PSI - Issue 33

Evgeny Lomakin et al. / Procedia Structural Integrity 33 (2021) 809–817 Lomakin E.V., Fedulov B.N. / Structural Integrity Procedia 00 (2019) 000–000

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3. Tension of the strip with angle cuts In this study, it is proposed to consider the problem of stretching a strip weakened by V-shape notches under plane strain conditions (Fig. 1). The strip is stretched by the force P . Value of the velocity of stretching of the strip away from the notches is assumed to be equal to V , edges of the cuts are free from load. The depth of the cuts is assumed to be arbitrary, but deep enough, otherwise the proposed type of plastic regions presented in Fig.1 may not be realized, namely, there may be no plastic deformations on the median line OM until the limit state is reached. For the plasticity condition, the form of ���� is chosen in the linear form (2).

Fig. 1. Section of a stripe with V-shape cuts

3.1 Analytical solution Using methods described in [5-7] it is possible to obtain kinematically admissible solution for the stress field. Thus, in ODMN region, the solution has the following form: �� � �� � ��� � � ��� �� � � � ��� � � ��� , �� � �� � � � � � �� ��� � � ��� �� � � � ��� � � ��� , �� � �, (7) where � – angle between x axis and boundary (free edge of cuts), and – constants from eq. (1) and (2), � � √3 √� � � .