Plastic Wave Propagation in Linearly Work-Hardening Materials

1973 ◽  
Vol 40 (4) ◽  
pp. 1045-1049 ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Work Hardening ◽  
Wave Speed ◽  
Plane Waves ◽  
Plastic Wave ◽  
Combined Stress ◽  
Hardening Material ◽  
One Dimensional ◽  
Simple Waves ◽  
Torsional Waves ◽  
Thin Walled Tube

The combined longitudinal and torsional waves in a linearly work-hardening thin-walled tube are studied. Explicit solutions are obtained for the stress paths in the stress space for the simple waves. The stress paths are all “similar”, and hence a proportionality property in the solutions exists for simple waves as well as for a more general initial and boundary-value problem. The same results apply to any type of plane waves of combined stress. Thus the “linearity” in the solutions of one-dimensional plastic waves in a thin rod of a linearly work-hardening material is not completely lost in the solutions of combined stress waves. Depending on whether the plastic wave speed cp is larger, equal, or smaller than c2, the nature of the solutions to a given combined stress wave problem can be quite different. Examples are given to illustrate this point.

Elastic-Plastic Boundaries in Combined Longitudinal and Torsional Plastic Wave Propagation

1968 ◽  
Vol 35 (4) ◽  
pp. 782-786 ◽  
Author(s):  
R. J. Clifton
Keyword(s):  
Wave Propagation ◽  
Time Derivative ◽  
Plastic Wave ◽  
Wave Speeds ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Simple Waves ◽  
Thin Walled Tube ◽  
Loading And Unloading ◽  
All Speeds

Assuming a one-dimensional rate independent theory of combined longitudinal and torsional plastic wave propagation in a thin-walled tube, restrictions are obtained on the possible speeds of elastic-plastic boundaries. These restrictions are shown to depend on the type of discontinuity at the boundary and on whether loading or unloading is occurring. The range of unloading (loading) wave speeds for the case when the nth time derivative of the solution is the first derivative that is discontinuous across the boundary is the complement of the range of unloading (loading) wave speeds for the case when the first discontinuity is in the (n + 1)th time derivative. Thus all speeds are possible for elastic-plastic boundaries corresponding to either loading or unloading. The general features of the discontinuities associated with loading and unloading boundaries are established, and examples are presented of unloading boundaries overtaking simple waves.

Biaxial Plastic Simple Waves With Combined Kinematic and Isotropic Hardening

1970 ◽  
Vol 37 (4) ◽  
pp. 1100-1106 ◽  
Author(s):  
R. P. Goel ◽  
L. E. Malvern
Keyword(s):  
Wave Speed ◽  
Cylindrical Tube ◽  
Simple Wave ◽  
Isotropic Hardening ◽  
Hardening Material ◽  
One Dimensional ◽  
Shear Wave Speed ◽  
Simple Waves ◽  
Thin Walled ◽  
Elastic Shear

The study of one-dimensional combined longitudinal and torsional plastic wave propagation in a thin-walled cylindrical tube of isotropic-hardening material was first carried out by Clifton. In this paper, the same problem is studied for a combined kinematic and isotropic hardening material. Simple wave solutions are obtained. In some cases, a discontinuity in shear stress occurs, propagating at the elastic shear-wave speed c2, followed by a slow plastic simple wave.

A One-Dimensional, Two-Phase Flow Model for Taylor Impact Specimens

1991 ◽  
Vol 113 (2) ◽  
pp. 228-235 ◽  
Author(s):  
S. E. Jones ◽  
P. P. Gillis ◽  
J. C. Foster ◽  
L. L. Wilson
Keyword(s):  
Wave Speed ◽  
Second Phase ◽  
Plastic Wave ◽  
Two Phase ◽  
Strain Rate Effects ◽  
One Dimensional ◽  
Rate Effects ◽  
Taylor Impact ◽  
Dynamic Yield ◽  
Two Phases

In this paper, a simple theoretical analysis of an old problem is presented. The analysis is more complete than earlier versions, but retains the mathematical simplicity of the earlier versions. The major thrust is to separate the material response into two phases. The first phase is dominated by strain rate effects and has a variable plastic wave speed. The second phase is dominated by strain hardening effects and has a constant plastic wave speed. Estimates for dynamic yield stress, strain, strainrate, and plastic wave speed during both phases are given. Comparisons with several experiments on OFHC copper are included.

scholarly journals Mathematical modelling of elastoplasticity at high stress

2012 ◽  
Vol 468 (2148) ◽  
pp. 3842-3863 ◽  
Author(s):  
P. D. Howell ◽  
H. Ockendon ◽  
J.R. Ockendon
Keyword(s):  
Mathematical Model ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Wave Speed ◽  
High Stress ◽  
Plastic Wave ◽  
Simple Mathematical Model ◽  
One Dimensional ◽  
Plastic Compression ◽  
Elastoplastic Wave

This study describes a simple mathematical model for one-dimensional elastoplastic wave propagation in a metal in the regime where the applied stress greatly exceeds the yield stress. Attention is focused on the increasing ductility that occurs in the over-driven limit when the plastic wave speed approaches the elastic wave speed. Our model predicts that a plastic compression wave is unable to travel faster than the elastic wave speed, and instead splits into a compressive elastoplastic shock followed by a plastic expansion wave.

Plastic Wave Speeds in Isotropically Work-Hardening Materials

1977 ◽  
Vol 44 (1) ◽  
pp. 68-72 ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Work Hardening ◽  
Wave Speed ◽  
Three Dimensional ◽  
Yield Condition ◽  
Elastic Response ◽  
Plastic Wave ◽  
Wave Speeds ◽  
Shear Wave Speed ◽  
Perfectly Plastic ◽  
Von Mises

Plastic wave speeds in materials whose elastic response is linear and isotropic while the plastic flow is incompressible and isotropically work-hardening are obtained. One of the three plastic wave speeds is identical to the elastic shear wave speed regardless of the form of the yield condition. The other two plastic wave speeds, cf and cs, are determined for materials obeying the von Mises yield condition. The dependence of cf and cs on the stress state and the direction of propagation is investigated in detail. The largest and smallest cf and cs, and the directions along which they occur are also presented. For materials obeying the Tresca’s yield condition, it is shown that one can obtain the corresponding results by simply specializing the results for the von Mises materials. Unlike in one-dimensional analyses where the plastic wave speed becomes zero for perfectly plastic solids, the three-dimensional analyses show that the ratio of cf to c1, where c1 is the elastic dilatation wave speed, is always larger than 3/7 for the von Mises materials and 1/2 for the Tresca’s materials. For most materials under moderate loadings, this ratio is much higher.

On the theory of electrohydrodynamically driven capillary jets

1997 ◽  
Vol 335 ◽  
pp. 165-188 ◽  
Author(s):  
ALFONSO M. GAÑÁN-CALVO
Keyword(s):  
Surface Charge ◽  
Electric Fields ◽  
Gas Flow ◽  
Wave Speed ◽  
Propagation Speed ◽  
Field Equations ◽  
Steady Regime ◽  
One Dimensional ◽  
Relaxation Effects ◽  
Capillary Jets

Electrohydrodynamically (EHD) driven capillary jets are analysed in this work in the parametrical limit of negligible charge relaxation effects, i.e. when the electric relaxation time of the liquid is small compared to the hydrodynamic times. This regime can be found in the electrospraying of liquids when Taylor's charged capillary jets are formed in a steady regime. A quasi-one-dimensional EHD model comprising temporal balance equations of mass, momentum, charge, the capillary balance across the surface, and the inner and outer electric fields equations is presented. The steady forms of the temporal equations take into account surface charge convection as well as Ohmic bulk conduction, inner and outer electric field equations, momentum and pressure balances. Other existing models are also compared. The propagation speed of surface disturbances is obtained using classical techniques. It is shown here that, in contrast with previous models, surface charge convection provokes a difference between the upstream and the downstream wave speed values, the upstream wave speed, to some extent, being delayed. Subcritical, supercritical and convectively unstable regions are then identified. The supercritical nature of the microjets emitted from Taylor's cones is highlighted, and the point where the jet switches from a stable to a convectively unstable regime (i.e. where the propagation speed of perturbations become zero) is identified. The electric current carried by those jets is an eigenvalue of the problem, almost independent of the boundary conditions downstream, in an analogous way to the gas flow in convergent–divergent nozzles exiting into very low pressure. The EHD model is applied to an experiment and the relevant physical quantities of the phenomenon are obtained. The EHD hypotheses of the model are then checked and confirmed within the limits of the one-dimensional assumptions.

Matter-wave solitons supported by quadrupole–quadrupole interactions and anisotropic discrete lattices

2018 ◽  
Vol 32 (09) ◽  
pp. 1850107 ◽  
Author(s):  
Rong-Xuan Zhong ◽  
Nan Huang ◽  
Huang-Wu Li ◽  
He-Xiang He ◽  
Jian-Tao Lü ◽  
...  
Keyword(s):  
Optical Lattices ◽  
Chemical Potential ◽  
Plane Waves ◽  
Einstein Condensate ◽  
Matter Wave ◽  
Linear Dispersion ◽  
One Dimensional ◽  
Bose Einstein Condensate ◽  
Discrete Lattices ◽  
Discrete Solitons

We numerically and analytically investigate the formations and features of two-dimensional discrete Bose–Einstein condensate solitons, which are constructed by quadrupole–quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.

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