Strain-Rate Effects in the Dynamic Buckling of a Simple Elastic-Plastic Model

1997 ◽  
Vol 64 (1) ◽  
pp. 193-200 ◽  
Author(s):  
D. Karagiozova ◽  
N. Jones
Keyword(s):  
Strain Rate ◽  
Plastic Material ◽  
Rate Sensitivity ◽  
Dynamic Buckling ◽  
Strain Rate Effects ◽  
Plastic Model ◽  
Elastic Plastic ◽  
Rate Effects ◽  
Elastic Plastic Material ◽  
The Impact

The phenomenon of dynamic buckling is examined when the influence of material strain-rate sensitivity is retained in the basic equations for a simple elastic-plastic model with linear strain hardening when subjected to an impact by a mass. Two approaches are proposed for taking into account the material strain-rate effects and both use the Cowper-Symonds constitutive equation. The critical impact velocities depend on the impact mass and are determined for a wholly elastic material, a strain-rate insensitive elastic-plastic material and an elastic-plastic material with a dynamic yield force together with linear or nonlinear hardening due to the strain-rate effects. The results obtained show that both strain-rate sensitive models predict impact velocities which are higher than those predicted by the strain-rate insensitive idealization and that the influence of any initial imperfections is important for the three material models considered.

scholarly journals Characterization of Impacts of Elastic-plastic Spheres

2020 ◽  
Vol 64 (2) ◽  
pp. 165-171
Author(s):  
Bence Szabó ◽  
Attila Kossa
Keyword(s):  
Plastic Material ◽  
Analytical Models ◽  
Material Models ◽  
Elastic Plastic ◽  
Analytical Functions ◽  
Elastic Plastic Material ◽  
Explicit Dynamic ◽  
The Impact ◽  
The Given

This work presents explicit dynamic finite element simulations of various impacts of elastic-plastic solid spheres with flat walls. Different  analytical models describing the mechanics of the impact phenomenon are also presented. Elastic and elastic-plastic material models for the sphere and the wall are considered during the analyses. The applicability of these different models is demonstrated and their accuracies are investigated. Closed-form analytical functions are proposed to describe the relationship between the initial velocity of the sphere and the investigated contact characteristics for the given material models. Analysis is carried out to study the effect of the friction coefficient as well as the angle of impact for various cases.

scholarly journals Numerical and Theoretical Analysis of the Inertia Effects and Interfacial Friction in SHPB Test Systems

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4809
Author(s):  
Pei Pei ◽  
Zhongcai Pei ◽  
Zhiyong Tang
Keyword(s):  
Theoretical Analysis ◽  
Elastic Material ◽  
Plastic Material ◽  
Inertia Effects ◽  
Elastic Plastic ◽  
Rate Dependent ◽  
Hardening Modulus ◽  
Structural Applications ◽  
Elastic Plastic Material ◽  
The Impact

The dynamic properties of materials should be analyzed for the material selection and safety design of robots used in the army and other protective structural applications. Split Hopkinson pressure bars (SHPB) is a widely used system for measuring the dynamic behavior of materials between 102 and 104 s−1 strain rates. In order to obtain accurate dynamic parameters of materials, the influences of friction and inertia should be considered in the SHPB tests. In this study, the effects of the friction conditions, specimen shape, and specimen configuration on the SHPB results are numerically investigated for rate-independent material, rate-dependent elastic-plastic material, and rate-dependent visco-elastic material. High-strength steel DP500 and polymethylmethacrylate are the representative materials for the latter two materials. The rate-independent material used the same elastic modulus and hardening modulus as the rate-dependent visco-elastic material but without strain rate effects for comparison. The impact velocities were 3 and 10 m/s. The results show that friction and inertia can produce a significant increase in the flow stress, and their effects are affected by impact velocities. Rate-dependent visco-elasticity material specimen is the most sensitive material to friction and inertia effects among these three materials (rate-independent material, rate-dependent elastic-plastic material, and rate-dependent visco-elastic material). A theoretical analysis based on the conservation of energy is conducted to quantitatively analyze the relationship between the stress measured in the specimen and friction as well as inertia effects. Furthermore, the methods to reduce the influence of friction and inertia effects on the experimental results are further analyzed.

On the Nature of Normality of Plastic Strain Rate and Convexity of Yield Surfaces in Plasticity

1975 ◽  
Vol 42 (1) ◽  
pp. 61-66 ◽  
Author(s):  
P. M. Naghdi ◽  
J. A. Trapp
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Plastic Material ◽  
Plastic Strain Rate ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Rigid Plastic Material ◽  
Yield Surfaces ◽  
Elastic Plastic Material ◽  
Special Case

Within the scope of the purely mechanical theory of plasticity, in a previous paper we have derived two inequalities which place restrictions on the constitutive equation for the rate of plastic strain in a finitely deformed elastic-plastic material. Here we take up the matter further, elaborate on the nature of the previously derived restrictions and obtain some additional results pertaining to the normality of the plastic strain rate and convexity of yield surfaces. Although in the main our discussions are carried out in the context of finite deformation, the nature of the restrictions for infinitesimal deformation is also examined. A special case of an elastic-plastic material in which the stress response is characterized by the stress rate and that of a rigid-plastic material are given detailed attention.

Viscous–elastic–plastic modelling of one-dimensional time-dependent behaviour of clays

1989 ◽  
Vol 26 (2) ◽  
pp. 199-209 ◽  
Author(s):  
J.-H. Yin ◽  
J. Graham
Keyword(s):  
Strain Rate ◽  
Constitutive Models ◽  
Constitutive Modelling ◽  
Time Dependent ◽  
Creep Tests ◽  
Strain Rate Effects ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Constant Rate ◽  
Rate Effects

Increased attention has recently been directed towards the influence of time and strain-rate effects on the behaviour of clays in one-dimensional (1-D) laboratory consolidation. The improved understanding coming from these studies must now be incorporated into improved constitutive models that can be used for analysis of foundation settlements. This paper presents a 1-D model for stepped loading using a new concept for establishing "equivalent times" during time-dependent straining. This model is then developed into a general constitutive equation for continuous loading. The model uses three parameters, λ, κ, and ψ, that can be easily found using conventional oedometer tests.The general model has been used to develop analytical solutions for creep tests, relaxation tests, constant rate of strain (CRSN) tests, and tests with constant rate of stress (CRSS). Results from three different clays have been used to examine the validity of the model. Key words: consolidation, constitutive modelling, elastic-plastic, viscous, time, creep, strain rate, relaxation.

Mechanical Behavior of a Rephosphorized Steel for Car Body Applications: Effects of Temperature, Strain Rate, and Pretreatment

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Yu Cao ◽  
Johan Ahlström ◽  
Birger Karlsson
Keyword(s):  
Strain Rate ◽  
Mechanical Behavior ◽  
Rate Sensitivity ◽  
Uniaxial Tensile ◽  
Good Precision ◽  
Interstitial Free ◽  
Softening Effect ◽  
Strain Rate Effects ◽  
Uniaxial Tensile Testing ◽  
Rate Effects

Temperature and strain rate effects on the mechanical behavior of commercial rephosphorized, interstitial free steel have been investigated by uniaxial tensile testing, covering temperatures ranging from −60°C to +100°C and strain rates from 1×10−4 s−1 to 1×102 s−1 encompassing most conditions experienced in automotive crash situations. The effect of prestraining to 3.5% with or without successive annealing at 180°C for 30 min has also been evaluated. These treatments were used to simulate pressing of the plates and the paint-bake cycle in the production of car bodies. Yield and ultimate tensile strengths, ductility including uniform and total elongation and area reduction, thermal softening effect at high strain rate, and strain rate sensitivity of stress were determined and discussed in all cases. It was found that the Voce equation [σ=σs−(σs−σ0)exp(ε/ε0)] can be fitted to the experimental true stress-true plastic strain data with good precision. The parameter values in this equation were evaluated and discussed. Furthermore, temperature and strain rate effects were examined in terms of thermal and athermal components of the flow stresses. Finally, a thermal activation analysis was performed.

From Dislocation Cores to high Temperature Strain rate Effects in L12 Compounds

1990 ◽  
Vol 213 ◽  
Author(s):  
V. Vitek ◽  
Y. Sodani ◽  
J. Cserti
Keyword(s):  
Strain Rate ◽  
Yield Stress ◽  
Rate Sensitivity ◽  
Physical Models ◽  
Strain Rate Effects ◽  
Screw Dislocations ◽  
The Core ◽  
Rate Effects ◽  
Temperature Dependences ◽  
Further Development

ABSTRACTIt is now generally accepted that in many L12 compounds the yielding behavior is controlled by the special features of the cores of screw dislocations. In this paper we first summarize results of the atomistic studies of the core structures of the <110> screw dislocations in these compounds. At this point we show that, depending on the atomic bonding, two distinct classes of L12 alloys exist. In the first, represented by alloys like Ni3Al, a glissile configuration of the core exists on {111} planes although a sessile configuration is energetically more favored. In the second class, represented by alloys like Pt3A1 and A13Ti modified by alloying into L12 structure, the cores of screw dislocations are always sessile. Using the results of the atomistic studies we present physical models explaining the temperature dependences of the yield stress in both classes of L12 alloys. At this point we also present a further development of the model for the anomalous temperature dependence of the yield stress in alloys like Ni3A1, originally put forward by Paidar et al. [15]. In this development strain rate effects are included and it is shown that the model explains not only the orientation dependences of the yield stress in the anomalous regime but also the very low strain rate sensitivity observed in this regime.

Elastic, Finite Deflection and Strain Rate Effects in a Mode Approximation Technique for Plastic Deformation of Pulse Loaded Structures

1980 ◽  
Vol 22 (4) ◽  
pp. 189-197 ◽  
Author(s):  
P. S. Symonds
Keyword(s):  
Strain Rate ◽  
General Scheme ◽  
Rate Sensitivity ◽  
Finite Geometry ◽  
Approximation Technique ◽  
Test Results ◽  
Rigid Plastic ◽  
Strain Rate Effects ◽  
Rate Effects ◽  
Clamped Beams

A general scheme is proposed for including effects of elastic deformation, finite geometry changes, and strain rate sensitivity in a simple approximate scheme for estimating maximum transient and permanent deformations in structures subjected to load pulses of high intensity. The method is applied here to fully clamped beams of mild steel subjected to explosive loading. Comparisons are made between estimates from the present method and test results, as well as with estimates by various rigid-plastic methods and (to a limited extent) with results from numerical methods.

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