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Surface wrinkling of the twinning induced plasticity steel during the tensile and torsion tests
Materials and Design 60 (2014) 146–152
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Surface wrinkling of the twinning induced plasticity steel during the tensile and torsion tests S. Khoddam a,⇑, H. Beladi a, P.D. Hodgson a, A. Zarei-Hanzaki b a b
Institute for Frontier Materials, Deakin University, Geelong, Victoria 3216, Australia School of Metallurgy and Material Engineering, University of Tehran, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 16 January 2014 Accepted 26 March 2014 Available online 4 April 2014 Keywords: Twinning induced plasticity steel Tensile test Torsion test Twinning Bifurcation
a b s t r a c t ‘Heterogeneous twinning’ is defined as plastic deformation due to the formation and progress of twins resulting in surface wrinkles on the deforming part when the initial grain size is relatively large compared to the typical size of the part. In the case of a Twinning Induced Plasticity (TWIP) steel with an initial grain size of 160 m, the heterogeneous twinning generated visible wrinkles, an orange peel effect, under medium uni-axial strains. The heterogeneous twinning did not occur in the material subjected to high shear strains. The complications resulting from this phenomenon on strain hardening characterization of the TWIP steels using two commonly used mechanical tests, tensile and torsion are discussed along with some experimental aspects of heterogeneous twinning. Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.
1. Introduction A very important feature of coarse-grained TWIP steel is its inhomogeneous deformation behavior at both the macroscopic and microscopic scales. The macroscopic heterogeneous deformation is known as the ‘‘orange peel effect’’ (see for example [1]) and the microscopic one has been attributed to surface discontinuities that nucleate in coarse slip bands and bulk voids [2,3]. Owing to the inhomogeneous deformation of the material, a careful selection of the test to characterize its flow behavior is necessary. Also, careful treatment of the test results is essential for a meaningful description of the material behavior. The tension test has been widely used to characterize the flow behavior of metals at room temperature. The maximum elongation of the most commonly used metals at room temperature during typical manufacturing processes rarely exceeds 15%. As a result, for most of structural and some cold forming applications, the flow description characterized by the tensile test should be sufficient. One disadvantage associated with the tensile test is the occurrence of the necking leading to stress triaxiality which makes the post necking data of no practical use. Also, the pre-necking, usable portion of the flow curve obtained from the tensile test does not adequately describe large deformations such as those experienced during Severe Plastic Deformation (SPD) processes (e.g. [4]). An example of heterogeneous twinning is the twinning induced ⇑ Corresponding author. Tel.: +61 3 5227 1102; fax: +61 3 5227 1103. E-mail address: [email protected] (S. Khoddam). http://dx.doi.org/10.1016/j.matdes.2014.03.063 0261-3069/Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.
plasticity deformation during a tensile sample with relatively large grain size compared to its gauge diameter. Dini et al. showed grain size dependence behavior of the TWIP steel during the tensile test [5]; the tensile test is unsuitable when a large grain TWIP sample is involved. As a result of this, heterogeneous twinning, contributes significantly to the deformation. Mechanisms responsible for high cold formability and strain hardening in Fe–Mn steels are still under discussion [6–10]. Both dynamic strain aging (DSA) and mechanical twinning have been considered to play significant roles in the high elongation and the work hardening behavior. The former event has been interpreted as the interaction between mobile dislocations and C–Mn bonds [7]. Verbeken et al. [8] and Bracke et al. [9] substantiated the first hypothesis by suppressing DSA in a Fe–22Mn–0.6C steel by substituting carbon with nitrogen while the stacking fault energy was kept constant. The resultant mechanical properties were quite similar. The second argument was supported by the fact that the occurrence of mechanical twinning during deformation will reduce the mean free path of dislocation. This could be interpreted as a dynamic Hall–Petch effect (see for example [10]). Allain et al. [11] have also suggested that the high strain hardening rate can be attributed to mechanical twinning. Bouaziz et al. [12] argued that a kinematic origin linked to the TWIP effect is the main reason for the high strain hardening rate. Barbier et al. [13] carried out tensile tests on a fine grained steel and categorized the evolving high strain hardening rate into five stages, related to the microstructure and texture evolutions and characteristics.
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During the tensile deformation of high Mn steels, the formation of twins which is responsible for the extraordinary cold formability of the alloy at room temperatures, postpones the occurrence of necking. As twins start to form, they introduce twin boundaries that obstruct dislocation motion (similar to obstruction due to ordinary grain boundaries). This is known as the Hall–Petch effect of twins. In addition, the twinning shear converts glissile dislocations into sessile ones making those regions harder [14]. If a local neck initiates at any position of the gauge length, the strain induced twins are also preferentially formed there causing an intensive local strain hardening near the neck. Thus, excessive deformation of this region is prevented. Initiation of necking in other weaker areas will be arrested by the same mechanism. This repeated process of local necking results in a high elongation to failure as well as high strength. Consequently, the instability region of the flow curve obtained from the tensile test is less obvious. This could make interpretation of the flow curve obtained by the tensile test even more complex. Owing to the complex deformation mechanism of the TWIP steel samples during the tensile test, the parallel deformation streamlines are disturbed even at the early stages of deformation. This invalidates the uniaxial straining assumption and, therefore, the use of the standard processing techniques to interpret the test data can produce an inaccurate flow description. The macroscopic heterogeneous deformation at the surface of the test is also a serious problem for ‘‘stress corrosion cracking’’ studies of the TWIP steels using the tensile test. These tests are performed using a tensile sample exposed to a corrosive environment [15,16]. Contribution of the surface irregularities and local stress concentration can significantly overwhelm the corrosion rate, the crack initiation and growth and eventually invalidate the test. The complex deformation mechanism has been mathematically modeled using bifurcation theory [17], but the model is not convenient for general applications. Alternatively, the torsion test can be used to characterize the strain hardening even in the presence of the heterogeneous twinning. Despite the occurrence of the heterogeneous twinning during the torsion test, the axisymmetric nature of the loading and shear deformation minimize the bifurcation phenomenon considerably. Thanks to a higher achievable ultimate plastic strain which is inherent to the test, flow characterization using the torsion test is especially useful to describe the TWIP steel behavior during the SPD processes (e.g. [18]) where shear is the dominant mode of deformation. In the literature, the physical model for cold deformation of high Mn steels [11] and mechanism for their unstable plastic flow [19] have mostly been investigated based on tensile tests. In this investigation, both tensile and torsion tests were carried out for assessing cold work hardening behavior of the material and the errors associated with each method will be discussed. It will be shown that owing to two different vector fields in the two tests, unstable deformation (manifested as heterogeneous twinning) is prevented during the torsion test. Due to the complications in the tensile test for the TWIP steels discussed in the current work, the torsion test will be recommended to avoid the heterogeneous twinning and to meaningfully characterize the TWIP steel flow behavior.
2. Description of heterogeneous twinning Heterogeneous and localized plastic deformation can cause a number of dynamic phenomena, on both the macroscopic (e.g. necking) and microscopic (e.g. shear bands and surface instabilities) scales. ‘‘Heterogeneous twinning’’ is an example of such phenomena. Heterogeneous twinning is a mode of deformation and differs from specific strain mechanisms such as dislocation
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glide or twin nucleation. Heterogeneous twinning depends on the path of deformation and its loading. An interesting indicator of heterogeneous twinning is the occurrence of surface waves. Such surface irregularities have been predicted by continuum theory [17], and are experimentally observed as wrinkles, for example on the surface of pressurized cylinders [20] and in the case of tensile tests on Hadfield steel [2]. Heterogeneous twinning during tensile testing of a coarse grained TWIP steels has been attributed to the ‘‘bifurcation phenomena’’ [21] and is considered as the induced bifurcation during plastic deformation of the alloy. Similar phenomena have been studied using ‘‘bifurcation analysis’’. Given a part that is constrained to plane deformation and is subjected to tension in one direction, the presence of an initial coarse grain in the undeformed structure facilitates the occurrence of bifurcation [17] (heterogeneous twinning). From a mathematical point of view, bifurcation explains how a sudden topological or qualitative change in the behavior of a structure occurs [22]. Assuming a system described by a vector field, a bifurcation occurs when a small smooth change is made to the bifurcation parameter values. Given the initial one dimensional (axial) material flow in the gauge section of the deforming tensile sample as the vector field, the non-axial strain component induced by a typical heterogeneous twin comprises the bifurcation parameter. As a result of the twinning, simultaneously starting at every deformation point, a small and smooth change is made to the one dimensional velocity field. The bifurcation phenomenon results in surface instabilities and heterogeneous deformation of the tensile sample in high Mn steels. This becomes more visible, when the average grain size of a material exceeds a threshold so that the ‘‘grain size’’ to ‘‘the deforming part size’’ ratio becomes statistically significant. Consequently, the material can no longer be considered truly polycrystalline and exhibits mechanical behavior transitional between that of single-crystals and that of polycrystalline materials. Hill and Hutchinson formulated the tensile test as a standard bifurcation problem [17] based on different constitutive behaviors. Their constitutive description included two instantaneous moduli, namely l for shearing parallel to the geometric axes and l* for shearing at 45° to them. As far as torsional loading is concerned, the theoretical approach, as described above, requires the inclusion of a microstructural parameter (e.g. grain size) and development of a dedicated bifurcation analysis to provide a better description of the wavelength of the phenomenon. Such an approach is inconvenient for general applications and is not dealt with in the current work. Here we present a simple explanation on why heterogeneous twinning is not promoted by the torsional loading. Fig. 1 shows the gauge section of a torsion sample (only a half section shown) and the radius dependant nature of the plastic strain in the sample twisted by a twist angle of h. Upon deformation of a material point in torsion sample due to twinning, its position changes. Due to the linear increase of the effective strain with radius (i.e. e is proportional to r in Fig. 1c), work hardening increases in the radial direction and therefore the twin cannot easily move toward the gauge surface. This constraint, for the case of torsional loading, promotes formation of ‘‘tangential twins’’ and prevents the bifurcation effect (and heterogeneous twinning). This is due to the fact that the initial one dimensional (tangential) vector field in the gauge section of the deforming torsion sample cannot be perturbed by a non-tangential strain component. In the following sections, we will present experimental results for coarse grain TWIP steel subjected to the both loading types. It will be experimentally shown that torsional loading prevents the bifurcation effect (and heterogeneous twinning) while uniaxial loading promotes the deformation mode.
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(a)
(b)
Fixed
(c)
using strain rates of e_ ¼ 0:012; 0:006 and 0.0002 s1 and the samples were deformed up to fracture. The torsion flow behaviors of the TWIP steel samples, overlaid with the tensile results are shown in Fig. 2. For conversion of torque-twist data to the effective stress–strain, the post processing techniques described in [24] and [25] were used. The tensile data were processed assuming a homogeneous deformation in the samples and using the standard post processing techniques. The true stress, r, and true strain, e, were calculated using the following relationships:
e ¼ ln
L0 þ x L0
θ
3. Experimental studies, results and discussion 3.1. Experimental procedures The investigated TWIP steel (with a major alloying composition (wt.%) of Mn: 26.34, C: 0.018C, Al: 4.84Al, Si: 3.56) was produced by casting followed by an electro slag re-melting (ESR) process to homogenize the material and to minimize its porosity and inclusions. The ESR piece then underwent a number of hot and cold rolling stages, and heat treatments. This produced a homogenized slab with a mean grain size of 160 lm which was subsequently used to produce torsion and tensile samples. Round samples with 3 mm diameter and 25 mm length for torsion and with 4.6 mm diameter and 17 mm length for tension were machined along the hot rolling direction from the TWIP steel. While these samples were used for flow behavior characterization, flat square tensile samples of 10 1 mm cross section and 50 mm length were also prepared for an easier observation of wrinkle formation on the gauge section during the test. The microstructure of the deformed specimens was examined on tangential sections at a depth of 100 lm below the surface of the specimen gauge at a region 3 mm far from necking to avoid any complex deformation modes induced due to the necking. Microstructural characterization was carried out using electron back-scattered diffraction (EBSD) on a field emission scanning electron microscope (FE-SEM; Zeiss-SUPRA 55-VP) integrated with a Zeiss angle selective backscattered (AsB) electron detector. The latter provides greater spatial resolution over traditional high angle collection detectors and enables the observation of detailed microstructural information such as mechanical twins and substructure dislocations. This technique requires a careful adjustment of different variables such as working distance and operating voltage to reveal the microstructure in detail. Further information regarding this technique can be found in [23]. For the current observation, the optimum condition was found at a working distance of 10 mm and an operating voltage of 10 kV. The sample was prepared by standard mechanical polishing followed by a colloidal silica slurry polish. The instrument was equipped with a fully automated EBSD device attachment. Data acquisition and post processing were performed using the TexSEM Laboratories, Inc. software (TSL). The EBSD maps were acquired using a spatial step size of 0.1 lm.
The torsion tests were carried out with strain rates of
e_ ¼ 0:0125 and 0.0033 s1 and the tensile tests were performed
ð2Þ
where ri, r0, L0 and x are instantaneous and initial gauge radii of the sample, initial gauge length and elongation, respectively. A number of very low strain rate torsion and tensile tests ðe_ 6 0:002Þ at room temperature indicated a zero strain rate hardening effect for the range. Fig. 2 compares the flow stresses obtained from the two tests in which different yield stresses and hardening effects are evident. The sources of discrepancies between flow stresses obtained from torsion test and other mechanical tests have been discussed by Lin [26], Jonas et al. [27], Khoddam et al. [28] and Kaspar et al. [29]. It has been shown [27] that the texture related correction factor between the two tests is not constant and increases with strain. Also, deformation outside the gauge section in the torsion test changes with strain [28]. It has been suggested to use the effective gauge length to minimize the discrepancies [30] but use of a strain dependant gauge length is not convenient. Apart from the typical differences mentioned in the existing literature, the significantly different yield stresses and hardening behaviors shown in Fig. 2 may be partly due to different development of twins during the two tests. This could be also attributed to the instabilities caused by the excessive ‘‘heterogeneous twinning’’ and change of cross section in the tensile sample. Experimental observations related to the hypothesis will be presented later in this work in Section 3.3. Hill and Hutchinson’s detailed formulation [17] is useful to understand the occurrence of the bifurcation during the tensile test but cannot
1300 1200 1100 1000 900 800 700 600
torsion 1, torsion 2, tension 1, tension 2, tension 3,
500 400 300
.
ε = 0.0125 s . ε = 0.0033 s-1 . -1 ε = 0.0012 s . -1 ε = 0.0006 s . ε = 0.0002 s-1 -1
200 100 0
3.2. Flow behavior of high Mn steel under torsion and tension tests
ð1Þ
sffiffiffiffiffiffiffiffiffiffiffiffiffi! L0 ri ¼ r0 L0 þ x
F r¼ 2 pr i
True stress σ , MPa
Fig. 1. Torsion sample (only half section shown) before deformation (a), deformed by a twist angle of h (b) and radius dependant strain distribution in the radial and longitudinal directions (c).
0.2
0.4
0.6
0.8
1
1.2
True strain, ε Fig. 2. Strain hardening of the TWIP steel under three different strain rates at torsion and tensile testing modes.
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be used as a method to correct the tensile test data for material characterization. One can conclude from other bifurcation related works (e.g. [1,2,7,10,21]) that the tensile test is inappropriate to characterize TWIP steel cold forming behavior. This highlights the importance of using the torsion test as an alternative method to avoid the bifurcation issues. Fig. 3 shows different levels of wrinkling on a torsion sample (Fig. 3a) and a tensile sample (Fig. 3b). Fig. 4 shows the wrinkles at the surface of the flat square tensile sample. It was difficult to exactly pinpoint the onset of the wrinkles but, visual monitoring during tensile testing along with interrupted tests indicated that they were readily observable when the plastic strain exceeded 0.05 in the flat square tensile samples. Similar visible wrinkling has been reported during tensile fracture of Hadfield steel [1,2]. It can be seen that despite a higher ultimate strains of eu = 1.1 and 1.2 in the case of torsion (as compared to that of tensile sample in which the ultimate strain is lower; eut = 0.55) the wrinkling on the tensile sample is much more prominent. Similar strain hardening indices n 0.29, for both tensile and torsion test results were found prior to an ultimate tensile strain of eu = 0.55 (see Fig. 2). Different yield strength and true stresses under tensile loading are shown in Fig. 2. It is clear that at the same strains, the effective yield strength and effective plastic stresses under tensile and torsional loading are not similar. Comparing the strain hardening indices for the torsion test after eut = 0.55, one can see that the index reduces significantly under the higher strain rate of e_ ¼ 0:0125 s1 . This could be due to a lower rate of
Fig. 3. Wrinkling on the surface of (a) the torsion sample and (b) the cylindrical tensile sample; macroscopic observations of the fractured tensile samples.
Fig. 4. Wrinkling on the surface of the flat square type tensile sample after fracture.
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dynamic recovery in the high strain regime (e > eut) and high strain rate compared to those of low strain regime (e < eut) and low strain rate. The torsion test results show a rate sensitivity in the strain rate range investigated ðe_ ¼ 0:0033 and 0:0125 s1 Þ. The torsion results with higher rate, e_ ¼ 0:0125 s1 , indicate a near zero strain hardening index for e > 0.62.Curtze et al. [31] studied the effect of strain rate sensitivity for three different TWIP steels. They showed noticeable rate sensitivity behavior for strain rates above 103 s1 and that the sensitivity increases with increasing strain rate. The tensile tests in Fig. 2 were performed under very low strain rates ðe_ < 1:2 103 Þ with no significant rate sensitivity. The rate sensitive behavior for the torsion tests shown in Fig. 2 can be explained by noting their higher strain rates; 3:3 103 < e_ < 12:5 103 . The rate sensitivity trend in Fig. 2 complies well with the reported results in [31]
3.3. Microhardness across the cross section The kinematic solution of the torsion test is based on a linear tangential velocity distribution in the radial direction, Vh, with Vh = 0 at r = 0 and Vh = r0h at r = ro where ro and h are the gauge radius and angular velocity, respectively (Fig. 1c). For the case of the tensile test, a uniform axial velocity field, Vz, develops in the circular gauge cross section. Given a constant velocity of the test’s crosshead, Vz is expected to increase during the test due to the volume constancy principle. However, the gauge cross sections for both tests should remain circular throughout the tests for the specified kinematic solutions. Fig. 5a and b shows the cross section of the TWIP steel test samples after deformation under torsional and tensile loads, respectively. Fig. 5a shows a circular cross section of the torsion TWIP sample for which the radius has not changed due to the heterogeneous twinning during deformation. Fig. 5b shows that the circular cross section of the tensile test has changed into an ellipse after deformation. The semi-major and the semi-minor axes of the ellipse are denoted by r1 and r2 respectively. Also, a fictitious radius r3 in Fig. 5b shows an imaginary reference circular cross section whose radius was calculated based on the standard tensile test calculations using an ultimate strain of eut = 0.55. Change of cross section in the tensile samples can be attributed to the material’s processing history. This included hot and cold rolling stages prior to their machining which resulted in the formation of flattened and elongated grains in the rolling direction. A combination of the rolling and normalizing of the electro slag remelted material is usually sufficient to produce an equiaxed grain structure. However, given the unstable nature of the bifurcation and heterogeneous twinning for the tensile deformation and a relatively small sample size, 4.6 mm in diameter, even a small portion of retained flattened and elongated grains can facilitate the propagation of the twins along a preferred axis to cause the cross section change. Fig. 6a and b shows the post deformation micro hardness distribution across the radii of the TWIP torsion and tension samples, respectively. The unchanged geometry of the TWIP torsion sample in Fig. 5a and a radial linear increase in the Fig. 6a are in agreement with the described kinematic solution of the torsion test in which a linear radial gradient of velocity is assumed. Non-uniform micro hardness distributions in Fig. 6b in the tensile test show work hardening across the elliptical deformed cross section. The changes in work hardening have been shown in Fig. 6b along r1 and r2 radii which are one half of the major and minor axes, respectively. Both results of Figs. 5b and 6b indicate a rather complex deformation in the tensile sample which cannot be explained using the standard kinematic solution of the tensile test described above.
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440 420 400 380 360 340 320 300 280 260 240 220 200
380
(a)
Torsoin,direction1, Torsoin,direction2, Torsoin,direction1, Torsoin,direction2,
0
0.2
0.4
0.6
0.8
1
.ε =0.0125s .ε =0.0125s .ε =0.0033s . ε =0.0033s
1.2
-1 -1 -1 -1
1.4
Distance from the centre, mm
Micro hardness, Vickers
Micro hardness, Vickers
Fig. 5. TWIP steel test sample cross section change during (a) torsion; r0 = 1.5 mm (unchanged) and (b) tension; major radius r1 = 2.89 mm, minor radius r2 = 1.84 mm and homogenous radius r3 = 1.80 mm.
(b)
360 340 320 300 280
tension1 ,along major radius tension1, along minor radius tension2, alongmajorradius tension2, along minor radius
260 240
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Distance from the centre, mm
Fig. 6. Microhardness distribution along the radial direction from the center to the surface of deformed sample of the TWIP steel subjected to different deformation modes: (a) torsion test and (b) tensile test.
A qualitative explanation on why the work hardening (micro hardness values) in the deformed tensile samples has increased along the major and minor axes will follow. The velocity in the tensile gauge section of the TWIP samples can be resolved in axial, radial and tangential components with the radial and tangential components resulting from twins progressing randomly in all directions, including tangential and radial. In the case of heterogeneous twinning, these components are significant enough in comparison with the main axial component to be treated as bifurcation parameters. The magnitude of these parameters is proportional to the ratio of the mean grain size to the gauge radius. The progress of the heterogeneous twinning in an unstable fashion at the periphery of the samples results in the formation of the wrinkles. Depending on the distribution of the large grain sizes, inclusions, imperfections etc. the bifurcation parameters along the semimajor and semi-minor axes of the ellipse are not necessarily equal. As shown in the hardness distribution results in Fig. 6b, the work hardening of a typical point in the ellipse cross section increases with their distance from the center along the semi-axes. Quantitative estimation of the new component is rather complex and requires a comprehensive bifurcation analysis. As a result, the simple theory of the tensile test cannot be applied to post process the tensile test results. Therefore, the work hardening and flow characterization of the TWIP steel in the tensile test should be re-considered carefully. The torsion test results shown in Figs. 5a and 6a indicate that the test results are less affected by the heterogeneous twinning and the test is more suitable compared to the tensile test for flow characterization of the TWIP steels.
For a better comparison of the deformation mechanisms in the two test conditions, the microstructures were examined using electron back-scattered diffraction (EBSD) along with assessments of deformed gauge sections and their results will be presented next. 3.4. Comparative study of the deformed microstructures According to the results shown in Figs. 5 and 6, the maximum heterogeneous propagation of the twins is expected at the periphery section of the tensile sample. To access comparable strains at both the samples for microscopic study, the torsion sample was machined about 1 mm deep (0.5 6 r 6 1.5 mm) to study the strain equivalent pffiffiffi to tensile strain [28] at fracture of (0.4 6 eu 6 1.2) using e ¼ rh= 3l where r, h and l are radius (mm), twist angle (rad) and length (mm) of torsion sample (Fig. 1c) . The initial microstructure of the alloy consisted of fully recrystallized grains with an average size of 160 lm. The microstructure examinations revealed that the mechanical twinning was extensively formed during deformation of samples subjected to both torsion and tensile deformation modes. The thickness of mechanical twins was very fine (i.e. 20 nm) and they mainly nucleated at grain boundaries and propagated across the grains (Figs. 7–9). They were mainly formed in a coordinated manner, as a group of nearly parallel twins of specific orientation (Fig. 7). Due to three-dimensional nature of the grains, a more precise investigation of twin nucleation and propagation requires three dimensional observations. As the twin thickness of 20 nm is smaller than the spatial resolution of EBSD map (i.e. the step size), they
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Fig. 7. AsB image of the mechanical twins formed in the sample subjected to the tensile testing.
Fig. 8. (a) EBSD band contrast image of the sample subjected to the tensile testing. (b) inverse pole figure and (c) stereographic standard triangle of dashed region in (a). (c and d) (1 1 1) pole figures of the grain and the adjacent mechanical twins. Dashed and solid lines are the coincidence of a plane twin normal and the trace of the twin, respectively. Black and red lines in (a) are high angle boundaries with a misorientation greater than 15° and mechanical twin boundaries, respectively. TD and ND represent the tensile direction and normal direction, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 9. EBSD band contrast (a) inverse pole figure (b) images of the sample subjected to the torsion loading. Black and red lines in (a) are high angle boundaries with a misorientation greater than 15° and mechanical twin boundaries, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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could not be readily indexed by EBSD. Hence, the band contrast quality image was used to partly reveal the mechanical twins (Figs. 8a and 9a). The observed twin regions delineated by red lines in Figs. 8a and 9a, in fact, consisted of organized aligned twins of a given orientation (Figs. 8b and 9b). The mechanical twins had a misorientation angle of 60° ± 2.5° about the [1 1 1] misorientation axis, similar to the annealing twins [32]. The mechanical twins could, however, be differentiated from annealing twins based on their morphology and size. There would be one or more twin variants formed in a given grain depending on the grain orientation [32]. Fig. 8 shows a crystallographic analysis of the EBSD map of a grain containing two twin variants with different traces under the tensile testing condition. The triangle stereographic standard along the tensile axis (TD) revealed that the orientation of the grain was such that its h5 3 3i direction was parallel to the tensile axis. In addition, the twins had different orientations in respect to the tensile direction (Fig. 8c). The deformation mode had a strong effect on the twin distribution. The mechanical twinning was found to be uniformly distributed within grains for the sample subjected to the torsion (Fig. 9). In contrast, they were much more scattered in the tensile sample. In addition, shear bands were widely seen in the microstructure of the tensile sample, crossing prior grain boundaries and interestingly containing fine mechanical twins (as shown by the arrows in Fig. 8). However, there was no sign of shear band formation in the torsion specimen. The formation of shear bands could be the reason behind the deformation non-homogeneity in tension compared with torsion. 4. Conclusions Significant surface alterations, ‘‘heterogeneous twinning’’, developed during uni-axial tensile straining of a TWIP steel sample. Visual inspection of the tensile specimens showed that the surfaces were wrinkled (rumpled) at the start of the plastic deformation (yielding). The material accommodated two times higher shearing strains without producing such surface alterations in torsion. It was also noticed that the tensile straining changed the cross section of round TWIP steel sample to an ellipse whereas under the pure shear straining, the circular cross section remained unchanged. Micro hardness distribution data across the tensile and torsion samples showed heterogeneous deformation in the TWIP tensile sample. Also, misorientation of the grain boundaries under tension and torsional straining were compared. The twins in torsion samples were distributed more uniformly compared to that of tensile samples. This indicates that shear straining can effectively prevent the heterogeneous twinning compared to the uni-axial straining and to allow accumulation of more deformation without developing visual surface waves. It was shown that under tensile straining, the true stress-true plastic strain curve is only an inaccurate indicative of the average mechanical response of the material, and it does not reflect local behavior. According to the evidence presented here, the true stress-true plastic strain results of the TWIP steel cannot be reliably identified based on the tensile test and standard data conversion techniques. It was shown that the tensile test results cannot be easily post processed for flow characterization of the steel. Alternatively, the torsion test proved to suffer less from this effect. References [1] Abbasi M, Kheirandish S, Kharrazi Y, Hejazi J. The fracture and plastic deformation of aluminum alloyed Hadfield steels. Mater Sci Eng A 2009;513–514:72–6.
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Mater Sci Eng: A 2009;500:196–206. [14] El Kadiri H, Oppedal AL. A crystal plasticity theory for latent hardening by glide twinning through dislocation transmutation and twin accommodation effects. J Mech Phys Solids 2010;58:613–24. [15] Kannan MB, Raman RKS, Khoddam S, Liyanaarachchi S. Corrosion behavior of twinning-induced plasticity (TWIP) steel. Mater Corros 2013;64:231–5. [16] Kannan MB, Raman RKS, Khoddam S. Comparative studies on the corrosion properties of a Fe–Mn–Al–Si steel and an interstitial-free steel. Corros Sci 2008;50:2879–84. [17] Hill R, Hutchinson JW. Bifurcation phenomena in the plane tension test. J Mech Phys Solids 1975;23:239–64. [18] Bagherpour E, Reihanian M, Ebrahimi R. On the capability of severe plastic deformation of twining induced plasticity (TWIP) steel. Mater Des 2012;36:391–5. [19] Lebedkina TA, Lebyodkin MA, Chateau JP, Jacques A, Allain S. On the mechanism of unstable plastic flow in an austenitic FeMnC TWIP steel. Mater Sci Eng A 2009;519:147–54. [20] Tvergaard V, Needleman A, Lo KK. Flow localization in the plane strain tensile test. J Mech Phys Solids 1981;29:115–42. [21] Rittel D, Roman I. Tensile deformation of coarse-grained cast austenitic manganese steels. Mater Sci Eng A 1989;110:77–87. [22] Blanchart P, Devaney RL, Hall GR. Differential equations. 3rd ed. Thomson Higher Education; 2006. [23] Hilditch T, Beladi H, Hodgson P, Stanford N. Role of microstructure in the low cycle fatigue of multi-phase steels. Mater Sci Eng: A 2012;534:288–96. [24] Khoddam S, Hodgson PD. A heuristic model selection scheme for representing hot flow data using the hot torsion test results. Mater Des 2010;31:2011–7. [25] Khoddam S, Hodgson PD. Conversion of the hot torsion test results into flow curve with multiple regimes of hardening. J Mater Process Technol 2004;153– 154:839–45. [26] Lin YC, Chen X-M. A critical review of experimental results and constitutive descriptions for metals and alloys in hot working. Mater Des 2011;32:1733–59. [27] Jonas JJ, Canova GR, Shrivastava S, Christodoulou N. Sources of the discrepancy between the flow curves determined in torsion and in axisymmetric tension and compression testing. In: Lee HE, Mallett RL, editors. Plasticity of Metals at Finite Strain: Theory, Experiment and Computation, Proceedings of Research Workshop. Stanford University, N.Y.: Rensselaer Polytechnic Institute, N.Y.; 1981. p. 206–22. [28] Khoddam S, Lam YC, Thomson PF. The effect of specimen geometry on the accuracy of the constitutive equation derived from the hot torsion test. Steel Res 1995;66:45–9. [29] Kaspar R, Muller PM, Philipp FD, Backmann G. Hot stress–strain curves of steel determined by different kinds of deformation. Steel Res 1993;64:611–7. [30] Khoddam S. Variations of effective length of the hot torsion test specimen with deformation. J Mater Process Technol 2006;177:465–8. [31] Curtze S, Kuokkala VT. 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Surface wrinkling of the twinning induced plasticity steel during the tensile and torsion tests S. Khoddam a,⇑, H. Beladi a, P.D. Hodgson a, A. Zarei-Hanzaki b a b
Institute for Frontier Materials, Deakin University, Geelong, Victoria 3216, Australia School of Metallurgy and Material Engineering, University of Tehran, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 16 January 2014 Accepted 26 March 2014 Available online 4 April 2014 Keywords: Twinning induced plasticity steel Tensile test Torsion test Twinning Bifurcation
a b s t r a c t ‘Heterogeneous twinning’ is defined as plastic deformation due to the formation and progress of twins resulting in surface wrinkles on the deforming part when the initial grain size is relatively large compared to the typical size of the part. In the case of a Twinning Induced Plasticity (TWIP) steel with an initial grain size of 160 m, the heterogeneous twinning generated visible wrinkles, an orange peel effect, under medium uni-axial strains. The heterogeneous twinning did not occur in the material subjected to high shear strains. The complications resulting from this phenomenon on strain hardening characterization of the TWIP steels using two commonly used mechanical tests, tensile and torsion are discussed along with some experimental aspects of heterogeneous twinning. Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.
1. Introduction A very important feature of coarse-grained TWIP steel is its inhomogeneous deformation behavior at both the macroscopic and microscopic scales. The macroscopic heterogeneous deformation is known as the ‘‘orange peel effect’’ (see for example [1]) and the microscopic one has been attributed to surface discontinuities that nucleate in coarse slip bands and bulk voids [2,3]. Owing to the inhomogeneous deformation of the material, a careful selection of the test to characterize its flow behavior is necessary. Also, careful treatment of the test results is essential for a meaningful description of the material behavior. The tension test has been widely used to characterize the flow behavior of metals at room temperature. The maximum elongation of the most commonly used metals at room temperature during typical manufacturing processes rarely exceeds 15%. As a result, for most of structural and some cold forming applications, the flow description characterized by the tensile test should be sufficient. One disadvantage associated with the tensile test is the occurrence of the necking leading to stress triaxiality which makes the post necking data of no practical use. Also, the pre-necking, usable portion of the flow curve obtained from the tensile test does not adequately describe large deformations such as those experienced during Severe Plastic Deformation (SPD) processes (e.g. [4]). An example of heterogeneous twinning is the twinning induced ⇑ Corresponding author. Tel.: +61 3 5227 1102; fax: +61 3 5227 1103. E-mail address: [email protected] (S. Khoddam). http://dx.doi.org/10.1016/j.matdes.2014.03.063 0261-3069/Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.
plasticity deformation during a tensile sample with relatively large grain size compared to its gauge diameter. Dini et al. showed grain size dependence behavior of the TWIP steel during the tensile test [5]; the tensile test is unsuitable when a large grain TWIP sample is involved. As a result of this, heterogeneous twinning, contributes significantly to the deformation. Mechanisms responsible for high cold formability and strain hardening in Fe–Mn steels are still under discussion [6–10]. Both dynamic strain aging (DSA) and mechanical twinning have been considered to play significant roles in the high elongation and the work hardening behavior. The former event has been interpreted as the interaction between mobile dislocations and C–Mn bonds [7]. Verbeken et al. [8] and Bracke et al. [9] substantiated the first hypothesis by suppressing DSA in a Fe–22Mn–0.6C steel by substituting carbon with nitrogen while the stacking fault energy was kept constant. The resultant mechanical properties were quite similar. The second argument was supported by the fact that the occurrence of mechanical twinning during deformation will reduce the mean free path of dislocation. This could be interpreted as a dynamic Hall–Petch effect (see for example [10]). Allain et al. [11] have also suggested that the high strain hardening rate can be attributed to mechanical twinning. Bouaziz et al. [12] argued that a kinematic origin linked to the TWIP effect is the main reason for the high strain hardening rate. Barbier et al. [13] carried out tensile tests on a fine grained steel and categorized the evolving high strain hardening rate into five stages, related to the microstructure and texture evolutions and characteristics.
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During the tensile deformation of high Mn steels, the formation of twins which is responsible for the extraordinary cold formability of the alloy at room temperatures, postpones the occurrence of necking. As twins start to form, they introduce twin boundaries that obstruct dislocation motion (similar to obstruction due to ordinary grain boundaries). This is known as the Hall–Petch effect of twins. In addition, the twinning shear converts glissile dislocations into sessile ones making those regions harder [14]. If a local neck initiates at any position of the gauge length, the strain induced twins are also preferentially formed there causing an intensive local strain hardening near the neck. Thus, excessive deformation of this region is prevented. Initiation of necking in other weaker areas will be arrested by the same mechanism. This repeated process of local necking results in a high elongation to failure as well as high strength. Consequently, the instability region of the flow curve obtained from the tensile test is less obvious. This could make interpretation of the flow curve obtained by the tensile test even more complex. Owing to the complex deformation mechanism of the TWIP steel samples during the tensile test, the parallel deformation streamlines are disturbed even at the early stages of deformation. This invalidates the uniaxial straining assumption and, therefore, the use of the standard processing techniques to interpret the test data can produce an inaccurate flow description. The macroscopic heterogeneous deformation at the surface of the test is also a serious problem for ‘‘stress corrosion cracking’’ studies of the TWIP steels using the tensile test. These tests are performed using a tensile sample exposed to a corrosive environment [15,16]. Contribution of the surface irregularities and local stress concentration can significantly overwhelm the corrosion rate, the crack initiation and growth and eventually invalidate the test. The complex deformation mechanism has been mathematically modeled using bifurcation theory [17], but the model is not convenient for general applications. Alternatively, the torsion test can be used to characterize the strain hardening even in the presence of the heterogeneous twinning. Despite the occurrence of the heterogeneous twinning during the torsion test, the axisymmetric nature of the loading and shear deformation minimize the bifurcation phenomenon considerably. Thanks to a higher achievable ultimate plastic strain which is inherent to the test, flow characterization using the torsion test is especially useful to describe the TWIP steel behavior during the SPD processes (e.g. [18]) where shear is the dominant mode of deformation. In the literature, the physical model for cold deformation of high Mn steels [11] and mechanism for their unstable plastic flow [19] have mostly been investigated based on tensile tests. In this investigation, both tensile and torsion tests were carried out for assessing cold work hardening behavior of the material and the errors associated with each method will be discussed. It will be shown that owing to two different vector fields in the two tests, unstable deformation (manifested as heterogeneous twinning) is prevented during the torsion test. Due to the complications in the tensile test for the TWIP steels discussed in the current work, the torsion test will be recommended to avoid the heterogeneous twinning and to meaningfully characterize the TWIP steel flow behavior.
2. Description of heterogeneous twinning Heterogeneous and localized plastic deformation can cause a number of dynamic phenomena, on both the macroscopic (e.g. necking) and microscopic (e.g. shear bands and surface instabilities) scales. ‘‘Heterogeneous twinning’’ is an example of such phenomena. Heterogeneous twinning is a mode of deformation and differs from specific strain mechanisms such as dislocation
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glide or twin nucleation. Heterogeneous twinning depends on the path of deformation and its loading. An interesting indicator of heterogeneous twinning is the occurrence of surface waves. Such surface irregularities have been predicted by continuum theory [17], and are experimentally observed as wrinkles, for example on the surface of pressurized cylinders [20] and in the case of tensile tests on Hadfield steel [2]. Heterogeneous twinning during tensile testing of a coarse grained TWIP steels has been attributed to the ‘‘bifurcation phenomena’’ [21] and is considered as the induced bifurcation during plastic deformation of the alloy. Similar phenomena have been studied using ‘‘bifurcation analysis’’. Given a part that is constrained to plane deformation and is subjected to tension in one direction, the presence of an initial coarse grain in the undeformed structure facilitates the occurrence of bifurcation [17] (heterogeneous twinning). From a mathematical point of view, bifurcation explains how a sudden topological or qualitative change in the behavior of a structure occurs [22]. Assuming a system described by a vector field, a bifurcation occurs when a small smooth change is made to the bifurcation parameter values. Given the initial one dimensional (axial) material flow in the gauge section of the deforming tensile sample as the vector field, the non-axial strain component induced by a typical heterogeneous twin comprises the bifurcation parameter. As a result of the twinning, simultaneously starting at every deformation point, a small and smooth change is made to the one dimensional velocity field. The bifurcation phenomenon results in surface instabilities and heterogeneous deformation of the tensile sample in high Mn steels. This becomes more visible, when the average grain size of a material exceeds a threshold so that the ‘‘grain size’’ to ‘‘the deforming part size’’ ratio becomes statistically significant. Consequently, the material can no longer be considered truly polycrystalline and exhibits mechanical behavior transitional between that of single-crystals and that of polycrystalline materials. Hill and Hutchinson formulated the tensile test as a standard bifurcation problem [17] based on different constitutive behaviors. Their constitutive description included two instantaneous moduli, namely l for shearing parallel to the geometric axes and l* for shearing at 45° to them. As far as torsional loading is concerned, the theoretical approach, as described above, requires the inclusion of a microstructural parameter (e.g. grain size) and development of a dedicated bifurcation analysis to provide a better description of the wavelength of the phenomenon. Such an approach is inconvenient for general applications and is not dealt with in the current work. Here we present a simple explanation on why heterogeneous twinning is not promoted by the torsional loading. Fig. 1 shows the gauge section of a torsion sample (only a half section shown) and the radius dependant nature of the plastic strain in the sample twisted by a twist angle of h. Upon deformation of a material point in torsion sample due to twinning, its position changes. Due to the linear increase of the effective strain with radius (i.e. e is proportional to r in Fig. 1c), work hardening increases in the radial direction and therefore the twin cannot easily move toward the gauge surface. This constraint, for the case of torsional loading, promotes formation of ‘‘tangential twins’’ and prevents the bifurcation effect (and heterogeneous twinning). This is due to the fact that the initial one dimensional (tangential) vector field in the gauge section of the deforming torsion sample cannot be perturbed by a non-tangential strain component. In the following sections, we will present experimental results for coarse grain TWIP steel subjected to the both loading types. It will be experimentally shown that torsional loading prevents the bifurcation effect (and heterogeneous twinning) while uniaxial loading promotes the deformation mode.
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(a)
(b)
Fixed
(c)
using strain rates of e_ ¼ 0:012; 0:006 and 0.0002 s1 and the samples were deformed up to fracture. The torsion flow behaviors of the TWIP steel samples, overlaid with the tensile results are shown in Fig. 2. For conversion of torque-twist data to the effective stress–strain, the post processing techniques described in [24] and [25] were used. The tensile data were processed assuming a homogeneous deformation in the samples and using the standard post processing techniques. The true stress, r, and true strain, e, were calculated using the following relationships:
e ¼ ln
L0 þ x L0
θ
3. Experimental studies, results and discussion 3.1. Experimental procedures The investigated TWIP steel (with a major alloying composition (wt.%) of Mn: 26.34, C: 0.018C, Al: 4.84Al, Si: 3.56) was produced by casting followed by an electro slag re-melting (ESR) process to homogenize the material and to minimize its porosity and inclusions. The ESR piece then underwent a number of hot and cold rolling stages, and heat treatments. This produced a homogenized slab with a mean grain size of 160 lm which was subsequently used to produce torsion and tensile samples. Round samples with 3 mm diameter and 25 mm length for torsion and with 4.6 mm diameter and 17 mm length for tension were machined along the hot rolling direction from the TWIP steel. While these samples were used for flow behavior characterization, flat square tensile samples of 10 1 mm cross section and 50 mm length were also prepared for an easier observation of wrinkle formation on the gauge section during the test. The microstructure of the deformed specimens was examined on tangential sections at a depth of 100 lm below the surface of the specimen gauge at a region 3 mm far from necking to avoid any complex deformation modes induced due to the necking. Microstructural characterization was carried out using electron back-scattered diffraction (EBSD) on a field emission scanning electron microscope (FE-SEM; Zeiss-SUPRA 55-VP) integrated with a Zeiss angle selective backscattered (AsB) electron detector. The latter provides greater spatial resolution over traditional high angle collection detectors and enables the observation of detailed microstructural information such as mechanical twins and substructure dislocations. This technique requires a careful adjustment of different variables such as working distance and operating voltage to reveal the microstructure in detail. Further information regarding this technique can be found in [23]. For the current observation, the optimum condition was found at a working distance of 10 mm and an operating voltage of 10 kV. The sample was prepared by standard mechanical polishing followed by a colloidal silica slurry polish. The instrument was equipped with a fully automated EBSD device attachment. Data acquisition and post processing were performed using the TexSEM Laboratories, Inc. software (TSL). The EBSD maps were acquired using a spatial step size of 0.1 lm.
The torsion tests were carried out with strain rates of
e_ ¼ 0:0125 and 0.0033 s1 and the tensile tests were performed
ð2Þ
where ri, r0, L0 and x are instantaneous and initial gauge radii of the sample, initial gauge length and elongation, respectively. A number of very low strain rate torsion and tensile tests ðe_ 6 0:002Þ at room temperature indicated a zero strain rate hardening effect for the range. Fig. 2 compares the flow stresses obtained from the two tests in which different yield stresses and hardening effects are evident. The sources of discrepancies between flow stresses obtained from torsion test and other mechanical tests have been discussed by Lin [26], Jonas et al. [27], Khoddam et al. [28] and Kaspar et al. [29]. It has been shown [27] that the texture related correction factor between the two tests is not constant and increases with strain. Also, deformation outside the gauge section in the torsion test changes with strain [28]. It has been suggested to use the effective gauge length to minimize the discrepancies [30] but use of a strain dependant gauge length is not convenient. Apart from the typical differences mentioned in the existing literature, the significantly different yield stresses and hardening behaviors shown in Fig. 2 may be partly due to different development of twins during the two tests. This could be also attributed to the instabilities caused by the excessive ‘‘heterogeneous twinning’’ and change of cross section in the tensile sample. Experimental observations related to the hypothesis will be presented later in this work in Section 3.3. Hill and Hutchinson’s detailed formulation [17] is useful to understand the occurrence of the bifurcation during the tensile test but cannot
1300 1200 1100 1000 900 800 700 600
torsion 1, torsion 2, tension 1, tension 2, tension 3,
500 400 300
.
ε = 0.0125 s . ε = 0.0033 s-1 . -1 ε = 0.0012 s . -1 ε = 0.0006 s . ε = 0.0002 s-1 -1
200 100 0
3.2. Flow behavior of high Mn steel under torsion and tension tests
ð1Þ
sffiffiffiffiffiffiffiffiffiffiffiffiffi! L0 ri ¼ r0 L0 þ x
F r¼ 2 pr i
True stress σ , MPa
Fig. 1. Torsion sample (only half section shown) before deformation (a), deformed by a twist angle of h (b) and radius dependant strain distribution in the radial and longitudinal directions (c).
0.2
0.4
0.6
0.8
1
1.2
True strain, ε Fig. 2. Strain hardening of the TWIP steel under three different strain rates at torsion and tensile testing modes.
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be used as a method to correct the tensile test data for material characterization. One can conclude from other bifurcation related works (e.g. [1,2,7,10,21]) that the tensile test is inappropriate to characterize TWIP steel cold forming behavior. This highlights the importance of using the torsion test as an alternative method to avoid the bifurcation issues. Fig. 3 shows different levels of wrinkling on a torsion sample (Fig. 3a) and a tensile sample (Fig. 3b). Fig. 4 shows the wrinkles at the surface of the flat square tensile sample. It was difficult to exactly pinpoint the onset of the wrinkles but, visual monitoring during tensile testing along with interrupted tests indicated that they were readily observable when the plastic strain exceeded 0.05 in the flat square tensile samples. Similar visible wrinkling has been reported during tensile fracture of Hadfield steel [1,2]. It can be seen that despite a higher ultimate strains of eu = 1.1 and 1.2 in the case of torsion (as compared to that of tensile sample in which the ultimate strain is lower; eut = 0.55) the wrinkling on the tensile sample is much more prominent. Similar strain hardening indices n 0.29, for both tensile and torsion test results were found prior to an ultimate tensile strain of eu = 0.55 (see Fig. 2). Different yield strength and true stresses under tensile loading are shown in Fig. 2. It is clear that at the same strains, the effective yield strength and effective plastic stresses under tensile and torsional loading are not similar. Comparing the strain hardening indices for the torsion test after eut = 0.55, one can see that the index reduces significantly under the higher strain rate of e_ ¼ 0:0125 s1 . This could be due to a lower rate of
Fig. 3. Wrinkling on the surface of (a) the torsion sample and (b) the cylindrical tensile sample; macroscopic observations of the fractured tensile samples.
Fig. 4. Wrinkling on the surface of the flat square type tensile sample after fracture.
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dynamic recovery in the high strain regime (e > eut) and high strain rate compared to those of low strain regime (e < eut) and low strain rate. The torsion test results show a rate sensitivity in the strain rate range investigated ðe_ ¼ 0:0033 and 0:0125 s1 Þ. The torsion results with higher rate, e_ ¼ 0:0125 s1 , indicate a near zero strain hardening index for e > 0.62.Curtze et al. [31] studied the effect of strain rate sensitivity for three different TWIP steels. They showed noticeable rate sensitivity behavior for strain rates above 103 s1 and that the sensitivity increases with increasing strain rate. The tensile tests in Fig. 2 were performed under very low strain rates ðe_ < 1:2 103 Þ with no significant rate sensitivity. The rate sensitive behavior for the torsion tests shown in Fig. 2 can be explained by noting their higher strain rates; 3:3 103 < e_ < 12:5 103 . The rate sensitivity trend in Fig. 2 complies well with the reported results in [31]
3.3. Microhardness across the cross section The kinematic solution of the torsion test is based on a linear tangential velocity distribution in the radial direction, Vh, with Vh = 0 at r = 0 and Vh = r0h at r = ro where ro and h are the gauge radius and angular velocity, respectively (Fig. 1c). For the case of the tensile test, a uniform axial velocity field, Vz, develops in the circular gauge cross section. Given a constant velocity of the test’s crosshead, Vz is expected to increase during the test due to the volume constancy principle. However, the gauge cross sections for both tests should remain circular throughout the tests for the specified kinematic solutions. Fig. 5a and b shows the cross section of the TWIP steel test samples after deformation under torsional and tensile loads, respectively. Fig. 5a shows a circular cross section of the torsion TWIP sample for which the radius has not changed due to the heterogeneous twinning during deformation. Fig. 5b shows that the circular cross section of the tensile test has changed into an ellipse after deformation. The semi-major and the semi-minor axes of the ellipse are denoted by r1 and r2 respectively. Also, a fictitious radius r3 in Fig. 5b shows an imaginary reference circular cross section whose radius was calculated based on the standard tensile test calculations using an ultimate strain of eut = 0.55. Change of cross section in the tensile samples can be attributed to the material’s processing history. This included hot and cold rolling stages prior to their machining which resulted in the formation of flattened and elongated grains in the rolling direction. A combination of the rolling and normalizing of the electro slag remelted material is usually sufficient to produce an equiaxed grain structure. However, given the unstable nature of the bifurcation and heterogeneous twinning for the tensile deformation and a relatively small sample size, 4.6 mm in diameter, even a small portion of retained flattened and elongated grains can facilitate the propagation of the twins along a preferred axis to cause the cross section change. Fig. 6a and b shows the post deformation micro hardness distribution across the radii of the TWIP torsion and tension samples, respectively. The unchanged geometry of the TWIP torsion sample in Fig. 5a and a radial linear increase in the Fig. 6a are in agreement with the described kinematic solution of the torsion test in which a linear radial gradient of velocity is assumed. Non-uniform micro hardness distributions in Fig. 6b in the tensile test show work hardening across the elliptical deformed cross section. The changes in work hardening have been shown in Fig. 6b along r1 and r2 radii which are one half of the major and minor axes, respectively. Both results of Figs. 5b and 6b indicate a rather complex deformation in the tensile sample which cannot be explained using the standard kinematic solution of the tensile test described above.
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440 420 400 380 360 340 320 300 280 260 240 220 200
380
(a)
Torsoin,direction1, Torsoin,direction2, Torsoin,direction1, Torsoin,direction2,
0
0.2
0.4
0.6
0.8
1
.ε =0.0125s .ε =0.0125s .ε =0.0033s . ε =0.0033s
1.2
-1 -1 -1 -1
1.4
Distance from the centre, mm
Micro hardness, Vickers
Micro hardness, Vickers
Fig. 5. TWIP steel test sample cross section change during (a) torsion; r0 = 1.5 mm (unchanged) and (b) tension; major radius r1 = 2.89 mm, minor radius r2 = 1.84 mm and homogenous radius r3 = 1.80 mm.
(b)
360 340 320 300 280
tension1 ,along major radius tension1, along minor radius tension2, alongmajorradius tension2, along minor radius
260 240
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Distance from the centre, mm
Fig. 6. Microhardness distribution along the radial direction from the center to the surface of deformed sample of the TWIP steel subjected to different deformation modes: (a) torsion test and (b) tensile test.
A qualitative explanation on why the work hardening (micro hardness values) in the deformed tensile samples has increased along the major and minor axes will follow. The velocity in the tensile gauge section of the TWIP samples can be resolved in axial, radial and tangential components with the radial and tangential components resulting from twins progressing randomly in all directions, including tangential and radial. In the case of heterogeneous twinning, these components are significant enough in comparison with the main axial component to be treated as bifurcation parameters. The magnitude of these parameters is proportional to the ratio of the mean grain size to the gauge radius. The progress of the heterogeneous twinning in an unstable fashion at the periphery of the samples results in the formation of the wrinkles. Depending on the distribution of the large grain sizes, inclusions, imperfections etc. the bifurcation parameters along the semimajor and semi-minor axes of the ellipse are not necessarily equal. As shown in the hardness distribution results in Fig. 6b, the work hardening of a typical point in the ellipse cross section increases with their distance from the center along the semi-axes. Quantitative estimation of the new component is rather complex and requires a comprehensive bifurcation analysis. As a result, the simple theory of the tensile test cannot be applied to post process the tensile test results. Therefore, the work hardening and flow characterization of the TWIP steel in the tensile test should be re-considered carefully. The torsion test results shown in Figs. 5a and 6a indicate that the test results are less affected by the heterogeneous twinning and the test is more suitable compared to the tensile test for flow characterization of the TWIP steels.
For a better comparison of the deformation mechanisms in the two test conditions, the microstructures were examined using electron back-scattered diffraction (EBSD) along with assessments of deformed gauge sections and their results will be presented next. 3.4. Comparative study of the deformed microstructures According to the results shown in Figs. 5 and 6, the maximum heterogeneous propagation of the twins is expected at the periphery section of the tensile sample. To access comparable strains at both the samples for microscopic study, the torsion sample was machined about 1 mm deep (0.5 6 r 6 1.5 mm) to study the strain equivalent pffiffiffi to tensile strain [28] at fracture of (0.4 6 eu 6 1.2) using e ¼ rh= 3l where r, h and l are radius (mm), twist angle (rad) and length (mm) of torsion sample (Fig. 1c) . The initial microstructure of the alloy consisted of fully recrystallized grains with an average size of 160 lm. The microstructure examinations revealed that the mechanical twinning was extensively formed during deformation of samples subjected to both torsion and tensile deformation modes. The thickness of mechanical twins was very fine (i.e. 20 nm) and they mainly nucleated at grain boundaries and propagated across the grains (Figs. 7–9). They were mainly formed in a coordinated manner, as a group of nearly parallel twins of specific orientation (Fig. 7). Due to three-dimensional nature of the grains, a more precise investigation of twin nucleation and propagation requires three dimensional observations. As the twin thickness of 20 nm is smaller than the spatial resolution of EBSD map (i.e. the step size), they
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Fig. 7. AsB image of the mechanical twins formed in the sample subjected to the tensile testing.
Fig. 8. (a) EBSD band contrast image of the sample subjected to the tensile testing. (b) inverse pole figure and (c) stereographic standard triangle of dashed region in (a). (c and d) (1 1 1) pole figures of the grain and the adjacent mechanical twins. Dashed and solid lines are the coincidence of a plane twin normal and the trace of the twin, respectively. Black and red lines in (a) are high angle boundaries with a misorientation greater than 15° and mechanical twin boundaries, respectively. TD and ND represent the tensile direction and normal direction, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 9. EBSD band contrast (a) inverse pole figure (b) images of the sample subjected to the torsion loading. Black and red lines in (a) are high angle boundaries with a misorientation greater than 15° and mechanical twin boundaries, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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could not be readily indexed by EBSD. Hence, the band contrast quality image was used to partly reveal the mechanical twins (Figs. 8a and 9a). The observed twin regions delineated by red lines in Figs. 8a and 9a, in fact, consisted of organized aligned twins of a given orientation (Figs. 8b and 9b). The mechanical twins had a misorientation angle of 60° ± 2.5° about the [1 1 1] misorientation axis, similar to the annealing twins [32]. The mechanical twins could, however, be differentiated from annealing twins based on their morphology and size. There would be one or more twin variants formed in a given grain depending on the grain orientation [32]. Fig. 8 shows a crystallographic analysis of the EBSD map of a grain containing two twin variants with different traces under the tensile testing condition. The triangle stereographic standard along the tensile axis (TD) revealed that the orientation of the grain was such that its h5 3 3i direction was parallel to the tensile axis. In addition, the twins had different orientations in respect to the tensile direction (Fig. 8c). The deformation mode had a strong effect on the twin distribution. The mechanical twinning was found to be uniformly distributed within grains for the sample subjected to the torsion (Fig. 9). In contrast, they were much more scattered in the tensile sample. In addition, shear bands were widely seen in the microstructure of the tensile sample, crossing prior grain boundaries and interestingly containing fine mechanical twins (as shown by the arrows in Fig. 8). However, there was no sign of shear band formation in the torsion specimen. The formation of shear bands could be the reason behind the deformation non-homogeneity in tension compared with torsion. 4. Conclusions Significant surface alterations, ‘‘heterogeneous twinning’’, developed during uni-axial tensile straining of a TWIP steel sample. Visual inspection of the tensile specimens showed that the surfaces were wrinkled (rumpled) at the start of the plastic deformation (yielding). The material accommodated two times higher shearing strains without producing such surface alterations in torsion. It was also noticed that the tensile straining changed the cross section of round TWIP steel sample to an ellipse whereas under the pure shear straining, the circular cross section remained unchanged. Micro hardness distribution data across the tensile and torsion samples showed heterogeneous deformation in the TWIP tensile sample. Also, misorientation of the grain boundaries under tension and torsional straining were compared. The twins in torsion samples were distributed more uniformly compared to that of tensile samples. This indicates that shear straining can effectively prevent the heterogeneous twinning compared to the uni-axial straining and to allow accumulation of more deformation without developing visual surface waves. It was shown that under tensile straining, the true stress-true plastic strain curve is only an inaccurate indicative of the average mechanical response of the material, and it does not reflect local behavior. According to the evidence presented here, the true stress-true plastic strain results of the TWIP steel cannot be reliably identified based on the tensile test and standard data conversion techniques. It was shown that the tensile test results cannot be easily post processed for flow characterization of the steel. Alternatively, the torsion test proved to suffer less from this effect. References [1] Abbasi M, Kheirandish S, Kharrazi Y, Hejazi J. The fracture and plastic deformation of aluminum alloyed Hadfield steels. Mater Sci Eng A 2009;513–514:72–6.
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