A dislocation model, accurately describing the uniaxial plastic stress-strain behavior of dual phase (DP) steels, is proposed and the impact of martensite content and ferrite grain size in four commercially produced DP steels is analyzed. It is assumed that the plastic deformation process is localized to the ferrite. This is taken into account by introducing a nonhomogeneity parameter, , that specifies the volume fraction of ferrite taking active part in the plastic deformation process. It is found that the larger the martensite content the smaller the initial volume fraction of active ferrite which yields a higher initial deformation hardening rate. This explains the high energy absorbing capacity of DP steels with high volume fractions of martensite. Further, the effect of ferrite grain size strengthening in DP steels is important. The flow stress grain size sensitivity for DP steels is observed to be 7 times larger than that for single phase ferrite. 1. Background The usage of advanced high strength steels, AHSS, has made it possible for the automotive industry to reduce weight and improve safety of vehicles. AHSS include steel types such as dual phase (DP), complex phase (CP), transformation induced plasticity (TRIP), and martensitic steels, of which DP steels are the most frequently used [1]. The properties of DP steels are characterized by a low yield strength due to the absence of Lüders bands and a high rate of deformation hardening, which results in a high tensile strength and good formability. DP steels also show a high energy absorbing ability which implies a good crashworthiness [2–5]. The explanation to the materials behavior is to be found in the microstructure, which in DP steels mainly consists of two phases: ferrite and martensite. A number of attempts, for example, [6–10], have been made to physically describe the stress-strain behavior of DP steels. In most cases empirical relationships have been used but some physical models have been developed. One frequently used concept is the Ashby-model [11], which is based on the assumption that the dislocations can be placed in two categories: statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) with pile ups of dislocations in arrays. Unfortunately, these arrays have never been observed in high stacking fault energy crystals like ferrite. This has also been pointed out by Mughrabi [12] who further states that, “The increasing number of SGP (strain gradient plasticity) theories confirms that the search for a really satisfactory theory is still going on.
References
[1]
C. Federici, S. Maggi, and S. Rigoni, The Use of Advanced High Strength Steel Sheets in the Automotive Industry, Fiat Auto—Engineering & Design, Turin, Italy, 2005.
[2]
J. R. Fekete, J. N. Hall, D. J. Meuleman, and M. Rupp, “Progress in implementation of advanced high-strength steels into vehicle structures,” Iron & Steel Technology, vol. 5, no. 10, pp. 55–64, 2008.
[3]
R. Koehr, ULSAB-AVC Advenced Vehicle Concepts Overview Report, in Safe, Affordable, Fuel Efficient Vehicle Concepts for the 21st Century Designed in Steel, Porsche Engineering Services, Detroit, Mich, USA, 2002.
[4]
P. Tsipouridis, E. Werner, C. Krempaszky, and E. Tragl, “Formability of high strength dual-phase steels,” Steel Research International, vol. 77, no. 9-10, pp. 654–667, 2006.
[5]
M. Takahashi, “Development of high strength steels for automobiles,” Nippon Steel Technical Report, no. 88, pp. 2–7, 2003.
[6]
J. Bouquerel, K. Verbeken, and B. C. De Cooman, “Microstructure-based model for the static mechanical behaviour of multiphase steels,” Acta Materialia, vol. 54, no. 6, pp. 1443–1456, 2006.
[7]
V. Colla, M. De Sanctis, A. Dimatteo, G. Lovicu, A. Solina, and R. Valentini, “Strain hardening behavior of dual-phase steels,” Metallurgical and Materials Transactions A, vol. 40, no. 11, pp. 2557–2567, 2009.
[8]
Z. H. Cong, N. Jia, X. Sun, Y. Ren, J. Almer, and Y. D. Wang, “Stress and strain partitioning of ferrite and martensite during deformation,” Metallurgical and Materials Transactions A, vol. 40, no. 6, pp. 1383–1387, 2009.
[9]
Z. Jiang, Z. Guan, and J. Lian, “Effects of microstructural variables on the deformation behaviour of dual-phase steel,” Materials Science and Engineering A, vol. 190, no. 1-2, pp. 55–64, 1995.
[10]
C. Kim, “Modeling tensile deformation of dual-phase steel,” Metallurgical Transactions A, vol. 19, no. 5, pp. 1263–1268, 1988.
[11]
M. F. Ashby, “The deformation of plastically non-homogeneous alloys,” in Strengthening Method in Crystals, A. Kelly and B. Nicholson, Eds., Applied Science Publishers LTD, London, UK, 1971.
[12]
H. Mughrabi, “Dual role of deformation-induced geometrically necessary dislocations with respect to lattice plane misorientations and/or long-range internal stresses,” Acta Materialia, vol. 54, no. 13, pp. 3417–3427, 2006.
[13]
H. Mughrabi, “On the current understanding of strain gradient plasticity,” Materials Science and Engineering A, vol. 387-389, no. 1-2, pp. 209–213, 2004.
[14]
D. A. Korzekwa, D. K. Matlock, and G. Krauss, “Dislocation substructure as a function of strain in a dual-phase steel,” Metallurgical Transactions A, vol. 15, no. 6, pp. 1221–1228, 1984.
[15]
G. I. Taylor, “The mechanism of plastic deformation of crystals. Part I. Theoretical,” Proceedings of the Royal Society A, vol. 145, pp. 362–387, 1934.
[16]
U. Liedl, S. Traint, and E. A. Werner, “An unexpected feature of the stress-strain diagram of dual-phase steel,” Computational Materials Science, vol. 25, no. 1-2, pp. 122–128, 2002.
[17]
J. M. Rigsbee, et al., “Structure-processing and structure-property relations in commercially processed dual-phase steels,” in Structure and Property of Dual-Phase Steels, R. A. Kot and J. W. Morrow, Eds., pp. 304–306, The Metallurgical Society of AIME, New Orleans, La, USA, 1979.
[18]
Y. Bergstr？m and Y. Granbom, A Dislocation Model for the Stress-Strain Behaviour of Dual-Phase Steel, International Deep Drawing Research Group, Oloftr？m, Sweden, 2008.
[19]
Y. Bergstr？m, “The plastic deformation of metals—a dislocation model and its applicability,” Reviews on Powder Metalurgy and Physical Ceramics, vol. 2, no. 2-3, pp. 79–265, 1983.
[20]
G. Krauss, STEELS: Heat Treatment and Processing Principles, ASM International, 1989.
[21]
A. R. Marder, “Deformation characteristics of dual-phase steels,” Metallurgical Transactions A, vol. 13, no. 1, pp. 85–92, 1982.
[22]
E. O. Hall, “The deformation and ageing of mild steel: III discussion of results,” Proceedings of the Physical Society. Section B, vol. 64, no. 9, pp. 747–753, 1951.
[23]
N. J. Petch, “The cleavage strength of polycrystals,” The Journal of the Iron and Steel Institute, vol. 174, pp. 25–28, 1953.
