Effect of Martensite Volume Fraction on Void Formation Leading to Ductile Fracture in Dual Phase Steels

Abstract

This study examines the ductile fracture of three dual-phase steels that contain low volume fractions of martensite (3.2%, 6.2% and 10%) and are composed of nearly the same quality of ferrite and martensite. The strains to rupture of the DP steel with 3.2% martensite are considerably higher than those of the DP steels with 6.2% and 10% martensite. The evolution of voids with respect to equivalent plastic strain, which is transformed from the thickness reduction of the specimen, was analyzed by SEM observation in fractured tensile specimens. The observation clarified the fact that the evolution of void size saturates at the specific strain in the DP steel with 3.2% martensite, whereas the void size in the DP steels with 6.2% and 10% martensite grows exponentially with strain. This significant favorable behavior of the DP steel with 3.2% martensite is probably caused by the relatively low heterogeneity of the stress and strain partitioning between the two phases, which allows attaining a significant higher ductility of this steel.

1. Introduction

High-strength steel sheets are widely used in automotive products to reduce weight and strengthen crashworthiness, although the increased strength is generally accompanied by deterioration in ductility, which renders their forming difficult.¹⁾

Among high-strength steels, dual-phase (DP) steels, which have hard martensite islands embedded into a soft ferrite matrix, are frequently used in the automotive industry, because of their high ductility and formability.^2,3,4,5) However, for the continuous prevailing of DP steels, their ductility needs to be increased to permit simple forming methods for conventional mild steels. Several authors have recently underlined the need to improve the stretch flangeability of DP steels, identified, for example, by the hole expansion ratio,^4,5) while other researchers have focused on the relationship between the ductility and microstructure of DP steels.^{6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)} This motivated us to analyze the damage accumulation mechanism in DP steels and its effect on ductility and formability.

A number of investigations suggest that the damage accumulation mechanism in DP steels is different from that in conventional mild steels, which exhibit void generation around ceramic or carbide inclusions.^21,22,23,24) Many investigations have shown that void formation in DP steels arises from martensite fracture, ferrite/martensite interface decohesion and, to a lesser extent, fracture along ferrite grain boundaries close to martensite islands.^{6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)} The investigations also suggest that martensite volume fraction affects void formation behavior. Ashemed et al.⁶⁾ reported that void formation was due to ferrite/martensite interface decohesion at a low martensite volume fraction (V_m), while the other two formation types occurred at high V_m values (about 32%). Szewczyk and Gurland¹²⁾ reported that for a V_m of approximately 16%, voids were generated mostly at ferrite/martensite interfaces, with sites mostly located around densely distributed martensite islands. Avramovic-Cingara et a1.¹⁷⁾ analyzed the effect of martensite morphology on void formation behavior by conducting in-situ observations of specimens during tensile tests. They concluded that elongated martensite islands induced martensite fracture. Tomoda et al.¹⁸⁾ reported that a lower martensite hardness might change the void formation mechanism from martensite fracture to ferrite/martensite interface decohesion.

In the present study, we experimentally analyzed the quantitative effects of the martensite volume fraction V_m on void formation behavior and macro-scale fracture. Neither of these effects has been sufficiently investigated in previous studies, especially at relatively low V_m values (~10%) in DP steels. It is expected that clarification of these aspects will give some valuable suggestions on how to further increase DP steel ductility.

This paper is organized as follows. Section 2 presents the materials used for this study: three types of DP steels, with V_m in the range of 3 to 10% and the ferrite and martensite having nearly the same quality in all three materials, were analyzed. Section 3 presents observations of void nucleation and growth, and shows the evolutions of area fraction, number, and void size in the three DP steels. The results are discussed in Section 4. Finally, study conclusions are presented in Section 5.

2. Materials

Three grades of dual-phase steel sheets having a thickness of 1.8 mm were analyzed. Hereafter, they are called DP1, DP2 and DP3. The chemical composition, thermo-mechanical treatment, microstructures and mechanical properties of these materials are presented immediately below.

2.1. Chemical Composition

Table 1 shows the chemical compositions of the three materials, while Table 2 gives the chemical compositions of the martensite and ferrite phases. The chemical composition of each phase was calculated by assuming that (i) the ferrite phase contains 0.02% carbon, which corresponds to the solubility of carbon in ferrite in the Fe–C system at 996 K; and (ii) Si and Mn are evenly distributed in both phases. The chemical compositions of the martensite and ferrite phases, shown in Table 2 for DP1, DP2 and DP3, are similar.

Table 1. Chemical compositions of the three materials.

	C [mass%]	Si [mass%]	Mn [mass%]
DP1	0.038	0.50	1.50
DP2	0.048	0.50	1.50
DP3	0.067	0.50	1.50

Table 2. Chemical compositions of ferrite and martensite.

	DP1	DP2	DP3
Ferrite	0.02 C - 0.5 Si -1.5 Mn
Martensite	0.58 C	0.48 C	0.49 C
	0.5 Si	0.5 Si	0.5 Si
	1.5 Mn	1.5 Mn	1.5 Mn

2.2. Thermo-mechanical Treatment

Figure 1 shows the thermo-mechanical conditions for DP1, DP2 and DP3. The samples were vacuum-melted in the laboratory, then thinned to 30 mm by hot rolling. After holding for 1 hour at 1423 K, the samples were hot rolled to 1.8 mm in six passes over 1073 K, air-cooled to 923 K, and then water-quenched to room temperature. Ferrite transformation occurred during the air-cooling process, and martensite transformation during the water-quenching process. The thermo-mechanical conditions for the three steels were assumed to result in similar ferrite/martensite strength differences and similar strengths at the ferrite/martensite interfaces.

Fig. 1.

Heat pattern for the three types of DP steels. Ms denotes the martensite start temperature.

2.3. Microstructures

The microstructures of the three materials are shown in Fig. 2. As indicated in Table 3, their martensite volume fractions increase in the order DP1, DP2, DP3. It is worth noting that the number density of martensite islands is almost proportional with martensite volume fraction, whereas the difference in mode area (the most frequent area) between DP1, DP2 and DP3 is relatively small. As shown in Fig. 3, the histograms of the martensite island areas reveal a gradual but moderate deviation towards large martensite islands in the order DP1, DP2, DP3. This is confirmed by the areas of the five largest martensite islands in Table 3.

Fig. 2.

Micrographs of DP1, DP2 and DP3, with martensite islands colored in white. (Online version in color.)

Table 3. Volume fraction, number density, and island size of martensite for the three materials.

	DP1	DP2	DP3
Volume fraction [%]	3.2	6.1	10
Number density of islands [/104μm2]	26	44	75
Mode area of islands [μm2]	2.7	3.0	3.3
Average area of the largest 5 islands [μm2]	22.5	26.2	35.4

Fig. 3.

Histogram of the area of martensite islands. (Online version in color.)

Considering this quantitative analysis of first-order statistical attributes of the microstructures, as well as the fact that the three DP steel grades have almost the same chemical composition of martensite and ferrite and are produced by the same heat-treatment histories, it may reasonably be assumed that the difference in the pattern and development of ductile fractures between the three grades arises mainly from their different martensite volume fractions, which were, in the present case, almost proportional with their number density of martensite islands. We hope that this restricted context will simplify analysis of the damage processes that precede the ductile fracture of DP steels, at least within the range of the relatively low martensite volume fractions considered in this paper.

2.4. Mechanical Properties

Table 4 shows mechanical properties obtained through tensile tests using the specimen in Fig. 4, where tensile force is along the transverse direction of the rolled sheets, cross head speed is 0.02 mm/s, and gauge length is 50 mm. Strain components to rupture were evaluated for the initial thickness of the cross section of the specimen, t₀, and the minimum thickness of the cross section of the ruptured specimen, t, using the formula   

$$\begin{array}{l}{\epsilon }_{xx}=ln\left(\frac{t_0}{t}\right),\hspace{0.17em}\hspace{0.17em}{\epsilon }_{yy}=0,\hspace{0.17em}\hspace{0.17em}{\epsilon }_{zz}=ln\left(\frac{t}{t_0}\right),\\ {\epsilon }_{xy}=0,\hspace{0.17em}\hspace{0.17em}{\epsilon }_{yz}=0,\hspace{0.17em}\hspace{0.17em}{\epsilon }_{zx}=0\hspace{0.17em}\hspace{0.17em}.\end{array}$$(1)

This evaluation ignores elastic strain, and assumes the existence of isochoric plastic deformation and plane strain conditions at the center of specimen width. The von Mises equivalent plastic strain $\overline{\epsilon }$ can be derived from these strain components using the formula   

$$\overline{\epsilon }=\sqrt{\frac{2}{3}\left({\epsilon }_{xx}^2+{\epsilon }_{yy}^2+{\epsilon }_{zz}^2+2{\epsilon }_{xy}^2\right)}.$$(2)

Table 4. Mechanical properties of the DP steels.

	DP1	DP2	DP3
Yield Stress [MPa]	283	314	300
Tensile Strength [MPa]	490	585	633
Uniform Elongation	0.196	0.168	0.149
Equivalent plastic strain to rupture	1.48	1.01	0.740

Fig. 4.

Specimen geometry for uniaxial tensile tests.

Figure 5 shows uniaxial tensile stress–strain curves obtained for the three DP steels. Yield stresses are almost independent of the martensite volume fraction, thus confirming that DP steel yield stresses are determined mainly by the ferrite phase. Actually, as shown in Fig. 5, the yield stress of all three materials is almost the same as the yield stress of single-phase ferrite having the composition shown in Table 2. However, after the beginning of plastic deformation, flow stress increases more rapidly at larger martensite volume fractions, and tensile strengths follow the same trend.

Fig. 5.

Stress–strain curves of the steels DP1, DP2, DP3 and of their ferrite phase. (Online version in color.)

Table 4 shows how both uniform elongations and strains to rupture decrease with increasing martensite volume fraction. It should also be noted that DP1 strain to rupture is significantly larger than that of DP2 or DP3, whereas the difference in their uniform elongations is relatively small.

3. Void Observations

3.1. Observation Technique

Fractured tensile specimens were observed using a scanning electron microscope (SEM). Observation areas were centered in the width direction of the specimens, and situated at a distance equal to a quarter of the thickness from the specimen surface (see Fig. 6). The specimens were electrochemically polished to obtain clear void images.

Fig. 6.

Schematic image of observed points on the cross sections of the tensile specimen.

Observations were conducted at five points situated at distances of 50, 500, 1000, 2000, and 4500 μm from the fractured surface. Voids were weighed up using three SEM images with a total area of 14400 μm², centered on each observation point. Equations (1) and (2) enable conversion of the specimen thickness at each observation point into corresponding equivalent strains.

3.2. Results

The reflected electron images of voids at three different strains in DP1, DP2 and DP3 are shown in Fig. 7. As indicated by Figs. 7(b-1)–7(b-3) and 7(c-1)–7(c-3), void areas in DP2 and DP3 increase significantly with equivalent strains derived from Eqs. (1) and (2). On the other hand, the area of the voids in DP1 seems similar in Figs. 7(a-1)–7(a-3), although the corresponding equivalent strains increase from 0.57 to 1.4. As for the sites of void formation, although the choice of observation point spatial positions and SEM micrograph resolution for this study did not permit unambiguous recognition of the nucleation mechanism for all voids, we can state beyond any reasonable doubt that the void formation observed in the three DP steels arises predominantly from ferrite/martensite interface decohesion (cf. Fig. 8(a)) and, to a lesser extent, from the fracture of martensite islands (cf. Fig. 8(b)). This finding is actually supported by most of the literature devoted to the ductile fracture of DP steels containing relatively low martensite volume fractions.^{6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)}

Fig. 7.

SEM images of voids.

Fig. 8.

Types of void formation.

To quantitatively analyze void formation behavior, evolution of the void area fraction vs. equivalent strain is shown in Fig. 9. The difference in the void area fractions among the three materials is rather small up to about 0.4 equivalent strain, but increases thereafter and becomes quite substantial at large strains. For DP2 and DP3, the void area fraction increases very rapidly with progressing deformation. These results are supported by other authors,^{12,13,14,15,16,17)} who have reported that void volume fraction increases exponentially in the central neck part of tensile specimens, due to high stress triaxiality. On the other hand, the increase is less significant for DP1, which shows a quasi-constant void area fraction over the whole strain range.

Fig. 9.

Area fraction of voids vs. equivalent strain.

In the following discussion, we split the evolution of the void area fraction into evolutions of the number density of voids and of the void size.

Figure 10(a) shows the variation of the number density of voids with strain, while Fig. 10(b) shows the same variation normalized by the number density of martensite islands of each material indicated in Table 3. Clearly, as shown by Fig. 10(a), increasing the martensite volume fraction from DP1 to DP3 induces a higher number density of voids at any equivalent strain. It is also worth noting that the number density of voids in DP1 increases definitely with progressing strain, unlike the void area fraction.

Fig. 10.

Void number density vs. equivalent strain.

On the other hand, the difference between the three materials is no longer visible in Fig. 10(b), after normalization with the number density of martensite islands, thus supporting the conjecture that the number of voids is mainly determined by, and increases with, the number of martensite islands. It is also worthy of note that the ratio of the number density of voids to the number density of martensite islands increases almost linearly with the equivalent strain for all three materials, and hence reaches its maximum in DP1, which has the highest strain to rupture. Finally, the fact that this ratio exceeds unity shows that one martensite island may have two or even more sites of void nucleation.

Figure 11 shows the evolution of the void size with strain. As shown in Fig. 11(a), the evolution of mode void size (i.e. the void size most frequently observed around each observation point), is almost the same for all three materials, and remains nearly constant throughout deformation. This agrees with similar results reported by Maire et al.¹⁵⁾ On the other hand, as already seen above, void size itself increases with the martensite volume fraction and progressing strain. Inspection of Fig. 11(b), which shows the evolution of the average void size of the five largest voids in each deformation, permits clarification of this apparent paradox. Indeed, it will be seen that the largest voids grow rapidly with the equivalent strain for DP2, and even more significantly for DP3. On the other hand, growth of the largest voids in DP1 is much slower than in DP2 or DP3. Actually, growth of the largest voids in DP1 saturates is below 4 μm², at an equivalent strain of about 0.8. These different growth rates of the largest voids contribute decisively to the difference in the evolutions of the void area fractions among the three materials. As a matter of fact, the difference in the number density of voids in the three materials is relatively small compared with the difference in their largest void sizes.

Fig. 11.

Void size vs. equivalent strain.

4. Discussion

As indicated in Sect. 2.4, increasing the martensite volume fraction decreases strain to rupture to a greater extent than does uniform elongation. Indeed, the strain to rupture of DP1 is significantly larger than that of DP2 or DP3, although the difference in uniform elongations among the three materials is relatively small. The void observations presented in Sect. 3.2 substantiate these findings. Thus, Fig. 9 shows that the void area fraction remains very low at equivalent strains corresponding to uniform elongation, while further deformation leads to large void area fractions before rupture in DP2 and DP3. On the other hand, the almost constant void area fraction at large strains in DP1 presumably prevents a sudden softening of the material, thus contributing to remarkably higher strains to rupture in comparison with the other two DP steels.

To the best of our knowledge, an evolution of the void area fraction like that in DP1 has not yet been observed. Actually, most results of this type reported in the literature^{12,13,14,15,16,17)} indicate an exponential evolution of void volume fraction with progressing strain, like in DP2 and DP3. The genuine void evolution in DP1 is presumably due in the first place to the relatively large separation distances between the martensite islands, which render possible accommodation of the overall deformation of the specimen mainly by ferrite deformation. Consequently, microstructural strain and stress levels in the martensite islands remain by and large below what would be necessary for martensite fracture. This circumstance is also favored in DP1 over DP2 and DP3 by the lower flow stress level, as well as by the lower probability of clustering and/or alignment of martensite islands due to their lower number density. The rare occurrence of the martensite islands in DP1 may also explain why the size of the largest voids remains significantly smaller than in the other two steels, especially at large strains. Apparently, the strain and stress partitioning between ferrite and martensite in DP1 can gradually generate voids at the interfaces between the two phases, but is not able to promote the growth and coalescence of such voids. Consequently, as we have seen in Sect. 3.2, while the number density of voids in DP1 increases steadily with strain, void size saturates at a rather low strain level.

On the other hand, the other two steels develop a more customary pattern of void formation and growth, with an increased contribution of martensite fracture and a rather rapid growth of the largest voids before macroscopic fracture of the specimen, both of these phenomena being more pronounced in DP3 than in DP2.

It has been repeatedly stressed in the literature^25,26,27) that the microstructural stress and strain heterogeneity that are due to martensite volume fraction and hardness, as well as the strength difference between the two phases, are the main sources of void formation and development in DP steels. In this study, we tried to simplify this complex problem by choosing three materials that have almost identical compositions for the two phases and were subjected to very similar heat-treatment patterns. Even so, an interpretation of the SEM observations of the void evolutions would benefit from a coupling with numerical simulations that provide a quantitative assessment of stress and strain distribution around the voids, using the real 2D and 3D morphology of the martensite islands. In addition, combining post-mortem techniques with in-situ observations of void development,²⁰⁾ and increasing micrograph resolution, would allow a more accurate evaluation of the processes of void nucleation, growth and coalescence. Both of these lines of research are currently under investigation by the present authors and will be addressed in future publications.

5. Conclusions

In this study, the ductile fracture of three types of DP steel was investigated, in relation with void generation and growth. The three steel grades, denoted DP1, DP2 and DP3, differed only in their martensite volume fraction, which amounts to 3.2%, 6.1% and 10%, respectively. The main conclusions of this study are:

(i) Martensite volume fraction affects strain to fracture to a greater extent than uniform elongation, presumably because the voids are mainly nucleated at strains that exceed the uniform elongation.

(ii) The pattern of void generation and development in DP1 (i.e., at a low martensite volume fraction), remarkably improves strain to fracture. This pattern is dominated by voids generated at the ferrite/martensite interface, which has a relatively small size and reaches saturation at high strains.

(iii) This special behavior of DP1 is most likely caused by the large spacing between the martensite islands, which allows the accommodation of overall strains mainly by plastic deformation of the ferrite. Consequently, with progressing deformation, microstructural stresses may become larger than the strength of the ferrite/martensite interfaces, but not large enough to produce either the fracture of martensite islands or a significant void growth and coalescence.

(iv) The increase of the martensite volume fraction from DP1 to DP2 and then to DP3 leads to a gradual intensification of the role played by initial martensite fracture in void growth and coalescence, especially for the largest voids.

Acknowledgment

We thank Prof. Teodosiu and the members of the VCAD System Research Program, RIKEN, Japan, for their cooperation and assistance during this study.

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