PSI - Issue 40

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Sergey Smirnov et al. / Procedia Structural Integrity 40 (2022) 378–384 Sergey Smirnov, Marina Myasnikova / Structural Integrity Procedia 00 (2022) 000 – 000

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Fig. 3. The brass microstructure and model: (a) a photograph of the brass microstructure, 140×160 µm ; (b) a microcell surrounded by a buffer layer.

The strain resistance of the buffer layer was assumed equal to that of the brass. The strain resistance of the brass constituents was determined by the microindentation technique (Smirnov et al. (2001)) based on the identification of the stress-strain dependence by experimental results and a numerical solution to the inverse problem. The stress strain curves for the brass and its constituents can be found in (Smirnov et al. (2016)). The numerical simulation of the deformation of the metal matrix composite and the brass was conducted in the quasi-static statement. The boundary conditions, ensuring the uniaxial loading conditions of the MMC model and upsetting of the brass model under plane strain were specified in displacements of the faces of the buffer layer of each computational model. The simulation yielded stress tensor mp  and strain increment mp  tensor data in each node of the finite element models. The data were further used to determine the stress stiffness coefficient i i i k T   and the Lode-Nadai coefficient 2 3 1 3 2 i i i i i          at each finite-element mesh node of the models at the i -th computation step. Here, i  denotes the mean normal (hydrostatic) stress, i T denotes tangential stress intensity equal to the shear yield stress in the plastic region; 1  , 2  and 3  denote principal stresses at the i -th computational step. The equivalent (von Mises) strain increment at the i -th computation step is expressed in terms of the strain tensor component . Thereafter, the whole accumulated equivalent strain  in every node is computed as the total of equivalent strain increments after n computational steps of deformation ( i = 1… n ). The phenomenological theory authored by Vadim Kolmogorov (Kolmogorov (2001)) was applied to studying material damage accumulation. This theory assumes that material damage  ranges between 0 and 1, where 0 means undeformed material and 1 implies material failure and crack emergence. Material damage at a computational step of deformation is equal to the ratio between the increment of accumulated equivalent strain and ultimate equivalent strain to fracture f  , and damage accumulation follows a linear law. A node was considered to be fractured if the damage level in the node reaches 1. The condition of fracture after n steps is stated as follows: increments mp  obtained at this step as 2 3 i mp mp    



n

    1 , i i k 

1

 



(1)



f

i

i

