Deformation and strain hardening behavior of powder metallurgical TRIP steel under quasi-static biaxial-planar loading

Author’s Accepted Manuscript Deformation and strain hardening behavior of powder metallurgical TRIP steel under quasi-static biaxial-planar loading. D. Kulawinski, S. Ackermann, A. Seupel, T. Lippmann, S. Henkel, M. Kuna, A. Weidner, H. Biermann www.elsevier.com/locate/msea

PII: DOI: Reference:

S0921-5093(15)30137-4 http://dx.doi.org/10.1016/j.msea.2015.06.083 MSA32521

To appear in: Materials Science & Engineering A Received date: 20 May 2015 Revised date: 10 June 2015 Accepted date: 25 June 2015 Cite this article as: D. Kulawinski, S. Ackermann, A. Seupel, T. Lippmann, S. Henkel, M. Kuna, A. Weidner and H. Biermann, Deformation and strain hardening behavior of powder metallurgical TRIP steel under quasi-static biaxialplanar loading., Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2015.06.083 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Deformation and strain hardening behavior of powder metallurgical TRIP steel under quasi-static biaxial-planar loading. D. Kulawinskia1, S. Ackermanna, A. Seupelb, T. Lippmanna, S. Henkela, M. Kunab, A. Weidnera, H. Biermanna a) Institute of Materials Engineering, Technische Universität Bergakademie Freiberg, Gustav-Zeuner-Str. 5, 09599 Freiberg, Germany b) Institute of Mechanics and Fluid Dynamics, Technische Universität Bergakademie Freiberg, Lampadiusstraße 4, 09599 Freiberg, Germany Abstract The present paper investigates a metastable austenitic stainless steel under different biaxial-planar load paths by using a cruciform specimen geometry. The material behavior was described by stress-strain curves and initial yield surface. Furthermore, the hardening behavior was determined by load sequence tests. To investigate the influence of the stress state on the martensite formation a ferrite sensor as well as electron backscatter diffraction measurements were used. Two cruciform specimen geometries were utilized and compared for the considered load cases. The stress state within the cruciform specimens was evaluated by an elastic unloading procedure with subsequent calculation of the stress components. Isotropic initial yielding and non-isotropic hardening were found. A recommendation for the use of the cruciform specimen geometry with respect to the load case is given. Keywords: TRIP-steel, biaxial stress-strain curves, load paths, initial yield surface, cruciform specimen geometry Introduction With the sheet metal forming process, complex-shaped parts for e.g. the automotive industry are manufactured. For this purpose the material behavior by means of the stress1

Corresponding author. Tel.: +49 3731 39 3457; fax: +49 3731 39 37 03.

E-mail address: [email protected] (D. Kulawinski). URL: http://www.iwt.tu-freiberg.de (D. Kulawinski).

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strain curves for different stress states as well as the initial yield surface and the strain hardening behavior are required [1, 2]. This database is needed to formulate adequate material models, which can be used to simulate the sheet metal forming process, e. g. by performing a finite element analysis (FEA) [3]. One opportunity to determine the material behavior under multiaxial stress state is biaxial testing. The biaxial stress state can be realized e.g. with the bulge test [4], with the tensiontorsion test [5] and with the biaxial-planar test [1]. The bulge test and the tension-torsion test are the commonly used testing methods to set biaxial stress states. With the bulge test the material behavior can be determined up to large strains, although there are limitations for the range of the stress states and the calculation of the strain state. For the tensiontorsion test a limitation of the range in the principal stress plane also exists, but the stress state can be calculated directly [5]. In order to overcome the limitations on the achievable stress states and defined homogeneous in-plane stress states, biaxial-planar testing with cruciform specimens is the most appropriate experimental method [1, 5]. However, the stress state cannot be calculated directly from the applied force due to the unknown effective cross-sectional area. In literature, this problem is solved by Grandlund [6] and Gozzi [7] with the assumption of a cross-sectional area of the cruciform specimen which depends on the stress state and the deformation. Therefore, a previous finite element simulation was done [6, 7]. In the present study the stress calculation was solved experimentally by a partial unloading method wherein the elastic strains were determined. Afterwards the principal stresses were calculated using Hooke’s law for the plane stress state [8]. In the present study, a powder metallurgically produced metastable austenitic stainless TRIP (TRansformation Induced Plasticity) steel, which provides both an excellent strength as well as ductility [9], was characterized under biaxial-planar loading using two cruciform specimen geometries. During deformation the metastable austenite shows a martensitic phase transformation [10, 11]. According to Iwamoto et al. [12], Perdahcioğlu et al. [13] as well as Beese and Mohr [14] this phase transformation depends on the applied stress state. The initial yield surface for austenitic stainless steels was found to be isotropic by Mohr and Jacquemin [15] as well as Page 2

Oswald [16] and Olsson [17]. With subsequent deformation the yield surface gets nonisotropic due to the martensitic phase transformation and furthermore a kinematic hardening is present. This can be explained by the formation of a texture which was investigated by Cakmak et al. [18, 19]. The aim of the present study was to investigate the initial yield surface and the influence of different stress states and load paths on the stress-strain curves, the strain hardening behavior as well as the martensitic phase transformation. Two cruciform specimen geometries were used to realize a biaxial-planar loading of the material. The stress was calculated by the partial unloading method [8]. The feasibility of this method was investigated for both cruciform specimen geometries. Differences in the stress and strain distribution within the gauge area of the two specimen types concerning the measured initial yield points were additionally analyzed by means of finite element calculations. Furthermore, sequential load paths were realized to determine a part of the subsequent yield surface and characterize the hardening behavior. Material The metastable austenitic stainless TRIP steel was high alloyed with the chemical composition given in Tab. 1. At first the material was cast to ingots by the company ACTech (Freiberg, Germany). These ingots were used for gas atomization under nitrogen by the company TSL (Bitterfeld, Germany), which yielded to an average diameter of 26.3 µm. Finally, the powder was pressed in circular blanks (discs) with a diameter of 150 mm. Subsequently, the discs were sintered under vacuum condictions at 1250 °C with a pressure of 30 MPa for 30 minutes using the hot pressing technique at the Fraunhofer Institute for Ceramic Technologies and Systems (Dresden, Germany). Due to the sinter process with a final cooling rate of 5 K/min a mainly austenitic initial state of the material with small amounts of δ-ferrite of 0.1-0.4% was obtained. These amounts of -ferrite were measured by the ferrite sensor as well as by microstructural investigations at the optical microscope. The microstructure of the material was fine grained with an average grain size of 10 µm, see Fig. 1c.

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Due to a larger cruciform specimen size of 340 x 340 x 5 mm³, the discs with a diameter of 140 mm were inserted into plates of a commercial austenitic stainless steel 1.4301 (X5CrNi18.10). Therefore, the discs were fixed by an interference fit and afterwards both materials were welded together by electron beam, see Fig. 1b. The position of the powder metallurgical (PM) austenitic steel within the supporting plate is shown in Fig. 1a. According to Fig. 1b, the weld had a very good connection to both materials without any cracks and defects. Subsequent to the welding, the plates were milled to a final thickness of 5 mm. After that, the cruciform specimens were cut out of the plate by water jet (cf. Figs. 2b and 2c). Experimental procedure and stress evaluation The tests were carried out on a servo hydraulic 250 kN biaxial-planar tension-compression machine (Instron 8800), see Fig. 2a, which was equipped with a biaxial orthogonal extensometer (Sandner, Germany). The extensometer was attached onto the surface in the center of the cruciform specimen. Furthermore, on the opposite surface the ferrite sensor measuring device Fischerscope MMS PC (Fischer, Germany) was applied. Hence, the formation of ’-martensite during deformation was measured. The exact ’-martensite content was calculated according to the study of Talonen et al. [21] by multiplying the value of the measuring system with a factor of 1.7. Cruciform geometries for the quasi-static biaxial-planar testing have been introduced by Gozzi et al. [7, 22], who developed the specimen shape on a basis of FE simulations with the aim to create a homogeneous stress and strain field within the gauge area. Gozzi et al. [7, 22] have suggested two cruciform specimen geometries to achieve the best stress and strain distribution within the gauge area. In this study also two cruciform specimen geometries were used, which differ in the numbers of slits and in the transition radius. The geometry with the three slits in Fig. 2b had a transition radius of 7 mm, whereas the geometry with two slits, Fig. 2c, had a radius of 10 mm. Furthermore, there are differences in the length of the slits. For the specimen with three slits, the middle slit was longer than the outer slits. The slits of the two slit specimen had the same length and were shorter compared to the three slit specimen. In Page 4

particular, due to a homogenous stress and strain distribution at the yield strength under a load ratio of = 1 the specimen with three slits was used. For the specimen with two slits also a homogenous stress and strain distribution was archived but without a stress and strain concentration. Therefore, higher strains until failure with two slits specimen can be reached and measured. With both geometries the quasi-static tests were carried out at different load ratios ( is the quotient of the force in axes 2 and 1,

) under force control, so that the load ratios

were almost constant during the tests. The parameters of the tests and the respective specimen geometry are summarized in Tab. 2. Quadrants are indicated in Fig. 3. Besides the tests with a constant load ratio, sequential tests with changing load ratios were performed to investigate the subsequent yielding. According to Kuroda and Tvergaard [23] as well as own work [8], a part of the yield surface can be determined by this method. Therefore, a sequential test was carried out with the load ratios according to Tab. 3 for both cruciform specimen geometries. For every segment a incremental load ratios was given, which defines the load path within the principal force plane to reach the next predefined load ratio. For visualization of the sequential tests the load paths are shown in the principal force plane in Fig. 3. Segments of constant incremental load ratio

are numerated and points of

change are marked by circles. In order to prevent buckling, supporting plates are clamped around the cruciform specimens in the case of compression at one axis. Uniaxial reference tests were carried out with flat and cylindrical specimens by using a servo hydraulic testing machine (MTS Landmark 250) and a tension module (Kammrath & Weiss). The microstructure was analyzed after deformation by scanning electron microscopy (SEM) as well as electron backscatter diffraction (EBSD) measurements. Therefore, the samples were grounded and vibration polished. With the EBSD measurements the development of the phases within the microstructure was examined. Page 5

Calculation of the stress state The stress calculation was solved by the elastic unloading method, which determines the elastic

and plastic part

of the total strain

in both loading axis

1 and 2 from the compliance during simultaneous unloading in both axes. For the planar biaxial testing, a plane stress condition can be assumed and both stress components were calculated using Hooke’s law for the isotropic elastic behavior with knowledge of elastic constants as the Young’s modulus E

and Poisson’s ratio

el

, according to equation (1). The values of the elastic constants were determined by the pulse-echo method of the ultrasonic technique according to the standard DIN EN 843-2. ;

(1)

The distortion energy criterion according to von Mises was assumed for the estimation of the equivalent stress

eq

and the true equivalent plastic strain

eq-pl.

For the present biaxial

loading case the deformation takes place within the principal normal directions so that the equivalent stress was calculated by using equation (2). (2)

√

The definition of the equivalent plastic strain for this biaxial stress state is given by equation (3). In the whole study, the elongation values were given as true strain.

√ (

)

(3)

In more detail, the partial unloading method was discussed by the authors’ group for quasistatic testing [8] as well as for low cycle fatigue testing [20]. Simulation of both specimens under shear loading = -1 A finite element analysis (FEA) was utilized to determine the stress and strain distribution at the initial plastic yielding in the measurement zone of both specimen types for the shear loading case ( = -1). The software package ABAQUS/Standard [25] was used to perform a Page 6

geometric linear quasi-static FEA. As material behavior, an elasto-plastic constitutive law for small deformation theory was considered. Isotropic, rate independent elastic and plastic properties were assumed. The yield function was given by the distortion energy hypothesis according to von Mises. Hardening was taken into account by using the uniaxial hardening curve of the considered material as a pointwise input. The elastic properties were described by Young’s modulus

and Poisson’s ratio

.

A plane stress state was assumed. Therefore, a 2D analysis seems to be sufficient. Quad elements with bilinear shape functions and full integration scheme were used for discretization (CPS4 elements). Due to the symmetry of the boundary value problem, only one quarter of the specimen was modeled. The gauge area in the center of the specimen (6.5 x 6.5 mm, highlighted in Fig. 9) was meshed with square shaped elements having an element size of 0.5 mm. Between the slits in the center of the specimens, a similar mesh quality was applied. The slits themselves had a finite radius of 0.15 mm at their ends. Twelve finite elements were distributed over the corresponding half cycle. A coarser mesh was used for the rest of the structure. According to the symmetry, displacement boundary conditions are incorporated as illustrated in Fig. 9. Setting the origin specimens, the symmetry conditions were:

in the bottom left corner of the . At the

clamp of the specimen, the displacement of the edges in the respective direction of loading was coupled to a reference point via a kinematic constraint (EQUATION). Unit forces for the considered shear loading case were prescribed at the reference point as loading boundary conditions:

. Using the default arc length method of ABAQUS (RIKS-

algorithm), the forces were proportionally varied with respect to a solution dependent load factor. This method was chosen to terminate the calculation, when a certain deformation state of the measurement area was reached. Here, a displacement value of a finite element node was checked. This node corresponds to the point, where the measurement of the experiments was performed on the 1-axis of the specimen. The displacement value was chosen in a way that an equivalent plastic strain of about 0.2% has been evolved in the measurement area.

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Results and Discussion Biaxial-planar tests with constant load ratio Uniaxial reference tests in tension and compression were carried out with flat as well as cylindrical samples. In all tensile tests for both uniaxial as well as biaxial-planar loading the values of the initial yield strength according to the commonly used 0.2 % yield stress definition were determined, cf. Tab. 4 and Fig. 4. According to the uniaxial tests the material had a yield strength of approximately 288 MPa with standard deviation of about ± 21 MPa in tension and ± 28 MPa in compression loading. Therefore, the standard deviation was also indicated besides the average value of the yield strength of all tests in the yield surface in Fig. 4. Furthermore, the points according to the symmetry condition of the loading were added within Fig. 4. The investigated powder metallurgical TRIP steel shows an initial yield surface which can be described by the distortion energy hypothesis according to von Mises very well. Thus, an almost isotropic yield of the TRIP steel exists. Obviously, the specimen with the two slits leads to higher equivalent yield strength than the cruciform geometry with three slits. The differences in yield strength for both specimens were small within quadrant I. However, the stress states within quadrant II. and IV. lead to differences of the equivalent yield strength up to 90 MPa between both specimen geometries. Due to the differences in the yield strength between both cruciform specimen geometries, the stress-strain curves were compared to the uniaxial reference data for each geometry individually in Fig. 5a and b. The comparison of the biaxial-planar tests with the specimen with three slits in Fig. 5a shows for all stress states a yielding at lower stresses than the uniaxial test. However, the strain hardening for the biaxial stress states was higher than in the uniaxial test. For the load ratios of 0 (III.) and 0.5 (I. or III.) only a true equivalent plastic strain of about 2.7 % as well as 4.5 %, respectively, can be achieved within the cruciform specimen until failure occurs. In the case of usage of the specimen with the two slits, the comparison with the uniaxial reference test shows a lower yield point for the load ratio = 1 and nearly the same yield stress for the load ratios of 0.5 as well as -1. The strain hardening behavior under Page 8

biaxial-planar loading is nearly equal to the uniaxial test. Only the equibiaxial loading = 0.5 leads to a stronger strain hardening. On the basis of these results obtained by the specimen with two slits, the material behavior seems to obey best the distortion energy hypothesis according to von Mises. Furthermore, the specimen with two slits enables higher elongations than the specimen with three slits. In the case of shear loading with a load ratio of = -1 a true equivalent plastic strain of about 20 % was achieved. However, it should be noted that the uniaxial tests have very large scatter, which was also present in the biaxialplanar tests. Due to this large scatter it can be concluded that the stress calculation according to the partial unloading method was able to determine the material behavior on basis of the stress-strain curve. Regarding the martensite evolution, less than 1 % of martensite volume fraction was measured at a true equivalent plastic strain of about 5 %. In Fig. 6, the martensite formation is shown versus the equivalent plastic strain. In general, the formation of ’-martensite under uniaxial tension was the lowest. For the loading case with a load ratio of 0.5 the highest formation of ’-martensite was determined, followed by load ratios of -1, 1 and 0. Furthermore, it can be recognized that the compression loadings (load ratios in the third quadrant) show smaller amounts of ’-martensite fraction than under tensile loading (first quadrant). The slower kinetics for ’-martensite phase transformation can be attributed to the compression loading, since this stress state suppresses ’-martensite formation due to its volume expansion [19]. Because of the small amount of martensite volume fraction within the microstructure, it is questionable whether the results can be extrapolated to larger martensite volume fractions. Therefore, a material with lower austenite stability is necessary. Biaxial-planar sequential tests The determination of the strain hardening behavior and the subsequent yielding in dependence on load sequence effects is based on two sequential tests. One of these tests was carried out on the specimen with two slits and is shown in Fig. 7. Fig. 7a shows the stress path of the sequential test within the principal stress plane. The corresponding stress-strain curve as well as the evolution of ’-martensite are shown in Fig. 7b. Page 9

In addition to the stress path in Fig. 7a, the yield surfaces at 0.5 % and 2 % equivalent plastic strain with 345 MPa and 438 MPa, respectively according to the von Mises criterion under the assumption of isotropic hardening were included. The stress path after changing the loading direction at 0.5 % equivalent plastic strain runs along the yield surface (345 MPa). However, this part is limited to the segments 1, 2, 3 according to Tab. 3, so that only a section of the yield surface can be described by this method. This result is similar to the investigations of Kuwabara et al. [24] and own work [8] and is consistent to the theory of Kuroda and Tvergaard [22]. Adjacent to this section, the stress path switches into the elastic region inside the yield surface. With a further deformation according to segment 6 (cf. Tab. 3) the formation of ’-martensite was induced, see Fig. 7b. After an equivalent strain of 1.1% the loading direction was changed again. In the following course (segments 7 – 11) a continuous hardening with a further ’-martensite formation occurred. To illustrate this behavior, the stress path is compared to the yield surface for equivalent stress of 438 MPa in Fig. 7a. However, no congruence between both can be found, see Fig. 7a. Obviously, the already formed martensite seems to be responsible for this behavior. After all segments, the material was loaded again at a load ratio of = -0.3 until the extensometer lost contact to the surface and a reapplication was not possible. The second sequential test was carried out using the specimen with three slits. The stress path within the principal stress plane as well as the corresponding stress-strain curve and the evolution of ’-martensite are shown in Fig. 8a and b, respectively. In this sequential test, the change of the loading directions was performed at a equivalent strain of 2 % according to Tab. 3. In addition to the stress path, the yield surface at the point of change of the load direction with an equivalent stress of 350 MPa was plotted in Fig. 8a. Up to this point the formation of ’-martensite occurred so that a volume fraction of 0.3 % was already present. When the loading direction was switched the stress path runs within the elastic region for the segments 1, 2, 3 and 4 according to Tab. 3. Segment 5 (Tab. 3) leads to a further plastic deformation up to 2.5 % with concomitant formation of ’martensite. For this point a subsequent yield surface with the corresponding equivalent stress of 378 MPa was included in Fig. 8a. The following change of the loading direction Page 10

(segment 6 in Tab. 3) shows a congruent course with the subsequent yield surface. However, with the next changes of the loading directions a continuous hardening with a further ’-martensite formation in comparison to the subsequent yield surface was present, see Figs. 8a and b. Within the segments 7 to 9 a strong hardening with nearly no plastic deformation was measured, see Fig. 8b, so that an elastic material behavior was present. This effect can be explained by kinematic hardening. Therefore, the yield surface (red ellipse) for an equivalent stress of 378 MPa with a shift of

MPa and

MPa

was included in Fig. 8a. The stress path is congruent with the hypothesis of the kinematic hardening. Consequently, the previous load path and the corresponding martensite evolution leads to a kinematic hardening. This demonstrates that the partial unloading method was able to measure load sequence effects. In both sequential tests, the formation of martensite prevents a matching curve of the yield surface and the stress path after a change of the loading directions. Due to this, it is assumed that the formation of ’-martensite is oriented within the microstructure in dependence of the stress state. With the change of the stress state other slip systems were activated which intersect with the martensite and lead to a strain hardening. A detailed examination is given by the EBSD measurements within the microstructure section. For this reason, the strain hardening behavior is a combination of isotropic as well as kinematic hardening so that anisotropic yield surface is assumed to be present. As long as no formation of ’-martensite occurs, the material and hardening behavior can be assumed as isotropic. The same behavior with an initial isotropic yielding and a kinematic hardening by further deformation was also found by various authors [8, 15, 16, 17, 24]. Simulation of both specimen under shear loading = -1 Within the shear loading case

= -1 a high difference of 90 MPa for values of the yield

strength between both specimen shapes was obtained. In Fig. 9 the FEA is shown for both specimen shapes. For each cruciform specimen with two (cf. Fig 9b) as well as three slits (cf. Fig. 9a), the equivalent plastic strains of a large part of the specimens are shown. Furthermore, the distribution of the equivalent plastic strain and the principal stress in axis

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1

is shown in Fig. 9 for the gauge area (6.5 x 6.5 mm²), at whose two vertices (black

points) two arms of the extensometer were located. For the cruciform specimen with three slits a stress and strain localization between the two center slits of the load transmission arms was observed. Therefore, the achievable values of strain were limited to a low level for the specimen with three slits. Within the gauge area a strong gradient of the equivalent plastic strain was present. The stress distribution, however, seemed somewhat more homogeneous. For this reason, the stress was underestimated at the yield point of 0.2 % strain. The cruciform specimen with two slits shows a significantly lower stress and strain localization between the two slits of the load transmission arms. Therefore, the specimen with two slits enables higher equivalent plastic strains before fracture than the specimen with three slits. This observation explains the results observed on the biaxial-planar tests at the shear loading case = -1. In the gauge area of the specimen with two slits a gradient of the equivalent strain was present, wherein the strain decreases towards the edge of the measuring field. In contrast, the stress

1

shows a homogeneous stress distribution along the

considered loading direction. Due to the stress and equivalent plastic strain distribution, the yield strength for the specimen with two slits was overestimated at the yield point. However, the error is supposedly to be smaller than for the specimen with three slits. Likewise, the results for the yield strength were more reliable. Based on the experimental results from the measurements and the FEA, the specimen with two slits has to be preferred for the shear loading case = -1 as well as for the determination of the material behavior at high equivalent strains. Microstructure The microstructure after biaxial deformation was investigated in detail for specimens with three slits after shear loading ( = -1) and equibiaxial tensile loading ( = 1 in the first quadrant) by SEM using backscattered electron (BSE) contrast as well as electron backscatter diffraction (EBSD). Fig. 10 shows the microstructure after shear loading (a) and the equibiaxial tensile loading (b) of specimens deformed up to a true equivalent plastic Page 12

strain of 8.6 % (a) and 8 % (b), respectively. First of all, the SEM micrographs were taken in backscattered electron (BSE) contrast reveal clearly both the formation of deformation bands (DB) within the austenitic matrix as well as the ’-nuclei formed inside the deformation bands. This is in good agreement with literature and uniaxial tests [26]. Uniaxial monotonic tests [27] revealed that these DBs are areas of strain localization, which is caused by the movement of partial dislocations forming largely extended stacking faults. With increasing plastic deformation, the thickness of the deformation bands, the density of stacking faults as well as the localized strain is increasing. The intersection points of individual DBs or even individual stacking faults on different slip planes are favored places for the formation of ’-nuclei. This is again accompanied by an increase of the localized plastic strain, however, depending on the crystallographic orientation of ’-nuclei with respect to the specimen surface and loading axis. Furthermore, significant differences between the two different loading cases become obvious. The austenitic grains at

= -1 (Fig. 10a) are nearly completely covered by

deformation bands containing ’-martensite islands. In contrast, the density of deformation bands in the specimen at = 1 (Fig. 10b) is much less. Thus, individual deformation bands within the austenitic matrix can be distinguished. The density of ’-martensite islands is less as well. These observations were confirmed by EBSD measurements on an area of interest (AOI) of 130 × 80 µm² with a step size of 0.2 µm on both specimens shown as phase maps in Fig. 11. The EBSD measurements reveal significant features differentiating the two loading cases: (i) the number of austenitic grains (red) containing deformation bands (yellow), (ii) the density of deformation bands within individual austenitic grains, (iii) the thickness of deformation bands and (iv) the amount of ’-martensite (blue). Thus, it is obvious that under shear loading conditions the formation of deformation bands exhibiting a hexagonal structure due to high density of stacking faults is more intense. Some individual former austenitic grains are covered completely by hexagonal deformation bands since their density and/or their thickness are much more pronounced than under equibiaxial tensile loading conditions. In addition, the volume fraction of deformation-induced ’-martensite is Page 13

significantly higher. This observation is in good agreement with measurements of the ferromagnetic phase fraction by a ferrite sensor. In addition to the phase maps, Fig. 11 contains schematic drawings of the individual load cases ( = –1 , and

= 1) regarding the arrangement of the two loading axis (A, B) with

respect to the specimen axes (x, y, z) as well as the assumed traces of activated slip planes on the specimen surface according to the assumption of Brown and Miller [28] on the orientation of surface cracks depending on different biaxial loading cases. Since the crack initiation and propagation is dominated by the formation of surface slip markings consisting of extrusions and intrusions, these orientations can be applied for the arrangements of slip traces as well. The observed deformation bands in the shear loading case are arranged in four main directions (within a scatter of parallel to 2, (iii) at + 45° to

1

5°): (i) parallel to

1,

(ii)

and (iv) at -45° to 1. In the equibiaxial tensile loading case,

similar slip trace arrangements were observed as in the shear loading case. However, the variation spread of slip traces around the arrangement according to (iii) and (iv) is much more pronounced depending on the exact position of the plane of maximum shear strain (according to Brown and Miller [28] and Itoh et al. [29]). Further differences becomes obvious regarding the crystallographic orientation of the grains containing deformation bands and deformation-induced ’-martensite. This is well demonstrated by inverse pole figure colored orientation maps shown in Fig. 12. Here, the orientation according to the specimen axis z was chosen, which represents the specimen surface normal direction. The other two specimen directions x and y are not suitable for this discussion since they are not aligned parallel to the loading axes. In addition, the inverse pole figures of the z-axis are plotted including only the orientation of grains containing deformation bands. Again, differences between the two loading cases become evident: (i) number of grains containing deformation bands, (ii) orientation of grains containing deformation bands and (iii) the orientation spread within individual austenitic grains due to the applied plastic deformation. Thus, the fraction of grains containing deformation bands after shear loading is twice of that after equibiaxial tensile loading. At = -1, the grain orientations containing deformation bands cover nearly the complete stereographic standard triangle (SST) except the orientations around the [-111] corner. Page 14

Obviously, grains with <111> surface normal are unfavorably oriented for the activation of deformation bands under both loading cases. In addition, the grain orientations containing deformation bands seems to be restricted to the <001> corner and the central part of the SST for the equibiaxial tensile loading case. Thus, it seems that at = 1 conditions, grain orientations within a band with a thickness of about 10-15° running parallel to the borderline between <111> and <110> are non-favorably oriented for martensitic phase transformation. The orientation dependence on the intensity of martensitic phase transformation is in agreement to observations of Cakmak et al. [18, 19], who investigated the orientation dependence of martensite evolution in a conventional austenitic stainless steel 304L deformed under biaxial torsion/tension and torsion/compression by detailed and thorough texture analysis. Finally, under both loading conditions a significant orientation spread within individual austenitic grains can be observed, which is even more pronounced under shear loading conditions at nearly similar equivalent von Mises strain. As a consequence of the above described observations, it can be assumed that the plastic deformation within the TRIP steel is significantly higher under shear loading conditions. This is further confirmed by the EBSD results regarding the developed local misorientation within austenitic grains, which is attributed to the defect content leading to lattice distortions. A parameter describing the local misorientation is the so-called KernalAverage-Misorientation (KAM) factor (given in a scale of 0° to 5° maximum). The KAM maps for the austenitic phase at the two different loading cases are shown in Fig. 13. The overall misorientation is much more pronounced after shear loading. Nearly all austenitic grains are characterized by a misorientation angle 1°

2.5°. Only few small areas are non-

distorted. In contrast, at equibiaxial tensile loading conditions the higher local misorientation values were mainly restricted to grain boundaries. In few grains, areas with higher misorientation are arranged similar to a cell structure, which is probably caused by the dislocation pattering. For a deeper understanding of the influence of grain orientation on the martensitic transformation under different biaxial loading conditions as well as on the local Page 15

misorientation and the dislocation pattering further detailed microstructural investigations will be published elsewhere including also all other loading cases beside = -1 and = 1 . This will include also detailed texture investigation both regarding the transforming austenite as well as the deformation-induced ’-martensite. Conclusion The present paper investigates the mechanical behavior of a metastable TRIP steel produced by powder metallurgy under biaxial-planar quasi-static loading. 1. The initial yield surface can be described very well by the distortion energy hypothesis according to von Mises. Thus, an isotropic material behavior is found for the TRIP steel studied in this work. 2. Biaxial material behavior was successfully characterized with both cruciform specimen geometries by measuring stress-strain curves whereby the partial unloading method was used. 3. The formation of ’-martensite is suppressed by compression loading so that transformation kinetics is reduced 4. The amount of formed ’-martensite content was measured. It can be assigned in descending order for the load ratios of 0.5, 1, -1, 0 and uniaxial loading. 5. An isotropic hardening behavior can be assumed as long as no ’-martensite is formed . 6. The orientation dependent formation of ’-martensite is assumed to cause a combined isotropic and kinematic hardening behavior. 7. The FEA and the results of the tests show that the specimen with two slits has to be preferred for the shear loading case = -1. Furthermore, the specimen geometry with two slits enables a material characterization for higher strains. Acknowledgements The authors thank the involved staff of the collaborative research center SFB 799 (B4, B2, C5) and the German Research Foundation (Deutsche Forschungsgemeinschaft) for financial support. In particular, the authors want to thank Dipl.-Ing. Reichel for the SEM Page 16

investigations as well as Dipl.-Ing. Harder for the support during the biaxial-planar testing. References [1]

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[10] G.B. Olson, M. Cohen, A general mechanism of martensitic nucleation: part II. FCC→BCC and other martensitic transformations, Metallurgical Transaction A, Volume 7, Issue A, 1976, Pages 1905–1914. [11] T. Angel, Formation of martensite in austenitic stainless steels: effects of deformation, temperature and composition, Journal of the Iron and Steel Institute, Volume 177, 1954, Pages 165–174. [12] T. Iwamoto, T. Tsuta and Y. Tomita, Investigation on deformation mode dependence of strain-induced martensitic transformation in TRIP steels and modelling of transformation kinetics, International Journal of Mechanical Sciences, Volume 40, 1998, Pages 173-18. [13] E. Perdahcioğlu, H. Geijselaers, M. Groen, Influence of plastic strain on deformation-induced martensitic transformations, Scripta Materialia, Volume 58, Issue 11, 2008, Pages 947–950. [14] A. M. Beese and D. Mohr, Effect of stress triaxiality and Lode angle on the kinetics of strain-induced austenite-to-martensite transformation, Acta Materialia, Volume 59, Issue 7, April 2011, Pages 2589-2600. [15] D. Mohr, J. Jacquemin, Large deformation of anisotropic austenitic stainless steel sheets at room temperature: multi-axial experiments and phenomenological modeling, Journal of the Mechanics and Physics of Solids, Volume56, Issue 10, 2008, Pages 2935–2956. [16] D. Mohr, M. Oswald, A new experimental technique for the multi-axial testing of advanced high strength steel sheets, Experimental Mechanics, Volume 48, Issue 1, 2008, Pages 65–77. [17] A. Olsson, Stainless steel plasticity – material modelling and structural applications. Ph.D. thesis, Luleå University of Technology, Sweden, 2001. [18] E. Cakmak, S. C. Vogel, H. Choo, Effect of martensitic phase transformation on the hardening behavior and texture evolution in a 304L stainless steel under compression at liquid nitrogen temperature, Materials Science and Engineering: A, Volume 589, Issue 1, 2014, Pages 235-241. [19] E. Cakmak, H. Choo, J.-Y. Kang and Y. Ren, Relationships Between the Phase Transformation Kinetics, Texture Evolution, and Microstructure Development in Page 18

a 304L Stainless Steel Under Biaxial Loading Conditions: Synchrotron X-ray and Electron

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Figure 1: a) Preparation of the plates with the dimension of 340 x 340 x 5 mm³ of the materials (X5CrNi18.10 and PM) by electron beam welding for the cruciform specimen. b) The weld between the PM (left) and the X5CrNi18.10 (right). c) The initial state of the investigated PM material.

Figure 2: Tension and compression biaxial-planar servohydraulic testing machine (a) and both used cruciform specimen geometries (b and c). b) Specimen geometry with three slits with the essential dimensions in mm, whereby the mid slit is longer than the outer slits and the radius between the load transmissions arms is 7 mm. c) Important dimensions in mm of the geometry with the two slits in which the slits are of the same length and the radius between the load transmissions arms is 10 mm.

Page 20

Figure 3: Load path of the biaxial-planar sequential tests, for details see Tab. 3, and some tests with constant load path.

Page 21

Figure 4: Yield surface of the studied steel with the yield strengths determined by uniaxial and biaxialplanar tests with both specimen geometries.

Figure 5: Comparison of the stress-strain curves of the biaxial-planar stress states with the uniaxial reference test for the specimen geometries a) with three slits and b) two slits.

Page 22

Figure 6: Comparison of the ’-martensite evolution of the biaxial-planar stress states with the uniaxial reference test for the specimen geometries with a) three slits and b) two slits.

Figure 7: a) Stress path within the principal stress plane of the sequential test with an initial load ratio of -0.3 at the cruciform specimen with two slits and b) the corresponding stress-strain curve and martensite evolution. In both plots regions with the corresponding segments according to Tab. 3 were included.

Page 23

Figure 8: a) Stress path within the principal stress plane of the sequential test with an initial load ratio of 0.3 at the cruciform specimen with three slits and b) the corresponding stress-strain curve and martensite evolution. In both plots regions with the corresponding segments according to Tab. 3 were included.

Page 24

Figure 9: FEM-images which show the stress and strain field within both cruciform specimen designs for a load ratio of -1. At the top pictures the strain field is shown for a large part of the specimen and the images below show the stress and strain field within the gauge area for the a) three slits specimen as well as b) two slits specimen.

Page 25

Figure 10: SEM micrographs using back scattered electron contrast for specimens with three slits after shear loading up to eq-pl = 8.6 % (a) and after equibiaxial tensile loading up to eq-pl = 8 % (b).

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Figure 11: EBSD phase map obtained on specimens with three slits after shear loading up to eq-pl = 8.6 % (a) and after equibiaxial tensile loading up to eq-pl = 8 % (b). Red – austenite, yellow – deformation bands with hexagonal structure, blue – ’-martensite, black dots – zero solutions, black lines – large angle grain boundaries (>10°). The arrangement of the two loading axes 1, 2 with respect to the specimen axis (x, y, z) as well as typical orientation of surface cracks are given in addition.

Page 27

Figure 12: Crystallographic orientation maps of the same AOI as shown in Fig. 11 for shear loading up to eq-pl = 8.6 % (a) and after equibiaxial tensile loading up to eq-pl = 8 % (b) using inverse pole figure coloring with respect to the surface normal direction. In addition, the inverse pole figures of the z-axis are shown including only grains containing deformation bands.

Page 28

Figure 13: Local misorientation developed within the austenitic matrix after shear loading (a) and equibiaxial tensile loading (b) of the same AOI as shown in Fig. 11 expressed by the Kernal-AverageMisorientation (KAM) factor.

Table 1: Chemical composition of the metastable austenitic TRIP steel

16Cr-6Mn-6Ni

Fe

Cr

Mn

Ni

C

N

Si

Mo & Al

wt.-%

Bal.

15.9

6.2

6.2

0.05

0.04

0.9

0.05

Table 2: Parameters of the quasi-static tests with constant load ratio

Cruciform specimen geometry

Load ratio

Three slits, see figure 2b

1 (I.), 0.5 (I.), -1(II.), 0 (III.), 0.5 (III.), 1(III.)

Two slits, see figure 2c

1 (I.), 0.5 (I.), -1(IV.)

(Quadrant in the principal force plane)

Page 29

Table 3: Sequential test parameters for both cruciform specimen geometries

Sequential test at the three slits specimen Segment 1

Load

ratio incremental

(Quadrant) -0.3 (II.) to -0.5 (II.)

load ratio

Sequential test at the two slits specimen Segment

1.34

1

Load

ratio incremental

(Quadrant) 0.3 (III.) to 0.2 (III.)

3.5

2

-0.5 (II.) to -1 (II.)

1.11

2

3

-1 (II.) to-2 (II.)

0.88

3

4

-2 (II.) to 4 (I.)

0.55

4

5

4 (I.) to 2 (I.)

0.48

5

-0.7 (II.)

-0.7

6

2 (I.)

2

6

-0.7 (II.) to -1 (II.)

1.14

7

2 (I.) to 4 (I.)

0.15

7

-1 (II.) to -3 (II.)

0.99

8

4 (I.) to -4 (II.)

0.55

8

-3 (II.) to -20 (II.)

0.62

9

-4 (II.) to-2 (II.)

0.73

9

-20 (II.) to 5 (I.)

0.44

10

-2 (II.) to -1 (II.)

0.88

11

-1 (II.) to -0.5 (II.)

1.11

12

-0.5 (II.) to -0.3 (II.)

0.2 (III.) to -0 (III.)

load ratio

-0 (III.) to -0.33 (II.) -0.33 (II.) to -0.7 (II.)

2.4 1.65 1.18

1.34

Page 30

Table 4: Values of the 0.2 % yield strength for the different stress states and specimen geometries

Uniaxial tensile tests Yield stress Rp0.2 and Stress state deviations in MPa 286 ± 21 Tension Compression -289 ± 28 Biaxial-planar quasi-static tests Specimen geometry

two slits

three slits

Load (quadrant) 1 (I.) 0.5 (I.) -1 (IV.) Sequential test -0.3 (II.) 1 (I.) 1 (I.) 1 (III.) 0 (III.) 0.5 (I.) 0.5 (III.) -1 (II.) Sequential test 0.3 (III.)

ratio Yield Stress in axis Yield Stress in axis Equivalent 1

1 in MPa

2

2 in MPa

stress

285 348 181

263 172 -175

275 302 312

-259

101

322

253 265 -293 -284 304 -284 -133

240 262 -282 -130 210 -192 124

247 264 288 246 270 251 223

-260

-143

226

yield in MPa eq

Page 31