PSI - Issue 43

Maroš Eckert et al. / Procedia Structural Integrity 43 (2023) 318–323 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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where the individual functional dependences f1 to f4 are defined by a polynomial dependence with the parameters given in Table 2.

Table 3. Constants of regression polynomial functions of material parameters for steel 100MnCrW4 F 1 ( ε ) F 2 ( ε ) F 3 ( ε )

F 4 ( ε )

D 0 = 0,02053 D 1 = -0,03577 D 2 = 0,08734 D 3 = -0,05492

E 0 = 3,1745 E 1 = 6,5989 E 2 = -46,3053 E 3 = 121,8473 E 4 = -139,2667 E 5 = 58,3584

F 0 = 326,1688 F 1 = 430,7578 F 2 = -2951,4895 F 3 = 7668,4699 F 4 = -8241,2172 F 5 = 3161,7272

G 0 = 27,0503 G 1 = 30,3846 G 2 = -213,4407 G 3 = 568,5267 G 4 = -617,4469 G 5 = 237,4956

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A comparison of experimental and predicted stress values for 100MnCrW4 material is shown in Fig. 4. The course of stresses was created based on equation (2), in which polynomial functions expressing the development of material parameters depending on the deformation were substituted. Two statistical parameters were used to assess the overall applicability of a given constitutive model. The first was the Pearson correlation coefficient R and the second was the average absolute percentage error of the forecast (hereinafter “ MAPE ” ), which is defined as: = 1 ∑| − | ∙ 100 =1 (3) where n s represents the number of all stress values. In this case, the Pearson correlation coefficient is R = 0.97885 and the value of MAPE = 17.28%, which can still be considered a good prediction (Fig. 4f). The largest deviations were achieved at the lowest form ing temperature of 800 °C, which means that the given temperature forms the limit temperature for the use of this model for the given steel.

1200 °C 1100 °C 1000 °C 900 °C 800 °C Model

1200 °C 1100 °C 1000 °C 900 °C 800 °C Model

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Strain rate = 0.1 s -1

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Strain rate = 0.001 s -1

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1200 °C 1100 °C 1000 °C 900 °C 800 °C Model

1200 °C 1100 °C 1000 °C 900 °C 800 °C Model

100 150 200 250 300 350 400 Stress (MPa)

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R = 0,97885 MARE = 17,28 %

Strain rate = 10 s -1

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d) f) Fig. 4. Comparison between measured and predicted flow stresses of 100MnCrW4 steel, a) strain rate 0.001 s -1 , b) strain rate 0.01 s -1 , c) strain rate 0.1 s -1 , d) strain rate 1 s -1 , e) strain rate 10 s -1 e)