Dynamic Plastic Response Research Articles

The interaction between pulse shape and strain hardening in dynamic plastic response

The effect of pulse shape on the dynamic plastic response of a single-degree-of-freedom system with rigid-strain-hardening behavior is investigated. The duration of response and final displacement are found to depend exactly on three parameters defined in terms of simple integrals of the pulse shape and material constants. These three parameters, however, lack an obvious physical interpretation. Consequently, a second set of three parameters is proposed which approximately accounts for the effect of pulse shape on the determination of the response duration and final displacement. Two of these parameters are the amplitude and duration of an equivalent rectangular pulse which has the same area and centroid as the applied pulse. The third parameter represents the amount of strain hardening and is determined from the strain-hardening coefficient and a measure of the effective pulse length.

Dynamic response of an infinitely large rigid-plastic plate impacted by a rigid cylinder with transverse shear and rotatory inertia

A theoretical solution for the dynamic response of an infinitely large, rigid-perfectly plastic plate with transverse shear force and rotatory inertia under a normal impact of a rigid flat-end cylinder is given herein. Embedding and perforation are investigated, and the numerical results indicate the influence of rotatory inertia and the transverse shear force on the dynamic plastic response of the plate.

Dynamic plastic response of circular plates in a damping medium

The motion of a simply supported circular plate of rigid-plastic material is studied. The motion is produced by a uniformly distributed impulsive velocity [Jones and de Oliveira, ASME J. appl. Mech. 47, 27–34 (1980)]. The material of the plate is assumed to obey the Tresca yield criterion with the inclusion of shear yield. The effect of damping by the surrounding medium on the plate motion is examined.

Dynamic Plastic Response of Circular Plates With Transverse Shear

Technical Briefs Dynamic Plastic Response of Circular Plates With Transverse Shear A. Kumar, A. Kumar Civil Engineering Department, Indian Institute of Technology Kanpur, Kanpur, India 208 016 Search for other works by this author on: This Site PubMed Google Scholar V. V. Krishna Reddy V. V. Krishna Reddy Civil Engineering Department, Indian Institute of Technology Kanpur, Kanpur, India 208 016 Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information A. Kumar Civil Engineering Department, Indian Institute of Technology Kanpur, Kanpur, India 208 016 V. V. Krishna Reddy Civil Engineering Department, Indian Institute of Technology Kanpur, Kanpur, India 208 016 J. Appl. Mech. Dec 1986, 53(4): 952-953 (2 pages) https://doi.org/10.1115/1.3171887 Published Online: December 1, 1986 Article history Received: March 3, 1986 Revised: May 21, 1986 Online: July 21, 2009

Dynamic plastic deformation of an infinite plate

A solution is derived for the dynamic plastic response of an infinite plate subjected to a general axisymmetric pressure pulse which varies both with position and time and is applied to a time-varying area of the plate. An approximation formula is obtained for the final plastic deformation in terms of simple integrals of the loading.

Bounds on the dynamic plastic behaviour of structures including transverse shear effects

The influence of transverse shear is an important factor in the dynamic plastic response of several practical problems. In fact, transverse shear effects play a vital role in the severance of structures at hard points and dominate the response of ideal fibre-reinforced structures as well as being potentially important for higher modal structural responses. It is demonstrated in this article that the simple bound theorems, which were developed for rigid plastic continua, can provide excellent estimates of the response durations and permanent displacements of impulsively loaded beams, circular plates and cylindrical shells when transverse shear effects are important. The bound theorems also provide exact agreement with the dynamic behaviour of the ideal fibre-reinforced structures which have been examined.

Stress wave experiments in plasticity

Plastic wave experiments are reviewed, beginning with the earliest experiments of Bell on the propagation of incremental waves in prestressed bars. Attention is directed to experiments in which the plastic wave profile at different distances of propagation is used to infer information on the dynamic plastic response of the material in which the wave is propagating. Plastic waves in bars, tubes, and plates are considered. Principal results are reviewed on such primary physical features as the velocity of propagation of incremental waves, the dynamic elastic limit, the wave profiles of finite amplitude waves, and the effects of nonproportional loading. Objectives for future research are suggested.

Euromech colloquim 217 dynamic plastic response of structures: to be held at Mátrafüred, Hungary, 13–16 October 1986

Euromech colloquim 217 dynamic plastic response of structures: to be held at Mátrafüred, Hungary, 13–16 October 1986

Pressure-shear waves in 6061-T6 aluminum and alpha-titanium

T he pressure-shear plate impact technique is used to study material behavior at high rates of deformation. In this technique, plastic waves of combined pressure and shear stresses are produced by impact of parallel plates skewed relative to their direction of approach. Commercially pure alpha-titanium and 6061-T6 aluminum are tested under a variety of pressure and shear tractions by using different combinations of impact velocities and angles of inclination. A laser interferometer system is used to monitor simultaneously the normal and transverse components of motion of a point at the rear surface of the target plate. The experimental results are compared with numerical solutions based on an elastic/viscoplastic model of the material. Both isotropic and kinematic strain hardening models are used in the computations. The results indicate that unlike the normal velocity profiles, the transverse velocity profiles are sensitive to the dynamic plastic response and, thus, can be used to study material behavior at high strain rates. For the materials tested the results suggest that the flow stress required for plastic straining increases markedly with increasing strain rate at strain rates above 10 4s −1. Hydrostatic pressure of the order that exists in the tests (up to 2 GPa) does not affect the plastic flow in 6061-T6 aluminum and appears to have at most a minor effect on the deformation of the titanium.

Parkes revisited: On rigid-plastic and elastic-plastic dynamic structural analysis

In this paper we re-examine a classical problem of rigid-plastic structural dynamics solved by Parkes [1], namely that of finding the deformations of a beam carrying a mass at its tip which is subjected to a short pulse loading. A considerable body of “elementary rigid-plastic theory” has been developed based on the neglect of elastic strain components, the idealization of perfectly plastic behavior (absence of strain hardening or strain rate sensitivity), and the assumption of linear field equations ignoring effects of geometry changes. This theory provides a valuable conceptual framework for problems of dynamic plastic structural response, although corrections are required for many practical applications; for example, Parkes introduced a correction for effects of high strain rates shown to be needed by his experiments on steel beams. The neglect of elastic strains — elastic moduli taken infinite — is a crucial assumption, and its validity is the subject of the present paper. We study it by making comparison between “exact” numerical solutions furnished by an advanced finite element computer program for an elastic-plastic beam, and the rigid-plastic solution slightly modified to allow for large deflections. Further insight is gained by comparisons also with a simplified elastic-plastic approach based on treatment of elastic and plastic action in artificially separated stages. The main conclusions are that the initial travelling-hinge phase of the rigid-plastic solution is essentially a fiction, but that the subsequent mode form phase is a prominent and significant feature of the late-time part of the “actual” elastic-plastic response.

Dynamic Plasticity

Recent advances in the understanding of the dynamic plastic response of crystalline solids are discussed. At the level of individual dislocations progress is being made on measurements of dislocation mobility at high stress levels and on elastodynamics solutions for transient dislocation motions. More progress is required on the understanding of changes in mobile dislocation density during dynamic plastic deformation. Widespread use of the Kolsky (or split-Hopkinson) bar has resulted in a reasonably clear picture of the dependence of flow stress on plastic strain rate for polycrystalline metals deformed at strain rates up to 103s−1. Influences of strain-rate history, temperature, and pressure require further investigation. At strain rates of approximately 103s−1’ to 105s−1 there is increasing evidence of a marked increase in flow stress with increasing strain rate. Pressure-shear plate impact experiments appear to be attractive for studying plastic response in this high strain-rate regime. Differences, if any, between stress-path effects at quasi-static strain rates and at strain rates of 103s−1 and higher remain poorly understood. Larger-than-predicted precursor decay observed in plate impact experiments on single crystals remains unresolved and of continuing fundamental interest; however, the importance of precursor decay measurements in determining dynamic plastic response appears to be diminishing because surface effects and limitations on the resolution of wave-front profiles represent serious constraints on the inferences that can be drawn from precursor decay measurements. Modeling of dynamic plastic response of polycrystals in terms of the response of slip systems is in an early stage of development. Kinematics of finite deformation by crystalline slip and consistent averaging techniques for modeling polycrystalline response are understood reasonably well. Increased emphasis on the understanding of the dynamic plastic response of single crystals and on the influence of microstructure appear desirable for sustained progress. Physically based models of wide applicability are required.

Dynamic axial plastic buckling of stringer stiffened cylindrical shells

A perturbation method of analysis has been used to examine the dynamic plastic buckling of a stringer-stiffened cylindrical shell subjected to an axial impact. It transpires that it is more efficient to place stiffeners on the outer shell surface rather than on the inner surface. Various results are presented to demonstrate the influence of the second moment of area, eccentricity, cross-sectional area and number of stiffeners on the dynamic plastic response.

Dynamic Plastic Response of Cylindrical Shells Under Gaussian Impulse

The determination of the inelastic response of cylindrical shells under general impulsive loads is of relevance to marine structures such as submarines, in analyzing their slamming damages. The present study is concerned with the plastic response of a simply supported cylindrical shell under a general axisymmetric impulsive load. The impulsive load is assumed to impart an axisymmetric velocity to the shell, with a Gaussian distribution along the longitudinal axis of the shell. A simplified Tresca yield condition is used. The shell response is determined for various forms of impulses ranging from a concentrated impulse to a uniform impulse over the entire length of the shell. Conclusions about the influence of geometry of the shell and the spatial distribution of impulse on the plastic behavior of cylindrical shells are presented.

Dynamic Plastic Response of Circular Plates With Transverse Shear and Rotatory Inertia

The response of a simply supported circular plate made from a rigid perfectly plastic material and subjected to a uniformly distributed impulsive velocity is developed herein. Plastic yielding of the material is controlled by a yield criterion which retains the transverse shear force as well as bending moments and the influence of rotatory inertia is included in the governing equations. Various equations and numerical results are presented which may be used to assess the importance of transverse shear effects and rotatory inertia for this particular problem.

Stress analysis of the strain rate hardening materials in axially symmetric field

This paper presents an analysis of a circular hollow cylinder composed of strain rate hardening plastic material subjected to a sudden internal pressure loading. Materials satisfying the constitutive relation, σ ∼ = σ 0 ϵ ∼ m and Levy-Mises equation are considered in the analysis. Dynamic and static analyses of axially symmetric material loaded under plane strain condition are described. The paper discusses the effect of strain rate hardening exponent, m, on the dynamic and static plastic response in the axially symmetric medium. A method is presented for the determination of the strain rate hardening exponent by measuring the hoop stress on the outer surface of a thin cylindrical specimen using the static solution.

The Influence of Rotatory Inertia and Transverse Shear on the Dynamic Plastic Behavior of Beams

The theoretical procedure presented herein examines the influence of retaining the transverse shear force in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Exact theoretical rigid perfectly plastic solutions are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively. It transpires that rotatory inertia might play a small, but not negligible, role on the response of these beams. The results in the various figures indicate that the greatest departure from an analysis which neglects rotatory inertia but retains the influence of the bending moment and transverse shear force in the yield condition is approximately 11 percent for the particular range of parameters considered.

A Numerical Procedure for the Dynamic Plastic Response of Beams with Rotatory Inertia and Transverse Shear Effects

ABSTRACT A numerical procedure is used to examine the influence of transverse shear forces in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Various results are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively, both of which are made from a rigid perfectly plastic material with yielding controlled by the Ilyushin-Shapiro ield criterion. Transverse shear effects lead to a dramatic reduction in the slopes of the deformed profiles for both beam problems. Moreover, the slope of the deformed profile underneath the striker in the impact problem is quite sensitive to the actual shape of a yield curve, while the maximum transverse displacement is less sensitive. The retention of rotatory inertia in the basic equations leads to further reductions up to 17 and 10% in the slopes and maximum transverse displacements, respectively.

Recent Progress in the Dynamic Plastic Behavior of Structures

Abstract : This article attempts to review the literature on the dynamic plastic response of structures published during the last three years, since the last survey by the author was published in the Shock and Vibration Digest(1). The review focuses largely on the behavior of simple structural components such as beams, plates and shells subjected to dynamic loads which produce extensive plastic flow of the material. In particular, recent work on the behavior of ideal fibre-reinforced beams, higher modal response of beams, the influence of transverse shear and rotatory inertia, approximate methods of analysis, rapidly heated structures, fluid-structure interaction and dynamic plastic buckling are discussed in detail. These topics are followed by a discussion of a few recent numerical studies on the dynamic plastic response of structures, and a brief survey of some recent experimental and theoretical investigations into the collision protection of vehicles. (Author)

Higher modal dynamic plastic behavior of beams loaded impulsively

It was demonstrated in a previous study 1 that the higher modal dynamic plastic response of beams may be a more efficient means of absorbing a given initial kinetic energy than a single modal response. Thus, the higher modal dynamic plastic response of impulsively loaded, fully clamped beams is examined herein, using various rigid perfectly plastic theoretical procedures and a numerical elastic-plastic computer code.

Dynamic Plastic Response of an Immersed Pipe

The dynamic plastic deformation of a rigid-ideally plastic pipe subjected to an internal pressure is reduced when the pipe is surrounded by a fluid. A method to determine the added (virtual) mass which reflects the resistance of the fluid being displaced by the deforming pipe is described herein. The expression for the added mass is derived in form of an integral which in turn is solved by means of numerical techniques recognizing the asymptotic behavior of the argument. A single parameter family of curves is given for the added mass. An approximation in the form of a polynomial is also computed for the added mass in order to simplify the subsequent determination of the plastic deformation of the pipe.