PSI - Issue 16

Ihor Dzioba et al. / Procedia Structural Integrity 16 (2019) 97–104 Ihor Dzioba, Sebastian Lipiec/ Structural Integrity Procedia 00 (2019) 000 – 000

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3. Details of numerical modeling and calibration of material constitutive relationship

The FEM calculations were performed on the numerical model of SENB specimen (Fig. 4a) with identical geometry dimensions to the experimental one ( W = 24 mm, S = 96 mm, B = 12 mm) using the Abaqus program. The SENB specimen was divided on 11 layers in thickness direction. The 8 nodes three-dimensional elements were used in calculation. Density of the elements net increases in the direction to crack tip. The crack tip is modelled as an arc with a radius of 0.012 mm. The possibility of transference was blocked according to the scheme shown in the Fig. 4b. The process of load simulation was generated by moving the high pin roller in – y axis direction. The roller position was taken from the experimental load-displacement curve. The displacement value corresponds to certain moments of loading process which were analyzed by Dzioba et al. (2018b).

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Fig. 4. The SENB specimen loading model (a) and boundary conditions (b) used in numerical calculation

During performing numerical calculations, especially when assessing areas are of high levels of deformation, it is necessary to calibrate the true stress-strain material (constitutive) relationship. The calibration of constitutive relationship was made according to Bai and Wierzbicki (2008, 2010) with taking into account the following additions introduced by Neimitz et al. (2018a, 2018b). The yield stress was defined according to the formula: = ̅̅̅( ̅ )[1 − ( − 0 )] ……... (1) where the function ̅( ̅̅̅̅) describes a relation between effective true stress and plastic strain; ƞ = is the triaxiality factor, is an average stress and is an effective stress ; ƞ 0 is a reference value of the triaxiality coefficient (for the uniaxial tensile test cylindrical specimen ,  0 = 1/3). The parameter ƞ in Eq. 1 must be determined experimentally . The equation described the effect of material weakness due to growth of voids and their merging was proposed by Neimitz et al. (2018a, 2018b) . ƞ ′ = ƞ [1 + ( _0 )( _ − _0 )] (2) In this equation , _0 is a value of plastic strain at which material weakness begins to occur, and _ are further plastic strain values . ( 0 ) is the Heaviside function . The diagrams of constitutive dependences for the material tested at T = 20 0 C with and without taking into account the effect of weakness are shown in Fig. 5a. It can be seen that only in the case of the constitutive dependence using which takes into account material weakening, the experimental and computational dependences of loading are similar (Fig. 5b).