PSI - Issue 30

L.A. Prokopyev et al. / Procedia Structural Integrity 30 (2020) 120–127

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Prokopyev L.A. et al. / Structural Integrity Procedia 00 (2020) 000–000 � � � � � � ��� �� � � �� � � � �� �� � � �� � � � �� �� � � �� � � � ��� �� � � � �� � � � �� � ��

(1)

� Т � � � √��� ���� Т � � � � � � � ��� Т � � � � � � � �� ���� � � � �

(2)

(3) For the values of stress intensity factor and T-stresses found by the finite element method, for five values of the cooling temperature, the specific volume � � and the linear size of the plastic zone along the crack extension line � are determined. The calculation results for each cooling temperature are shown in Table 2. Table 2. The results of calculating the stress intensity factor, T-stresses and dimensions of the plastic zone by finite element method in plane strain and plane stress states. Values of the fracture mechanics parameters from the finite element method 213 K 223 K 233 K 243 K 253 K � � Scheme No.1, ��√� 4,16 3,64 3,12 2,60 2,08 � � Scheme No.2, ��√� 5,55 4,86 4,17 3,47 2,78 � � Scheme No.1, �� 46,6 39,2 34,0 28,0 22,8 � � Scheme No.2, �� -62,8 -54,2 -47,1 -38,5 -31,0 � � , Scheme No.1, plane strain, �� � 0,0366 0,0283 0,0209 0,0146 0,0094 � � , Scheme No.1, plane stress, �� � 0,0763 0,0582 0,0427 0,0295 0,0189 � � , Scheme No.2, plane strain, �� � 0,0759 0,0574 0,0418 0,0286 0,0182 � � , Scheme No.2, plane stress, �� � 0,1303 0,1002 0,0739 0,0513 0,0330 � , Scheme No.1, plane strain, �� 0,0023 0,0017 0,0013 0,0009 0,0006 � , Scheme No.1, plane stress, �� 0,0151 0,0114 0,0083 0,0057 0,0036 � , Scheme No.2, plane strain, �� 0,0037 0,0028 0,0021 0,0015 0,0010 � , Scheme No.2, plane stress, ��� 0,0211 0,0165 0,0123 0,0087 0,0057 Since the purpose of this work is the relationship between the stress intensity factor and the parameters of the plastic zone, the stress intensity factor is used instead of the temperatures of the cooling zone in further calculations. The values of the plastic zone specific volume for five values of the stress intensity factor were also determined. The dependence of the plastic zone specific volume and the size along the crack extension line on the stress intensity factor is plotted. The dependences of the plastic zone specific volume and the plastic zone size along the crack extension line on the stress intensity factor are shown in Fig.5 and Fig.6. 4. Discussion For the two loading schemes, power-law dependences of the plastic zone volume on the stress intensity factor are obtained. By the finite element method, a model of low-temperature loading of a steel sheet with a centrally located crack at various cooling temperatures has been implemented; inaccuracy in calculating the fracture mechanics parameters by the finite element method for the standard loading scheme was no more than 0.15% compared to the method of boundary collocations. It should be noted from Fig.5, Fig.6 that for two schemes with the same stress intensity factor values, different power-law coefficients were obtained, which corresponds to the experimental Builo's results (2017).