On The Deformation Mechanisms in Single Crystal Hadfield Manganese Steels

Scripta Materialia, Vol. 38, No. 6, pp. 1009 –1015, 1998 Elsevier Science Ltd Copyright © 1998 Acta Metallurgica Inc. Printed in the USA. All rights reserved. 1359-6462/98 $19.00 1 .00

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ON THE DEFORMATION MECHANISMS IN SINGLE CRYSTAL HADFIELD MANGANESE STEELS I. Karaman, Huseyin Sehitoglu and Ken Gall Department of Mechanical and Industrial Engineering University of Illinois, Urbana, IL 61801, USA

Yuriy I. Chumlyakov Physics of Plasticity and Strength of Materials Laboratory Siberian Physical and Technical Institute, 634050 Tomsk, Russia (Received November 24, 1997) (Accepted in revised form December 12, 1997)

Introduction Austenitic manganese steel, so called Hadfield manganese steel, is frequently used in mining and railroad frog applications requiring excessive deformation and wear resistance. Although it was discovered more than a hundred years ago by Robert Hadfield, its deformation mechanisms, particularly Its work hardening ability, are still not completely understood. Previous studies [1– 4] attributed the work-hardening characteristics of this material due to dynamic strain aging [3] or an imperfect deformation twin, a so-called pseudotwin [1]. Unfortunately, these previous studies have all focused on polycrystalline Hadfield steels. To properly study the mechanisms of deformation in the absence of grain boundary or texture effects, single crystal specimens are required. The only published study to date on single crystal Hadfield steels is by Shtremel et al. [4] who investigated orientations in which slip is principal mechanism of deformation. They observed that only one slip system dominates in the plastic deformation of the ^010& and near ^012& orientations. They also noted that dislocations are stopped by collisions with stacking faults, creating similar work hardening characteristics as other fcc materials undergoing multiple slip. However, it is still necessary to consider crystallographic orientations where twinning will dominate the deformation since twinned regions have been observed in deformed polycrystals [1,2]. Experiments on traditional fcc single crystal materials have demonstrated that twins normally form after considerable levels of slip strains are developed [5]. However, since the study by Copley and Kear [6] on the effect of the applied stress on the stacking fault energy and partial dislocation separation, it has been realized that twinning may play an important role on the initial yielding of the fcc materials with low stacking fault energies. Previous studies of the authors on single crystal austenitic stainless steels with high nitrogen concentrations [7], showed that an increased nitrogen concentration decreased the stacking fault energy and caused twinning to be observed at the early stages of deformation.

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Figure 1. Resolved shear stress vs. resolved shear strain for Hadfield manganese steel under tension. The modeling result for the [111] orientation is also included. Details of modeling is explained in the text.

With this background, the purpose of this work is the following: (1) Observe the inelastic stress-strain behavior of Hadfield single crystals in orientations where twinning and slip are individually dominating or when they are competing deformation mechanisms. (2) Determine the microyield points of Hadfield single crystals and use micro-mechanical modeling to predict the stress-strain response of a single crystal undergoing micro-twinning. Experimental Procedure The material used in this study was commercial Hadfield manganese steel with a composition of Mn 12.34wt%, C 1.03wt% and Fe-balance. Single crystals were grown by the Bridgman technique in an He atmosphere, followed by homogenization in an inert gas at 1373 K for 24 hours. Electro-discharge machining was utilized to cut the regular dog-bone shaped flat tensile specimens with nominal dimensions of 8mm 3 3 mm 3 1mm. Specimens were then solution treated and water quenched from 1373 K after 1 hour. Tests were performed at room temperature. During testing, deformation surface relief was observed with a Questar QM100 long distance microscope. Uniaxial tension experiments were conducted with a screw driven ATS test machine equipped with a unique small specimen gripping system. For the measurement of microstrains, a miniature size MTS axial extensometer was employed. To distinguish twins from slip bands, the specimen surface was repolished and etched with a mixture of 80 g anhydrous sodium chromate and 400 ml glacial acetic acid. Results and Discussions In this study three different crystallographic orientations, ^001&, ^111&, and ^123& were chosen to exemplify different positions in a stereographic triangle for the tensile axis of single crystals. Resolved shear stress vs. inelastic shear strain plots for the three orientations are shown in Fig. 1. To calculate the resolved components of the stresses and strains, only the most favorable slip or twin systems were chosen as the dominant deformation system. There are two distinct yield points for all of the t-g curves, which can be denoted as the microyield and macroyield points. The hardening characteristics of the two

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TABLE I Some Important Parameters Extracted From Fig. 1. u0 is defined as ­t/­gin Between t0 and tcr. The Theoretical Elastic Moduli are for a Pure Fe Single Crystal. Tensile Directions

[111]

[001]

[123]

Schmid Factors for twinning Schmid Factors for slip Elastic Modulus-Theoretical Elastic Modulus-Experimental t0 (microyield) tcr (macroyield) tcr 2 t0 u0 (experimental u0 (model)

0.314 0.272 283.3 GPA 287 GPA 52 MPa 127 MPa 75 MPa 94.9 GPa 86.3 GPa

0.236 0.408 132.2 GPa 120 GPa 90 MPa 131 MPa 41 MPa 38.0 GPa —

0.471 0.466 220.4 GPa 217 GPa 61 MPa 138 MPa 77 MPa 250 GPa —

regions, one between micro and macroyielding and one beyond the macroyield point, are quite different. Subsequently, it can be implied that two distinct underlying mechanisms are responsible for the different hardening coefficients and two yield points. Table I emphasizes the orientation dependence of the deformation behavior of the single crystals by tabulating the exact values of the important parameters extracted from Fig. 1. Several parameters in Table I will be discussed later. In the [111] direction, the Schmid factor, m[111] 5 0.314 for the leading [121] partials is slightly higher than the Schmid factor, m[111] 5 0.272 for perfect [011] dislocations (Table I). Consequently, it can be argued that in this loading direction, twinning should initiate before slip. To determine which mechanism actually controls the macroscopic deformation in Figure 1, microscopic observations are necessary. In situ observations of deformation surface relief phenomenon are shown in Fig. 2 at approximately 3% inelastic strain. To distinguish whether or not the surface relief effects are due to twin or slip bands, the specimens were repolished and etched. Since the etchant attacks twin boundaries, it was easy to observe that the bands on specimen loaded along [111] direction are twin bands. In the [123] direction the Schmid factor for both twinning and slip are nearly identical (Table I). Therefore,

Figure 2. Deformation surface relief in a Hadfield single crystal loaded uniaxially along the [111] direction. After repolishing and etching the surfaces, it was revealed that black bands are aggregates of twin lamellae. Note the equal distances between nucleating twin bands.

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Figure 3. Schematic of the model for the crystal orientation of [111].

neither mechanism should be more pronounced over the other. Even using microscopy techniques it is difficult to determine if twinning dominates over slip or vice versa. The [001] orientation promotes easy glide, thus macroscopic deformation in Figure 1 is due to slip. This observation is consistent with the experimental results of Shtremel et al. [4] on Hadfield single crystals of this orientation. In the Luders type deformation region, thin twin bands form with almost equal distances from each other as it can be seen in Fig. 2. Twin bands were found to nucleate at the tips of existing twins or at the specimen edges. The nucleation of twin bands at the tips of pre-existing twin bands was observed in situ via enlarged versions of Fig. 2. This process of secondary twin formation is repeated along many of the tiny twin bands and subsequently leads to a macroscopic thickening of the twinned region. It is interesting to note that once the new twin is nucleated at the existing twin tip, the pre-existing twin stops growing. New twins can be realized as a continuation of old twins, however, there is an incoherency between the two twin boundaries. It should also be noted that the Boas-Schmid Law holds for the macroscopic yields points. At this point it is imperative to discuss the behavior of the three different crystallographic orientations in the micro-strain region. It is proposed that in the microstrain region the growth of small twinning and slip zones is responsible for the micro-yielding of the specimens. The large constraint provided by the surrounding elastic medium hinders the growth of the small inelastically deforming regions. Subsequently, the stress strain behavior in the micro-strain region demonstrates considerable hardening. To verify this proposed theory, micro-modeling was used to predict the stress-microstrain behavior of crystals loaded along [111] direction. The model incorporates Eshelby inclusion theory [8] and the classical minimum complementary free energy theorem to arrive at single crystal constitutive relationships. Anisotropic ellipsoidal inclusions, Fig. 3, were used to represent microscopic twin bands in crystals oriented along the [111] direction. A representative twinning system (m 5 [11# 2] and n 5 [1# 11]) is shown in Figure 3 that is identical to the experimentally observed twinned region shown in Figure 2. The dashed lines in Fig. 3 represents the trace of twinned regions in Fig. 2 which make a 54.7° angle with edge of the figure (with [112# ] direction, shown also in Fig. 3). The twining shear strain across the habit plane was taken as 0.707 and the stress-free transformation strain for Eshelby’s approach was calculated depending on this value. Since the twinning shear only occurs along a specified

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direction and not along conjugate directions, twelve possible twin systems, {111}^112# & were extracted from the Thompson tetrahedron. The anisotropic Eshelby’s tensor was used to calculate eigenstrains. Although explicit expressions for the anisotropic Green’s function are not available, it is possible to obtain an anisotropic Eshelby’s tensor using numerical integration and by assuming a uniform eigenstrain inside the inclusion. The yield criteria and growth rate of the twinned regions were obtained from a thermodynamical potential. The complementary free energy was modified for this case and is given as follows; C(Sij, f n) 5 Sij

O e f 2 21 S C n n ij

ij

ijkl

21

Skl 1

n

1 2V

E

int s int ij e ij dV

(1)

v

where S is the applied stress, en is the inelastic strain of the nth twin variant, fn is volume fraction of the nth twin variant, C is the elastic modulus tensor, and sijint and eijint represent the internal stress-strain field due to the formation of microscopic twinned inclusions. The superiority of this model is the consideration of the orientational dependence of the elastic properties and the use of the anisotropic Eshelby approach. Since we are interested in microyielding region in which elastic properties still have an effect on the flow behavior, orientational dependence plays a strong role on this region. Once the high inelastic strain levels are reached, the effect of this dependence will be impaired. The equivalent inclusion method [8] is employed to calculate equivalent eigenstrain for each possible twin variant and total eigenstrain is assumed uniform inside the inclusion. The thermodynamic driving force Fn 5 ­C/­fn on the nth microscopic twin variant is obtained from partial derivation of this complementary free energy with respect to fn. The evolution of fn versus the applied stress is determined from the consistency condition, dFn 5 0. More detailed information on modeling can be found in a recent paper of authors [9]. A reasonable agreement between experimental and modeling results is obtained on the strain hardening coefficient of the [111] orientation in microyielding region (Table I). Additionally, a comparison of the model with experimental results in the microflow region is also shown in Fig. 1. Since pure slip is the only deformation mechanism in the [001] direction, the stress-strain response was not modeled with the above approach. Additionally, stacking fault-dislocation and twin-slip interactions are more prominent in the [123] direction and they should be accounted for in any modeling effort which attempts to predict the proper hardening response. It should also be noted that after macroyielding, twinned regions span the gage section, elastic constraint is lost, and this modeling approach is no longer valid. At this point it is necessary to provide explanations for the different microscopic yield points in Table I. As previously mentioned, Copley and Kear [6] proposed a theory in which the applied stress may play an important role on the equilibrium stacking fault energy and separation of Shockley partial dislocations in fcc metals with low stacking fault energy. As a first approximation, effective stacking fault energy is defined as

geff 5 g0 1

m2 2 m1 sb 2

(2)

where g0 is the stacking fault energy per unit area under zero stress level, m2 and m1 are the absolute values of the Schmid factors of the trailing and leading Shockley partials respectively, b is the magnitude of their Burgers vector and s the applied stress. Since the stress required for twin nucleation depends on the stacking fault energy, it is clear that twinning will play a role along directions in which applied stress reduces the stacking fault energy as shown in recent studies [7,10]. They demonstrated that the main reason for the orientation dependence of the CRSS is the relationship between partial dislocation separation and the elastic interaction of the Shockley partial dislocations with impurity

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atoms. Since the athermal component of CRSS depends on the Burgers vector of partials and the equilibrium separation distance of them via elastic interaction term, CRSS decreases in directions (i.e. [111]) in which partial dislocation density is high and separation distance of them increases with applied stress. Contrarily, as equation 2 predicts along directions (i.e. [001]) in which the equilibrium separation distance decreases with applied stress, CRSS will increase which is consistent with experimental results (Fig. 1). In addition to the growth of microscopic deformation regions, microscopic yielding may also be accompanied by the difference between the elastic interactions of screw and edge dislocations with a solute atom. According to Fleischer’s classical analysis of the elastic interaction of screw and edge dislocations with a solute atom [11], elastic interaction of a solute atom with an edge dislocation is considerable larger than with a screw dislocation. This is due to the fact that the interstitials in FCC crystals have distortions of cubical symmetry. Therefore, screw dislocations are expected to be more mobile than edge dislocations before the macroyield point and thus they may be partially responsible for the microflow. Loretto and his colleagues [12] used a similar idea of elastic interaction difference between edge and screw dislocations to explain pre-yielding of Cu-0.4%Cr single crystals. They proposed that between macroyield and microyield points, edge components of the loops move to create dislocation slip while screw components are hindered by the Cr particles. If the interstitials are thought as very small particles, the study of Haberkorn et al. [13] supports our approach. Conclusions 1. Direct microscopic investigations during tensile tests revealed that in crystals oriented along [111] direction, twinning is the primary macroscopic deformation mode while slip governs the macroscopic deformation in the crystals oriented along the [001] direction. 2. Two different yield points, microyield and macroyield, were observed at small strains in single crystals of Hadfield manganese steel stressed in tension. Using an anisotropic Eshelby based micro-mechanical model for twinning, it was possible to predict the s-e response (in the [111] orientation) due to the growth of microscopic twin regions. The model properly predicts the experimentally observed decrease in the micro-hardening rate as the number and volume fraction of twinned regions increases. 3. Microyield points depend on the orientation of crystals due to effect of applied stress on the equilibrium separation of Shockley partial dislocations which affects the athermal component of the t0. The results are consistent with the model proposed by Copley & Kear. Acknowledgments This work was supported by the National Science Foundation contract CMS 94-14525, Mechanics and Materials Program, Arlington, Virginia. The Russian research is funded by grants from the International Science Foundation and Russian Fund for Basic Researches, grant No. 02-95-00350. References 1. 2. 3. 4. 5.

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