PSI - Issue 13

Andrzej Neimitz et al. / Procedia Structural Integrity 13 (2018) 862–867 Andrzej Neimitz et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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Fig. 4. The stress – strain curves after various stages of calibration.

When new constitutive equation, after calibration is implemented to the ABAQUS and the stress and strain field in front of the crack is computed, the stress distribution in front of the crack, after various calibration procedure is shown in Fig. 5. In Figs 5 several curves representing opening stress and accumulated effective plastic strains are shown. They include also the curves obtained numerically using uniaxial TS_LS curves without calibration, but applying two different extrapolation techniques of these curves beyond the stress maximum.

a)

b)

Fig. 5. a) opening stress distribution in front of the crack after the stress - strain curves calibration using C04, C1 various options of calibration and cylindrical specimens without calibration. Material N, temp. +20 º C. Central part of SENB specimen; b) accumulated effective plastic strain distributions in front of the crack after the stress - strain curves' calibration using C04, C1, PN, specimens with various options of calibration and cylindrical specimens without calibration. +20 º C. Central part of SENB specimen. In Fig.5 the curves a and b were obtained without calibration of the stress-strain curve. Other curves are after different calibration procedures. Usually, linear extrapolation without calibration leads to the results, which are not acceptable from the physical point of view, since the opening stress at the crack tip increases, while it is well known, that material at this region has been softened by the voids evolution. Sometimes, similar behaviour is observed after extrapolation using the power function. Moreover, extrapolation of the TS_LS curves by the power function is not always possible, in particular at low temperatures, e.g. see Figs 3. Thus, the process of calibration is necessary. Two methods of calibration were tested: with and without the effect of material softening, using four different specimen's geometries and two ways of the stress-strain curves extrapolation. The method of calibration has no essential influence on the values of the stress maximum in front of the crack. All maximum values obtained after testing 12 methods of calibration and shown in Fig. 5 for N material, were within the