇 . (22)

These expressions can be visualized in Figures 7 and 8, which describe the fraction of dynamic

recrystallization as a function of the processing parameters (Figure 7), and the dynamically

recrystallized grain size as a function of the processing parameters (Figure 8). In each figure, a),

b), and c) are shown for the initially pearlitic and ferritic, bainitic, and martensitic

microstructure, respectively. These figures also compare the model predictions and the

experimental data. Error bars are included in these plots as Standard Error(s) versus each

individual trend produced from the global model.

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Figure 7: The fraction of dynamic recrystallization for the initially a) pearlitic and ferritic, b) bainitic, and c) martensitic microstructure as a function of the processing parameters. A comparison of the model with the experimental data is shown.

Figure 8: The dynamically recrystallized grain size for the initially a) pearlitic and ferritic, b) bainitic, and c) martensitic microstructure as a function of the processing parameters. A comparison of the model with the experimental data is shown.

3.4 Correlation between Microstructure and Mechanical Properties:

Following the development of the microstructural model, the resulting microstructures

were incorporated into constitutive expressions for predicting the flow behavior of the material.

Typically, the Hall-Petch equation is used to relate grain size to the yield strength of a given

material. The form of this equation is shown as Equation 23:

𝜎𝜎 = 𝜎𝜎 + 𝑘𝑘 𝐷𝐷 / (23)

Where 𝜎𝜎 is the yield stress, D is the grain size of the material, and 𝜎𝜎 , 𝑘𝑘 are constants.

However, for very fine grain sizes (<1 µm) a departure from the typical Hall-Petch trend occurs.

Therefore, a modified equation valid for fine grain sizes is necessary, Equation 24 [35]:

𝜎𝜎 = + 𝛽𝛽 𝐷𝐷 (24)

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Where 𝛼𝛼 ,𝛽𝛽 are constants. For purposes of this study, a global equation of the following form is

used:

𝜎𝜎 = + 𝛽𝛽 𝐷𝐷 𝑋𝑋 (25)

Where 𝐷𝐷 ,𝑋𝑋 are defined previously in section 3.2. These terms are combined into the D

term to weight the effects of the fraction of dynamic recrystallization on the grain size and

ending yield stress. When this equation is solved for the experimental data, using model values

for 𝐷𝐷 , and  𝑋𝑋 , it takes the form:

𝜎𝜎 = . + 0.0001 𝐷𝐷 𝑋𝑋 (26)

Where 𝐷𝐷 is in microns. This solved equation is visualized in Figure 9, which shows the yield

stress as a function of 𝑋𝑋 ∗ 𝐷𝐷 (which are both dependent on the material’s processing

parameters). Error bars are included on the plot as Standard Error(s).

Figure 9: The yield stress for material as a function of the processing parameters. A comparison of the model with the experimental data is shown. Note that this modeling equation is applicable to all three initial microstructures.

4. Discussion:

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In this investigation, samples of 4140 steel billet material were processed to contain three

distinct microstructures prior to warm rolling. By varying the warm rolling process parameters

to induce varying levels of effective strain at temperatures between 866K and 973K, the effect of

the starting microstructure on the dynamic grain refinement characteristics was quantified. It was

shown that the initially pearlitic and ferritic microstructure could be transformed to a fully

martensitic microstructure when the cooling rate was on the order of 30 K/s (30 °C/s), while a

predominately bainitic microstructure was obtained when the cooling rate was on the order of

0.83 K/s (0.83 °C/s). Consistent with literature [36], 4140 steel transforms completely to

martensite when cooled from above 1023 K (750 °C) at cooling rates exceeding 16.7 K/s (16.7

°C/s). For a 100% bainitic transformation, a linear cooling rate between 0.083 K/s (0.083 °C/s)

and 0.0083/s (0.0083 °C/s) would be required. When producing the bainitic microstructures,

however, the actual measured cooling rate of approximately 0.83 K/s (0.83 °C/s) resulted in the

formation of 80-85% bainite, with the remainder transforming to martensite. The SEM images

shown in Figure 2 are consistent with the measured cooling rates as the fraction of bainite is

estimated to be approximately 85%, with the remainder being martensitic and retained austenite.

During the warm rolling process, the three initial microstructures behaved differently

with respect to their dynamic recrystallization kinetics. The initially pearlitic and ferritic

microstructure exhibited the most sluggish recrystallization kinetics. Although cementite

precipitates present in pearlite grains effectively pin dislocations, the comparatively large

spacings between precipitates form regions of ferrite where subgrain formation and rotation into

continuously dynamically recrystallized grains may occur. Moreover, within the ferrite grains,

no features exist to pin dislocations, and significant recovery is able to occur. These

microstructural features contribute to increasing the level of effective strain required to produce

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CDRX in those regions as the kinetics of deformation and recovery are in competition. As such,

the final levels of CDRX in these pearlitic/ferritic microstructures tends to be limited for the

range of effective strains evaluated in this study. On the other hand, the bainitic microstructure

contains a fine and homogeneous distribution of carbides throughout the microstructure. The

small interparticle spacings and homogeneous distribution of fine carbides confers a high degree

of dislocation pinning throughout the microstructure. This also serves to limit the degree of

degree of dislocation recovery occurring during deformation since the magnitude of dislocation

travel is limited by the interparticle spacings. This limits the size of the subgrain structures that

can form and promotes relatively high levels of dynamic recrystallization as a function of

effective strain. Finally, the 4140 samples with the martensitic starting microstructures exhibited

the highest tendency to dynamically recrystallize during warm rolling. Heating the martensitic

samples up to the warm rolling temperatures resulted in tempering of the martensite and

precipitates of carbides with extremely fine interparticle spacings. Not only did this

microstructure possess a homogeneous dispersion of carbides to pin dislocations, but the

increased grain boundary surface formed by the interlocking martensitic sheaves also promoted

CDRX during deformation. In addition to forming sub-grain structures that are limited by the

size of the carbide spacings, these elongated sheaves also appear to fragment and form discrete

grains during deformation. The combination of these factors decreased the amount of effective

strain required to dynamically recrystallize the majority of the volume fraction. It should be

noted that despite the difference in starting microstructure, the dynamically recrystallized grains

appeared to be ferritic and the resulting microstructure consisted of ferrite and carbides in all

three cases.

23

As expected, the tensile tests demonstrated that the yield strength of the warm rolled

4140 samples decreased as the warm rolling temperature increased [37]. In addition, the initially

pearlitic and bainitic samples experienced an increase in ductility corresponding with the

decrease in yield strength. Interestingly, the initially bainitic sample rolled at 977 K (704 °C)

exhibited the most tensile ductility out of all the samples tested with 11.7% strain. Following

yield, the plastic flow behavior in this sample was characterized by a lack of both hardening and

softening behavior. The increased ductility associated with this sample could likely be attributed

to the microstructure being comprised of a nearly homogeneous distribution of sub-micron

grains, Figure 5. The observed tensile flow behavior is characteristic of superplastic flow

behavior where macroscopic strains are largely being accommodated via grain boundary sliding

and rotation with minimal dislocation activity. Under these conditions, the ductility of the

microstructures was effectively extended. Although the samples with initially martensitic

microstructures were found to exhibit similar grain sizes and magnitudes of the flow stresses

when compared to the initially bainitic samples, the warm rolled martensitic samples

experienced a decrease in the overall ductility as the rolling temperature increased. It is possible

that the decreases in ductility as a function of temperature could be attributed to temper

embrittlement of 4140. Since molybdenum and chromium are known to react to form carbides

(most effectively at temperatures above 813 K (540 °C) [38], softening of the alloy is mitigated

at all tempering temperatures. In conventional Cr-Mo steels, carbides are often utilized to assist

in preventing grain growth and alloying the steel with chromium and molybdenum additions

retards the coalescence of carbides. However, molybdenum additions are also utilized to mitigate

the effects of temper embrittlement. When Cr-Mo carbides form in alloy steels containing low

levels of molybdenum, such as 4140, the corresponding depletion of the Mo from the ferrite

24

renders the alloy susceptible to temper embrittlement. As a result, 4140 is susceptible to temper

embrittlement when the martensitic structure is tempered at temperatures between 728 K and 868

K (455 °C and 595 °C). Since this coincides with temperature range used for warm rolling and

embrittlement could not be avoided in 4140 at the lower rolling temperatures. In order to remove

the susceptibility for temper embrittlement in this alloy, a slight increase in the molybdenum

content would be required to prevent harmful inclusions from segregating to the grain

boundaries. For example, 4340 steel is not susceptible to temper embrittlement as its

molybdenum content is slightly higher than that of 4140, and its chromium content slightly

lower. As such, the molybdenum is able to sufficiently counteract the effects of the chromium,

while the addition of nickel provides some weak solid solution strengthening [38].

Constitutive models developed to describe the microstructural transformations occurring

via dynamic recrystallization during warm rolling of 4140 steel were observed to be in good

agreement with the experimental data as the effects of both deformation temperature and

effective strain were effectively captured. These models also correctly predict the difference in

behavior associated with varying the initial microstructures. Although some discrepancies in the

models can be observed at higher temperatures, this can likely be attributed to the occurrence of

grain growth. Model predictions for the size of the dynamically recrystallized grains are

consistent with the observations that lower rolling temperatures produce finer dynamically

recrystallized grains. It should be noted that the error bars shown in Figures 7 and 8 were

generated versus each individual trend computed by the global model; the error bars shown may

be larger than expected as a result.

The yield stress model can be observed to be in good agreement with the experimental

data. Assuming complete recrystallization, this model can be used to accurately predict the yield

25

stress of warm rolled 4140 steel containing grain sizes between ~0.2 and 1.0 microns. For grain

sizes above 1 micron, the typical Hall-Petch equation likely be valid. In the yield stress model,

Xdrx is factored in as a correction for the level of recrystallization present in the material.

Although the degree of dynamic recrystallization was limited in the samples possessing the

initially pearlitic and ferritic microstructure due to recrystallization predominately occurring

within the pearlite phase fraction (unless significantly higher effective strains are provided), the

corresponding yield stresses were still comparable to the other two initial microstructures.

Successfully coupling the microstructural process models with the yield stress model is

significant, in that the strength of the material can be directly estimated based on the initial

microstructure and the processing parameters.

5. Conclusions:

This investigation showed that the starting microstructure of 4140 steel plays a major role

in the development of thermal – mechanical processes capable of producing sub-micron grain

sizes. Starting with a tempered martensitic microstructure, warm rolling resulted in recrystallized

grain sizes in the range of 0.5-0.8 microns, and required the least effective strain to achieve high

levels of recrystallization. Warm rolling of bainitic 4140 samples also induced high levels of

recrystallization and had dynamically recrystallized grain sizes slightly larger than that of the

initially martensitic samples, in the range of 0.6-0.9 microns. When the starting microstructure

was predominately comprised of pearlite and ferrite, the resulting warm rolled microstructure

appeared to exhibit a limited level of dynamic recrystallization (~50%) unless significant

effective strain would be supplied at a high rate. Dynamically recrystallized grain sizes for these

samples ranged from 0.7-1.0 microns. Constitutive models were developed that describe the

26

microstructural changes occurring in 4140 steel as a function of deformation temperature,

effective strain and starting microstructure.

The dynamically recrystallized microstructures containing submicron grains were found

to possess yield strengths ranging from approximately 600 MPa up to 1160 MPa following warm

rolling to an overall height reduction of 80%. As expected, the magnitudes of the yield strengths

were observed to increase as the rolling temperature decreased. A modified Hall-Petch model

was developed to estimate the yield stress as a function of grain size. Ductility in these samples

increased with temperature, except in the samples with the martensitic starting structures, where

temper embrittlement likely occurred. It should be noted that the reported yield strength values

were measured from as-rolled material and these strength levels may potentially be enhanced

even further with appropriate heat treatments.

Acknowledgements:

The authors would like to acknowledge the Forging Foundation (FIERF)/Forging Industry

Association and the Armour College of Engineering, a college of the Illinois Institute of

Technology, for providing funding to support this research.

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