PSI - Issue 13

Andrzej Neimitz et al. / Procedia Structural Integrity 13 (2018) 862–867

867

Andrzej Neimitz et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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range 1287-1297 MPa The location of the stress maximum has been also almost the same. Without calibration, the stress maximum is 1319 or 1324 MPa for the linear and power function extrapolation respectively. Large differences are in the stress distributions just in front of the crack, as expected and noticable differences are observed in the case of accumulated effective plastic strains distributions. These strains can be about 15% higher when the effect of the softening is included and when they are compared with the strains computed using the constitutive equation without calibration. Similar behaviour to that shown in Figs 5 was observed for other materials and temperatures. When the SEN(B) specimen is used to calibrate the constitutive equation, very good agreement between numerical and experimental curves is obtained. However, when the constitutive equation obtained after calibration is used to compute the stress field in front of the crack, the result is almost the same as for the material without calibration. Calibration using the SEN(B) specimens reflects the “average” behaviour of th e entire specimen, not the local field in front of the crack. 3. Conclusions Several conclusions can be drawn after numerous calibrations of the original stress – strain curves: 1) Linear approximation of the last segment of the TS-LS curve and further extrapolation of this line to large strains leads to favourable results for all tested specimens, materials and temperatures, provided the calibration procedure including material softening is performed. 2) Approximation of the entire plastic part of the TS_LS curve by a power function and further extrapolation can be used for ductile materials at room temperature and for planar specimens (Fig. 1c). When the microstructure or temperature constrains plastic deformation, the power function approximation is not recommended before the calibration according to the Bai-Wierzbicki procedure. 3) The geometrical details of the notched cylindrical specimens are not important for calibration of the constitutive curve when the constitutive equation is used to compute the stress and strain fields in front of the crack. 4) Calibration of the constitutive equation, including material softening, leads to significant correction of the stress field in front of the crack with respect to the field obtained without TS-LS calibration. 5) When the test temperature is lower, differences between calibrated and uncalibrated constitutive equations are smaller. 6) It is possible to obtain constitutive equation after calibration with the same set of α, , and m coefficients for all four specimen geometries discussed so far. Such a constitutive equation leads to acceptable agreement between the experimental and numerically obtained curves (Neimitz et al. (2018)). However, much better results can be obtained if the calibration is performed using each specimen geometry separately. To our knowledge, a universal function that can be used to calibrate TS-LS curves for different specimen geometries, does not currently exist. 7) When studying the stress distribution in front of the crack, selection of the specimen geometry, to perform calibration, must depend on a region along the crack front; e.g., the notched cylindrical specimen would be better for the analysis in the central part of the fractured specimen, and the specimen shown in Fig. 1b would probably be better for the region close to the fractured specimen surface. Acknowledgements This research was performed with financial support from the Polish National Science Committee (NCN), grant no. UMO-2014/15/B/ST8/00205. Bai, Y., Wierzbicki, T., 2008. A new model plasticity and fracture with pressure and Lode dependence. International Journal of Plasticity 24, 1071 – 1096. Algarni, M., Bai, Y., Choi, Y., 2015. A study of Inconel 718 dependency on stress triaxiality and Lode angle in plastic deformation and ductile fracture. Engineering Fracture Mechanics 147, 140 – 157. Bai, Y., Wierzbicki, T., 2010. Application of extended Mohr – Coulomb criterion to ductile fracture. International Journal of Fracture 161, 1 – 20. Neimitz, A., Galkiewicz, J., Dzioba, I., 2018. Calibration of constitutive equations under conditions of large strains and stress triaxiality. Archives of Civil and Mechanical Engineering18/4, 1123 – 1135. References