Influence of martensite content and morphology on tensile and impact properties of high-martensite dual-phase steels

Influence of Martensite Content and Morphologyon Tensile and Impact Properties of High-MartensiteDual-Phase Steels

A. BAG, K.K. RAY, and E.S. DWARAKADASA

A series of dual-phase (DP) steels containing finely dispersed martensite with different volumefractions of martensite (Vm) were produced by intermediate quenching of a boron- and vanadium-containing microalloyed steel. The volume fraction of martensite was varied from 0.3 to 0.8 bychanging the intercritical annealing temperature. The tensile and impact properties of these steelswere 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 excellentmechanical properties, including high impact toughness values, with an optimum in properties obtainedat ,0.55 Vm. A further increase in Vm was found to decrease the yield and tensile strengths as wellas the impact properties. It was shown that models developed on the basis of a rule of mixtures areinadequate in capturing the tensile properties of DP steels with Vm . 0.55. Jaoul–Crussard analysesof the work-hardening behavior of the high–martensite volume fraction DP steels show three distinctstages of plastic deformation.

I. INTRODUCTION banded martensite. In particular, this work focuses on under-standing the tensile and impact properties of high-martensiteDUAL-PHASE (DP) steels have a composite micro-(.0.25) DP steels.structure of martensite and ferrite and exhibit a good combi-

nation of strength and ductility and a high work-hardeningrate. Most of the research work on DP steels conducted so II. EXPERIMENTAL PROCEDUREfar was directed toward understanding the role of chemistry(primarily, variations in C, Mn, Si, and V) and microstruc- A microalloyed steel supplied by Swedish Steel (Oxelo-

sund, Sweden) was selected as the starting material for mak-tural variables on the steel’s tensile and formability charac-teristics.[1,2,3] It is now established that the microstructural ing DP microstructures. The as-received steel was in the

form of 14-mm-thick hot-rolled plates in a quenched andparameters of significance are the volume fraction, size, anddistribution of the constituent phases. However, most of tempered condition. The chemical composition of the steel,

determined using various chemical analysis techniques, isthe research work conducted to date has been focused onmicrostructures containing a volume fraction of martensite shown in Table I. Specimen blanks, 210 3 70 3 14 mm in

size, were subjected to either intermediate quench (IQ) or(Vm) less than 0.25.[2,3] The lack of research interest in high-Vm DP steels can be attributed to the earlier observation that step quench (SQ) heat-treatment schedules. The IQ treatment

consisted of a double quench operation; the specimens werethe ductility and impact toughness of these materials degraderapidly with increasing martensite content above 0.25.[4] first soaked at 920 8C for 30 minutes and were quenched

in a 9 pct iced brine solution (27 8C). These were then heldThe degradation of ductility and impact toughness of high-Vm-containing DP steels has been attributed to the formation at different intercritical temperatures (ICTs) of 730 8C, 740

8C, 760 8C, 780 8C, 800 8C, 820 8C, 840 8C, and 850 8C forof coarse martensite phases. This observation suggests thatit may be possible to improve the ductility and toughness 60 minutes and were finally quenched in oil (25 8C). In the

SQ treatment, the specimen blanks were first austenitizedby developing microstructures with very fine grains and auniform distribution of ferrite and martensite phases. Dual- at 920 8C for 30 minutes, furnace cooled to the required

intercritical temperatures (760 8C, 780 8C, 800 8C, and 820phase steels containing such microstructures are obtained inthis work by adopting suitable heat-treatment procedures. 8C), held for 60 minutes, and quenched in oil (25 8C). These

heat-treatment procedures are schematically shown in FigureThe present investigation examines the tensile and impactproperties of these steels and compares them to those of 1. The temperature control for the intercritical soaking treat-

ments was maintained within 62 8C. Precautions were takenconventionally processed DP steel containing coarse orto obtain uniformity of cooling during all the quenchingoperations by continuous stirring of the oil bath. In order todistinguish the specimens subjected to varied heat-treatment

A. BAG, formerly Manager and Head, Materials Science Laboratory,schedules, they were identified with code numbers, asR&D Centre, Bharat Earth Movers Limited, Kolar Gold Fields, 563115described in Table II. These designations are followed in allIndia, is with the School of Mechanical and Production Engineering, Nan-

yang Technological University, Singapore 639798. K.K. RAY, Professor, subsequent discussions.is with the Department of Metallurgical and Materials Engineering, Indian Several stereological measurements were carried out toInstitute of Technology, Kharagpur - 721 302, India. E. S. DWARAKA- estimate (1) the volume fraction of inclusion (JIS G0555DASA, Professor, is with the Department of Metallurgy, Indian Institute

standard),[5] (2) the volume fractions of ferrite (Vf) and mar-of Science, Bangalore - 560 012, India.Manuscript submitted July 7, 1998. tensite (using a manual point-counting technique as well as

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 30A, MAY 1999—1193

Table I. Chemical Composition of the Steel (Weight Percent)

Elements C Mn S P Si Cr Mo V B N

Wt pct 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 adiameter of 8.75 mm and a gage length of 60 mm. All testswere conducted at room temperature with nominal strainrates of 1023/s using a servohydraulic universal testingmachine. Impact tests were carried out on standard CharpyV-notch bars of 55 mm length in the transverse-longitudinalorientation (with respect to the rolling direction). These testswere carried out at room temperature (25 8C) using a standardpendulum-type impact testing machine. Fracture surfaces ofthe impact and the tensile specimens were coated with goldprior to examining them in a scanning electron microscope.

(a)III. RESULTS

A. Microstructure

Representative optical microstructures of IQ-conditionedand SQ-conditioned specimens are shown in Figures 2 and3, respectively. The morphological distribution of constituentphases is similar to those reported for conventional DPsteels.[7] The ferrite and martensite in SQ specimens exhib-ited banded microstructures with blocky regions of thephases (Figure 3). The IQ specimens did not exhibit anybanding and the ferritic regions in these specimens appearto be encapsulated by both globular and plate martensitethat is finely dispersed. However, the IQ steel containing0.78 Vm shows coarse martensite (Figure 2(d)).

(b) Microstructures prepared at low ICTs show fine particlesFig. 1—Schematic representation of heat-treatment schedules for (a) IQ of undissolved carbides. These precipitates are formed dur-and (b) SQ treatments. ing the reheating process to the ICT, wherein the quenched

martensite gets tempered, then partly dissociates into ferriteplus carbide, and then reverts to the ferrite, austenite, andundissolved carbide upon reaching the ICT. Upon quenchingautomatic areal analysis with an image analyzer), (3) the

prior austenite grain size (PAGS), using the random intercept from the ICT after the 1-hour holding, the austenite trans-forms to ferrite and martensite. The amount of carbidesmethod, and (4) the mean free path of ferrite and martensite

(lf and lm respectively) by linear-intercept analysis.[6] The decreases from the A73 (Figure 2(a)) through A76 (Figure2(b)) specimens and such carbides are not present in speci-amount of retained austenite was estimated by X-ray diffrac-

tion analysis. mens A80 through A84, as shown in Figures 2(c) and 2(d).

Table II. Heat-Treatment Schedules for Achieving Varied DP Structures

Austenitizing Treatment IntercriticalType of Heat for 30 Min at 920 8C Soaking Temperature Final Cooling

Treatment Specimen Code Followed by Cooling in (8C) for 60 Min Media

Intermediate quenching A73 iced-brine solution 730 oilA74 740A76 760A78 780A80 800A82 820A84 840A85 850

Step quenching B76 furnace 760B78 780B80 800B82 820

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Fig. 2—Typical optical micrographs of IQ-treated DP steels showing distribution of martensite (black needle/block), undissolved carbide (black dot), andferrite (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 B. Tensile Propertiesdistinct relation to the temperature of intercritical treatments.

The variation in the yield strength (sy) and ultimate tensileThe average volume fraction of inclusions in steel was foundstrength (st) of IQ and SQ steels with Vm are shown into be ,0.3 pct. The volume fractions of sulfide and oxideFigure 6(a). The values of the uniform elongation (Dlu) andinclusions were estimated separately and found to be 0.07the total elongation (Dlt) are given in Figure 6(b). Each dataand 0.24 pct, respectively. The sulfide inclusions were foundpoint in Figures 6(a) and (b) represents the average valuesto be elongated in nature, indicating the rolled condition ofobtained from three specimens. The scatter (above the mean)the virgin steel plate.in experimental data is found to be well within 3 pct. AsThe microstructures of both the IQ and SQ specimensseen from Figures 6(a) and (b), the tensile strength of thewere found to contain 2 to 3 pct retained austenite. Dual-IQ steels increases with increasing Vm, peaking at aroundphase steels often contain retained austenite in addition to,0.55 Vm, and then gradually decreasing with a furtherferrite and martensite. The presence of this phase in smallincrease in Vm. The yield strength appears to reach a plateaupercentages in different microstructures is not expected toabove ,0.5 Vm. However, a sharp increase in the sy and stinfluence the mechanical properties. The PAGS on the trans-of IQ steel with 0.78 Vm, vis-a-vis those of ,0.6 Vm steel,verse and longitudinal directions was almost identical inis noticeable, whereas its ductility (as characterized by Dlunature, and the average value was found to be 11.04 6 4.67and Dlt) decreases substantially.mm, which corresponds to the ASTM grain-size number

In contrast to the IQ steels, sy increases, whereas stof ,10.remains approximately constant with increasing Vm in SQThe dependence of martensite content on ICT is shownsteels (Figure 6(a)). Commensurately, the uniform elonga-in Figure 4; the Vm increases approximately linearly withtion decreases, whereas the total elongation remains constantincreasing ICT. The mean free path of ferrite and the mean(Figure 6(b)). When compared to the IQ steels of similarfree path of martensite in IQ steel specimens are shown inVm, the SQ steels have higher strength but lower ductility.Figure 5 as a function of Vm. As expected, lf decreases,Clearly, these results indicate that steels containing eitherwhereas lm increases, with increasing Vm. These variationscoarse (as in 0.78 Vm IQ steels) or banded (as in all the SQare observed to obey power law–type relationships (Figuresteels examined) martensitic structures will have inferior5) It is noted here that the lf and lm values in the IQ steelsductility to the DP steels containing finely dispersedare at least one order of magnitude less than those in the

SQ steels. martensite.

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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- andSQ-conditioned DP steels. Fig. 5—Mean free path of ferrite and martensite as a function of volume

fraction of martesite for IQ-treated steels.

C. Impact Toughness relatively coarser ferrite with carbide precipitates, whereas,for Vm . 0.6, the low Gc value is due to coarser martensite.The values of average Charpy V-notched impact energy

(Gc) of the IQ and SQ specimens were plotted against the The range of Vm over which high values of Gc are measuredcorresponds to the microstructure comprised mostly ofmartensite content in Figure 7. For the case of IQ steel, the

Gc value increases with increasing Vm, peaks around ,0.55 refined ferrite and martensite (as shown in Figure 2) withoutany carbide precipitation in ferrite. Hence, it can be con-Vm, and then decreases. This result is in agreement with the

trends in the tensile properties of these steels. The lower cluded that higher toughness values in IQ specimens areassociated with finer martensite and finer precipitate-freetoughness for specimens containing Vm , 0.5 is due to

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(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) dimplefracture at high Vm (Vm 5 0.6).

(b)that IQ steels with very high Vm do not have favorableFig. 6—(a) Strength and (b) percentage of elongation as a function ofmechanical properties.volume fraction of martensite for IQ- and SQ-conditioned DP steels.

From Figure 7, it is seen that the impact toughness of theSQ specimens (7 to 20 J for 0.45 , Vm , 0.66) is muchinferior to the IQ specimens with a similar Vm. An interestingobservation that can be made from Figure 7 is that the Gc

of the SQ specimens also increases approximately linearlywith increasing Vm. This is in contradiction to some of theprevious reports, wherein a steep drop in Gc values wasobserved for DP steels with a Vm higher than ,0.15.[7]

Because of the observation of significantly lower Gc valuesof SQ steels compared to those of the IQ steels, we havenot conducted any further investigation to explore themechanical behavior of SQ steels.

D. Fractography

Scanning electron micrographs of fractured tensile IQspecimens containing a Vm of 0.38 and 0.6 are shown inFigures 8(a) and (b), respectively. These fractographs depictFig. 7—Charpy impact energy vs volume fraction of martensite for IQ-

and SQ-conditioned DP steels. predominantly cleavage fracture at a low Vm (Figure 8(a))and predominantly dimpled fracture at a high Vm (Figure8(b)). The change in fracture morphologies with Vm is ingeneral agreement with the variation in ductility with Vm.ferrite. The present observations are in agreement with the

hypothesis of Kang and Kwon[4] that fine distribution of Previous works[7,8] on fractographic observations of DPsteels indicate that, during tensile deformation, ferritemartensite enhances toughness of DP steels. When the

matrensitic content is increased from ,0.6 to ,0.78, a sharp deforms first and facilitates the nucleation of cracks eitherat precipitates present in it or at ferrite-martensite interfaces.drop in measured impact energy is noticeable. This observa-

tion, in combination with that of the tensile results, indicates Subsequently, these cracks propagate either by cleavage or

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dimple mode, depending on the state of stress present in the where stf and stm are the tensile strengths of the ferrite andthe martensite, respectively. If stf and stm are assumed tomicrostructure. In the IQ steels, the ferrite was found to be

dispersed with fine carbide precipitates for Vm , 0.45. be invariant with respect to the amount, nature, and morphol-ogy of the respective phases, Eq. [1] predicts a linear relationHence, crack initiation in these microstructures can be con-

sidered to take place predominantly at the precipitates. between st and Vm. On comparison, the experimental resultsobtained in this work appear to agree with the suggestedStress-controlled growth of the cracks within the ferrite

phase, favored by high internal stresses, leads to cleavage empirical expression of Byun and Kim,[11] up to a Vm of,0.5. However, they do not obey any of the predicted trendsfracture.

The crack initiation sites for a Vm of around 0.5 are consid- above 0.5 Vm. Beyond this level of Vm, the experimentalresults show that the tensile strength decreases with increas-ered to be located at the ferrite-martensite interfaces, because

of the absence of precipitates in this microstructure. In addi- ing martensite content, whereas the models predict increas-ing strengths.tion, since the internal stresses in these microstructures are

of low magnitudes, the nucleated cracks grow in a stable Chang and Preban[12] proposed an alternate model toexplain the variation between sy and Vm. In their model, theymanner, leading to larger dimple sizes. As the martensite

content increases further, the number of crack nucleation determined that the mean free path of ferrite will influence sy

through a Hall–Petch-type expression,sites increases, but the growth of these cracks depends onthe local stress state. At a very high Vm, the number of crack

sy 5 s0y 1 Kyl21/2f [2]initiation sites is large, and the stress distribution in the

microstructure is uniform. This results in a larger number where s0y is a reference frictional stress and Ky is theof fine dimples Figure 8(b)). Finally, it is noted that frac- dislocation-locking constant. Both soy and Ky are functionstographic observations on SQ specimens indicate extensive of Vm. Calculated results of sy vs Vm, following the workcleavage regions that are almost identical to those reported of Chang and Preban,[12] show reasonable agreement within literature for such steels. the current experimental results on IQ steels, but again, only

up to a Vm of 0.5. This model predicts an increasing sy valuewith a Vm above 0.5, whereas the experimental results onIV. DISCUSSIONthe IQ indicate a plateau in sy.

In contrast to the trends in IQ steels, the behavior of SQA. Evolution of Microstructuressteels can be explained in a rather straightforward manner

The morphology and dispersion of the martensite in the using a unidirectional composite analogy (wherein the elasticIQ heat-treated microstructure depends on the process of modulus of the fibers and the matrix are the same). Sincereversion of austenite from the initial tempered martensite. the yielding of ferrite dominates the yield strength of SQThe nucleation of austenite from the tempered martensite steels tested along the rolling direction, a decrease in lf withcan occur at different sites, such as (1) the prior austenite increasing Vm leads to higher sy (according to Eq.[2]). Thisgrain boundaries, (2) the carbide precipitates on prior austen- rationalizes the experimental trends in sy. Similarly, the inde-ite grain boundaries, (3) the spheroids in ferrite, and (4) the pendence of tensile strength of the SQ DP steels with Vm canfine carbide arrays formed on the prior martensitic plate/ be rationalized if we assume that the strength of martensitelath boundaries. dominates the overall strength of DP steels and that the

The morphology of the ferritic and martensitic regions in martensite strength remains invariant with lm (in particular,the SQ specimens depends on the formation of ferritic because of the very high values of lm).regions in the austenitic matrix while cooling from 920 8C However, the trends in the properties of IQ steels cannotto the ICT. The nucleation of ferrite starts at austenite grain be rationalized using the composite analogy or any of theboundaries, and these nuclei grow inside the austenite matrix models that are available in the literature. An examinationto yield distinct regions of ferrite. On quenching from ICT, of the earlier modeling work indicates the following com-austenite transforms to martensite, and the domain bound- plexities in understanding the stress-strain behavior of DParies of austenite get transferred to the product phase. The steels.resultant martensite can have both plate and lath morphology,

(1) Chang and Preban[12] emphasize that the prediction ofthe latter being predominant in specimens treated at lowerstrength (both yield and tensile) values of DP steelsintercritical temperatures. The starting configurations of theshould incorporate their dependence on the mean freeaustenitic domains, thus, lead to the varied morphologies ofpath of ferrite. This contention is based on the assump-martensite in the DP microstructures processed via the IQtion that plastic deformation in DP steels remains pri-and SQ routes. The problem of banding does not appear inmarily confined to the ferritic regions. On the contrary,the IQ-treated samples, because of the existence of a largein-situ observation of tensile fracture in DP steels bynumber of different types of nucleation sites for austeniteSu et al.[13] shows necking of martensitic region, indicat-in the martensitic microstructure.ing that plastic deformation of martensite is alsoimportant. Despite this observation, the influence of the

B. Yield and Tensile Strengths mean free path of martensite on the st-Vm relationshas not been understood yet. Balliger and Gladman[14]

The variation in tensile strength of DP steels, in terms ofindicated this possibility in their analysis conducted fol-the martensite content, has been empirically modeled inlowing Ashby’s report.[15]

earlier investigations,[9,10,11] formulated on the basis of the(2) The strength-microstructure relations in DP steels haverule of mixtures,

often been treated with a continuum-mechanicsst 5 stf(1 2 Vm) 1 stmVm [1] approach with isostress[16] or isostrain analysis.[17] These

1198—VOLUME 30A, MAY 1999 METALLURGICAL AND MATERIALS TRANSACTIONS A

models may be suitable, to some extent, for DP steelscontaining dilute concentrations of martensite and whenthe microstructure resembles that of fiber-reinforcedcomposites with nondeformable fibers and a continuousmatrix. For conventional DP steels prepared by the SQroute, which usually contain a banded structure, or DPsteels with dilute martensitic contents (Vm , 0.25), theapplicability of these models could be satisfactory. ButDP steels prepared by the IQ route and with a higherVm neither exhibit a banded microstructure nor showany continuous matrix of ferrite, especially for Vm .0.5. Hence, the applicability of simple continuummechanics–based analyses to predict st as a function ofVm for IQ specimens could be questionable.

(3) Araki et al.[18] formulated theoretical equations basedFig. 9—Variation of yield strength with respect to mean free path of mar-on continuum mechanics to describe the flow stress oftensite in log-log scale.DP steels, emphasizing its work-hardening behavior and

considering martensite as a ductile phase. These investi-gators found that such theoretical equations are applica-

distribution of the phases in a two-phase alloy, it can beble only up to Vm ' 0.2. If the DP steel is consideredconsidered jointly with Vm to construct a model to describeas a mixture of two ductile phases, several other phenom-the tensile properties of DP steels. Secondly, it is importantena such as unrelaxed plastic incompatibility, plasticto treat both the phases in a DP steel as deformable, contribut-relaxation, and yielding of martensite need to be incorpo-ing to the overall sy and st characteristics of the steel.rated.[19,20,21] This is in addition to the appropriate con-

Following the aforementioned assumption, a fundamentalsiderations of stress and strain partitioning duringunderstanding of the variations of sf(lf) and sm(lm) isdeformation.[11] Bhattacharyya et al.[22] have consideredrequired to develop suitable models. Unfortunately, veryadditional factors like the shape of martensite and ther-little is now known about sf(lf) and sm(lm) when internalmal mismatch between the phases of a DP steel in orderstresses are present. In the absence of such data, it can beto predict the stress-strain response of DP steels moreassumed, with a reasonable degree of accuracy, that sf(lf)accurately. However, their work does not suggest anyand sm(lm) follow a Hall–Petch kind of relationship suchrelation between sy vs Vm in DP steels, but only pointsas the one given in Eq. [2]. This simplification emergesto some important additional factors which were notfrom the fact that finer microstructural constituents usuallyconsidered by the earlier investigators for explaining thelead to higher strength. Many studies on the grain size ordeformation response.mean free path dependence of the strength of ferrite in poly-(4) Kim[23] considered the internal stresses developed duringcrystalline iron or mild steel have shown such a relationshipdeformation and formed during transformation of aus-to be valid. Contradictory views also exist about the choicetenite to martensite in DP steels, in order to formulateof the exponent for l; that of 20.5 is debatable. For example,an analytical model based on a continuum-mechanicsHansen[24] has indicated the possibility of this exponent rang-approach. This model also predicts a continuous increaseing from 20.5 to 1. Further, in fine lamellar structures, aof the strength of DP steel with an increase in Vm andseries of investigations[25,26] indicate that strength is morecannot explain the present results. Byun and Kim[11]

meaningfully expressed by a l21 type dependence.made a similar analysis of stress-strain behavior of DPObservation of Figure 5 indicates that lf decreases withsteels, which considered inhomogeneous distribution of

increasing Vm and appears to reach a steady-state valuestress and strain in the ferrite and martensite phases ofbetween 0.5 and 0.6 Vm. Similarly, Figure 6(a) indicates thatDP steels.a steady value in sy is reached for the same range in Vm.Guided by this observation, the variation in log sy is plottedThe previous discussion leads to the conclusion that there

are several factors that need to be taken into account to against log lf in Figure 9. It can be seen that a power-lawrelation between sy and lf exists, implying that yielding ofpredict the tensile and yield strengths of DP steels in a

generalized manner. From this discussion, it is obvious that ferrite determines the yield strength of the DP steels. Thisobservation is physically meaningful since ferrite has a sig-the strength of ferrite and martensite are not unique values

over any range of Vm but are functions of the chemistry, nificantly lower yield strength than that of martensite. How-ever, the experimental results suggest that the power-lawshape, and contiguity of phases; of the internal stresses due

to phase transformation and plastic incompatibility; and of exponent is ,20.25 and not 20.5 (Eq. [2]), as used byChang and Preban.[12] However, a mechanistic understandingthe precipitate volume fraction, etc. Developing a general-

ized theoretical model that incorporates all these factors is of the observed exponent is yet to be developed.Attempts were made to rationalize the experimental trendsa difficult task. A simplifying assumption that can be made

is that the mean free path (l) is the single most significant in st vs Vm using simple relations such as the rule of mixtures(both the upper-and lower- bound analysis with isostrain orfactor of all the independent variables, influencing the tensile

and the yield strengths. This assumption is based on the isostress assumptions, respectively, were conducted). Thecalculations performed always show an increasing value ofobservation that the development and distribution of all types

of stresses in ferrite or martensite in a DP steel depend on st with increasing Vm, depending on the constituent proper-ties used. At best, these calculations predict properties tothis parameter. Since l is governed by the amount and the

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 30A, MAY 1999—1199

reach a steady-state value; however, the constants extracted to 3 mm for 0.33 , Vm , 0.77. If we assume that it isessential for both lf and lm to be fine for the DP steel toare not physically meaningful. An increasing and then

decreasing trend has never been able to be simulated using show the highest ductility, a microstructure containing aVm , 0.55 should show a maximum in Dlu and Dlt, becausethis approach. These computations, albeit unsuccessful, led

to the conclusion that the rule of mixtures cannot be applied lf and lm are minimum for this composition (,1.0 mm).Away, from Vm , 0.55, either lf or lm increases and causesto predict the strength of high-martensite-containing DP

steels having contiguous and complex microstructures. Dlu and Dlt to decrease.It is interesting to note that the analysis of Byun andMore-sophisticated methodologies are required to predict

trends that match the experiments. Further efforts are under- Kim[11] is in reasonable agreement with the present experi-mental trends. They have analyzed the long-range internalway in this direction.stresses arising from unrelaxed plastic incompatibility in DPmicrostructures and hypothesized that the average of internal

C. Ductility stresses over the composite volume of DP microstructuresfor Vm , 0.5 is zero. Hence, one can expect a higher DluThe ductility of the DP microstructures has been examinedand Dlt at this microstructural state. This explanation appearsin terms of the uniform elongation and the total elongationto satisfactorily rationalize the present maxima of Dlu and(Figure 6(b)). Most of the previous observations on theDlt in its variation with Vm, but fails to explain the previousductility of DP steels indicate that both Dlu and Dlt decreaseresults on conventional DP steels. An additional conditionwith Vm. Davies[9] has shown that, with an increase in Vm,that is required to be satisfied is for the average internalDlu decreases rapidly up to about Vm ' 50 and that, abovestresses to be zero only when the magnitudes of the internalVm ' 50, the rate of decrease substantially reduces. Daviesstresses in ferrite and martensite are equal (signs being oppo-has supported this observation using the theories ofsite). Such a situation would require a finer distribution ofMileiko[27] and Garmong and Thompson[28] to describe thethe phases of a DP steel. In most of the previous reports onmechanical properties of fiber composites made of two duc-conventional DP steels, the microstructures do not representtile phases. Marder[29] observed a linear variation betweenthis distribution and, hence, the contention of Byun andDlu and Vm and explained his results using the isostressKim fails.analysis of Speich and Miller.[17] Jiang et al.[30] developed

an expression for Dlt in terms of Vm, considering the two-stage work-hardening behavior of DP steels, and suggested D. Work-Hardening Behaviora nonlinear monotonic variation between these parameters.

Early work[9,36,37] on the work-hardening behavior of DPThe observation of a maximum in Dlu at Vm , 40 for asteels contended that the flow stress of these materials obeyspredeformed DP steel by Liu et al.[31] indicates a trend thatthe Hollomon’s equation, which is commonly used to ana-is intermediate between the predictions of Marder[10] andlyze the work-hardening behavior of metallic materialsJiang et al. These investigators suggest that the type of(especially to cross-check the magnitude of uniformmartensite present dictates the ductility of DP steels (twinnedelongation),vs lath) and conclude that a finer microstructure exhibits

higher ductility. s 5 K«n [4]The explanation rendered by Fan and Miodownik[32] for

where s and « are the true stress and true strain, respectively;the variation of Dlu and Dlt with Vm is significantly differentn is the work-hardening exponent; and K is the strengthfrom those described in the preceding paragraph. Using topo-coefficient. The condition of tensile instability indicates thatgraphic transformation and a three-microstructural-elementDlu should be equal to n if the work hardening of the materialbody, these investigators suggested that Dlt can becan be expressed by an average value for any tensile defor-expressed asmation between yield and maximum load.

Dlt 5 (Dlf0 1 K fl21/4

f )F f 1 (Dlm0 1 K ml21/4

m )F m

[3]The computed values of n and Dlu are plotted in Figure

10 against Vm. It is noted from this figure that, except for1 (Dlfm

0 1 K fml21/4fm )F fm

where (Dl f0 1 K fl21/4

f ), (Dlm0 1 K ml21/4

m ), and (Dl fm0 1

K fml21/4fm ) control the ductility of the predominantly ferritic,

martensitic, and ferrito-martensitic topographical regions ofthe DP microstructures, and F f, F m, and F fm representparameters related to the different regions. The suffixes f,m, and fm represent the ferrite, martensite, and ferrito-mar-tensitic domains, respectively. Using the empirical Eq. [3],Fan and Miodownik[32] demonstrated that Dlt exhibits a mini-mum in its variation with Vm at around Vm , 0.6; such adescription closely describes several publishedresults.[33,34,35] The present observation of the variation ofDlt with Vm is exactly opposite the trend predicted by usingthe parameters given by Fan and Miodownik.

The experimental trends in Dlu and Dlt with Vm observedin the present investigation are in agreement only with thatreported by Liu et al.[31] The microstructures of IQ steels in Fig. 10—Variation of strain-hardening exponent (n) and uniform strain as

a function of volume percentage of martensite for IQ-conditioned DP steels.this work are very fine, with lf and lm in the range from 1

1200—VOLUME 30A, MAY 1999 METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 12—Crussard–Jaoul plot of ds/d« vs strain (in logarithmic scale) toFig. 11—Typical log-log plots of true stress vs true strain for estimated reveal various stages of work hardening.strain-hardening exponent (n) for IQ-treated steels.

the case of Vm 5 0.64, the values of n are always significantly cross-slip and dynamic recovery together with martens-higher than Dlu. This observation is in contradiction to that itic deformation.of Davies,[9] who has reported a good agreement between

However, using the modified J–C analysis, Jiang et al.[30]n and Dlu. This observed deviation can be attributed either

observed only two stages of work-hardening behavior into a nonlinear variation of ln s with ln « or to the possibilitysteels containing Vm . 0.3.of different stages of work hardening. Typical plots of ln s

Experimental results obtained in the present work werevs ln« are shown in Figure 11, and these indeed reflect asubjected to both the J–C and modified J–C analyses. Typi-nonlinear variation between ln s and ln «.cal results are presented in Figure 12. These plots indicateSeveral previous investigators[17,38–40] indicated that work-that the flow-stress behavior of the high-Vm DP steels canhardening behavior in the DP steels occurs in three differentbe described using a three-stage work-hardening behavior.stages. This is revealed by the Jaoul–Crussard (J–C) analy-All the present results are obtained on DP microstructuresses, which are based on the following two equations:[30,40]

containing Vm . 0.33. Hence, the observed three stages maybe due to different work-hardening mechanisms associateds 5 s0 1 K 8«n8 [5]with the finer distribution of constituent phases. It is hypothe-

« 5 «0 1 K9sn9 [6] sized that the results can be rationalized with the followingdeformation mechanisms.where s0 and «0 are reference true stress and true strain,

respectively. Differentiating the previous equations with (1) Stage I is due to homogeneous deformation of ferrite.respect to « and expressing in logarithmic forms, we get The rate of work hardening is high in this stage when

Vm , 0.5, because undissolved carbide particles impedeln 1ds

d«2 5 ln K 8 1 ln n8 1 (n8 2 1) ln « [7] the glide of dislocations in the ferrite phase. Thepossibility of martensite deformation is not ruled out.

(2) Stage II is due to a condition of going throughandminimum plastic incompatibility, resulting in lowerinternal stresses and, thus, enhancing easy flow of

ln 1dsd«2 5 (1 2 n8) ln s 2 ln (K9n9) [8] dislocations.

(3) Stage III consists of simultaneous deformation of ferriterespectively. Analyses of true stress–strain data using Eqs. and martensite associated with dynamic recovery.[7] and [8] are referred to as the J–C analysis and modified

Specific evidence has not been obtained to support theJ–C analysis, respectively. Using both these analyses, Sam-previous hypothesis; however, some experimental observa-uel[40] has been able to reveal the three stages of work harden-tions extend support to this view.[41] First, the slope ofing in DP steels. These stages of work hardening in DP steelsthe ln ds/d« vs ln « plots in stage I, for the A73 throughhave been attributed[17,38–40] to the following mechanisms ofA78 specimens, are lower than the slopes for the A80deformation.through A84 specimens. This observation implies a higherwork-hardening rate in stage I for samples containing a(1) Stage I consists of homogeneous deformation of the

ferrite matrix by the glide of mobile dislocations present lower Vm than for those containing a higher Vm. Lowerwork-hardening rates with higher Vm are attributed to annear the martensitic regions.

(2) Stage II covers a diminished work hardening with con- ease of the dislocation flow, owing to the absence ofbarriers such as the undissolved carbide particles. Secondly,strained ferrite deformation and with possible transfor-

mation of retained austenite to martensite. the slope of ln ds/d« vs ln « in stage I and stage III,for specimens containing a higher Vm, are similar. This(3) Stage III consists of ferrite deformation with attendant

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 30A, MAY 1999—1201

4. S. Kang and H. Kwon: Metall. Trans. A, 1987, vol. 18A, pp. 1587-92.is indicative of simultaneous deformation of both the5. Japanise Industrial Standard, JIS GO555, 1977, p. 321.phases. The presence of stage II may be due to dynamic6. E.E. Underwood: Quantitative Stereology, Addision-Wesley, Reading,

changes of internal stresses during plastic deformation; MA, 1970, p. 82.however, no conclusive support could be obtained to 7. R.G. Davies: Metall. Trans. A, 1979, vol. 10A, pp. 113-18.

8. F.H. Samuel, D. Daniel, and O. Sudre: Mater. Sci. Eng., 1987, vol.explain this stage of deformation in an appropriate manner.92, pp. 43-62.

9. R.G. Davies: Metall. Trans. A, 1978, vol. 9A, pp. 671-79.10. A.R. Marder: Metall. Trans. A, 1982, vol. 13A, pp. 85-92.V. CONCLUSIONS11. T.S. Byun and I.S. Kim: J. Mater. Sci., 1993, vol. 28, pp. 2923-32.12. P.H. Chang and A.G. Preban: Acta Metall., 1985, vol. 33, pp.On the basis of the experimental work that has been carried

897-903.out and presented in this article, the following conclusions13. M. Su, S.M. Sun, and D.Z. Yang: Scripta Metall., 1987, vol. 21, pp.can be drawn. 801-04.14. N.K. Balliger and T. Gladman: Met. Sci., 1981, vol. 15, pp.1. Dual-phase steels containing approximately equal

95-108.amounts of finely dispersed ferrite and martensite phases 15. M.F. Ashby: Strengthening Metals in Crystals, Elsevier, London, 1971,exhibit the optimum combinations of high strength and pp. 137-92.

16. I. Tamura: Trans. ISI, Jpn., 1973, vol. 13, pp. 283-92.ductility with high impact toughness.17. G.R. Speich and R.L. Miller: in Structure and Properties of Dual-2. The impact toughness values of DP steels with finely

Phase Steels, R.A. Kot and J.W. Morris, eds., AIME, New York, NY,dispersed constituents are much superior to those with a 1979, p. 145.coarse or banded martensite and exhibit a peak for a Vm 18. K. Araki, Y. Takada, and K. Nakokai: Trans. ISI Jpn., 1977, vol. 17,

p. 710.of 0.5 to 0.6. Higher toughness values in IQ specimens19. K. Tanaka and T. Mori: Acta Metall., 1970, vol. 18, pp. 931-41.are associated with finer martensite and finer precipitate-20. L.M. Brown and W.M. Stobbs: Phil. Mag., 1971, vol. 23, p.free ferrite.

1185.3. The variation in tensile properties, such as the yield and 21. M.F. Ashby: Phil. Mag., 1966, vol. 14, p. 1157.

tensile strength, and ductility with martensite content in 22. A. Bhattacharyya, T. Sakaki, and G.J. Weng: Metall. Trans. A, 1993,vol. 24A, pp. 301-14.the IQ steels exhibit an unusual nature. The peak in

23. C. Kim: Metall. Trans. A, 1988, vol. 19A, pp. 1263-68.tensile properties emerges due to finer microstructural24. N. Hansen: Metall. Trans. A, 1985, vol. 16A, pp. 2167-90.constituents and due to the possible absence of average 25. M. Dollar, I.M. Bernstein, and A.W. Thompson: Acta Metall., 1988,

internal stress over the composite microstructure vol. 36, pp. 311-20.26. J. Gil Sevillano: ICSMA-5 Proc., Achen, P. Hassen et al., eds., Perga-volume.

mon Press, Oxford, United Kingdom, 1979, p. 819.4. The calculated work-hardening exponent differs signifi-27. S.T. Mileiko: J. Mater. Sci., 1969, vol. 4, pp. 974-77.cantly from the uniform elongation obtained from the28. G. Garmong and R.B. Thompson: Metall. Trans., 1973, vol. 4, pp.

true stress–true strain curves. This deviation is due 863-73.to the presence of three stages of work-hardening during 29. A.R. Marder: Metall. Trans. A, 1981, vol. 12A, pp. 1569-79.

30. Z. Jiang, Z. Guan, and J. Lian: J. Mater. Sci., 1993, vol. 28, p.plastic deformation with different work-hardening rates.1814.

31. J. Liu, Z. Jiang, and J. Lian: Mater. Sci. Technol., 1991, vol. 7, pp.527-31.

32. Z. Fan and A.P. Miodownik: Scripta Metall., 1993, vol. 28, pp.ACKNOWLEDGMENTS895-900.

This work was carried out at Bharat Earth Movers Limited 33. A.H. Nakagawa and G. Thomas: Metall. Trans. A, 1985, vol. 16A,pp. 831-40.(BEML) as part of AB’s Ph.D. thesis dissertation with the

34. R.M. Ramage, K.V. Jata, G.I. Shiflet, and E.A. Starke, Jr.: Metall.Indian Institute of Technology (Kharagpur, India). AB isTrans. A, 1987, vol. 18A, pp. 1291-98.grateful to the management of BEML for support rendered

35. Y.L. Su and J. Gurland: Mater. Sci. Eng., 1987, vol. 95, pp.during the course of this work. AB also appreciates the help 151-65.of Dr. U. Ramamurty for redrawing the graphs. 36. P.E. Repas: Dual-Phase and Cold Pressing Vanadium Steels in the

Automobile Industry, Vanitec, Berlin, 1978, p. 13.37. R. Lagneborg: Dual-Phase and Cold Pressing Vanadium Steels in the

Automobile Industry, Vanitec, Berlin, 1978, p. 43.REFERENCES38. G.R. Speich: in Fundamental of Dual-Phase Steels, R.A. Kot and B.L.

Bramfitt, eds., AIME, New York, NY, 1981, p. 3.1. Dual-Phase and Cold Pressing Vanadium Steels in the AutomobileIndustry, Vanitec, Berlin, 1978. 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. Kot2. Structure and Properties of Dual-Phase Steels, R.A. Kot and J.W.Morris, eds., AIME, New York, NY, 1979. and J.W. Morris, eds., AIME, New York, NY, 1979, p. 304.

40. F.H. Samuel: Mater. Sci. Engg., 1987, vol. 92, pp. L1-L4.3. Fundamental of Dual-Phase Steels, R.A. Kot and B.L. Bramfitt, eds.,AIME, New York, NY, 1981. 41. A. Bag: Ph.D. Dissertation, IIT, Kharagpur, India, 1996.

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