A modelling of plastic deformations growth under impact, based on a numerical solution of the plane stress state problem

Аuthors

Bogdanov V. R.^1*, Sulym G. T.^2**

1. National Transport University, Suvorova str., Kyiv, 01010, Ukraine
2. Lviv Ivan Franko National University, Universitetska str., Lviv, 79000, Ukraine

*e-mail: vladislav_bogdanov@hotmail.com
**e-mail: sulym@franko.lviv.ua

Abstract

A new finite-difference method of numerical solution for dynamic plane problems of elastic-plasticity theory taking into account unloading processes is proposed. A plane stress state for the three-point bar bending is considered and some solutions for the bars with rectangular cross-sections and the middle notch modeling the crack have been obtained. The plastic strain areas around the crack tips in different alloys are compared.
The considered specimen is loaded by the impact of the absolutely rigid striker. Due to the short interaction time the dynamic load can be approximated by the pressure at the contact area varying in time as a linear function. Both the contact and bearing areas are constant. The theory of non-isothermal flow of strengthening plastic media, the Huber-Mizes yield criteria, and the hypothesis of short-term creep are used. We also suppose that the material is strengthening during the elastic-plastic deformation process. The successive approximation approach is used for the physically nonlinear problems solution together with the variable- step finite difference schema.
The numerical solutions are computed for compact specimens made of RPV steel 15Х2НМФА, aluminum, titanium and silver. The areas of plastic deformations at the top of the notch-crack for the alloys with different shear and bulk modulus are compared. It is shown that rising of the ratio between the shear and bulk modulus results rising of plastic zones at the top of crack-notches.

Keywords:

compact specimen, plastic deformation, marginal incision, plane problem, impact loading

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