UDK 669.14.018.8:620.17:519.68 ISSN 1580-2949 Original scientific article/Izvirni znanstveni članek MTAEC9, 45(4)369(2011) PREDICTION OF THE MECHANICAL PROPERTIES OF CAST Cr-Ni-Mo STAINLESS STEELS WITH A TWO-PHASE MICROSTRUCTURE NAPOVED MEHANSKIH LASTNOSTI LITIH Cr-Ni-Mo NERJAVNIH JEKEL Z DVOFAZNO MIKROSTRUKTURO Milan Maleševic, Jelena V. Tuma, Borivoj Suštaršič, Predrag Borkovic Institute of Metals and Technology, Lepi pot 11, 1000 Ljubljana, Slovenia milan.malesevic@imt.si Prejem rokopisa - received: 2011-03-07; sprejem za objavo - accepted for publication: 2011-03-15 The results of mechanical tests on Cr-Ni-Mo stainless steels were analyzed to find a correlation between the Charpy-V impact toughness (CVN), the Vickers hardness (HV5) and the tensile strength Rm with the time and temperature of isothermal ageing. These tests were performed on three alloys with different chemical compositions and delta ferrite contents. The alloys were designated as the volume fractions of A (2 %), B (11 %) and C (with 27 % of delta ferrite). All the results were then described with the most suitable function. After that, a computer program for the prediction (calculating) of the mechanical properties (impact toughness CVN, Vickers hardness HV5 and tensile strength Rm) was made. The program application was written in the Visual Basic 6 environment. With this program it is possible to predict the change of the CVN, HV5 and Rm of Cr-Ni-Mo stainless steels depending on time, aging temperature and the delta ferrite content of the material for aging temperatures from 290 °C to 350 °C (step 10 °C), and delta ferrite content from 2 % to 27 % (step 1 %). To avoid mistakes and to focus on a time period of practical importance, the aging time is limited to 40 years. The principle used here allows us to predict the mechanical properties of other materials with any other chemical composition. However, the confirmation of this requires additional experimental data. Keywords: Cr-Ni-Mo stainless steels, impact toughness, Vickers hardness, tensile strength, delta ferrite content, empirical method, program application, Visual Basic 6 Na osnovi mehanskih preizkusov na Cr-Ni-Mo nerjavnem jeklu smo izvršili analizo vpliva temperature in časa izotermnega žarjenja na Charpy-V udarno žilavost (CVN), trdoto po Vikersu (HV5) in natezno trdnost (Rm). Mehanske preizkuse smo izvršili pri treh zlitinah z različno kemijsko sestavo in vsebnostjo delta ferita. Zlitine smo označili z volumenskimi deleži A (2 %), B (11 %) in C (27 % delta ferita). Vse eksperimentalne rezultate smo opisali z najbolj primerno empirično funkcijo. Potem smo izdelali računalniški program za napoved (izračun) mehanskih lasnosti (CVN, HV5 in Rm) v odvisnosti od časa in temperature izotermnega žarjenja (staranja). Programska aplikacija je napisana v okolju Visual Basic 6. S tem programom je mogoče predvideti spremembo CVN, HV5 in Rm Cr-Ni-Mo nerjavnega jekla, odvisno od časa, temperature staranja in vsebnosti delta ferita v materijalu, za temperature staranja od 290 °C do 350 °C (korak 10 °C) in vsebnosti delta ferita od 2 % do 27 % (korak 1 %). Da bi se izognili napakam in se osredinili na časovno obdobje, ki ima praktični pomen, je čas omejen za obdobje 40 let. Z uporabo istega načela je tudi mogoče napovedati mehanske lastnosti drugih materialov z drugačno kemično sestavo. Za potrditev tega potrebujemo nove eksperimentalne podatke. Ključne besede: nerjavna jekla Cr-Ni-Mo, udarna žilavost, trdota po Vikersu, natezna trdnost, vsebnost delta ferita, empirična metoda, programska aplikacija, Visual Basic 6 1 INTRODUCTION 2 EXPERIMENTAL PART 2.1 Experimental data The idea is to make a computer-program application able to simulate the process of aging of Cr-Ni-Mo stain- The results obtained on three different alloys, desig- less steels with a two-phase microstructure. These steels nated as A (with the volume fraction 2 % of ^-ferrite), B are used for the structural elements of older nuclear (11 %) and C (27 %) were used 4. The alloys were aged power plants 1,2,3. On the basis of the input data (aging (isothermally annealed) for up to two years at three time, aging temperature and delta ferrite content of the different temperatures, 290 °C, 320 °C and 350 °C, for steel) this program calculates and predicts the impact one day, seven days, one month, six months, one year toughness, hardness and tensile strength of a given steel. and two years. The impact toughness (Table 3), Vickers It is also able to draw diagrams for the change of each hardness (Table 4) and tensile strength (Table 5) were mechanical property with respect to the aging time. This determined on these samples. The tests were also program is based on pure experimental results and performed before the aging. All the tests were performed methods. at room temperature (20 °C). The average delta ferrite content (Table 2) was determined with a FERITSCOPE MP30, Fisher, Germany. Table 1: Average chemical composition of the selected alloys in volume fractions (0/%) Tabela 1: Povpre~na kemi~na sestava izbranih zlitin (0/%) Table 5: Average tensile strength Rm /MPa Tabela 5: Povpre~na natezna trdnost Rm /MPa A B C C 0.06 0.07 0.06 Si 0.43 0.67 1.68 Mn 1.59 1.04 0.67 P 0.03 0.03 0.03 S 0.01 0.01 0.01 Cr 18.0 21.7 20.8 Ni 11.9 11.0 9.0 Mo 1.84 2.03 2.46 Table 2: Average delta ferrite content (0/%) Tabela 2: Povpre~na vsebnost delta ferita (0/%) Table 3: Average Charpy impact toughness; CVN/J Tabela 3: Povpre~na udarna zilavost po Charpyju; CVN/J Alloy A B C Delta ferrite content 2 11 27 Alloy A B C Initial state 130 134 107 Aging time (h) Aging temperature 290 °C 24 138 109 127 168 163 87 123 720 119 117 120 4320 101 108 113 8760 149 103 61 17520 121 62 53 Aging time (h) Agin g temperature 3 20 °C 24 145 112 106 168 112 80 108 720 106 94 54 4320 176 57 33 8760 113 33 48 17520 105 34 30 Aging time (h) Agin g temperature 3 50 °C 24 155 112 103 168 102 69 76 720 155 47 28 4320 145 50 19 8760 100 34 21 17520 99 38 14 Table 4: Average Vickers hardness HV/HV5 Tabela 4: Povpre~na trdota po Vickersu HV/HV5 Alloy A B C Initial state 138 174 207 Aging time (h) Agin g temperature 290 °C 24 135 167 208 168 132 171 213 720 139 170 210 4320 132 166 207 8760 140 164 208 17520 133 174 218 Aging time (h) Aging temperature 320 °C 24 134 169 208 168 133 168 212 720 134 172 220 4320 134 173 221 8760 134 175 224 17520 139 183 238 Aging time (h) Aging temperature 350 °C 24 133 163 210 168 141 174 214 720 139 182 228 4320 131 181 230 8760 134 181 233 17520 153 187 248 Alloy A B C Initial state 371 556 684 Aging time (h) Agin; g temperature 290 °C 24 472 552 675 168 489 560 714 720 503 550 712 4320 501 561 682 8760 501 561 732 17520 479 560 705 Aging time (h) Agin; g temperature 320 °C 24 481 546 666 168 494 556 717 720 480 570 732 4320 490 568 722 8760 491 580 696 17520 492 604 765 Aging time (h) Agin; g temperature 350 °C 24 488 560 695 168 485 563 713 720 490 571 733 4320 486 594 766 8760 485 608 760 17520 495 610 824 2.2 Modelling of the functions The methodology of this procedure is explained on the alloy C and the impact-toughness results, as an example. All the results were introduced into a diagram and the characteristic points of the impact-toughness functions for all three aging temperatures are generated. For this operation we used a simple program for drawing diagrams called Graph 5. The distribution of these characteristic points is shown in Figure 1. Each point represents the average value of the impact toughness obtained by the Charpy-V test. Then the program generates automatically the most suitable and optimum function (Figure 2), which for the impact toughness is: a+b ■ t CVN =--^ (1) 1+c ■ t+d ■ t2 The most suitable and appropriate selected empirical functions describing the change of hardness and tensile strength with time at a constant temperature are: HV = a-t" (2) Rm = a ■ tb (3) where CVN (J) is the impact Charpy-V toughness, a, b, c, d are the empirically determined materials coefficients, and t (h) is the time 2.3 Creating a database of functions Only functions for the temperatures 290 °C, 320 °C and 350 °C could be developed from the available experimental data. However, the goal was also to predict the changes of the impact toughness at intermediate temperatures in between the experimental temperatures, i.e., for (300, 310, 330 and 340) °C. It was assumed that the Figure 1: Distribution of the impact-toughness characteristic points of alloy C, at 290, 320 and 350°C Slika 1: Karakteristične točke udarne žilavosti zlitine C, pri (290, 320 in 350) °C ■ ■ CVTT (J) C C 290 C C 320 C 3^ C 350 4 , * - =- -- ♦ —1-^— 0 \ -1- "^T^ 1 1 tai) Figure 4: Calculating the points for the (300, 310, 330 and 340) °C functions Slika 4: Izračun točk za funkcije (300, 310, 330 in 340) °C between 290 °C and 320°C are marked. The same principle is used for the temperatures between 320 °C and 350°C and the relation (5) was obtained. (CVN290 - CVN320 )::(CVN290 - CVNx^) = (320 - 290):(x1 - 290) ^(CyN290 - CVN^ ) ■ (320 - 290) = (CVN290 - CVN320)(x1 - 290) ^CVN - CVN - (CVN 290 - CVN 32")-( X' - 290) (4) ^CVN290 cviyx1 - 320 - 290 >CVNX - (CVN290 - CVN320) ■ (x1 - 290) Figure 2: Impact-toughness functions of alloy C, at (290, 320 and 350) °C Slika 2: Funkcije udarne žilavosti zlitine C, pri (290, 320 in 350) °C functions of the temperatures 300 °C and 310 °C lie between the functions for 290 °C and 310 °C, while the functions for 330 °C and 340 °C lie between 320 °C and 350 °C. For the determination of the characteristic points of the functions for intermediate temperatures some characteristic mathematical relations were used. The relation (4) is determined on the basis of the diagram in Figure 3, where all the important points for the temperatures 320 - 290 (CVN32„ - CVN35„):(CVN32„ - CVN^ )- (350 - 320):(x1 - 320) ^(CVN320 - CVN^^) ■ (350 - 320)- (CVN320 - CVN350 )(x1 - 320) (CVN320 - CVN350). (X1 - 320) ^CVN320 - CVN^ 1 - (5) >CVNX - (CVN320 - CVN3 350 - 320 0)■(X1- 320) 350 - 320 With the help of these two relations (4 and 5) all the characteristic points for all the functions were calculated. During the next step the functions were determined and generated. These functions now describe the way that the impact toughness of alloy C changes with time, at ageing temperatures of (290, 300, 310, 320, 330, 340 and 350) °C. The same principle as for the impact toughness was used to determine the functions for the Vickers hardness (2) and the tensile strength (3), for all three alloys A, B Figure 3: Characteristic values from equation (4) Slika 3: Značilne vrednosti iz enačbe (4) Figure 5: Generating the functions for (300, 310, 330 and 340) °C Slika 5: Prikaz generiranja funkcij od (300, 310, 330 in 340) °C Figure 6: All C functions from 290 °C to 350 °C Slika 6: Vse C funkcije od 290 °C do 350 °C Figure 7: Functions of alloy A (blue), B (green) and C (red) at an aging temperature of 290 °C Slika 7: Funkcije zlitin A (modra), B (zelena) in C (rde~a) pri temperaturi staranja 290 °C Figure 8: Calculating the points for functions with a delta ferrite content between (2, 11 and 27) %, at an aging temperature of 290°C Slika 8: Izra~un to~k za funkcije z vsebnostjo delta ferita med (2, 11 in 27) % pri temperaturi staranja 290 °C and C. Subsequently, the functions had to be divided according to the temperatures, i.e., divided into 7 groups for the ageing temperatures (290, 300, 310, 320, 330, 340 and 350) °C. The functions of the alloys A, B and C at the ageing temperature of 290 °C are shown in Figure 7. At the next step the functions for the alloys which have a delta ferrite content between the three characte- Figure 9: Generating the functions for all delta ferrite contents between (2, 11 and 27) %, at an aging temperature of 290 °C Slika 9: Generiranje funkcij za vse vsebnosti delta ferita med (2, 11 in 27) %, pri temperaturi 290 °C Figure 10: Functions for delta ferrite contents between (2, 11 and 27) %, at an aging temperature of 290 °C Slika 10: Funkcije za vsebnosti delta ferrita med (2, 11 in 27) %, pri temperature staranja 290 °C Figure 11: Functions of Vickers hardness for delta ferrite contents between (2, 11 and 27) % and an aging temperature of 290°C Slika 11: Funkcije Vickersove trdote za vsebnosti delta ferita med (2, 11 in 27) % in temperaturo staranja 290 °C ristic values of (2, 22 and 27) %, were determined by covering of all the delta ferrite contents between 2 % and 27 % (step 1). This is shown in Figures 8, 9 and 10. The same principle is used for calculating the functions for the Vickers hardness and tensile strength changes. These Figure 12: Functions of tensile strength for delta ferrite contents between 2 % and 27 % and an aging temperature of 290°C Slika 12: Funkcije natezne trdnosti za vsebnosti delta ferita med 2 % in 27 % ter temperaturo staranja Figure 13: Database of functions of the impact toughness Slika 13: Baza podatkov funkcij udarne žilavosti Figure 15: Database of functions of the tensile strength Slika 15: Baza podatkov funkcij natezne trdnosti functions (the example of the aging temperature of 290 °C) are shown in Figures 11 and 12. 2.3.1 Saving the functions in the Microsoft Office Access database As we can see, the selected functions are determined with different coefficients. The functions for the impact toughness with four, and functions for Vickers hardness and tensile strength with only two, coefficients. For this reason, all the functions are saved into the database simply by saving their coefficients. Examples of functions saved are shown in Figures 13,14 and 15. 2.4 Program application The program application was written in the Visual Basic 6 environment and was connected, using the Figure 14: Database of functions of the Vickers hardness Slika 14: Baza podatkov funkcij Vickersove trdote Figure 16: Main window of the "AgeSoft6" program Slika 16: Glavno okno "AgeSoft6" programa Figure 17: Calculated values Slika 17: Izra~unane vrednosti program code, with Microsoft Office database of functions. The main window of this program, called "AgeSoft6", is shown in Figure 16. The working principle of "AgeSoft6" is very simple. The user first inputs the "input data" and then on the basis of the input data, the software selects the appropriate function from the database. Next, the software includes the function coefficients into the equation, written in program code and calculates the results. Except for the modes for calculating the mechanical properties, there is also a mode for drawing the diagrams that show us how each function of each mechanical property changes over time. One example with calculated values and the CVN-t diagram for the alloy with 27 % of delta ferrite, aged at 320 °C for 10 000 h, is shown in Figure 17. 3 RESULTS AND DISCUSSION With this program it is possible to predict the affect of the ageing time, temperature and the content of delta ferrite, for ageing temperatures from 290 °C to 350 °C (step of 10 °C) and delta ferrite contents from 2 % to 27 % (step of 1 %) on the Charpy impact toughness (CVN), Vickers hardness (HV5) and tensile strength (Rm) of Cr-Ni-Mo stainless steels. Experimental results were available for an ageing time of 2 years. These results were used for the developing of functions that describe the change of the mechanical properties also for ageing times longer than 2 years. With the help of these functions the program calculates the mechanical properties for up to 40 years (350 400 h) of ageing. However, mistakes in the results can occur, due to possible technical mistakes during the mechanical tests performed. If the calculated value of the CVN is lower than 20 J the program gives an alarm with a warning that the CVN is below a critical value. 4 CONCLUSIONS The developed program is purely empirical and is made on the basis of the experimental data obtained for Cr-Ni-Mo stainless steels, so it corresponds in principle only to these kinds of steels with these chemical properties and ageing conditions. To have more value the program must be more universal. Therefore, in the next stage of the development of this program, experimental data for cast Cr-Ni duplex stainless steels will be used. The creation of a universal computer program that describes the ageing behaviour of any type of steel is probably too optimistic and at the moment this task is too difficult. 5 REFERENCES 1 Jelena V. Tuma, Borivoj Su{tar{i~, Franc Vodopivec: The effect of ageing temperature and time on the mechanical properties of Fe-NiCrMo alloys with different contents of delta ferrite, Nucl. Eng. Des., 238 (2008) 7, 1511-1517 2 Jelena V. Tuma, Borivoj Su{tar{i~, Roman Celin, Franc Vodopivec: The mechanical properties of two-phase Fe-NiCrMo alloys at room temperature and 290 °C after ageing in the temperature range 290-350 °C, Mater. Tehnol. 43 (2009) 4, 179-187 3 Roman Celin, Jelena V. Tuma, Boris Arzen{ek: Effects of ageing a two-phase Fe-NiCrMo alloy on the strain hardening at room temperature and at 290 °C, Mater. Tehnol. 43 (2009) 5, 251-255 4B. Su{tar{i~, J. V. Tuma, D. Kmeti~, R. Celin, B. Arzen{ek, B. Breskvar, F. Vodopivec, M. Godec, T. Drglin, J. Janovec, I. Nagli~, R. Sturm, L. Kosec, B. Kosec, P. Skraba, N. Grubeljak, P. McGui-ness, B. Saje, Z. Ra~i~, S. Sumlaj: Research of structural brittleness of two-phase stainless steels, Final report on the results of research project, Institute of metals and technology, University of Ljubljana, NTF-Department for materials and metallurgy, Ljubljana, 2004. 5 Graph - is an open source application used to draw mathematical graphs in a coordinate system. The program makes it very easy to visualize a function and paste it into another program. It is also possible to do some mathematical calculations on the functions. Copyright © 2009 by Ivan Johansen