Application of the energy-based criterion to the simulation of the fracture of the steel structures.

*(Russian. English summary)*Zbl 1413.74005Summary: In this work we develop a energy balance model for inelastic deformation process of metals. The changes in the material structure are taken into account with the help of a tensorial variable having the physical meaning of additional strain induced by initiation of defects. The introduction of such a parameter allows one to calculate the stored energy value and develop an energy-based fracture criterion. We consider two ways of derivation of the constitutive equations for plastic and structural strain. The first method is based on the principles of linear nonequilibrium thermodynamics, the second one is the analogue of the flow plasticity theory. The developed thermomechanical model includes an equilibrium equation, a geometric relation for the strain tensor, Hooke’s law, the constitutive equations for the structural and the plastic strain and energy balance equation. It is assumed that fracture in the material takes place when the stored energy reaches a critical value in some volume of the material. The application of such an approach to fracture problems of metals is illustrated by two numerical examples. The first example is a crack path simulation in the steel shaft with initial crack oriented at a certain angle to the shaft axis. The second example is simulation of the crack initiation and propagation in a steel bearing bracket. The obtained results are in agreement with the previously published results and could be used for the simulation of fracture of real structures.

##### MSC:

74A45 | Theories of fracture and damage |

74B05 | Classical linear elasticity |

74R20 | Anelastic fracture and damage |

##### Keywords:

stored energy; numerical simulation; fracture of solids; thermodynamics of inelastic deformation; AISI 304 steel##### Software:

PROCRACK
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\textit{A. A. Kostina} et al., Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 20, No. 4, 656--674 (2016; Zbl 1413.74005)

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