Damage micromechanisms in dual phase steel investigated with combined phase and absorption contrast tomography Accepted Manuscript Damage micromechanisms in dual phase steel investigated with combined[.]
Accepted Manuscript Damage micromechanisms in dual-phase steel investigated with combined phaseand absorption-contrast tomography Hiroyuki Toda, Akihide Takijiri, Masafumi Azuma, Shohei Yabu, Kunio Hayashi, Dowon Seo, Masakazu Kobayashi, Kyosuke Hirayama, Akihisa Takeuchi, Kentaro Uesugi PII: S1359-6454(17)30010-1 DOI: 10.1016/j.actamat.2017.01.010 Reference: AM 13472 To appear in: Acta Materialia Received Date: 30 September 2016 Revised Date: January 2017 Accepted Date: January 2017 Please cite this article as: H Toda, A Takijiri, M Azuma, S Yabu, K Hayashi, D Seo, M Kobayashi, K Hirayama, A Takeuchi, K Uesugi, Damage micromechanisms in dual-phase steel investigated with combined phase- and absorption-contrast tomography, Acta Materialia (2017), doi: 10.1016/ j.actamat.2017.01.010 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 proof before it is published in its final 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 M AN U SC RI PT ACCEPTED MANUSCRIPT K 1.0 0.5 -0.5 -1.0 TE D AC C EP (a) 3D martensitic network together with Gaussian curvature distribution used for tracking 0.7 0.6 0.5 0.4 0.3 0.2 0.1 175 µm εeq (b) 3D local strain map in the martensitic phase for an applied strain change of 11.4 % ACCEPTED MANUSCRIPT Damage micromechanisms in dual-phase steel investigated with combined phase- and absorption-contrast tomography Hiroyuki Toda1*, Akihide Takijiri2, Masafumi Azuma3, Shohei Yabu3, Kunio Hayashi3, Dowon Seo1, RI PT Masakazu Kobayashi2, Kyosuke Hirayama1, Akihisa Takeuchi4 and Kentaro Uesugi4 Department of Mechanical Engineering, 3D/4D Structural Materials Research Centre, Kyushu University, 744, Motooka, Nishi ward, Fukuoka city, FUKUOKA 819-0395, Japan Department of Mechanical Engineering, Toyohashi University of Technology, 1-1, Hibarigaoka, Tempaku, Toyohashi city, AICHI 441-8580, Japan Steel Research Laboratories, Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu city, CHIBA 293-8511, Japan M AN U SC Japan Synchrotron Radiation Research Institute, 1-1-1, Kouto, Sayo-cho, Sayo-gun, HYOGO 679-5148, Japan Abstract: The single-distance phase retrieval technique was applied to contrast-enhanced imaging of the dual-phase microstructure of a ferrite/martensite dual-phase with only 1.4 % difference in density TE D between the two phases Each high-resolution absorption-contrast image was registered with a corresponding phase-contrast image, to analyse damage evolution behaviour The loading step at which each microvoid was nucleated was identified by tracking the microvoid throughout tension, together with its nucleation site Premature damage initiation was observed at a relatively early stage EP at various nucleation sites, such as the ferrite interior, martensitic interior and ferrite/martensite interfaces; however, the subsequent growth of such microvoids was relatively moderate On the other AC C hand, microvoids were also initiated later due to martensitic cracking after the maximum load was reached, and these microvoids subsequently exhibited rapid growth The martensite cracking induced additional damage evolution mainly along nearby ferrite/martensite interfaces and intersections between the martensite and the ferrite grain boundary It is notable that the microvoids originating from martensitic cracking exhibited characteristic shear-dominated growth under macroscopic tension, whereas those originating from the other nucleation sites exhibited traditional triaxiality-dominated growth It was concluded that the ductile fracture was dominated by the substantial force driving the growth of microvoids located on morphologically characteristic martensitic particles Keywords: dual-phase; microtomography; phase-contrast imaging; microvoid; ductile fracture ACCEPTED MANUSCRIPT INTRODUCTION In general, the ductile fracture process in alloys consists of nucleation, growth and coalescence of microvoids The nucleation of microvoids is attributable to particle fracture and/or particle/matrix interfacial decohesion It is well known that particle cracking is more apt to occur in the case of coarser particles, while interfacial decohesion is more frequently observed in the case of finer particles RI PT [1] The ductile fracture process might also be interrelated with various microstructural heterogeneities, such as pre-existing microdefects [2,3], particle clustering [4], microstructural anisotropy [5] and dual-phase (hereinafter DP) microstructures [6-11] It is reasonable to assume that the ductile fracture process is appreciably affected in the case of DP SC microstructures, especially when the deformation resistance of a harder phase is significantly higher than that of a softer matrix A good example of such a DP microstructure is seen in DP steels that consist of a hard martensitic phase and a soft ferritic phase In spite of extensive research activity, a M AN U variety of interpretations remain concerning the micromechanisms of damage nucleation in DP steels The reported origins of microvoid nucleation are classified as ferrite/martensite interfacial decohesion [6-8], ferrite grain-boundary decohesion [9] and martensitic cracking [10] It can be inferred that the reported differences among the damage micromechanisms may be partly attributable to various microstructural differences, such as martensitic volume fraction and carbon content in the martensitic phase Each of the above-listed studies employed SEM observation of polished specimen surfaces or TE D sections It is interesting to note that close similarities may exist among the SEM micrographs presented as evidence for the respective damage micromechanisms advocated in the abovementioned studies It is therefore conceivable that the different postulated damage micromechanisms might be more or less ascribed to different interpretations of an originally identical phenomenon EP With the advent of state-of-the-art imaging techniques, a thorough understanding of the detailed damage processes is expected, even when practical materials with three-dimensional (hereinafter 3D) complexity in their DP microstructures are investigated Phase-contrast X-ray microtomography AC C (hereinafter XMT) techniques are capable of revealing such DP microstructures with reasonable spatial resolution For example, Landron et al employed the X-ray holotomography technique to a DP steel, and succeeded in clearly separating the ferritic and martensitic phases at the initial unloading stage [12] The present authors applied the single-distance phase retrieval technique to 3D observations of a DP stainless steel consisting of austenitic and ferritic phases [11,13], and found that a limited number of microvoids, initiated at later stages from fine particles located on ferrite/austenite boundaries, exhibited enormous growth, thereby inducing macroscopic ductile fracture This was attributable to the high driving force for microvoid growth at morphologically specific ferrite/austenite boundaries Application of this technique to the controversial interpretation of damage micromechanisms in ferrite/martensite DP steels is of great interest In the present study, a ferrite/martensite DP steel, with a relatively coarse and interconnected martensitic phase, was ACCEPTED MANUSCRIPT evaluated as a model material Experimental 2.1 Material used A DP steel with a chemical composition of 0.01 C, 0.1 Mn and balance iron in mass %, was prepared A rolled plate was maintained at 1373 K for 100 sec for recrystallization, followed by RI PT maintenance at 1073 K for 100 sec, and then water-quenched to obtain a martensitic phase Fig shows an optical micrograph of the investigated steel The average volume equivalent diameter (i.e., the diameter of a sphere with volume equal to that of a non-spherical particle), and the volume fraction of martensitic particles, VfM, were 18.3 µm and 29.9 %, respectively Parallel-piped tensile specimens, SC which had nominal dimensions of 600 × 600 µm2 in the gauge section, were sampled in parallel to the rolling direction, using an electro discharge machining apparatus The gauge section was manually M AN U polished to obtain the almost circular cross-section shown below in Fig 2.2 3D imaging The XMT experiments were performed at the BL20XU beamline of SPring-8 A monochromatic X-ray beam of 37.7 keV was produced by a liquid nitrogen-cooled Si (111) double crystal monochromator A miniature material test rig was positioned approximately 240 m from the X-ray source The sample-to-detector distance, L, was 65 mm for the absorption-contrast XMT, and was TE D varied between 200 and 800 mm for the phase-contrast XMT, for screening purposes A CMOS camera (ORCA Flush 4.0, Hamamatsu Photonics K K.) of 4.0 megapixels, with a 10 µm thick Lu2SiO5:Ce scintillator, was used for acquiring the projection images; and a 20× objective lens was used to obtain an effective pixel size of 6.5 àm ì 6.5 µm Exposure time was 0.8 sec The stress-strain EP curve obtained during the tensile test performed at a loading rate of 0.0005 mm/sec is shown in Fig The absorption-contrast XMT scans were repeated times before fracture, while maintaining displacement The phase-contrast XMT scans were obtained times at the loading steps indicated in AC C Fig The slope of the elastic part of the stress-strain-curve appears low due to small stiffness of the miniature material test rig used, which is mainly attributed to the usage of a polymer tube as a load frame instead of metallic pillars The vertical drops in load that are observed in Fig indicate inherent relaxation behaviour of the material during the tomographic scans A total of 1,800 and 3,600 radiographs, scanning 180°, were obtained in the absorption-contrast and phase-contrast XMT scans, respectively; and 10 blank images were captured every 18º in each phase-contrast XMT scan, for background subtraction purposes, in order to eliminate ring artefacts introduced due to beam drift A propagation-based single-distance phase retrieval algorithm using Paganin’s method was applied, to reconstruct a projected distribution of the complex X-ray refractive index from a single projection image per projection [14-16] Noise, spatial resolution, and contrast between the two phases were quantitatively evaluated in the reconstructed slices, in order to optimise ACCEPTED MANUSCRIPT imaging and phase retrieval conditions, such as propagation distance, X-ray energy, and parameters for the phase retrieval process A conventional filtered backprojection algorithm was then employed to reconstruct image slices for both the absorption-contrast and phase-contrast images Isotropic voxels with 0.5 µm edges were achieved in both the reconstructed slices To employ the phase retrieval algorithm in the case of DP materials, a priori knowledge of δi and βi (i.e., the refractive index and extinction coefficient in the complex refractive index for the ith phase), RI PT as well as the total projected thickness of the sample, are required In order to accurately determine the in-situ densities of the ferritic and martensitic phases, the carbon concentration in the martensitic phase was estimated by randomly measuring micro-Vickers hardness in both of the phases The measured hardness was HV599 and HV236 for the martensitic and ferritic phases, respectively The SC carbon concentration was estimated to be 0.33 % for the martensitic phase [17], resulting in a carbon concentration of 0.001 % for the ferritic phase The density values were accordingly calculated as 7.87 density difference of 1.4 % between them 2.3 Image analyses M AN U g/cm3 and 7.76 g/cm3 for the ferritic and martensitic phases, respectively, implying a relatively small 2.3.1 3D volume rendering and qualitative image analysis The grey value in the absorption-contrast XMT images was calibrated such that the linear absorption coefficients of 0-42 cm-1 fell within an 8-bit grey-scale range To estimate the volume of TE D individual microvoids and particles with sub-voxel accuracy, facetted iso-intensity surfaces of pentagonal shape were computed on the basis of the Marching Cubes algorithm To suppress inaccuracies originating from image noise, only features over voxels in volume were counted as particles and microvoids in the XMT images EP The modulation transfer function (MTF), derived from the edge response function [18] at the ferrite/martensite interfaces, was measured, in order to determine the spatial resolution at a % contrast ratio in the phase-contrast XMT images It has been reported by the present authors that AC C reasonable agreement was observed between the results of interface-based MTF calculations and those obtained with 3D test patterns [19] Noise was also measured in the phase-contrast images, by determining the standard deviation within a given region of interest (30 pixels × 30 pixels × 10 regions) for each image In order to evaluate the efficiency of the single-distance phase retrieval technique, contrast was defined by substituting average grey values between the ferritic and martensitic phases 2.3.2 Microvoid analysis Precise image registration was performed before microvoid tracking, using a transformation matrix by means of which the sum of the distances between identical particles captured at neighbouring loading steps was minimised Microvoids were tracked in reverse chronological order, from the last loading step (shown in Fig 2) to the initial unloaded state, by employing the microstructural tracking ACCEPTED MANUSCRIPT technique [20, 21] The coefficients α, β and γ in the matching probability parameter used in the microstructural tracking technique were determined as 0.8, 0.1 and 0.1, respectively, after systematically optimising the conditions in a preliminary trial When a given microvoid could not be further tracked beneath a specific applied strain level, the microvoid was assumed to have been nucleated at that applied strain level The phase-contrast images were then used for identifying its nucleation site (i.e., ferritic interior, martensitic interior, intergranular fracture in ferrite, RI PT ferrite/martensite interface, or an intersection between the martensite and the ferritic grain boundary) Since grain boundaries are typically invisible in the XMT technique, the serial sectioning technique was employed in the university for identifying the ferritic grain boundary after the absorption-contrast and phase-contrast XMT scans of the tensile test had been interrupted at the last loading step shown in SC Fig in the synchrotron radiation facility Since the density difference between the ferritic and martensitic phases is too small to accurately segment the two phases, the serial sectioning technique was also utilised for verifying the microvoid nucleation sites A region of 600 àm ì 1,000 àm ì100 M AN U µm was precisely registered between the absorption-contrast XMT image and the two-dimensional (hereinafter 2D) image stack obtained in the serial sectioning process, for the images captured at the final loading-stage A JEOL JSM-6500F-based TSL™ EBSD facility was used to carry out EBSD orientation mapping around microvoids on the cross-sections A 15 kV accelerating voltage was selected, with a working distance of 23 mm and a measurement pitch of 0.2 µm Particles have linear absorption coefficients similar to microvoids and pre-existing pores It is TE D therefore difficult to distinguish between pre-existing pores and particles, and also difficult to detect microvoid nucleation during the reverse tracking process when microvoids are nucleated from particles Microvoid nucleation was therefore defined in the present study identically to the previous study [11], where a specific thresholding value in volume expansion (i.e., 1.71 times in volume) is EP used for detecting microvoid initiation AC C Damage evolution behaviour 3.1 Observation of DP structure An identical virtual cross-section captured at different L values was evaluated The two phases were not distinguished when L < 500 mm The contrast between the two phases was gradually enhanced with increasing L, along with improvement in the signal-to-noise ratio, while the substantial spatial resolution was per contra reduced, as has also been reported in the literature [11] The largest difference (26.5) in averaged 8-bit grey values between the two phases was obtained at L = 700 mm, while the average spatial resolution measured at ferrite/martensite interfaces was 2.8 µm Fig shows the optimised 3D images before and after the phase retrieval process, together with a corresponding absorption-contrast image It is to be noted that the dual phase microstructure is somewhat observable ACCEPTED MANUSCRIPT simply by separating the sample and image detector by a comparatively large distance (i.e., L = 700 mm), even before the phase retrieval shown in Fig (b) It appears, however, most likely that only the interfaces are highlighted in Fig (b), with pairs of black and white fringes caused by Fresnel diffraction, and that the internal grey values are similar between the two phases Although the phase-retrieved image exhibits a reasonable signal-to-noise ratio and enhanced contrast between the two phases (Fig (c)), image segmentation was not possible without applying a 3D median-based RI PT filter, due to the remaining ring artefacts Although the median-based filter used (i.e., × × 7) preserved the DP microstructure reasonably well, it slightly degraded the spatial resolution, from 2.8 µm to 3.2 µm; however, this still appeared competent to depict the morphology of martensitic particles in the present study Overall, the DP microstructure was recognised and analysed reasonably well, difference of 1.4 % between the two phases SC after the single-distance phase retrieval algorithm was applied, in spite of the relatively small density It is also to be noted that the imaged microvoids in Fig (c) have obviously been enlarged M AN U compared to Fig (a), in which the sample and the image detector are moderately separated Such enlargement is attributable to X-ray divergence and X-ray deflection Absorption-contrast images such as that shown in Fig (a) were used for the quantitative assessment of damage evolution behaviour, due to their higher spatial resolution and the loss of quantitative size capability in the phase-contrast images TE D 3.2 Microvoid initiation and growth behaviour Fig shows a series of 3D perspective views of microvoids during the in-situ tensile test The underlying ferritic and martensitic phases are not displayed The microstructural features shown in Fig are mainly microvoids, but may contain some pre-existing particles such as MnS, which has a linear EP absorption coefficient one third as large as those of the ferritic and martensitic phases Obviously rapid increases in the number density and size of microvoids are observed in Fig (d) – (g), after the uniform elongation of the specimen is truncated after the onset of macroscopic neck formation around AC C the maximum load level The abrupt damage evolution is also detected in Fig 5, after an applied strain of 23.9 % is reached, with rapid increases both in the microvoid volume fraction and in the fraction of microvoids coarser than µm A limited number of extremely coarse microvoids observed in Fig are significantly elongated, exhibiting complex shape It is also noteworthy that the majority of the elongated coarse microvoids are oriented in oblique directions (e.g., 45°) with respect to the loading direction The results of the reverse microvoid tracking are summarised in Fig and Table Noteworthy is the presence of microvoids that exhibited rapid growth after being initiated at an applied strain of 23.9 %, while microvoids initiated at the other loading steps (especially those nucleated at less than ε = 8.1 %) exhibited rather dormant growth, as shown in Fig (a) and (b) As a result, the majority of ACCEPTED MANUSCRIPT coarse microvoids (i.e., > µm) observed at the final loading step were nucleated at an applied strain of 23.9 %, except for some limited nucleation and growth in the necked area during the final localised deformation Closer examination of Fig revealed early microvoid nucleation, without significant growth, at fine MnS particles located mainly at ferrite/martensite interfaces Interfacial damage nucleation is later activated after the maximum load is reached, as shown in Table Intergranular and transgranular cracking in the ferrite interior is also observed, to a lesser extent Microvoids that were RI PT initiated at an applied strain of 23.9 %, and then showed characteristic rapid growth, were originated from martensitic cracking Such microvoids were observed even outside the necked area The martensitic cracking was not extensively observed after an applied strain of 23.9 %, whereas microvoid nucleation at ferrite/martensite interfaces still remained active, though only in the necked SC area, until the final rupture The data in Fig was analysed according to the microvoid nucleation sites, as shown in Fig It is interesting to note that microvoids nucleated due to martensitic cracking tended to grow rapidly compared to those nucleated at the other nucleation sites Especially moderate M AN U growth was observed in the case of the microvoids nucleated in the interior of the ferritic phase The total volume fraction of microvoids nucleated due to martensitic cracking was approximately six times that of the second most common nucleation site (i.e., intersections between martensite and the ferrite grain boundary) just before the final rupture The microvoids initiated due to martensitic cracking exhibited characteristically low sphericity (Fig (c)), as in the elongated microvoids observed in Fig TE D These tendencies are confirmed in Fig 8, where the growth curves of individual microvoids have been collated and classified according to their nucleation site Wider variation in growth rate is apparent in the case of microvoids nucleated due to martensitic cracking The four microvoids with high growth rates (indicated by arrows in Figs (g) and (c)) were nucleated due to martensitic loading direction EP cracking at an applied strain of 23.9 %, and later propagated in oblique directions with respect to the AC C 3.3 Details of the microvoid initiation sites in the martensitic phase The largest microvoid seen in Fig (g) has been extracted in Fig 9, together with adjacent martensitic particles The microvoids shown in Fig were nucleated where the martensitic phase exhibited morphological complexity such as a notch or neck No such morphological features were obvious at the other nucleation sites This tendency is confirmed in Fig 10, where the shape and orientation of cracked and uncracked martensitic particles have been quantified The degree of necking was defined by dividing the minimum cross-sectional area, d, by the average value measured for 100 µm along the longitudinal axis, D It is clearly demonstrated that necked portions were sampled as a result of intense strain localisation, and that the driving forces for subsequent rapid growth may arise from stress redistribution after martensitic cracking In order to quantitatively evaluate the effects of martensitic morphology, 3D strain mapping was performed for the interior of the martensitic phase ACCEPTED MANUSCRIPT Tetrahedrons, whose vertices were sites of morphological features such as concave and convex portions of the martensitic phase, were generated by the Delaunay tessellation technique; and normal and shear strains were then calculated based on the deformation of each tetrahedron, assuming a linear displacement field inside it The local strain distribution was illustrated in the form of a 3-D colour contour map, as shown in Fig 11 It is interesting to note, in this figure, that although the macroscopic reach more than five times this strain level in equivalent strain RI PT applied strain range is only 11.4 % (i.e., between the 3rd and the last loading steps), high strain regions Figs 12 (a) and (b) show a cross-section of the identical martensite particle, analysed using the EBSD technique There is little evidence, in this figure, that microstructural features inside the martensite, such as blocks, packets or their boundaries, have marked influence on the martensitic SC cracking In summary, the significant strain variation due to morphological complexity is the main cause of the martensitic cracking identified in Figs – 10 and Table Fig 13 shows the strain localisation in the ferritic phase around a cracked martensite particle A M AN U wide region of more than 100 µm is characterised by the strain localisation in the ferrite interior, especially along nearby ferritic grain and phase boundaries, as indicated by the white and yellow arrows, respectively, in Fig 13 (b) It is reasonable to assume that further damage evolution is triggered due to preceding martensitic cracking, according to the mechanism whereby potential crack initiation sites, such as the ferritic grain boundary, ferrite/martensite interfaces, and dispersion particles in the ferrite interior, are characterised by a large strain region In the case of these crack TE D nucleation sites, Table suggests that the grain boundary in the ferritic phase and the ferrite/martensite interface can act as more detrimental stress risers, causing succeeding damage evolution along phase and grain boundaries Notably, although it is not especially common, remarkable strain localisation was observed at intersections between the martensite and the ferritic grain boundary (the uppermost AC C Discussion EP white arrow in Fig 13 (b)) It has been generally understood that ductile fracture is divided into three stages: microvoid nucleation, growth and coalescence The onset of coalescence is defined by a critical microvoid volume fraction, fc, in the traditional Gurson-type models [22], whereas the former two stages undergo simultaneous evolution The values of fc reported for DP steels vary, from 0.08 (tensile strength, σUTS of 950-1000 MPa, VfM of 0.55) [23], to 0.014 (σUTS of 704 MPa, VfM of 0.18) [24], and 2.5 × 10-4 (σUTS~1000 MPa, VfM of 0.11) [25], presumably depending on VfM, the initial void volume fraction and the maximum void volume fraction per unit volume that can be nucleated (i.e., volume fraction of all the particles with potential for microvoid nucleation), In the present study, the VfM value for the last loading step was approximately 2.4 × 10-4 (Fig (a)), suggesting that the microvoid coalescence occurring at an applied strain of 23.9 % This seems to be consistent with the present experimental result As was summarised in Section 1, a variety of microvoid nucleation mechanisms have been EP advocated in the literature, mainly through the employment of 2D observation techniques [6-10] In the present study, all the proposed microvoid nucleation mechanisms were actually observed in the damage and fracture process of the investigated DP steel Table and Figs and 8, however, indicate AC C that and varied significantly with the different nucleation sites It is reasonable to assume that was being affected by inhomogeneous strain distribution, which inherently arises due to the complexity of a DP structure Delayed microvoid initiation due to martensitic cracking was observed just after the maximum load was reached, and such microvoids exhibited rapid growth in comparison to the microvoids initiated at the other sites A similar pattern was observed by the present authors in the case of DP stainless steel [11], in which microvoids initiated on ferrite/austenite boundaries after the maximum load showed enormous growth, thereby inducing macroscopic ductile fracture In terms of microvoid nucleation, it is reasonable to assume that there exists some local variation in the abovementioned damage parameters, with respect to the DP structure, which alters the balance among the competitive microvoid nucleation sites It seems, however, more ACCEPTED MANUSCRIPT important that the nucleation process has little influence on macroscopic mechanical properties The major differences between the DP steels of the present and previous studies are deformation resistance and the volume fraction of the secondary phase It is reasonable to assume that the hard martensitic phase, which is somehow interconnected in spite of the relatively low volume fraction (i.e., 29.9 %), induced stress concentration in the investigated DP steel It can be considered that martensitic cracking is less apt to occur than the damage initiation from the other sites, given that the hard RI PT martensitic phase could tolerate loading without significant deformation in the investigated DP steel However, once morphologically weak martensitic particles are preferentially fractured, stress redistribution to the weaker ferritic matrix can cause the rapid growth of existing microvoids On the other hand, in the DP stainless steel investigated in our previous study [11], intense shear localisation SC was observed in thin oblong ferritic film that was sandwiched between two or more slender austenitic particles There, enormous growth of a limited number of microvoids was observed at the ferrite/pearlite boundaries after maximum load was reached, due to the characteristic morphology of M AN U the ferritic phase Although the dominant mechanisms may be different, the finding common to the two DP steel studies is that damage evolution is controlled by the rapid growth of microvoids that are nucleated at specific nucleation sites Although Eq does not contain variables that can indicate localised characteristics of microvoid growth, it is evident that local driving forces for microvoid growth can undergo significant variation Microvoid growth has been phenomenologically postulated to depend on the existence and degree TE D of the triaxial stress state [27] A triaxial driving force for microvoid growth is assumed to arise due to the formation of a macroscopic neck under tension, which can be estimated by the well-known Bridgeman’s equation [28] However, the moderate microvoid growth here observed before the onset of necking, and the subsequent rapid growth of a limited number of microvoids, are not explained by EP that mechanism Another possible source of stress triaxiality would be plastic constraint around harder phases For example, Katani et al demonstrated, through their 2D image-based finite element simulations based on the Gurson damage model, that stress triaxiality is more than twice as elevated at AC C phase boundaries [23] However, the rapid microvoid growth in oblique directions, observed here (Figs and 9), cannot simply be explained by the development of stress triaxiality It has been recognised in recent years that the Gurson-type damage models are unable to model ductile fracture under shear-dominated stress states with low stress triaxiality [29] It is well known that microvoid growth in a narrow shear band that is inclined away from the loading direction is typically observed during the cutting of sheet metal, but is also sometimes observed even in simple tensile tests [30] Here, microvoids are flattened out to form microcracks, which are rotated and elongated; and finally neighbouring microvoids coalesce to induce the final rupture This would appear to bear some affinity to the oblique elongation of a limited number of microvoids in the present study, as well as to the propagation of microvoids through the very narrow ferritic channels observed in the previous study [11] Nahshon and Hutchinson have extended the Gurson-type model to ACCEPTED MANUSCRIPT phenomenologically model localisation and fracture under shear-dominated stress states [31] is expressed in their model as follows: = (1 − )(// + 01 2 * # 345 ! 45 67 , (4) * RI PT where f is the microvoid volume fraction, (// the rate of plastic volume change, kω a constant expressing the magnitude of the damage growth rate in shear (1.1 for a steel with a yield stress (415 MPa) similar to that of the present DP steel [32]), ω the deviatoric stress state parameter, sij the stress * deviator, ( 8 the plastic strain rate, and σe the effective stress In this model, the first term corresponds SC to the microvoid growth in the original Gurson-type model, and the second term expresses the contribution from shear It is assumed, here, that the void volume fraction is an effective damage parameter, and that void growth mechanisms (i.e., the first term) are inactive Void distortion and M AN U rotation contributes to softening, and constitutes material degradation As an extreme case, if a pure shear state (i.e., ω = 1) is assumed, Eq becomes: = 01 9// /√3 , * * (5) where 9// is the plastic shear strain rate This implies that the damage growth rate in shear is linearly TE D proportional to the plastic shear strain rate It can be inferred, from the co-existence of elongated and rather spherical microvoids in Fig 4, that triaxiality can vary locally, which might cause a transition from shear-dominated to traditional triaxiality-dominated damage evolution, within a single specimen In Fig 14, the microvoid size data for the last loading step shown in Fig were reorganised as a EP function of microvoid shape according to the microvoid nucleation sites In Fig 14, the magnitude of elongation is expressed as sphericity [2], which is related to the form and elongation Here, the AC C sphericity, S, was around 0.6 for a prolate spheroid of in the ratio of polar to equatorial radius It can be seen that remarkably elongated microvoids (i.e., with sphericity of less than 6) are associated, with few exceptions, with the martensitic phase, and especially with martensitic cracking The microvoids that originated from martensitic cracking exhibited an average S of 0.50, which corresponds to a prolate spheroid of 16 in aspect ratio, and of 1.49 × 10-4; whereas those originating from the ferritic interior exhibited an average S of 0.77 and of 0.82 × 10-4 Such disparity is directly reflected in the respective local deformation rates described in Eqs and 5, resulting in very high estimated plastic shear strain rates, of the order of unity, for the elongated microvoids under local shear Summary ACCEPTED MANUSCRIPT Combined phase- and absorption-contrast tomography has been applied to a DP steel The single-distance phase retrieval technique has been successfully employed to visualise, in 3D, ferrite/martensite DP structure with a significantly small density difference Microvoid nucleation, growth and coalescence behaviours have been quantitatively investigated by tracking all the microvoids to reveal microstructure/damage evolution relationships under tension Premature damage initiation was observed at a relatively early stage at various nucleation sites, RI PT such as the ferrite interior, martensitic interior and ferrite/martensite interfaces; however, the subsequent growth of such microvoids was relatively moderate On the other hand, microvoids initiated due to martensitic cracking near the point of maximum load subsequently exhibited characteristically rapid growth The martensitic cracking induced additional damage evolution mainly SC along nearby ferrite/martensite interfaces and intersections between the martensite and the ferrite grain boundary It is noteworthy that the microvoids originating from martensitic cracking exhibited characteristic shear-dominated growth in oblique directions under macroscopic tension, whereas those M AN U originating from the other nucleation sites exhibited traditional triaxiality-dominated growth, forming rather spherical microvoids It can be inferred from such co-existence of elongated and rather spherical microvoids that triaxiality can vary locally, causing a transition from shear-dominated to traditional triaxiality-dominated damage evolution, within a single specimen Although in the present study, a DP steel, with the relatively coarse martensitic phase, was evaluated as a model material due to the limitation in the spatial resolution of the phase-contrast XMT images, a similar tendency is expected in TE D practical DP steels as far as morphologically weak martensitic particles, which are shown in Figs and 11, are preferentially fractured in DP steels with relatively low martensite volume fraction EP Acknowledgements The synchrotron experiments were performed with the approval of JASRI, through proposal numbers 2012B1629, 2014B1681 and 2015A0076 The authors are grateful to Mr T Saeki for AC C conducting some of the image-based analyses References [1] P.F Thomason, A theory for ductile fracture by internal necking of cavities, J Inst Metals, 96 (1968) 360-365 [2] H Toda, H Oogo, K Horikawa, K Uesugi, A Takeuchi, Y Suzuki, M Nakazawa, Y Aoki, M Kobayashi, The true origin of ductile fracture in aluminum alloys, Metall and Mater Trans A, 45 (2014) 765-776 [3] T.F Morgeneyer, M.J Starink, I Sinclair, Evolution of voids during ductile crack propagation in an aluminium alloy sheet toughness test studied by synchrotron radiation computed tomography, Acta ACCEPTED MANUSCRIPT Mater., 56 (2008) 1671-1679 [4] D Steglich, W Brocks, J Heerens and T Pardoen, Anisotropic ductile fracture of Al 2024 alloys, Engng Fract Mech., 75 (2008) 3692-3706 [5] C.Y Tang, C.L Chow, W Shen and W.H Tai, Development of a damage-based criterion for ductile fracture prediction in sheet metal forming, J of Mater Proc Tech., 91 (1999) 270-277 [6] E Ahmad, T Manzoor, M.M.A Ziai, and N Hussain, Effect of martensite morphology on tensile RI PT deformation of dual-phase steel, J of Mater Engng and Prfm., 21 (2012) 382-387 [7] G Avramovic-Cingara, Ch.A.R Saleh, M.K Jain and D.S Wilkinson, Void nucleation and growth in dual-phase steel 600 during uniaxial tensile testing, Metall Mater Trans A, 40A (2009) 3117-3127 [8] M Erdogan, The effect of new ferrite content on the tensile fracture behaviour of dual phase steels, SC J Mater Sci., 37 (2002) 3623-3630 [9] J Kadkhodapour, A Butz, S Ziaei Rad, Mechanisms of void formation during tensile testing in a commercial dual-phase steel, Acta Mater., 59 (2011) 2575-2588 M AN U [10] D.L Steinbrunner, D.K Matlock, and G Krauss, Void formation during tensile testing of dual phase steels, Metall Trans A, 19A (1988) 579-589 [11] H Toda, F Tomizato, R Harasaki, D Seo, M Kobayashi, A Takeuchi and K Uesugi, 3D fracture behaviours in dual-phase stainless steel, ISIJ Int., 56(2016), 883–892 [12] C Landron, E Maire, J Adrien, H Suhonen, P Cloetens and O Bouaziz, Non-destructive 3-D reconstruction of the martensitic phase in a dual-phase steel using synchrotron holotomography, TE D Scripta Mater., 66 (2012) 1077-1080 [13] H Toda, D Seo, M Kobayashi and A Hosokawa, Assessment of ductile fracture via 3D/4D image-based approaches, Proc of 4th Int Sympo on Steel Sci., (2014) in press [14] D Paganin, S.C Mayo, T.E Gureyev, P.R Miller, and S.W Wilkins, Simultaneous phase and 33–40 EP amplitude extraction from a single defocused image of a homogeneous object, J Microsc., 206 (2002) [15] M.A Beltran, D.M Paganin, K Uesugi and M.J Kitchen, 2D and 3D X-ray phase retrieval of AC C multi-material objects using a single defocus distance, Optics Express, 18(2010) 6423-6436 [16] S.C Mayo, A.W Stevenson and S.W Wilkins, In-line phase-contrast X-ray imaging and tomography for materials science, Materials, (2012) 937-965 [17] The Iron and Steel Institute of Japan, Steel Handbook Vol 4, (1981) 22-23 [18] I.A Cunningham and A Fenster, A method for modulation transfer function determination from edge profiles with correction for finite-element differentiation, Med Phys 14 (1987) 533-537 [19] H Toda, F Tomizato, F Zeismann, Y Motoyashiki-Besel, K Uesugi, A Takeuchi, Y Suzuki, M Kobayashi and A Bruckner-Foit, High-resolution observation of steel using X-ray tomography technique, ISIJ Int., 52 (2012) 516-521 ACCEPTED MANUSCRIPT [20] M Kobayashi, H Toda, Y Kawai, T Ohgaki, K Uesugi, D.S Wilkinson, T Kobayashi, Y Aoki, M Nakazawa, High-density three-dimensional mapping of internal strain by tracking microstructural features, Acta Mater., 56 (2008) 2167-2181 [21] H Toda, E Maire, Y Aoki, and M Kobayashi, Three-dimensional strain mapping using in-situ X-ray synchrotron microtomography, J Strain Anal Eng Des., 46 (2011) 549-561 [22] C.C Chu, A Needleman, Void nucleation effects in biaxially stretched sheets, J of Engng Mater RI PT and Tech 102 (1980), 249-256 [23] S Katani, S Ziaei-Rad, N Nouri, N Saeidi, J Kadkhodapour, N Torabian, S Schauder, Microstructure modelling of dual-phase steel using SEM micrographs and Voronoi polycrystal models, Metallogr Microstruct Anal., 2(2013) 156-169 of a dual-phase sheet steel, ISIJ Int., 52 (2012) 743-752 SC [24] O West, J Lian, S Münstermann, W Bleck, Numerical determination of the damage parameters [25] T Balan, X Lemoine, E Maire, A Habraken, Implementation of a damage evolution law for M AN U dual-phase steels in Gurson-type models, Mater and Dsgn., 88(2013) 1213-1222 [26] K.L Nielsen, V Tvergaard, Ductile shear failure or plug failure of spot welds modelled by modified Gurson model, Engng Fract Mech., 77 (2010), 1031-1047 [27] J.R Rice and D.M Tracey, On the ductile enlargement of voids in triaxial stress fields, J Mech Phys Solids, 35 (1969) 201-217 [28] R.D Thomson and J.W Hancock, Ductile failure by void nucleation, growth and coalescence, Int TE D J of Fract., 26 (1984) 99-112 [29] Y Bao and T Wierzbicki, On fracture locus in the equivalent strain and stress triaxiality space, Int J of Mech Sci., 46 (2004) 81–98 [30] J.P Bandstra, D.M Goto and D.A Koss, Ductile failure as a result of a void-sheet instability: EP experiment and computational modelling, Mater Sci Engng., A249 (1998) 46–54 [31] K Nahshon, J.W Hutchinson, Modification of the Gurson Model for shear failure, European J of Mech - A/Solids, 27 (2008) 1–17 AC C [32] Z Xue, J Faleskog, J.W Hutchinson, Tension–torsion fracture experiments – Part II: Simulations with the extended Gurson model and a ductile fracture criterion based on plastic strain, Int J of Solids and Struct., 50 (2013) 4258–4269 ACCEPTED MANUSCRIPT Caption list Table Percentage of initiated microvoids at different applied strain levels The data were organised according to the void nucleation sites Fig An optical micrograph of the investigated DP steel M and α denote the martensitic and ferritic phases, respectively RI PT Fig Nominal stress - nominal strain curve obtained during the in-situ tensile test Fig 3D tomographic images obtained at varying camera distance, L, at the maximum load Each image shows a quarter of a virtual cross-section, with or without the phase retrieval process Fig 3D perspective views of microvoids at different load levels The underlying ferritic and SC martensitic phases are not displayed, and only microvoids are shown in red Fig Changes in volume fraction and size distribution of microvoids as a function of applied strain Fig Growth behaviour and shape of microvoids that were initiated at different applied strain levels different applied strain levels M AN U Size distributions at the last loading step are shown in (c) for microvoids that had been nucleated at Fig Growth behaviour of microvoids initiated at different nucleation sites Diameter distributions at the last loading step are shown in (d) for voids nucleated at different nucleation sites Fig Growth behaviour of individual microvoids extracted from a unit box located at the center of the specimen The growth data were organised according to the microvoid nucleation sites: (a) TE D microvoids nucleated in the ferritic phase, which has been classified into intergranular (IG) and transgranular (TG) fracture; (b) the interfaces between the ferritic and martensitic phases, in which the intersections between martensite and the ferritic grain boundaries have been distinguished; and (c) the martensite fracture itself EP Fig 3D perspective views of a typical microvoid The underlying ferritic phase is not displayed, and only the microvoid and the martensitic phase are shown Fig 10 Characteristics of 25 randomly selected martensitic particles, in terms of shape (i.e., the degree AC C of necking) and inclination angle with respect to the tensile axis Fig 11 Results of 3D strain mapping of cracked martensite, which has been measured between an applied strain of 16.4 and 27.8 % (a) is a spatial distribution of Gaussian curvature value that has been superposed on the extracted image of a martensitic phase region (b) is a 3D contour of equivalent strain Circles in (a) denote morphological features used for the 3D strain mapping Fig 12 Photomicrograph and inverse pole figure map of the normal direction, analysed using the EBSD method Shown is a microvoid initiated from martensitic cracking (a) is a SEM micrograph of the identical cross-section as in (b) In (b), the white dashed lines are the block boundaries of the martensitic microstructure, and the yellow lines are ferrite/martensite interfaces Fig 13 Inverse pole figure map of the normal direction, analysed with the EBSD method Shown is a microvoid initiated from martensitic cracking (a) is an IPF map, and (b) is a KAM map ACCEPTED MANUSCRIPT Fig 14 Characteristics of microvoids extracted from the same unit box as in Fig Microvoid size AC C EP TE D M AN U SC RI PT data were organised according to the microvoid nucleation sites as a function of their morphology M AN U SC RI PT ACCEPTED MANUSCRIPT α TE D M 100 µm AC C EP Fig An optical micrograph of the investigated DP steel M and α denote the martensitic and ferritic phases, respectively SC RI PT ACCEPTED MANUSCRIPT 500 400 300 200 M AN U 600 Absorption-contrast Phase- and absorption-contrast TE D Nominal stress, σ / MPa 700 100 10 20 30 Nominal strain, ε (%) Fig Nominal stress - nominal strain curve obtained during the in-situ tensile test AC C EP ... applied strain change of 11.4 % ACCEPTED MANUSCRIPT Damage micromechanisms in dual- phase steel investigated with combined phase- and absorption- contrast tomography Hiroyuki Toda1*, Akihide Takijiri2,... Stevenson and S.W Wilkins, In- line phase- contrast X-ray imaging and tomography for materials science, Materials, (2012) 937-965 [17] The Iron and Steel Institute of Japan, Steel Handbook Vol 4, (1981)... existing microvoids On the other hand, in the DP stainless steel investigated in our previous study [11], intense shear localisation SC was observed in thin oblong ferritic film that was sandwiched