Damage micromechanisms in dual phase steel investigated with combined phase and absorption contrast tomography

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[.]

Damage micromechanisms in dual-phase steel investigated with combined

phase-and 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: 4 January 2017

Accepted Date: 5 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 toour customers we are providing this early version of the manuscript The manuscript will undergocopyediting, typesetting, and review of the resulting proof before it is published in its final form Pleasenote that during the production process errors may be discovered which could affect the content, and alllegal disclaimers that apply to the journal pertain

(a) 3D martensitic network

together with Gaussian

curvature distribution used

for tracking

(b) 3D local strain map in themartensitic phase for an appliedstrain change of 11.4 %

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 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

It is reasonable to assume that the ductile fracture process is appreciably affected in the case of DP 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 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 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

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 (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

of martensitic particles, Vf

M, were 18.3 µm and 29.9 %, respectively Parallel-piped tensile specimens, 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 polished to obtain the almost circular cross-section shown below in Fig 3

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

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 µm × 6.5 µm Exposure time was 0.8 sec The stress-strain curve obtained during the tensile test performed at a loading rate of 0.0005 mm/sec is shown in Fig 2 The absorption-contrast XMT scans were repeated 7 times before fracture, while maintaining displacement The phase-contrast XMT scans were obtained 3 times at the loading steps indicated in Fig 2 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 2 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

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),

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 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 g/cm3 and 7.76 g/cm3 for the ferritic and martensitic phases, respectively, implying a relatively small density difference of 1.4 % between them

2.3 Image analyses

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 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 9 voxels in volume were counted as particles and microvoids in the XMT images

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 5 % contrast ratio in the phase-contrast XMT images It has been reported by the present authors that 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

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 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 used for detecting microvoid initiation

3 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 3 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

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 3 (b) It appears, however, most likely that only the interfaces are highlighted in Fig 3 (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 3 (c)), image segmentation was not possible without applying a 3D median-based filter, due to the remaining ring artefacts Although the median-based filter used (i.e., 7 × 7 × 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, after the single-distance phase retrieval algorithm was applied, in spite of the relatively small density difference of 1.4 % between the two phases

It is also to be noted that the imaged microvoids in Fig 3 (c) have obviously been enlarged compared to Fig 3 (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 3 (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

3.2 Microvoid initiation and growth behaviour

Fig 4 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

4 are mainly microvoids, but may contain some pre-existing particles such as MnS, which has a linear 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 4 (d) – (g), after the uniform elongation of the specimen is truncated after the onset of macroscopic neck formation around 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 5 µm A limited number of extremely coarse microvoids observed in Fig 4 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 6 and Table 1 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 6 (a) and (b) As a result, the majority of

coarse microvoids (i.e., > 5 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 4 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 1 Intergranular and transgranular cracking in the ferrite interior is also observed, to a lesser extent Microvoids that were 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 area, until the final rupture The data in Fig 6 was analysed according to the microvoid nucleation sites, as shown in Fig 7 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 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 7 (c)), as in the elongated microvoids observed in Fig

4

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 4 (g) and 8 (c)) were nucleated due to martensitic cracking at an applied strain of 23.9 %, and later propagated in oblique directions with respect to the loading direction

3.3 Details of the microvoid initiation sites in the martensitic phase

The largest microvoid seen in Fig 4 (g) has been extracted in Fig 9, together with adjacent martensitic particles The microvoids shown in Fig 9 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

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 cracking In summary, the significant strain variation due to morphological complexity is the main cause of the martensitic cracking identified in Figs 7 – 10 and Table 1

Fig 13 shows the strain localisation in the ferritic phase around a cracked martensite particle A 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 nucleation sites, Table 1 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 white arrow in Fig 13 (b))

5 Discussion

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

M

of 0.11) [25], presumably depending on Vf

M, 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 Vf

M value for the last loading step was approximately 2.4 × 10-4 (Fig 5 (a)), suggesting that the microvoid coalescence

As was summarised in Section 1, a variety of microvoid nucleation mechanisms have been 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 1 and Figs 7 and 8, however, indicate 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

Microvoid growth has been phenomenologically postulated to depend on the existence and degree

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 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 phase boundaries [23] However, the rapid microvoid growth in oblique directions, observed here (Figs 4 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

deviator, (* the plastic strain rate, and σe the effective stress In this model, the first term corresponds

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 rotation contributes to softening, and constitutes material degradation As an extreme case, if a pure shear state (i.e., ω = 1) is assumed, Eq 4 becomes:

 = 019//*/√3 , (5)

where 9//* is the plastic shear strain rate This implies that the damage growth rate in shear is linearly 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 8 were reorganised as a 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

sphericity, S, was around 0.6 for a prolate spheroid of 9 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 4 and 5, resulting in very high estimated plastic shear strain rates, of the order of unity, for the elongated microvoids under local shear

6 Summary

Premature damage initiation was observed at a relatively early stage 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 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 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 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 practical DP steels as far as morphologically weak martensitic particles, which are shown in Figs 9 and 11, are preferentially fractured in DP steels with relatively low martensite volume fraction

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 conducting some of the image-based analyses

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