Relationship between Microstructure, Mechanical Properties and Damage Mechanisms in High Martensite Fraction Dual Phase Steels

ISIJ International, Vol. 55 (2015), ISIJ International, No. 10 Vol. 55 (2015), No. 10, pp. 2237–2246 Relationship between Microstructure, Mechanical Properties and Damage Mechanisms in High Martensite Fraction Dual Phase Steels Irina PUSHKAREVA,1)* Sébastien ALLAIN,2) Colin SCOTT,3) Abdelkrim REDJAÏMIA2) and Antoine MOULIN4) 1) Formerly IJL, UMR CNRS-UL 7198. Now at CANMET MATERIALS, Natural Resources Canada, 183 Longwood Road South, Hamilton, ON, L8P 0A5 Canada. 2) IJL, UMR CNRS-UL 7198, Parc de Saurupt, CS 50840, F-54011 Nancy Cedex, France. 3) Fomerly Arcelor Research SA. Now at CANMET MATERIALS, Natural Resources Canada, 183 Longwood Road South, Hamilton, ON, L8P 0A5 Canada. 4) Arcelor Research SA, Voie Romaine – BP 30320, F-57283 Maizières-lèsMetz, France. (Received on April 1, 2015; accepted on July 2, 2015; J-STAGE Advance published date: August 28, 2015) The relationships between microstructure, mechanical properties and damage mechanisms in asquenched and in quenched-and-tempered high martensite fraction ( > 60%) dual phase (DP) steels were investigated. The mechanical behaviour was determined by tensile and hole expansion (HE) tests. In the as-quenched condition, the HE ratio decreased with increasing ferrite content and showed a non-linear inverse relation to the uniform elongation. Tempering significantly improved the HE ratio for all studied martensite fractions; the increase in HE was found to be monotonic for tempering temperatures between 230°C and 460°C, even though the yield stress dependence was complex in this range. Tempering studies showed that, at constant martensite fractions, there was a linear dependence between the HE ratio and the ductile fracture strain, εf. However, the parameters of the linear relation changed significantly when the martensite fraction was varied. The dominant damage mechanism in simple tensile tests evolved from ferrite/martensite or martensite/martensite interface decohesion in the as-quenched state to martensite/ carbide interface decohesion after tempering. The damage mechanisms were qualitatively described using the Beremin local criteria. KEY WORDS: dual-phase steel; mechanical properties; microstructure; fracture; modelling. 1. Hole Expansion (HE) test is the most widely used to determine stretch-flange formability limits. This is a technological method for evaluating the suitability of sheet steel for forming ‘flanges’ which is representative of the processes used under industrial production conditions.4,5) According to literature data, the HE behaviour of high strength steels is determined by microstructural heterogeneities.2,6) As previously stated, DP steel microstructures consist of ferrite and martensite with very different mechanical properties. Strain incompatibilities generated at ferrite/ martensite interfaces during deformation can promote local boundary decohesion, even at relatively low macroscopic strains. This can lead to poor damage response, especially when compared to homogeneous microstructures.2,6) This paper reports on high martensite fraction ( > 60%) DP steels in the as-quenched and quenched-and-tempered conditions. Results from tensile and HE tests are presented and interpreted with the aid of detailed microstructural analyses. These data are reconciled with the observed damage mechanisms on tensile samples through ex-situ SEM investigations of void distributions. Introduction In the automotive industry, environmental concerns require that vehicle fuel consumption and CO2 emissions have to be reduced as much as possible. It is therefore advantageous to lighten the body in white and chassis components by replacing existing parts using higher strength, thinner gauge alternatives with equivalent or improved structural/functional properties. Dual Phase (DP) steels are a class of advanced high strength steels (AHSS) characterized by a microstructure consisting of a mixture of hard martensite and softer ferrite which combines high strength with good ductility. Their excellent properties have made them the most widely used of all AHSS in the automotive sector; however, certain aspects of DP steel behaviour, notably the formability, limit the range of accessible parts.1,2) For cold stamped components the most important forming properties are deep drawability, bulgeability, stretch-flange formability and bendability.2,3) Various test methods are available to assess the formability of sheet material. Amongst these, the * Corresponding author: E-mail: ir.pushkareva@gmail.com DOI: http://dx.doi.org/10.2355/isijinternational.ISIJINT-2015-186 2237 © 2015 ISIJ ISIJ International, Vol. 55 (2015), No. 10 2. with a punch/die clearance of 12%. The burr at the hole edge was always positioned downwards. The hole was then expanded by a conical punch with a top angle of 60°. A clamping force was applied to the test piece to prevent any material draw-in during the test. The conical expansion tool was pressed upwards into the punched hole at a rate which enabled the operator to stop the test when the first visible crack traversed the full thickness of the cut edge. HE was then determined by the following formula: Experimental Procedure All of the experiments were carried out on an industrial Fe-0.15C-0.215Si-1.9Mn-0.195Cr wt.% 1.2 mm thick sheet in the cold rolled full hard condition. Samples were heated at 2.7°C/s to six different intercritical annealing temperatures (755, 760, 785, 790, 810 and 840°C), held at temperature for 130 s and then water quenched to room temperature. For tempering studies, the as-quenched specimens were then post-heated at 230°C, 380°C and 460°C for 240 seconds. The annealing and quenching experiments were carried out in a continuous annealing simulator where the temperature was controlled to ± 5°C over the entire homogeneous zone (10 cm by 6 cm). All the tempering treatments were performed in a salt bath. The resultant microstructures were characterised by optical microscopy in the plane defined by the rolling direction (RD) and normal direction (ND), after picral and metabisulfite etching, and the phase fractions were determined by an Aphelion® semi-automatic image analyzer. Transmission electron microscope (TEM) observations were carried out in a Philips CM200 field emission gun (FEG)-TEM on thin foils prepared in the plane of the sheet at ¼ thickness. The samples were mechanically polished to 50 μm, then prethinned to 20 μm by dimple grinding and finally reduced to electron transparency by twin-jet electropolishing using a solution consisting of 5% perchloric acid in acetic acid at a temperature of 15°C. Local carbon concentration measurements were made using a Gatan 666 Electron Energy Loss (EELS) spectrometer. The EELS experiments were carried out at a temperature of − 169°C in a liquid nitrogen cooling holder in order to eliminate carbon contamination on the specimen surface during analysis. The detection limit for carbon with this technique is of the order of 0.04 wt.% and the measurement relative error was < 5% for C concentrations between 0.2 and 0.8 wt.%.7) Flat tensile samples of 50 mm gauge length and 12.5 mm width were cut from the heat treated coupons with the tensile loading axis parallel to the transverse direction (TD) of the sheet and tested at a strain rate of 0.008 s − 1 following the European Standard EN 10002-1. A pair of tensile samples was cut from each annealed coupon. The sample to sample dispersion was found to be ± 20 MPa for YS (Yield stress) and UTS (Ultimate tensile strength) and ± 0.25% for UE (Uniform elongation) for each pair. The fracture strain (εf) of broken tensile samples was determined as follows: HE = where D0 is the initial hole diameter, and Dh is the hole diameter at fracture. Three samples were tested for each heat treatment condition. 3. Microstructural Characterisation The microstructure of the as-quenched samples after annealing at 755–790°C consisted of martensite bands (dark coloured) and (often) elongated ferrite grains (light coloured) (Fig. 1). These martensite bands were located in regions of high manganese and carbon segregation which formed in the initial as-cast microstructure and were then deformed into thin sheets or bands during the hot and cold rolling processes.8,9) At these high strength levels, martensite is the dominant phase and forms a continuous network around the ferrite islands.10) In samples annealed at temperatures of 810°C and higher, the ferrite volume fraction was approximately 1% and the microstructure was almost fully martensitic. X-ray diffraction measurements confirmed that no significant amounts of residual austenite were present in any of the samples.  S0  ε f = ln    Sf  where S0 is the initial section of the tensile specimen and Sf is the projected surface area at fracture corresponding to the narrowest part of the necked region. The microstructural damage analysis of tensile test specimens was carried out using a LEO 982 field emission gun (FEG) scanning electron microscope (SEM) in the plane defined by the TD and RD after nital or picral etching. The fracture surfaces were observed in a JEOL 6400 SEM. HE tests were carried out according to ISO TC 1644) specifications. A square sample 100 × 100 mm was cut from the heat treated coupon. Then a hole with diameter D0 = 10 mm was punched in the central part of the test piece © 2015 ISIJ Dh − D0 × 100% D0 Fig. 1. 2238 Optical micrographs of the as-quenched samples. Picral and Metabisulfite etching: the dark-etching phase is martensite, the light-etching phase is ferrite. ISIJ International, Vol. 55 (2015), No. 10 Table 1. Measured ferrite and martensite grain sizes in the RD × ND plane, martensite fractions and martensite carbon contents for different annealing temperatures. Annealing temperature, °C Ferrite grain size in RD, μm Thickness of martensite band in ND, μm Martensite fraction (measured), % Martensite carbon content (measured), wt.% 755 6 3 61 – 760 6 3 62 0.28 785 4 4 82 – 790 6 4 86 0.17 810 3 – 99 0.15 840 1 – 99 – Fig. 3. Evolution of the martensite (austenite) carbon content with annealing temperature. complete carbon partitioning at intercritical annealing temperatures above 760°C. The change (ortho → para) in the phase transformation kinetics at lower temperatures was attributed to incomplete Mn partitioning. A more detailed discussion of this phenomenon and the influence it has on the carbon profile at the martensite-ferrite interfaces was given in a previous publication.11) 4. Mechanical Properties Table 2 summarizes the average mechanical properties measured for various annealing and tempering temperatures in terms of yield strength (YS), ultimate tensile strength (UTS), uniform elongation (UE), hole expansion ratio (HE) and ductile fracture strain (εf). This data is discussed in the following sections. Fig. 2. Evolution of the martensite (austenite) fraction with annealing temperature. The numbered points show the measured martensite carbon concentrations (in wt.%). 4.1. Tensile Properties of As-quenched Samples The as-quenched material exhibited characteristic DP steel behaviour: continuous yielding, low YS/UTS ratio and absence of any yield plateau.12) Both the YS and the UTS increase with increasing martensite fraction (Fig. 4). However, the mean increase in UTS with increasing martensite fraction was 8.6 MPa/% martensite, which is a little more than half the value (15 MPa/% martensite) proposed by Davies.13) This is due to carbon dilution and the influence of the plastic behaviour of the martensite. The latter becomes dominant in DP steels containing high martensite fractions where the mean carbon content in martensite < 0.5 wt.%.14) A high dispersion was observed in both the uniform and total elongations of asquenched samples, nevertheless a clear trend of decreasing UE with increasing martensite content was found (Fig. 4) in agreement with other published data.15) For each annealing temperature, Table 1 contains the average experimental ferrite grain size measured in the RD × ND plane, the average thickness of the martensite bands measured parallel to ND in the same plane, the martensite volume fraction and its mean carbon content. The latter was obtained by Electron Energy Loss Spectroscopy (EELS) from thin foils in the TEM. The EELS values were the average of concentrations measured on at least 5 different martensite islands.11) The evolution of the experimental martensite fractions with annealing temperature is plotted in Fig. 2. On the same graph the orthoequilibrium austenite fractions and also the paraequilibrium curve calculated using ThermoCalc© with the TCFE7 database are superimposed. It can be seen that at lower annealing temperatures the experimental martensite (austenite) fraction is above the orthoequilibrium line and lies closer to the paraequilibrium value. As the intercritical temperature increased, the system tends to orthoequilibrium. In Fig. 3, the experimental martensite carbon contents from three annealing temperatures (indicated by the numbered points in Fig. 2) are compared with the theoretical values. The good agreement with orthoequilibrium indicates that the isothermal holding time of 130 s was sufficient to allow 4.2. Tensile Properties of Quenched and Tempered Samples The mechanical properties of DP steels are strongly altered by tempering.16) This is a complex phenomenon as several effects must be considered, i.e. ageing of the ferrite and martensite phases (which depends on the amount of 2239 © 2015 ISIJ ISIJ International, Vol. 55 (2015), No. 10 Table 2. Average mechanical properties as a function of annealing and tempering temperatures. Annealing temperature, °C Martensite fraction, % 755 61 760 Tempering temperature, °C YS, MPa UTS, MPa UE, % HE ratio, % Ductile fracture strain, εf 20 508 1 029 6.5 9 0.33 62 20 546 1 056 4.9 9 0.30 760 62 230 736 1 012 5.6 35 0.37 760 62 380 764 891 4.4 64 0.54 760 62 460 734 817 5.7 77 0.63 785 82 20 691 1 180 4.8 15 0.30 790 86 20 765 1 242 5.4 19 0.59 790 86 230 906 1 130 3.5 46 0.78 790 86 380 954 1 041 3.0 72 0.82 790 86 460 831 884 2.6 97 0.99 810 99 20 998 1 385 2.4 43 0.71 810 99 230 1 153 1 283 1.6 64 0.79 810 99 380 1 130 1 161 1.6 89 0.89 810 99 460 1 001 1 005 2.8 99 0.95 840 99 20 1 006 1 423 2.8 51 0.80 840 99 230 1 214 1 362 2.8 80 0.92 840 99 380 1 131 1 176 2.4 89 0.96 840 99 460 1 038 1 046 2.1 95 1.08 Fig. 5. YS evolution with tempering temperature. Fig. 4. Evolution of the YS, UTS and UE with martensite fraction in the as-quenched condition. of martensite) decreased. Other workers have reported very similar observations2,3) and have explained the increase in YS between the as-quenched state and tempering at 230°C by the relaxation of Type 2 transformation stresses, i.e. short range internal stresses arising from the martensite transformation. Hutchinson and co-workers used X-ray diffraction line broadening analysis to show that the mean internal stress was approximately 50% of the tensile strength for a range of as-quenched martensitic steels. In their model, regions where the local residual shear stresses are aligned near to 45° to the external loading direction yield first, contributing to the extended elasto-plastic transition and thus reducing the conventional 0.2% proof yield stress. carbon in solid solution and the density of mobile dislocations formed during quenching), tempering of martensite, and any interactions between the two such as the volume contraction of martensite. Figure 5 shows the evolution of YS with tempering temperature for each annealing temperature. In all cases, a well-defined yield point and a yield plateau appeared after tempering. The latter became more extended at higher tempering temperatures.1) The YS exhibited a clear maximum at tempering temperatures in the range 230–380°C and the peak YS appeared to shift to higher temperatures as the intercritical annealing temperature (volume fraction © 2015 ISIJ 2240 ISIJ International, Vol. 55 (2015), No. 10 Fig. 7. Fig. 6. UTS evolution with tempering temperature. The authors showed that tempering at 200°C or 225°C reduced these internal stresses by up to 20% compared to the as-quenched condition and thus introduced a significant increase in the 0.2% proof yield stress. The subsequent reduction of YS after tempering at 380 and 460°C is due to martensite softening which also results in reduction of UTS (Fig. 6). Regarding the UTS, it can be seen in Fig. 6 that, for all annealing temperatures tested, the UTS decreases rapidly as the tempering temperature increased. The softening rate appeared to be highest for samples annealed at the highest temperatures i.e. those containing the most martensite. This behaviour could be related to the fact that the initial martensite softening rate was inversely proportional to its strength (carbon content).19) That is to say, for a tempering interval of 240 s, higher carbon martensite remains significantly harder than lower carbon martensite. At longer annealing times this is clearly not the case.20) HE ratio evolution with tempering temperature for four different annealing temperatures. Fig. 8. Plot of the experimental HE ratio as a function of difference in hardness (ΔHv) between ferrite and martensite – comparison with literature data. 4.3. Hole Expansion Properties Before presenting the HE properties data the important effect of hole edge damage by punching must be discussed. It is well known that the hole punching operation can deteriorate the HE properties to an extent that depends on many parameters, most notably the punch/die clearance. However, Hasegawa et al.3) have shown that the difference in HE ratio between machined holes and punched holes remains constant for a range of different DP compositions and microstructures. Therefore, it is possible to compare HE ratios for different microstructures as long as the hole punching parameters and the sheet thickness are not varied, as is the case in the present study. From Table 2 and Fig. 7, it can be seen that HE ratio strongly increased with martensite fraction for as-quenched samples. The maximum HE value obtained was 50% for the almost fully martensitic steels and the minimum was 9% for the 61% martensite fraction steels. Tempering considerably improved the HE ratio as illustrated in Fig. 7. For example, the HE ratio for the 760°C-annealed sample increases from 9% in the asquenched state to 77% after tempering at 460°C. A similar trend was observed by Kamp and co-workers21) for two DP steels with chemical compositions close to the alloy studied here but with martensite volume fractions of only 30%. Thus it is possible to obtain the same target HE ratio starting from quite different ferrite/martensite fractions by appropriate adjustment of the tempering temperature. In Fig. 8 the relationship between the HE ratio and the difference in Vickers hardness (ΔHv) of the ferrite and martensite (see §5 for details) is shown for alloys annealed at 760°C and 810°C and then tempered at different temperatures. Plotted on the same graph is data taken from the work of Hasegawa et al.3) for a DP steel with a similar chemical composition and tempering parameters but containing 34% martensite. In both studies there appears to be a comparable linear correlation between the HE ratio and ΔHv for a given steel microstructure i.e. the HE ratio decreased with increasing ΔHv. Unfortunately the absolute HE values cannot be compared due to differing experimental procedures. Although the HE ratio can be improved using tempering treatments, tempering leads to an unwanted reduction in the 2241 © 2015 ISIJ ISIJ International, Vol. 55 (2015), No. 10 Fig. 9. Process map illustrating the relationship between HE ratio and UTS in the as-quenched (AQ) and quenched and tempered conditions. steel UTS. In Fig. 9, a process map showing the UTS-HE diagram is plotted for as-quenched and quenched and tempered states. This can be used to find the process parameters leading to the best compromise between the required UTS and HE ratios. The dashed arrows indicate the change in HE and UTS with tempering temperature at constant intercritical annealing temperature and the solid arrows show the variation due to changes in the annealing temperature at constant tempering temperature. Regarding the as-quenched state, an increase in the annealing temperature in the range 760°C–840°C led to an increase in UTS from 1 050 MPa to > 1 400 MPa, coupled with an increase in the HE from 10% to 50%. The above trend was the same for all tested tempering temperatures. In general, specimens quenched from higher temperatures gave higher values of UTS and HE ratios. Thus, the initial steel microstructure controlled the mechanical and damage behaviour after tempering. For the composition studied here: • Increasing the quenching temperature improved both UTS and HE ratio, • A wide range of HE ratios can be achieved at constant UTS by varying the annealing and tempering conditions. In order to obtain the best HE value, it is therefore advantageous to use the highest annealing and tempering temperatures compatible with the target UTS and the required uniform elongation. Fig. 10. correlate well with the HE ratio is the ductile fracture strain, εf, measured on broken tensile test samples. A general relation of this type has already been reported by Link et al.22) It can be seen from Fig. 10(a) that, for each intercritical annealing temperature, the HE ratio increases linearly with εf as the tempering temperature increases. The correlation coefficient for the data in Fig. 10(a) is 20 ± 3% HE/0.1 fracture strain. For martensite volume fractions fm ≥ 86% the data points could all be considered to lie along a single line, to within experimental error. However, samples annealed at 760°C (62% martensite) show a distinctly different behaviour with a similar tempering response but a markedly reduced fracture strain at constant HE ratio. This is an important observation as it clearly indicates that the HE/εf relation is not constant but contains a strong microstructure dependence, at least for DP steels with high martensite fraction. One possible explanation for this observation can be 4.4. Relationship between HE Ratio and the Ductile Fracture Strain From the previous sections it is obvious that standard uniaxial tensile test data is insufficient to predict the HE behaviour of DP steels. For example, it is impossible to reconcile the evolution of the HE ratio with martensite fraction for different tempering temperatures with the YS or UTS data shown in Figs. 5 and 6. It is also quite evident from Fig. 4 and Table 2 that the ductility measured through uniform elongation in tensile tests showed an inverse, nonlinear relationship with the HE ratio. One structure-sensitive mechanical property which does © 2015 ISIJ a) Correlation between fracture strain and HE for each annealing temperature and b) Dynamic fracture toughness K JD of a DP steel as a function of martensite volume fraction (data from Bag et al.23)). 2242 ISIJ International, Vol. 55 (2015), No. 10 taken from the dynamic fracture toughness results of similar high martensite fraction DP steels reported by Bag and coworkers.23) They carried out room temperature impact tests on standard (10 mm thick) Charpy samples cut from alloys with martensite fractions between 33% and 62% and found a sharp increase in KJD as the martensite fraction increased from 45% to 60% with a plateau before and after this region. Their data are plotted in Fig. 10(b) (points and solid line). The dotted line represents the expected increase in KJD as the martensite fraction is reduced towards 0%. Although there is no existing theoretical support for comparing low strain rate HE/εf data with high strain rate Charpy tests, there does appear to be a clear similarity in the KJD and HE/εf behaviour in Figs. 10(a) and 10(b) that merits further investigation. In Fig. 10(a) there is a constant HE/εf relation at fm ≥ 86% and a large shift to much lower fracture strains at fm = 62%. Bearing in mind the differences in the experimental conditions, this could well correspond to the region of reduced fracture toughness shown in Fig. 10(b). Assuming that to be the case, then we would expect that decreasing fm below 62% should result in little further change in HE/εf until some threshold ferrite content is attained whereupon the fracture strain should start to increase again. Recent work by Lai et al.24) suggests that this threshold occurs in the region 21% < fm < 36%. Consequently any HE/εf study where the range of fm is confined to one of the plateau regions would very probably conclude that there is no microstructural dependence. This is likely to be the case for the results reported by Link et al.22) although no figures for fm were given in their text. Further comparative tests at lower martensite fractions are required in order to validate this hypothesis. In conclusion it is clear that knowledge of εf alone is not sufficient to predict the HE behaviour of DP steels over a wide range of fm. However, if the as-quenched HE value is measured and the correlation coefficient is known then εf can safely be used to predict HE ratios after tempering. Fig. 11. SEM micrograph in RDxTD plane of broken tensile test samples showing a) voids at ferrite/martensite interfaces in the as-quenched sample annealed at 760°C, b) void in martensite in the as-quenched sample annealed at 810°C. Loading axis is parallel to TD. Arrows point at voids. 760°C-annealed as-quenched sample (containing the highest carbon martensite).9) In this specimen a mixed mode of damage was observed close to the edge of the fracture surface: some cleavage was present together with the dimpled areas. It is known that martensite toughness decreases with increasing carbon content and this may lead to the appearance of brittle cleavage.25–27) 4.5. Damage Mechanisms Void distributions were studied by SEM on broken tensile test samples polished in the plane defined by RD and TD and observed just behind the fracture surface. In an as-quenched 760°C annealed tensile test sample (62% martensite fraction) it was seen that the dominant damage mechanism was ferrite/martensite interface decohesion (Fig. 11(a)). In almost fully martensitic as-quenched 810°C-annealed samples the voids were often seen at martensite/martensite (prior austenite) grain boundaries. (Fig. 11(b)). Tempering altered the DP steel microstructure and led to a change in the damage mechanism – voids formed preferentially at tempered carbides inside the martensite (Fig. 12). For the 760°C-annealed sample tempered at 230°C ferrite/martensite interface decohesion remained the dominant mechanism (Fig. 12(a)) but this changed to internal martensite damage at carbide particles after tempering at 380°C (Fig. 12(b)). Further, for the 810°C annealed samples void formation at tempered carbides appeared at the lowest tempering temperature of 230°C (Fig. 12(c)). SEM fractography of as-quenched and quenched and tempered broken tensile test samples revealed ductile fractures with a dimpled fracture surface in all cases except the 5. Modelling Interface Decohesion in DP Steels Many studies of ductile damage mechanisms in DP steels have highlighted the importance of decohesion at the ferrite/martensite interface followed by the propagation of microcracks at the phase boundaries.8,28–32) This was the dominant behaviour in as-quenched samples in this study. However, depending on the martensite fraction (carbon content) and the tempering treatment, the major damage mechanism changed to void formation at tempered carbides in martensite. The latter mechanism is difficult to model as most of the important parameters such as the volume fraction of carbides, their size and shape distribution, the evolution of the matrix carbon concentration and the local stress triaxiality are not known. Instead, the description of the probability of interface decohesion at ferrite/martensite 2243 © 2015 ISIJ ISIJ International, Vol. 55 (2015), No. 10 σ C = Σ1 + X ................................ (1) Where Σ1 is the maximum principal stress and X is the kinematic hardening which represents the second-order internal stresses generated during plastic deformation of the DP composite. Σ1 is a function of the hydrostatic stress σh and the Von Mises equivalent stress σeq:34) 2 Σ1 = σ h + ⋅ σ eq ............................. (2) 3 In order to calculate the kinematic hardening X at the ferrite/martensite interface, a phenomenological approach involving a “law of mixtures” type description is used.35) If the macroscopic strain at the start of void nucleation, εn in a tensile test is measured then the kinematic hardening is: Xε n = fm (1 − fm )∆σ ε n ......................... (3) Where Δσεn is the difference in the flow stress of the two phases at the nucleation strain. It has been observed that the earliest interface voids tend to nucleate at high values of local ferrite strains (εn > 0.2).14,36) It is reasonable to propose that at this point the flow stress in martensite is nearly constant and that of ferrite is only slowly increasing. It is therefore possible, under these particular conditions, to use the Vickers hardness values to estimate Δσεn. Using the hardness conversion σ≈3HV, equation Eq. (3) can be rewritten as: Xε n = 3 ⋅ fm (1 − fm ) Hvm − Hvα ................. (4) Where Hvm and Hvα are the martensite and ferrite hardness values. In a similar manner, the value of σeq is determined through the martensite and ferrite hardnesses as follows:35) σ eq = 3 ⋅ [(1 − fm ) Hvα + fm Hvm ] ................. (5) The as-quenched and tempered martensite hardness values were taken from the work of Grange37) for given martensite carbon contents and tempering temperatures. Note however that in reference37) a tempering time of one hour was applied. The ferrite hardness was calculated using Hasegawa equation3) and is equal to 140 Hv. The hydrostatic stress can be found from the definition of triaxiality, T: σ h = T σ eq .................................. (6) According to Helbert et al. the local triaxiality Tloc at ferrite/martensite boundaries may be higher than the macroscopic triaxiality T due to kinematic hardening, X and we can write:38) Fig. 12. SEM micrograph in RD × TD plane of broken tensile test sample showing voids at tempered carbides in the a) 760°C-annealed sample after tempering at 230°C, b) 760°C-annealed sample after tempering at 460°C, c) 810°C-annealed sample after tempering at 230°C. Loading axis is parallel to TD. Arrows point at voids.  X  Tloc = T 1 +  ............................ (7)  σ eq  It can be seen that the local triaxiality Tloc increases with increasing X and so the probability of interface decohesion also rises. Thus, combining Eqs. (1), (2) and (6) the critical debonding stress can be determined as: phase boundaries as a function of the intercritical annealing and tempering parameters is presented below. It has been shown that, for inclusions larger than ~20 nm in diameter, the debonding criterion is the critical local stress.33) According to Beremin the maximum stress to which an inclusion is subjected, σc can be defined as:34) © 2015 ISIJ 2  σ c =  Tloc +  σ eq + Xε n ...................... (8) 3  2244 ISIJ International, Vol. 55 (2015), No. 10 specimen annealed at 760°C and tempered at 230°C was ferrite-martensite decohesion (Fig. 12(a)) changing to martensite/carbide decohesion after tempering at 380°C and 460°C (Fig. 12(b)). This implies that σc must lie between 1 272 MPa and 895 MPa. In the sample annealed at 810°C some ferrite-martensite decohesion was observed in the as-quenched state, but not after tempering at 230°C (Fig. 12(c)). Thus the lower limit for σc can be raised to 1 137 MPa. Reported values of critical interface strengths vary between 1 200 and 2 800 MPa.36,40) The results presented here are in good agreement with the lower value. Tempering strongly decreases the local interface stress so that the material becomes less susceptible to damage. The model predicts that, for the studied alloy, damage by ferrite/martensite interface decohesion should be completely suppressed at tempering temperatures above ~300°C. In summary, at low tempering temperatures σc is high, so the predominant damage mechanism is decohesion at ferrite-martensite boundaries. As the tempering temperature increases above ~300°C, σc decreases to below the critical interface strength and ferrite/martensite decohesion is suppressed. At this point a transition to martensite/carbide decohesion appears to be favoured. An attempt was made to extend the model to include internal martensite damage.9) This was based on the observation by Saeglitz and Krauss41) that the nucleation stress at fracture of low temperature tempered martensite appears to be rather constant with tempering temperature and time. The extension followed the Riedel approach42) to calculate the stresses exerted by a plastically deforming matrix on a brittle inclusion. A fitted Voce model was used to determine the equivalent stress in the matrix as a function of the martensite C content. This could then be used to calculate the critical nucleation strain εn for void formation (assuming a constant nucleation stress) again as a function of the C content. This type of approach is useful to explain the observed macroscopic HE behaviour in DP steels with a martensite matrix as it will always predict that εn decreases as the martensite C content increases. As-quenched steels with high martensite C contents (i.e. lower annealing temperatures) have low εn values and are thus susceptible to damage (low HE ratios). Tempering acts to precipitate carbides and reduce the martensite C concentration so εn increases and the damage resistance is improved (high HE ratio). The difficulty lies in the fact that the experimental observations show that void nucleation at carbides occurs first in lower carbon martensite (Figs. 12(a) and 12(c)). Capturing this behaviour is not possible using a simple mean field approach. More sophisticated modelling techniques coupled with detailed experiments to determine the evolution of the martensite microstructure with tempering (e.g. mean size and fraction of carbides formed, dislocation recovery rates) are required, which are beyond the scope of this work. Now, assuming a constant hardness value for ferrite and substituting the appropriate values for Hvm in equations (Eq. (4)) and (Eq. (5)) Xεn and σeq are calculated for three different experimental martensite fractions fm (62%, 86%, 99%). Substituting these data into Eq. (7) and taking T = 0.33 for uniaxial tension before necking gives Tloc and hence, using equation Eq. (8), the local interface stress σc. The values of Xεn and σc are plotted in Figs. 13(a) and 13(b) respectively as a function of tempering temperature for the three annealing conditions. Figure 13(a) shows that the kinematic hardening Xεn strongly decreases with increasing initial martensite fraction and with tempering temperature. This is in agreement with the work of Zhongua39) on the Bauschinger effect. The experimental HE ratios are superimposed on the same figure. Qualitatively, there appears to be a beneficial correlation between HE and decreasing internal stresses. Reducing Xεn decreases Tloc and thus decreases the interface stress σc which in turn retards the damage initiation and growth process, hence promoting better HE properties. Figure 13(b) shows the evolution of the local ferritemartensite interface stress σc with annealing and tempering temperatures. The major damage mechanism for the 6. Conclusions A systematic and detailed study of the microstructure and mechanical properties of as-quenched and quenched-andtempered dual phase steels with different ferrite/martensite ratios was carried out. It was shown that, at constant composition, the HE ratio of high strength (UTS > 1 000 MPa) Fig. 13. Calculated variation in the a) kinematic hardening X εn and b) interface stress σc at a void nucleation strain ε = εn as a function of tempering temperature (tempering time = 240 s). 2245 © 2015 ISIJ ISIJ International, Vol. 55 (2015), No. 10 Metall. Mater. Trans. A, 40A (2009), 3117. 9) I. Pushkareva: PhD thesis, Institut National Polytechnique de Lorraine, (2009). 10) B. Krebs: PhD thesis, L’Université Paul Verlaine de Metz, (2009). 11) I. Pushkareva, C. P. Scott, M. Gouné, N. Valle, A. Redjaïmia and A. 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Tempering studies showed that, at constant martensite fractions, there was a linear dependence between the HE ratio and the ductile fracture strain, εf, measured on tensile samples. However, when the martensite fraction changed then the correlation coefficient and most notably the offset were strongly altered. Thus it is clear that the HE ratio is microstructure dependent and cannot be predicted by tensile testing alone. In as-quenched samples the main damage mechanism was either decohesion at ferrite/martensite interfaces (for samples containing > 40% ferrite) or cavity formation at martensite/martensite interfaces (for samples containing < 1% ferrite). A significant change in the damage mechanism occurred after tempering. Here voids formed preferentially at carbide/martensite interfaces. A simple model based on Beremin local decohesion criteria was shown to describe qualitatively the transition in damage mechanisms. 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