Influence of Martensite Content and Morphology on Tensile and Impact Properties of High-Martensite Dual-Phase Steels A. BAG, K.K. RAY, and E.S. DWARAKADASA A series of dual-phase (DP) steels containing finely dispersed martensite with different volume fractions of martensite (Vm) were produced by intermediate quenching of a boron- and vanadiumcontaining microalloyed steel. The volume fraction of martensite was varied from 0.3 to 0.8 by changing the intercritical annealing temperature. The tensile and impact properties of these steels were studied and compared to those of step-quenched steels, which showed banded microstructures. The experimental results show that DP steels with finely dispersed microstructures have excellent mechanical properties, including high impact toughness values, with an optimum in properties obtained at ,0.55 Vm. A further increase in Vm was found to decrease the yield and tensile strengths as well as the impact properties. It was shown that models developed on the basis of a rule of mixtures are inadequate in capturing the tensile properties of DP steels with Vm . 0.55. Jaoul–Crussard analyses of the work-hardening behavior of the high–martensite volume fraction DP steels show three distinct stages of plastic deformation. I. INTRODUCTION DUAL-PHASE (DP) steels have a composite microstructure of martensite and ferrite and exhibit a good combination of strength and ductility and a high work-hardening rate. Most of the research work on DP steels conducted so far was directed toward understanding the role of chemistry (primarily, variations in C, Mn, Si, and V) and microstructural variables on the steel’s tensile and formability characteristics.[1,2,3] It is now established that the microstructural parameters of significance are the volume fraction, size, and distribution of the constituent phases. However, most of the research work conducted to date has been focused on microstructures containing a volume fraction of martensite (Vm) less than 0.25.[2,3] The lack of research interest in highVm DP steels can be attributed to the earlier observation that the ductility and impact toughness of these materials degrade rapidly with increasing martensite content above 0.25.[4] The degradation of ductility and impact toughness of highVm-containing DP steels has been attributed to the formation of coarse martensite phases. This observation suggests that it may be possible to improve the ductility and toughness by developing microstructures with very fine grains and a uniform distribution of ferrite and martensite phases. Dualphase steels containing such microstructures are obtained in this work by adopting suitable heat-treatment procedures. The present investigation examines the tensile and impact properties of these steels and compares them to those of conventionally processed DP steel containing coarse or A. BAG, formerly Manager and Head, Materials Science Laboratory, R&D Centre, Bharat Earth Movers Limited, Kolar Gold Fields, 563115 India, is with the School of Mechanical and Production Engineering, Nanyang Technological University, Singapore 639798. K.K. RAY, Professor, is with the Department of Metallurgical and Materials Engineering, Indian Institute of Technology, Kharagpur - 721 302, India. E. S. DWARAKADASA, Professor, is with the Department of Metallurgy, Indian Institute of Science, Bangalore - 560 012, India. Manuscript submitted July 7, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A banded martensite. In particular, this work focuses on understanding the tensile and impact properties of high-martensite (.0.25) DP steels. II. EXPERIMENTAL PROCEDURE A microalloyed steel supplied by Swedish Steel (Oxelosund, Sweden) was selected as the starting material for making DP microstructures. The as-received steel was in the form of 14-mm-thick hot-rolled plates in a quenched and tempered condition. The chemical composition of the steel, determined using various chemical analysis techniques, is shown in Table I. Specimen blanks, 210 3 70 3 14 mm in size, were subjected to either intermediate quench (IQ) or step quench (SQ) heat-treatment schedules. The IQ treatment consisted of a double quench operation; the specimens were first soaked at 920 8C for 30 minutes and were quenched in a 9 pct iced brine solution (27 8C). These were then held at different intercritical temperatures (ICTs) of 730 8C, 740 8C, 760 8C, 780 8C, 800 8C, 820 8C, 840 8C, and 850 8C for 60 minutes and were finally quenched in oil (25 8C). In the SQ treatment, the specimen blanks were first austenitized at 920 8C for 30 minutes, furnace cooled to the required intercritical temperatures (760 8C, 780 8C, 800 8C, and 820 8C), held for 60 minutes, and quenched in oil (25 8C). These heat-treatment procedures are schematically shown in Figure 1. The temperature control for the intercritical soaking treatments was maintained within 62 8C. Precautions were taken to obtain uniformity of cooling during all the quenching operations by continuous stirring of the oil bath. In order to distinguish the specimens subjected to varied heat-treatment schedules, they were identified with code numbers, as described in Table II. These designations are followed in all subsequent discussions. Several stereological measurements were carried out to estimate (1) the volume fraction of inclusion (JIS G0555 standard),[5] (2) the volume fractions of ferrite (Vf) and martensite (using a manual point-counting technique as well as VOLUME 30A, MAY 1999—1193 Table I. Chemical Composition of the Steel (Weight Percent) Elements Wt pct C Mn S P Si Cr Mo V B N 0.16 1.32 0.002 0.013 0.44 0.03 0.09 0.056 0.0019 0.4 Tensile tests were carried out on round specimens with a diameter of 8.75 mm and a gage length of 60 mm. All tests were conducted at room temperature with nominal strain rates of 1023/s using a servohydraulic universal testing machine. Impact tests were carried out on standard Charpy V-notch bars of 55 mm length in the transverse-longitudinal orientation (with respect to the rolling direction). These tests were carried out at room temperature (25 8C) using a standard pendulum-type impact testing machine. Fracture surfaces of the impact and the tensile specimens were coated with gold prior to examining them in a scanning electron microscope. (a) III. RESULTS A. Microstructure (b) Fig. 1—Schematic representation of heat-treatment schedules for (a) IQ and (b) SQ treatments. automatic areal analysis with an image analyzer), (3) the prior austenite grain size (PAGS), using the random intercept method, and (4) the mean free path of ferrite and martensite (lf and lm respectively) by linear-intercept analysis.[6] The amount of retained austenite was estimated by X-ray diffraction analysis. Representative optical microstructures of IQ-conditioned and SQ-conditioned specimens are shown in Figures 2 and 3, respectively. The morphological distribution of constituent phases is similar to those reported for conventional DP steels.[7] The ferrite and martensite in SQ specimens exhibited banded microstructures with blocky regions of the phases (Figure 3). The IQ specimens did not exhibit any banding and the ferritic regions in these specimens appear to be encapsulated by both globular and plate martensite that is finely dispersed. However, the IQ steel containing 0.78 Vm shows coarse martensite (Figure 2(d)). Microstructures prepared at low ICTs show fine particles of undissolved carbides. These precipitates are formed during the reheating process to the ICT, wherein the quenched martensite gets tempered, then partly dissociates into ferrite plus carbide, and then reverts to the ferrite, austenite, and undissolved carbide upon reaching the ICT. Upon quenching from the ICT after the 1-hour holding, the austenite transforms to ferrite and martensite. The amount of carbides decreases from the A73 (Figure 2(a)) through A76 (Figure 2(b)) specimens and such carbides are not present in specimens A80 through A84, as shown in Figures 2(c) and 2(d). Table II. Heat-Treatment Schedules for Achieving Varied DP Structures Type of Heat Treatment Intermediate quenching Step quenching 1194—VOLUME 30A, MAY 1999 Specimen Code A73 A74 A76 A78 A80 A82 A84 A85 B76 B78 B80 B82 Austenitizing Treatment for 30 Min at 920 8C Followed by Cooling in iced-brine solution furnace Intercritical Soaking Temperature (8C) for 60 Min 730 740 760 780 800 820 840 850 760 780 800 820 Final Cooling Media oil METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 2—Typical optical micrographs of IQ-treated DP steels showing distribution of martensite (black needle/block), undissolved carbide (black dot), and ferrite (white). Micrographs (a), (b), (c), and (d ) correspond to the microstructures obtained with ICT at 730 8C, 760 8C, 800 8C, and 840 8C, respectively. Thus, the amount of carbides in the ferritic regions bears a distinct relation to the temperature of intercritical treatments. The average volume fraction of inclusions in steel was found to be ,0.3 pct. The volume fractions of sulfide and oxide inclusions were estimated separately and found to be 0.07 and 0.24 pct, respectively. The sulfide inclusions were found to be elongated in nature, indicating the rolled condition of the virgin steel plate. The microstructures of both the IQ and SQ specimens were found to contain 2 to 3 pct retained austenite. Dualphase steels often contain retained austenite in addition to ferrite and martensite. The presence of this phase in small percentages in different microstructures is not expected to influence the mechanical properties. The PAGS on the transverse and longitudinal directions was almost identical in nature, and the average value was found to be 11.04 6 4.67 mm, which corresponds to the ASTM grain-size number of ,10. The dependence of martensite content on ICT is shown in Figure 4; the Vm increases approximately linearly with increasing ICT. The mean free path of ferrite and the mean free path of martensite in IQ steel specimens are shown in Figure 5 as a function of Vm. As expected, lf decreases, whereas lm increases, with increasing Vm. These variations are observed to obey power law–type relationships (Figure 5) It is noted here that the lf and lm values in the IQ steels are at least one order of magnitude less than those in the SQ steels. METALLURGICAL AND MATERIALS TRANSACTIONS A B. Tensile Properties The variation in the yield strength (sy) and ultimate tensile strength (st) of IQ and SQ steels with Vm are shown in Figure 6(a). The values of the uniform elongation (Dlu) and the total elongation (Dlt) are given in Figure 6(b). Each data point in Figures 6(a) and (b) represents the average values obtained from three specimens. The scatter (above the mean) in experimental data is found to be well within 3 pct. As seen from Figures 6(a) and (b), the tensile strength of the IQ steels increases with increasing Vm, peaking at around ,0.55 Vm, and then gradually decreasing with a further increase in Vm. The yield strength appears to reach a plateau above ,0.5 Vm. However, a sharp increase in the sy and st of IQ steel with 0.78 Vm, vis-à-vis those of ,0.6 Vm steel, is noticeable, whereas its ductility (as characterized by Dlu and Dlt) decreases substantially. In contrast to the IQ steels, sy increases, whereas st remains approximately constant with increasing Vm in SQ steels (Figure 6(a)). Commensurately, the uniform elongation decreases, whereas the total elongation remains constant (Figure 6(b)). When compared to the IQ steels of similar Vm, the SQ steels have higher strength but lower ductility. Clearly, these results indicate that steels containing either coarse (as in 0.78 Vm IQ steels) or banded (as in all the SQ steels examined) martensitic structures will have inferior ductility to the DP steels containing finely dispersed martensite. VOLUME 30A, MAY 1999—1195 Fig. 3—Typical optical micrographs of SQ-treated DP steels showing banded microstructure with blocky martensite (black) and ferrite (white) phases. Micrographs (a), (b), (c), and (d ) correspond to the microstructures obtained with ICT at 760 8C, 780 8C, 800 8C, and 820 8C, respectively. Fig. 4—Volume fraction of martensite as a function of ICT for IQ- and SQ-conditioned DP steels. C. Impact Toughness The values of average Charpy V-notched impact energy (Gc) of the IQ and SQ specimens were plotted against the martensite content in Figure 7. For the case of IQ steel, the Gc value increases with increasing Vm, peaks around ,0.55 Vm, and then decreases. This result is in agreement with the trends in the tensile properties of these steels. The lower toughness for specimens containing Vm , 0.5 is due to 1196—VOLUME 30A, MAY 1999 Fig. 5—Mean free path of ferrite and martensite as a function of volume fraction of martesite for IQ-treated steels. relatively coarser ferrite with carbide precipitates, whereas, for Vm . 0.6, the low Gc value is due to coarser martensite. The range of Vm over which high values of Gc are measured corresponds to the microstructure comprised mostly of refined ferrite and martensite (as shown in Figure 2) without any carbide precipitation in ferrite. Hence, it can be concluded that higher toughness values in IQ specimens are associated with finer martensite and finer precipitate-free METALLURGICAL AND MATERIALS TRANSACTIONS A (a) Fig. 8—Scanning electron fractographs of IQ-treated DP steels showing (a) predominantly cleavage fracture at low Vm (Vm 5 0.38) and (b) dimple fracture at high Vm (Vm 5 0.6). (b) Fig. 6—(a) Strength and (b) percentage of elongation as a function of volume fraction of martensite for IQ- and SQ-conditioned DP steels. that IQ steels with very high Vm do not have favorable mechanical properties. From Figure 7, it is seen that the impact toughness of the SQ specimens (7 to 20 J for 0.45 , Vm , 0.66) is much inferior to the IQ specimens with a similar Vm. An interesting observation that can be made from Figure 7 is that the Gc of the SQ specimens also increases approximately linearly with increasing Vm. This is in contradiction to some of the previous reports, wherein a steep drop in Gc values was observed for DP steels with a Vm higher than ,0.15.[7] Because of the observation of significantly lower Gc values of SQ steels compared to those of the IQ steels, we have not conducted any further investigation to explore the mechanical behavior of SQ steels. D. Fractography Fig. 7—Charpy impact energy vs volume fraction of martensite for IQand SQ-conditioned DP steels. ferrite. The present observations are in agreement with the hypothesis of Kang and Kwon[4] that fine distribution of martensite enhances toughness of DP steels. When the matrensitic content is increased from ,0.6 to ,0.78, a sharp drop in measured impact energy is noticeable. This observation, in combination with that of the tensile results, indicates METALLURGICAL AND MATERIALS TRANSACTIONS A Scanning electron micrographs of fractured tensile IQ specimens containing a Vm of 0.38 and 0.6 are shown in Figures 8(a) and (b), respectively. These fractographs depict predominantly cleavage fracture at a low Vm (Figure 8(a)) and predominantly dimpled fracture at a high Vm (Figure 8(b)). The change in fracture morphologies with Vm is in general agreement with the variation in ductility with Vm. Previous works[7,8] on fractographic observations of DP steels indicate that, during tensile deformation, ferrite deforms first and facilitates the nucleation of cracks either at precipitates present in it or at ferrite-martensite interfaces. Subsequently, these cracks propagate either by cleavage or VOLUME 30A, MAY 1999—1197 dimple mode, depending on the state of stress present in the microstructure. In the IQ steels, the ferrite was found to be dispersed with fine carbide precipitates for Vm , 0.45. Hence, crack initiation in these microstructures can be considered to take place predominantly at the precipitates. Stress-controlled growth of the cracks within the ferrite phase, favored by high internal stresses, leads to cleavage fracture. The crack initiation sites for a Vm of around 0.5 are considered to be located at the ferrite-martensite interfaces, because of the absence of precipitates in this microstructure. In addition, since the internal stresses in these microstructures are of low magnitudes, the nucleated cracks grow in a stable manner, leading to larger dimple sizes. As the martensite content increases further, the number of crack nucleation sites increases, but the growth of these cracks depends on the local stress state. At a very high Vm, the number of crack initiation sites is large, and the stress distribution in the microstructure is uniform. This results in a larger number of fine dimples Figure 8(b)). Finally, it is noted that fractographic observations on SQ specimens indicate extensive cleavage regions that are almost identical to those reported in literature for such steels. IV. DISCUSSION A. Evolution of Microstructures The morphology and dispersion of the martensite in the IQ heat-treated microstructure depends on the process of reversion of austenite from the initial tempered martensite. The nucleation of austenite from the tempered martensite can occur at different sites, such as (1) the prior austenite grain boundaries, (2) the carbide precipitates on prior austenite grain boundaries, (3) the spheroids in ferrite, and (4) the fine carbide arrays formed on the prior martensitic plate/ lath boundaries. The morphology of the ferritic and martensitic regions in the SQ specimens depends on the formation of ferritic regions in the austenitic matrix while cooling from 920 8C to the ICT. The nucleation of ferrite starts at austenite grain boundaries, and these nuclei grow inside the austenite matrix to yield distinct regions of ferrite. On quenching from ICT, austenite transforms to martensite, and the domain boundaries of austenite get transferred to the product phase. The resultant martensite can have both plate and lath morphology, the latter being predominant in specimens treated at lower intercritical temperatures. The starting configurations of the austenitic domains, thus, lead to the varied morphologies of martensite in the DP microstructures processed via the IQ and SQ routes. The problem of banding does not appear in the IQ-treated samples, because of the existence of a large number of different types of nucleation sites for austenite in the martensitic microstructure. B. Yield and Tensile Strengths The variation in tensile strength of DP steels, in terms of the martensite content, has been empirically modeled in earlier investigations,[9,10,11] formulated on the basis of the rule of mixtures, st 5 stf(1 2 Vm) 1 stmVm 1198—VOLUME 30A, MAY 1999 [1] where stf and stm are the tensile strengths of the ferrite and the martensite, respectively. If stf and stm are assumed to be invariant with respect to the amount, nature, and morphology of the respective phases, Eq. [1] predicts a linear relation between st and Vm. On comparison, the experimental results obtained in this work appear to agree with the suggested empirical expression of Byun and Kim,[11] up to a Vm of ,0.5. However, they do not obey any of the predicted trends above 0.5 Vm. Beyond this level of Vm, the experimental results show that the tensile strength decreases with increasing martensite content, whereas the models predict increasing strengths. Chang and Preban[12] proposed an alternate model to explain the variation between sy and Vm. In their model, they determined that the mean free path of ferrite will influence sy through a Hall–Petch-type expression, sy 5 s0y 1 Kyl21/2 f [2] where s0y is a reference frictional stress and Ky is the dislocation-locking constant. Both soy and Ky are functions of Vm. Calculated results of sy vs Vm, following the work of Chang and Preban,[12] show reasonable agreement with the current experimental results on IQ steels, but again, only up to a Vm of 0.5. This model predicts an increasing sy value with a Vm above 0.5, whereas the experimental results on the IQ indicate a plateau in sy. In contrast to the trends in IQ steels, the behavior of SQ steels can be explained in a rather straightforward manner using a unidirectional composite analogy (wherein the elastic modulus of the fibers and the matrix are the same). Since the yielding of ferrite dominates the yield strength of SQ steels tested along the rolling direction, a decrease in lf with increasing Vm leads to higher sy (according to Eq.[2]). This rationalizes the experimental trends in sy. Similarly, the independence of tensile strength of the SQ DP steels with Vm can be rationalized if we assume that the strength of martensite dominates the overall strength of DP steels and that the martensite strength remains invariant with lm (in particular, because of the very high values of lm). However, the trends in the properties of IQ steels cannot be rationalized using the composite analogy or any of the models that are available in the literature. An examination of the earlier modeling work indicates the following complexities in understanding the stress-strain behavior of DP steels. (1) Chang and Preban[12] emphasize that the prediction of strength (both yield and tensile) values of DP steels should incorporate their dependence on the mean free path of ferrite. This contention is based on the assumption that plastic deformation in DP steels remains primarily confined to the ferritic regions. On the contrary, in-situ observation of tensile fracture in DP steels by Su et al.[13] shows necking of martensitic region, indicating that plastic deformation of martensite is also important. Despite this observation, the influence of the mean free path of martensite on the st-Vm relations has not been understood yet. Balliger and Gladman[14] indicated this possibility in their analysis conducted following Ashby’s report.[15] (2) The strength-microstructure relations in DP steels have often been treated with a continuum-mechanics approach with isostress[16] or isostrain analysis.[17] These METALLURGICAL AND MATERIALS TRANSACTIONS A models may be suitable, to some extent, for DP steels containing dilute concentrations of martensite and when the microstructure resembles that of fiber-reinforced composites with nondeformable fibers and a continuous matrix. For conventional DP steels prepared by the SQ route, which usually contain a banded structure, or DP steels with dilute martensitic contents (Vm , 0.25), the applicability of these models could be satisfactory. But DP steels prepared by the IQ route and with a higher Vm neither exhibit a banded microstructure nor show any continuous matrix of ferrite, especially for Vm . 0.5. Hence, the applicability of simple continuum mechanics–based analyses to predict st as a function of Vm for IQ specimens could be questionable. (3) Araki et al.[18] formulated theoretical equations based on continuum mechanics to describe the flow stress of DP steels, emphasizing its work-hardening behavior and considering martensite as a ductile phase. These investigators found that such theoretical equations are applicable only up to Vm ' 0.2. If the DP steel is considered as a mixture of two ductile phases, several other phenomena such as unrelaxed plastic incompatibility, plastic relaxation, and yielding of martensite need to be incorporated.[19,20,21] This is in addition to the appropriate considerations of stress and strain partitioning during deformation.[11] Bhattacharyya et al.[22] have considered additional factors like the shape of martensite and thermal mismatch between the phases of a DP steel in order to predict the stress-strain response of DP steels more accurately. However, their work does not suggest any relation between sy vs Vm in DP steels, but only points to some important additional factors which were not considered by the earlier investigators for explaining the deformation response. (4) Kim[23] considered the internal stresses developed during deformation and formed during transformation of austenite to martensite in DP steels, in order to formulate an analytical model based on a continuum-mechanics approach. This model also predicts a continuous increase of the strength of DP steel with an increase in Vm and cannot explain the present results. Byun and Kim[11] made a similar analysis of stress-strain behavior of DP steels, which considered inhomogeneous distribution of stress and strain in the ferrite and martensite phases of DP steels. The previous discussion leads to the conclusion that there are several factors that need to be taken into account to predict the tensile and yield strengths of DP steels in a generalized manner. From this discussion, it is obvious that the strength of ferrite and martensite are not unique values over any range of Vm but are functions of the chemistry, shape, and contiguity of phases; of the internal stresses due to phase transformation and plastic incompatibility; and of the precipitate volume fraction, etc. Developing a generalized theoretical model that incorporates all these factors is a difficult task. A simplifying assumption that can be made is that the mean free path (l) is the single most significant factor of all the independent variables, influencing the tensile and the yield strengths. This assumption is based on the observation that the development and distribution of all types of stresses in ferrite or martensite in a DP steel depend on this parameter. Since l is governed by the amount and the METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 9—Variation of yield strength with respect to mean free path of martensite in log-log scale. distribution of the phases in a two-phase alloy, it can be considered jointly with Vm to construct a model to describe the tensile properties of DP steels. Secondly, it is important to treat both the phases in a DP steel as deformable, contributing to the overall sy and st characteristics of the steel. Following the aforementioned assumption, a fundamental understanding of the variations of sf(lf) and sm(lm) is required to develop suitable models. Unfortunately, very little is now known about sf(lf) and sm(lm) when internal stresses are present. In the absence of such data, it can be assumed, with a reasonable degree of accuracy, that sf(lf) and sm(lm) follow a Hall–Petch kind of relationship such as the one given in Eq. [2]. This simplification emerges from the fact that finer microstructural constituents usually lead to higher strength. Many studies on the grain size or mean free path dependence of the strength of ferrite in polycrystalline iron or mild steel have shown such a relationship to be valid. Contradictory views also exist about the choice of the exponent for l; that of 20.5 is debatable. For example, Hansen[24] has indicated the possibility of this exponent ranging from 20.5 to 1. Further, in fine lamellar structures, a series of investigations[25,26] indicate that strength is more meaningfully expressed by a l21 type dependence. Observation of Figure 5 indicates that lf decreases with increasing Vm and appears to reach a steady-state value between 0.5 and 0.6 Vm. Similarly, Figure 6(a) indicates that a steady value in sy is reached for the same range in Vm. Guided by this observation, the variation in log sy is plotted against log lf in Figure 9. It can be seen that a power-law relation between sy and lf exists, implying that yielding of ferrite determines the yield strength of the DP steels. This observation is physically meaningful since ferrite has a significantly lower yield strength than that of martensite. However, the experimental results suggest that the power-law exponent is ,20.25 and not 20.5 (Eq. [2]), as used by Chang and Preban.[12] However, a mechanistic understanding of the observed exponent is yet to be developed. Attempts were made to rationalize the experimental trends in st vs Vm using simple relations such as the rule of mixtures (both the upper-and lower- bound analysis with isostrain or isostress assumptions, respectively, were conducted). The calculations performed always show an increasing value of st with increasing Vm, depending on the constituent properties used. At best, these calculations predict properties to VOLUME 30A, MAY 1999—1199 reach a steady-state value; however, the constants extracted are not physically meaningful. An increasing and then decreasing trend has never been able to be simulated using this approach. These computations, albeit unsuccessful, led to the conclusion that the rule of mixtures cannot be applied to predict the strength of high-martensite-containing DP steels having contiguous and complex microstructures. More-sophisticated methodologies are required to predict trends that match the experiments. Further efforts are underway in this direction. C. Ductility The ductility of the DP microstructures has been examined in terms of the uniform elongation and the total elongation (Figure 6(b)). Most of the previous observations on the ductility of DP steels indicate that both Dlu and Dlt decrease with Vm. Davies[9] has shown that, with an increase in Vm, Dlu decreases rapidly up to about Vm ' 50 and that, above Vm ' 50, the rate of decrease substantially reduces. Davies has supported this observation using the theories of Mileiko[27] and Garmong and Thompson[28] to describe the mechanical properties of fiber composites made of two ductile phases. Marder[29] observed a linear variation between Dlu and Vm and explained his results using the isostress analysis of Speich and Miller.[17] Jiang et al.[30] developed an expression for Dlt in terms of Vm, considering the twostage work-hardening behavior of DP steels, and suggested a nonlinear monotonic variation between these parameters. The observation of a maximum in Dlu at Vm , 40 for a predeformed DP steel by Liu et al.[31] indicates a trend that is intermediate between the predictions of Marder[10] and Jiang et al. These investigators suggest that the type of martensite present dictates the ductility of DP steels (twinned vs lath) and conclude that a finer microstructure exhibits higher ductility. The explanation rendered by Fan and Miodownik[32] for the variation of Dlu and Dlt with Vm is significantly different from those described in the preceding paragraph. Using topographic transformation and a three-microstructural-element body, these investigators suggested that Dlt can be expressed as m 21/4 m Dlt 5 (Dlf0 1 K fl21/4 )F f 1 (Dl m f 0 1 K lm )F fm 21/4 fm 1 (Dl fm 0 1 K lfm )F [3] m 21/4 fm where (Dl f0 1 K fl21/4 ), (Dl m 1 f 0 1 K lm ), and (Dl 0 ) control the ductility of the predominantly ferritic, K fml21/4 fm martensitic, and ferrito-martensitic topographical regions of the DP microstructures, and F f, F m, and F fm represent parameters related to the different regions. The suffixes f, m, and fm represent the ferrite, martensite, and ferrito-martensitic domains, respectively. Using the empirical Eq. [3], Fan and Miodownik[32] demonstrated that Dlt exhibits a minimum in its variation with Vm at around Vm , 0.6; such a description closely describes several published results.[33,34,35] The present observation of the variation of Dlt with Vm is exactly opposite the trend predicted by using the parameters given by Fan and Miodownik. The experimental trends in Dlu and Dlt with Vm observed in the present investigation are in agreement only with that reported by Liu et al.[31] The microstructures of IQ steels in this work are very fine, with lf and lm in the range from 1 1200—VOLUME 30A, MAY 1999 to 3 mm for 0.33 , Vm , 0.77. If we assume that it is essential for both lf and lm to be fine for the DP steel to show the highest ductility, a microstructure containing a Vm , 0.55 should show a maximum in Dlu and Dlt, because lf and lm are minimum for this composition (,1.0 mm). Away, from Vm , 0.55, either lf or lm increases and causes Dlu and Dlt to decrease. It is interesting to note that the analysis of Byun and Kim[11] is in reasonable agreement with the present experimental trends. They have analyzed the long-range internal stresses arising from unrelaxed plastic incompatibility in DP microstructures and hypothesized that the average of internal stresses over the composite volume of DP microstructures for Vm , 0.5 is zero. Hence, one can expect a higher Dlu and Dlt at this microstructural state. This explanation appears to satisfactorily rationalize the present maxima of Dlu and Dlt in its variation with Vm, but fails to explain the previous results on conventional DP steels. An additional condition that is required to be satisfied is for the average internal stresses to be zero only when the magnitudes of the internal stresses in ferrite and martensite are equal (signs being opposite). Such a situation would require a finer distribution of the phases of a DP steel. In most of the previous reports on conventional DP steels, the microstructures do not represent this distribution and, hence, the contention of Byun and Kim fails. D. Work-Hardening Behavior Early work[9,36,37] on the work-hardening behavior of DP steels contended that the flow stress of these materials obeys the Hollomon’s equation, which is commonly used to analyze the work-hardening behavior of metallic materials (especially to cross-check the magnitude of uniform elongation), s 5 K«n [4] where s and « are the true stress and true strain, respectively; n is the work-hardening exponent; and K is the strength coefficient. The condition of tensile instability indicates that Dlu should be equal to n if the work hardening of the material can be expressed by an average value for any tensile deformation between yield and maximum load. The computed values of n and Dlu are plotted in Figure 10 against Vm. It is noted from this figure that, except for Fig. 10—Variation of strain-hardening exponent (n) and uniform strain as a function of volume percentage of martensite for IQ-conditioned DP steels. METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 11—Typical log-log plots of true stress vs true strain for estimated strain-hardening exponent (n) for IQ-treated steels. the case of Vm 5 0.64, the values of n are always significantly higher than Dlu. This observation is in contradiction to that of Davies,[9] who has reported a good agreement between n and Dlu. This observed deviation can be attributed either to a nonlinear variation of ln s with ln « or to the possibility of different stages of work hardening. Typical plots of ln s vs ln« are shown in Figure 11, and these indeed reflect a nonlinear variation between ln s and ln «. Several previous investigators[17,38–40] indicated that workhardening behavior in the DP steels occurs in three different stages. This is revealed by the Jaoul–Crussard (J–C) analyses, which are based on the following two equations:[30,40] s 5 s0 1 K 8«n8 [5] n9 [6] « 5 «0 1 K9s where s0 and «0 are reference true stress and true strain, respectively. Differentiating the previous equations with respect to « and expressing in logarithmic forms, we get ln 1d«2 5 ln K 8 1 ln n8 1 (n8 2 1) ln « [7] 1d«2 5 (1 2 n8) ln s 2 ln (K9n9) [8] ds and ln ds respectively. Analyses of true stress–strain data using Eqs. [7] and [8] are referred to as the J–C analysis and modified J–C analysis, respectively. Using both these analyses, Samuel[40] has been able to reveal the three stages of work hardening in DP steels. These stages of work hardening in DP steels have been attributed[17,38–40] to the following mechanisms of deformation. (1) Stage I consists of homogeneous deformation of the ferrite matrix by the glide of mobile dislocations present near the martensitic regions. (2) Stage II covers a diminished work hardening with constrained ferrite deformation and with possible transformation of retained austenite to martensite. (3) Stage III consists of ferrite deformation with attendant METALLURGICAL AND MATERIALS TRANSACTIONS A Fig. 12—Crussard–Jaoul plot of ds/d« vs strain (in logarithmic scale) to reveal various stages of work hardening. cross-slip and dynamic recovery together with martensitic deformation. However, using the modified J–C analysis, Jiang et al.[30] observed only two stages of work-hardening behavior in steels containing Vm . 0.3. Experimental results obtained in the present work were subjected to both the J–C and modified J–C analyses. Typical results are presented in Figure 12. These plots indicate that the flow-stress behavior of the high-Vm DP steels can be described using a three-stage work-hardening behavior. All the present results are obtained on DP microstructures containing Vm . 0.33. Hence, the observed three stages may be due to different work-hardening mechanisms associated with the finer distribution of constituent phases. It is hypothesized that the results can be rationalized with the following deformation mechanisms. (1) Stage I is due to homogeneous deformation of ferrite. The rate of work hardening is high in this stage when Vm , 0.5, because undissolved carbide particles impede the glide of dislocations in the ferrite phase. The possibility of martensite deformation is not ruled out. (2) Stage II is due to a condition of going through minimum plastic incompatibility, resulting in lower internal stresses and, thus, enhancing easy flow of dislocations. (3) Stage III consists of simultaneous deformation of ferrite and martensite associated with dynamic recovery. Specific evidence has not been obtained to support the previous hypothesis; however, some experimental observations extend support to this view.[41] First, the slope of the ln ds/d« vs ln « plots in stage I, for the A73 through A78 specimens, are lower than the slopes for the A80 through A84 specimens. This observation implies a higher work-hardening rate in stage I for samples containing a lower Vm than for those containing a higher Vm. Lower work-hardening rates with higher Vm are attributed to an ease of the dislocation flow, owing to the absence of barriers such as the undissolved carbide particles. Secondly, the slope of ln ds/d« vs ln « in stage I and stage III, for specimens containing a higher Vm, are similar. This VOLUME 30A, MAY 1999—1201 is indicative of simultaneous deformation of both the phases. The presence of stage II may be due to dynamic changes of internal stresses during plastic deformation; however, no conclusive support could be obtained to explain this stage of deformation in an appropriate manner. V. CONCLUSIONS On the basis of the experimental work that has been carried out and presented in this article, the following conclusions can be drawn. 1. Dual-phase steels containing approximately equal amounts of finely dispersed ferrite and martensite phases exhibit the optimum combinations of high strength and ductility with high impact toughness. 2. The impact toughness values of DP steels with finely dispersed constituents are much superior to those with a coarse or banded martensite and exhibit a peak for a Vm of 0.5 to 0.6. Higher toughness values in IQ specimens are associated with finer martensite and finer precipitatefree ferrite. 3. The variation in tensile properties, such as the yield and tensile strength, and ductility with martensite content in the IQ steels exhibit an unusual nature. The peak in tensile properties emerges due to finer microstructural constituents and due to the possible absence of average internal stress over the composite microstructure volume. 4. The calculated work-hardening exponent differs significantly from the uniform elongation obtained from the true stress–true strain curves. This deviation is due to the presence of three stages of work-hardening during plastic deformation with different work-hardening rates. ACKNOWLEDGMENTS This work was carried out at Bharat Earth Movers Limited (BEML) as part of AB’s Ph.D. thesis dissertation with the Indian Institute of Technology (Kharagpur, India). AB is grateful to the management of BEML for support rendered during the course of this work. AB also appreciates the help of Dr. U. Ramamurty for redrawing the graphs. REFERENCES 1. 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Lagneborg: Dual-Phase and Cold Pressing Vanadium Steels in the Automobile Industry, Vanitec, Berlin, 1978, p. 43. 38. G.R. Speich: in Fundamental of Dual-Phase Steels, R.A. Kot and B.L. Bramfitt, eds., AIME, New York, NY, 1981, p. 3. 39. J.M. Rigsbee, J.K. Abraham, A.T. Davenport, J.E. Franklin, and J.W. Pickens: in Structure and Properties of Dual-Phase Steels, R.A. Kot and J.W. Morris, eds., AIME, New York, NY, 1979, p. 304. 40. F.H. Samuel: Mater. Sci. Engg., 1987, vol. 92, pp. L1-L4. 41. A. Bag: Ph.D. Dissertation, IIT, Kharagpur, India, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS A