155 CORRELATION BETWEEN HARDNESS AND TENSILE PROPERTIES IN ULTRA-HIGH STRENGTH DUAL PHASE STEELS SHORT COMMUNICATION Martin Gaško 1,*, Gejza Rosenberg 1 1 Institute of materials research, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice - Slovakia * corresponding author: Tel.: +421 55 729 2473, e-mail: mgasko@imr.saske.sk Resume The possibility to predict yield strength, strength limit, fatigue live estimation as well as other mechanical properties depending on values of materials hardness is commonly known and it is often used in practice. The main aim of this contribution is to review the possibilities of application of correlation relationships between hardness and ultimate tensile strength of steel sheets in various structural states. The experiments were performed on advanced steels with structure which is composed from ferrite and martensite (dual phase steels). Available online: http://fstroj.uniza.sk/pdf/2011/27-2011.pdf Article info Article history: Received 27 May 2011 Accepted 28 July 2011 Online 3 November 2011 Keywords: Dual phase steel Vickers hardness Mechanical properties ISSN 1335-0803 1. Introduction Although, basically the hardness test of the metal materials evaluates only surface resistance of the material against the plastic deformation, the hardness test is frequently used because it represents cheap non-destructive and simple method for assessment of various material properties like yield strength, tensile strength, fatigue limit, but also distribution of residual strains and, in a case of brittle materials, fracture toughness [2-4]. In order to determine the relationship between the ultimate tensile strength (UTS) and hardness (H) a number of relations were established [2-4]. In practice, the simplest equation is most often used: UTS = H. k (1) where k is coefficient. In contribution [1], the coefficient was in range from 3.38 to 3.55 for steel, from 3.48 to 3.21 for brass and from 2.86 to 3.63 for nodular iron (the hardness was measured according to Brinell, HB). Fig. 1 shows the progress of UTS in dependence on HB for different materials [1-3]. For aluminium alloys, in comparison with steels, generally the smaller values of coefficient k are observed (Fig.1). This can be well seen from results mentioned in Fig. 1 based on work [3]. In this contribution the fact that the value of coefficient k, in dependence on microstructure state (SDAS secondary dendrite arm spacing), is in the range from 2.63 to 2.88 was found. At the steels, the coefficient k ranges the most frequently in the interval from 3.0 to 3.6. According to standard ČSN 420379, which is replaced now by STN EN ISO 18265, in dependence on applied heat treatment or heat mechanical treatment, the influence of microstructure on correlation of TS-HB is reflected by the ratio of yield strength and tensile strength of steel. By this standard [2], for the ratio YS/TS in range from 0.5 to 0.9 the coefficient k in the range from 3.54 to 3.21 (with increase the ratio YS/TS low value of k is recommended to use) is recommended to use. In present, there exist a number of correlation
156 M. Gaško, G. Rosenberg: Correlation between hardness and tensile properties UTS - HB UTS [MPa] Al-Si-Mg (A356) fine SDAS Brass Al-Si-Mg large SDAS Steel [2] Cast iron (nodular) Steel[1] 90 140 190 240 290 340 HB Fig. 1. Plot of ultimate tensile strength of various materials as a function of hardness [1-3] relationships HB UTS a HB YS type, where besides the empirical coefficients, many other material characteristics are involved. For example, the equations by Cahoon et al. are among the most known which include the strain hardening exponent [3]. The utilizing of the high strength steels constantly increases in the entire area of industry. The high demands on strength and plastic properties of the steel sheets for automotive industry intended for the autobody are placed. Among all advanced high strength steels the dual phase steels (DP) are most often used for automotiv industry. By comparison to conventional steels, DP steels have significantly better combination values of strength versus ductility and a very good compressibility. The high plasticity of DP steels is given by microstructure consisting of soft ferrite and hard martensite. In consequence of this, these steels are also known by low value of YS/TS ratio (mostly YS/TS = 0.6 to 0.7, valid even for steels with strength over the MPa) [5,6]. The main aim of this work was to find out how the individual composition of microstructure and low ratio YS/TS results in value of coefficient k and, at the same time, with which accuracy it is possible to predict YS and TS of these steels, by the Vickers hardness testing. 2. Experimental material For experiments five low carbon steels with carbon content C = 0.07-0.15 % and manganese content Mn = 1.0-1.8 % were used. All steels were processed with two modes of intercritical annealing consisting of heating on 750 C or C (10 minutes hold) and consequential quenching in water. The volume fraction of martensite was in range from 20 to 60 %. The tensile properties was measured on specimens, which were 120 mm long, and 10 mm wide, with starting measured length L 0 = 50 mm (thickness of specimens was in range from s = 1.0 to s = 1.2 mm). In this study the correlation of relationship in form TS - HV, YS - HV, YS/TS - as well as the correlation between strain hardening exponent and hardness: n - HV was examined. 3. Results and discussion Among the all studied correlations, as expected, the highest coefficient of correlation was found between hardness and strength. However, also in this case, the correlation coefficient did not attain the value R 2 = 0.9, therefore the interdependence between strength and hardness is relatively low. The results show that the prediction of UTS value based on the measurement of values of could be loaded
157 by considerable error. The biggest scatter of data is observed in the range from 270 to 325. The anticipated strength (UTS calculated from equation on Fig. 2) is in comparison with the strength based on tensile test measurement in the range UTS ±125 MPa. When we take into account all measured values mentioned in Fig.1, and the shape of correlation equation (1) then we detect that the coefficient k is in the range from 2.8 to 3.6. The correlation coefficient for the relation YS = f () is less than R 2 = 0.8. This result clearly shows that the prediction of the yield stress of steel through the measured values of hardness is loaded with larger error as it was in the case of strength prediction. Measured results in Fig. 3 indicate that the relation YS = f () at hardness over the 325 units is steeper. The slope in the established equations reaches more than three times higher values (Fig. 3). It is likely that for the YS - correlation using the equation in exponential form would be more suitable. Also in the relation YS / UTS = f (), for the same hardness, it is possible to observe the break. From the set of correlation equations it is clear that, for the hardness of about 330 units, the relation shows a minimum (Fig. 4). In practical terms we cannot speak about correlation of YS / UTS -, because correlation coefficient is low. The data in Fig. 4 show that in the range from 210 to 330 units of the values of ratio YS / UTS are in the range from 0.5 to 0.7, and the hardness from 370 to 430 units of results in the ratio YS / UTS = 0.7 to 0.85. U T S 1300 1100 900 700 y = 2,77x + 92,754 R 2 = 0,8786 UTS - Fig. 2. Ultimate tensile strength as a function of hardness y = 1,5703x + 76,165 R² = 0,5694 YS - y = 2,5009x - 181,44 R² = 0,7695 Y S y = 5,4035x - 1312,5 R² = 0,736 Fig. 3. Yield strength as a function of hardness
158 M. Gaško, G. Rosenberg: Correlation between hardness and tensile properties YS/U T S 0,9 0,8 0,7 0,6 0,5 y = -0,0003x + 0,6852 R 2 = 0,0562 YS/UTS - y = 0,0006x + 0,417 R 2 = 0,2303 y = 0,0027x - 0,3592 R 2 = 0,5422 0,4 Fig. 4. The yield strength to tensile strength ratio, as a function of hardness () n 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 y = -0,0003x + 0,2344 R² = 0,5518 n - 0,04 Fig. 5. The strain hardening exponent as a function of hardness () Fig. 5 shows the dependence of strain hardening exponent for hardness. Unlike Fig. 3 and Fig. 4 it is possible to describe the measured data by one equation, but with low correlation coefficient R 2 = 0.55. The practical use of correlation equation n -, referred in Fig. 5, is limited. It is proved by the fact that for the steels with n = 0.14 hardness from 225 up to 320 units was measured. From the measured results in this work it is evident that the possibility to predict mechanical properties of dual phase steels by means of the measured values of hardness is very limited, if not impossible. As seen in the Table 1, from known hardness of steels, also in this case it is possible to predict the strength of steel with the accuracy about ±10 % UTS. Also we can see the correlation coefficients and relationships among the hardness and other mechanical properties which suggest the possibility of using the hardness measurements. On the other hand, it should be noted that the measured data (in the case of relationship between hardness and ultimate tensile strength) are not very different from the results measured for different steels and different structural states observed by other authors [4, 7]. Table 1 Table of regression analysis for all data sets Relationship Best fit equation Coefficient of determination UTS= f (HB) y = 2.77x + 92.754 R 2 = 0.8786 YS = f (HB) y = 2.5009x 181.44 R² = 0.7695 YS/UTS=f(HB) y = 0.0006x + 0.417 R 2 = 0.2303 n = f(hb) y = -0.0003x + 0.2344 R² = 0.5518
159 UTS - HB U T S [M Pa] Al-Si-Mg (A356) fine SDAS Brass Al-Si-Mg large SDAS Steel [2] Cast iron (nodular) Steel[1] 90 140 190 240 290 340 HB DP Fig. 6. Dependence of ultimate tensile strength of various materials as a function of hardness [1-3] Evidence of this is Fig. 6 that is identical to Fig. 1, but complemented with the data measured in this work (values of were converted using the table of values for HB). 4. Conclusions In this work the possibility of prediction of selected mechanical properties of dual phase steels by means of Vickers hardness tests was verified. It was shown that from all correlation relations established in the work it is practically applicable only the correlation between hardness and UTS (on the basis of known values it is possible to predict the strength with an accuracy of ± 10%). Results of work clearly shows that for the prediction of mechanical properties of dual phase steels with higher accuracy the influence of the microstructural parameters in the correlation equations is necessary to include. That is the aim of our further research. Acknowledgements The authors are thankful to grant agency VEGA of SR for financial support of this work, which was realized within the frame of project with No. 2/0195/09. References [1] http://www.calce.umd.edu/tsfa/hardness_ad_. htm#6 [1 November 2011]. [2] ČSN 42 0379 (in Slovak) [3] L. Ceschini, A. Morri, A. Morri, G. Pivetti: Mater Des 32 (2011) 1367-1375. [4] E.J. Pavlina and C.J. Van Type: J. Mater. Eng. Perform, 17 (8) 6 888-893. [5] G. Rosenberg, K. Buríková, Ľ. Juhár: Manufact. Eng. 3 (9) 49-52. [6] Xin-sheng Liao, Xiao-dong Wang, Xu-fei Li, Yheng-hong Guo, Yong-hua Rong: Adv. Mater. Res. 97-101 (2010) 728-732. [7] J. Pavlina, C.J. Van Tyne: J. Mater. Eng. Perform. 17(6) (8) 888-893.