S.E. Jones

On the equation of motion of the undeformed section of a Taylor impact specimen

In this paper a one‐dimensional analysis is presented that leads to the appropriate equation of motion for the undeformed portion of a plastic, rigid rod after impact with a rigid anvil. This equation is used as a basis for deducing material properties of the rod material from post‐test measurements.

On the penetration of semi-infinite targets by long rods

Abstract T he one-dimensional eroding-rod penetration theory proposed by A. T ate ( J. Mech. Phys. Solids 15 , 387, 1967; 17 , 141, 1969) is modified in two ways. In the equation of motion of the rigid end of the rod, a proper accounting is made of mass transfer into the plastic region. Also, the mushroom strain at the deforming end of the rod is incorporated into the analysis. It is shown that this latter factor has a very substantial effect on calculated penetrations.

On some conservation laws of conservative and non-conservative dynamic systems

Abstract This study is concerned with the derivation of conservation laws of both conservative and non-coaservative dynaraical systems with finite numbers of degrees of freedom. First, the derivation of generators of the infinitesimal transformations of the generalized coordinates and time from Noethers basic identity is discussed. In the second part, a special class of conservation laws of conservative dynamical systems which are called action integral conservation laws is developed.

Some further results on the Taylor impact test

Abstract The impact of a rigid, plastic rod with a rigid anvil is analyzed as a one-dimensional problem. The material is assumed to strain-harden during plastic deformation and one hardening parameter is determined using post-test measurements of the deformation.

Stress distributions in the vicinity of a neck

The Bridgman analysis gives the stress distribution at the minimum cross section in a neck in a round tensile specimen. Consequently, the Bridgman analysis is essentially one dimensional since only radial variation (at constant axial position) is considered. In the present analysis the assumptions made by Bridgman are assumed valid for other cross sections close to the neck. A method suggested by Kaplan is then used to extend the Bridgman analysis to obtain the stresses as a function of both radial and axial position.

Linearly viscoplastic material

Viscoplastic material models which are based upon dislocation dynamics are so complex mathematically that they seldom yield closed‐form solutions to boundary value problems. Here we examine a material having a linear dependence of dislocation speed on stress. The boundary value problem corresponding to a constant crosshead speed tension test of this material remains highly nonlinear. However, an analytic solution to the problem is found in terms of tabulated functions and this solution is used to demonstrate some of the features of the response of the material during tension testing.

Impact of work-hardening cylinders on a rigid boundary

Abstract The problem of impacting a uniform cylinder of rigid-plastic work-hardening material is investigated. The elementary equations of motion are inverted through the Hodograph Transformation and an exact solution for plane plastic wave propagation is given. This solution is expressed in terms of the motion of the rigid-plastic interface and the current velocity of the rigid rod section. A simple example is discussed.

Upper yield points of non-linear viscoplastic materials

Abstract An approximate solution to the non-linear differential equation governing the behavior of a non-linear, viscoplastic material in tension is given. This solution is used to generate an accurate estimate for the upper yield point for the material. The results are compared to those previously obtained by other means.