Dynamic Plastic Behavior Research Articles

Recent Progress in the Dynamic Plastic Behaviour of Structures, Part Iv

Recent Progress in the Dynamic Plastic Behaviour of Structures, Part Iv

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.

Recent Progress in the Dynamic Plastic Behavior of Structures, Part III

Recent Progress in the Dynamic Plastic Behavior of Structures, Part III

Behavior of viscoplastic circular plates under Gaussian impulse

The dynamic plastic behavior of viscoplastic circular plates subjected to impulse loading is presented. The impulse is assumed to impart a transverse axisymmetric velocity with a spatial Gaussian distribution. The combined influence of membrane forces, bending moments and strain-rate sensitivity is considered in predicting the deformation. Numerical results are presented to show this influence on the rate of growth of plastic regimes, the deflection configuration and the total time of response. It is concluded that the spatial distribution of impulse has a considerable effect on the deformation response of the plate, and relatively small effect on the total time of response; furthermore, the simple bending theory is inadequate to reliably predict the response.

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.

Literature Review : Recent Progress in the Dynamic Plastic Behavior of Structures: Part II

Literature Review : Recent Progress in the Dynamic Plastic Behavior of Structures: Part II

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.

A study of the higher modal dynamic plastic response of beams

A theoretical and experimental investigation into the higher modal dynamic plastic response of fully clamped beams is reported herein. It is shown that the influence of geometry changes or finite-deflections is important which agrees with previous studies on the dynamic plastic behavior of uniformly loaded beams. It appears that the higher modal response of beams is a more efficient means of absorbing a given magnitude of kinetic energy than a single modal response.

Large Displacement Matrix Analysis of Elastic/Viscoplastic, Plane Frame Structures

Within the framework of lumped mass/elementary beam theory, a large displacement matrix analysis of elastic/perfectly viscoplastic plane frame structures undergoing primarily flexural deformations and following a constitutive power law is first formulated. A general purpose computer program based on the step-by-step computational procedure in conjunction with the fourth order Runge-Kutta integration technique is then developed. The computerized study is then used in an analytical/experimental correlation study of the dynamic response of a laboratory impact test problem of a mild steel plane frame dropped into a narrow rigid pole obstacle at 20 mph (32.2 km/hr); good analytical and experimental correlation results are obtained up to 2 percent of strain. An example problem of inelastic response of an automobile bumper (beam) subjected to impact loading is also given. Discussion of the results with regard to strain rate sensitivity effects on dynamic plastic behavior and comparison of the “exact” solution with those obtained under certain simplified approximations are made.

Dynamic plastic behavior of structures under impact loading investigated by the extended hamilton's principle

We propose the extended Hamilton's principle to investigate the dynamic plastic behavior of a beam or a plate under an impact loading. Material is assumed to be rigid perfectly plastic. The impact loading is given in the form of initial velocity. Good agreement between our numerical solutions and experimental results done by Parkes and Jones indicates that the proposed variational method is a powerful approximation method for the dynamic plasticity analysis. The effect of strain-rate sensitivity on the permanent deflection of a plate is investigated in some detail. Instead of nonlinear differential equations, nonlinear algebraic equations are solved in the proposed method.

Some experiments on the dynamic plastic behavior of shell intersections

An experimental investigation into the dynamic plastic behavior of some metal shell intersections is reported. The models consist of a cylindrical nozzle intersecting a hemispherical shell which is subjected to a uniformly distributed internal impulsive velocity field. The magnitude of the initial kinetic energy of the dynamic load is sufficient to cause inelastic behavior and small permanent displacements.

The dynamic plastic behavior of simply supported spherical shells

A theoretical study has been undertaken into the dynamic plastic response of simply supported shallow and deep spherical shells subjected to exponentially decaying pressure pulses. The shells were assumed to be made from a rigid perfectly plastic material and exact solutions were obtained for three approximate yield conditions.

An approximate theoretical study of the dynamic plastic behavior of shells

An approximate theoretical procedure is presented which may be used to estimate the dynamic plastic response of arbitrarily shaped shells. The influence of finite-deflections is retained in the analysis, but material elasticity, strain hardening and strain rate sensitivity are disregarded. The two particular cases of a complete spherical shell which is subjected to a spherically symmetric pressure pulse and a fully clamped cylindrical shell loaded impulsively are considered in some detail. It is observed that the predictions for these two cases agree favourably with the results of more exact rigid-plastic theories.

Dynamic Compressive Test for Determining Stress-Strain Relation of Material

An experimental method of determining the dynamic stress-strain relation of materials and the results of tests on specimens of annealed copper are reported in this paper. 1) Remarkable stress drops after the dynamic yield stress were observed in the stress-strain curves of copper in a certain range of strain rates. 2) The stress near the impact end of the specimen should be considered as three dimensional. In practice, however, if the ratio of specimen diameter to pulse length is reduced sufficiently, uniaxial stress state should be realized, so that this method can be employed to determine the dynamic characteristic of materials. Furthermore, a constitutive equation of metal was proposed from the standpoint of relaxation phenomenon. But for a more reasonable description of the dynamic plastic behavior of metals it may be necessary to take the strain history into consideration.

An experimental study into the dynamic plastic behaviour of wide beams and rectangular plates

An experimental programme was undertaken into the dynamic behaviour of wide beams and rectangular flat plates which were fully clamped and axially restrained at two ends. The initial energy of the uniformly distributed impulsive loads applied to the specimens was considerably greater than the corresponding static elastic strain energy capacities. Over 50 tests were conducted on mild steel and aluminium 6061-T6 specimens which had various L/H and L/B ratios. It appears that the permanent transverse deflections at the center of the beams and plates are essentially independent of the aspect ratios for L/B between 1 and 5. It is shown that an increase in strain-rate sensitivity of the material from which a wide beam or plate is made leads to smaller permanent deflections which agrees with earlier studies on beams. However, this effect is less important than the influence of geometry changes or finite-deflections when W 0/H > 1 approximately. It is concluded that the predictions of rigidplastic theories for fully clamped beams give reasonable engineering estimates of the permanent transverse deflections provided the influence of geometry changes and material strain-rate sensitivity is retained when appropriate.

A theoretical study of the dynamic plastic behavior of beams and plates with finite-deflections

An approximate theoretical procedure is developed herein in order to estimate the permanent transverse deflections of beams and arbitrarily shaped plates which are subjected to large dynamic loads. The influence of finite-deflections or geometry changes is retained in the analysis but elastic effects are disregarded. The particular case of a fully clamped rectangular plate acted on by a uniformly distributed dynamic pressure pulse is studied in some detail. It is observed that reasonable agreement between the theoretical predictions and the experimental results has been obtained for beams (β = 0) and rectangular plates (β = 0.593) which were made from a strain-rate insensitive material.

The dynamic plastic behavior of fully clamped rectangular plates

An experimental investigation was undertaken in order to study the behavior of fully-clamped rectangular plates when subjected to uniformly distributed impulsive velocities. The total energy of the dynamic loads was sufficiently large to cause plastic flow of the plate material and maximum permanent deflections from 0.2 to nearly seven times the corresponding plate thicknesses. All the rectangular plates had the same aspect ratio (B/L = 0.593) but various thicknesses (H), and were made from either hot-rolled mild steel or aluminum 6061-T6. The permanent deformed profiles of the plates are similar to the shape of the velocity field used by Wood [11] for calculating the minimum upper bound to the collapse pressure of a fully-clamped rectangular plate loaded with a uniformly distributed time-independent pressure. It is observed that a modification of the bending only prediction of Martin [13] provides adequate engineering estimates of the maximum permanent deflections up to the order of one-half of the corresponding plate thickness. For larger deflections, it is necessary to include the influence of geometry changes; and in the case of mild steel, material strain-rate sensitivity as well.

Finite deflection of a circular viscoplastic plate subject to projectile impact

A method is presented for the determination of the permanent deflection of plates subject to the impact of projectiles moving with velocities high enough to produce plastic deformations in association with finite deflections. The plate material is assumed to obey the Mises-Huber yield condition and its associated flow rule for static deformations and to behave as a viscoplastic solid for dynamic deformations, elastic strains being considered negligible. The method is illustrated by application to the case of a clamped plate struck at the center by a projectile of negligible radius. The relevance of the solution to experimental studies of the dynamic plastic behavior of plates is discussed.

Catastrophic Thermoplastic Shear

Dynamic plastic behavior of materials is influenced by internally generated temperature gradients. These gradients are a function of thermophysical properties as well as strain rate and shear strength. Criteria are presented for the prediction of catastrophic shear in materials. Catastrophic shear occurs when the local rate of change of temperature has a negative effect on strength which is equal to or greater than the positive effect of strain-hardening. Catastrophic slip is an influential deformation mechanism during high-speed machining and ballistic impact. Structural failure may occur during dynamic loading of components which are designed without regard to the specific sensitivity of certain materials to catastrophic shear.