Propagation of plane elastic-tough-plastic waves in the materialwith yield delay
Date
2017-01-01
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Lviv Politechnic Publishing House
Abstract
The use of electromechanical model of ideal elastic-tough-plastic material with
yield delay while investigating the propagation of plane one-dimensional waves is being considered.
The materials being investigated possesses the property of toughness only in the plastic region and is
elastic up to the plastic state. The solving of the problem is being carried out in the conditions of
one-parameter loading when the permanent (steady) uniformly distributed stress is being suddenly
applied to the boundary surface of non-deformed half-space. The value of applied stress exceeds the
limit level of elastic state in the case of static deformation and remains unchanged for the whole
region of disturbed half-space. In order to conduct the corresponding calculation the dependence
between the components the tensor of normal stress and linear deformations along the load axis is
being determined. The defining equations of elastic-tough-plastic medium behind the front of the
wave of transition from elastic to plastic state are being derived and the simple relationship for
determination of the time (duration) of yield delay is deduced. The basic solution of these equations
is obtained for the stresses in elastic and plastic region of the half-space. The special representation
of the basic pattern of changing of lateral (transverse) stresses and longitudinal deformations for the
region of active loading of material is defined. The distribution of velocities of the half-space points
in the plastic region is obtained. The difference between the characters of propagation of plane
elastic-plastic wave and the wave processes in the material with yield delay is shown.
It is noted that two different solutions are obtained despite of the simple type of loading. The
first one detects the strange character of medium’s behaviour when the material of disturbed halfspace
in the plastic region is in the state of “trembling”, which causes the pulsations of lateral
(transverse) stresses and the impulses of deformations along the axis that is normal to the boundary
surface of the half-space.
Description
Keywords
yield delay, plane elastic-tough-plastic waves, dynamic criterion of plasticity, plastic state, overstress, medium “trembling”
Citation
Andrusyk Y. Propagation of plane elastic-tough-plastic waves in the materialwith yield delay / Yaroslav Andrusyk // Ukrainian Journal Of Mechanical Engineering Andmaterials Science. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 3. — No 1. — P. 9–26.