Yang Li-ming

Mechanism of Strain Rate Effect Based on Dislocation Theory

Based on dislocation theory, we investigate the mechanism of strain rate effect. Strain rate effect and dislocation motion are bridged by Orowans relationship, and the stress dependence of dislocation velocity is considered as the dynamics relationship of dislocation motion. The mechanism of strain rate effect is then investigated qualitatively by using these two relationships although the kinematics relationship of dislocation motion is absent due to complicated styles of dislocation motion. The process of strain rate effect is interpreted and some details of strain rate effect are adequately discussed. The present analyses agree with the existing experimental results. Based on the analyses, we propose that strain rate criteria rather than stress criteria should be satisfied when a metal is fully yielded at a given strain rate.

CHAPTER 2 – Elementary Theory of One-Dimensional Stress Waves in Bars

This chapter discusses the primary one-dimensional theory of stress waves in bars. It begins by discussing the two coordinates that exist in continuum mechanics. These coordinates are used to study the movement of the medium. These are material coordinate system and spatial coordinate system. The authors use the material coordinate system (Lagrange system) to study the longitudinal motion of a bar with uniform cross section. Characteristic lines and the compatibility relationships along the characteristic lines are discussed with explanatory equations. In this discussion, the directional derivative method is used to deduce the equations of characteristics. Further, it explains the longitudinal stress waves propagating in a semi-infinite long bar. The chapter presents an insight into strong discontinuity, weak discontinuity, shock waves, and continuous waves. Dispersion effects induced by the transverse inertia are explained in one section. Finally, the last section concludes the chapter by describing the propagation of a simple kind of transverse wave, namely the elastic torsion wave in cylindrical bars. The torsion wave theory based on the invariable plane cross-section assumption leads solutions that are identical with Pochhammers elastodynamic exact solution.

Strain Rate Sensitivities of Face-Centred-Cubic Metals Using Molecular Dynamics Simulation

We use dislocation theory and molecular dynamics (MD) simulations to investigate the effect of atom properties on the macroscopic strain rate sensitivity of fcc metals. A method to analyse such effect is proposed. The stress dependence of dislocation velocity is identified as the key of such study and is obtained via 2-D MD simulations on the motion of an individual dislocation in an fcc metal. Combining the simulation results with Orowans relationship, it is concluded that strain rate sensitivities of fcc metals are mainly dependent on their atomic mass rather than the interatomic potential. The order of strain rate sensitivities of five fcc metals obtained by analysing is consistent with the experimental results available.

CHAPTER 12 – Numerical Methods for Stress Wave Propagation

To adapt to the rapid development and extensive application of numerical simulation by computer, a study of three numerical methods to solve the problems of stress wave propagation is required. This chapter incorporates these numerical methods along with the characteristics method. These numerical methods are finite difference method, and finite element method. These have been extensively used to solve the stress wave problems. As a rudiment, only elementary theories of these methods are introduced in the chapter. In addition, illustrations and features of these methods are presented by analyzing some simple examples. Among these three numerical methods, the characteristics method can be regarded as an “optimized” finite difference method.The chapter also discusses the advantages as well as the disadvantages of the numerical methods. First, the real influence of some variables on the results obtained may be concealed by such approximate methods. Second, the numerical errors, convergence, and stability involved in the numerical methods may encumber to understand and recognize the physical essence of the problem studied.

CHAPTER 6 – One-Dimensional Visco-Elastic Waves and Elastic-Visco-Plastic Waves

This chapter is devoted to the discussion on one-dimensional visco-elastic waves and elastic-visco-plastic waves. There are two types of stress wave theories. One is the rate-independent theory and the other one is the rate-dependent theory or strain-rate-dependent theory. The mechanical response of rate-dependent materials is separated into two parts. These are time-independent instantaneous response and the time-dependent non-instantaneous response. Macroscopically, all kinds of non-instantaneous responses may be attributed to or equivalent to some kinds of viscous responses induced by the so-called internal dissipative force. Thus, based on the elastic response, the visco-elastic wave theory has been correspondingly developed. This theory has been extensively applied to study polymer materials. In wave propagation, the viscous effect mainly results in the dispersion phenomenon and the absorption phenomenon. Based on the elastic–plastic response to take into account the viscous effects for both the elastic and the plastic parts, the corresponding visco-elastic-plastic wave theory has been developed. However, if the viscous effect is taken into account only for the plastic part, then correspondingly the elastic-visco-plastic wave theory has been developed.

CHAPTER 10 – Elastic–Plastic Waves Propagating in Beams under Transverse Impact (Bending Wave Theory)

This chapter discusses the theory of elasto-plastic waves propagating in beams under transverse impact (bending waves). The discussion is based on the theory of elasto-plastic waves propagating in flexible strings and considering bending resistance of structural element. Herein, the propagation of bending moment disturbances and shear disturbances are coupled with each other. These discussions are limited to the primary theory based on the assumptions of “plane cross-section” of beams and rate-independence of constitutive relations. The beam can be regarded as a string with un-negligible stiffness. The dynamic bending problem of beams can be described either by vibration approach or by wave propagation approach. In the present chapter, the bending wave propagation in beams is discussed. First, the elastic bending waves are briefly discussed, and then mainly the plastic bending waves is discussed. Similar to the situations of plastic longitudinal waves in bars, the plastic bending waves can be dealt with by elastic–plastic analysis, or by rigid-plastic approximate analysis. The chapter is limited to the discussions on the rate-independent bending wave theory, shear failure of beams under transverse impact, and the elemental theory based on the plane cross section assumption..

CHAPTER 9 – Elastic–Plastic Waves Propagating in Flexible Strings

This chapter discusses the theory of elasto-plastic waves in flexible strings under transverse impact as an example of interaction of longitudinal waves and transverse waves. A flexible string is such a simple structure component that only bears tension while its bending resistance is disregarded. In the classic theory of elastic waves propagating in flexible strings, only two simple kinds of elastic wave propagation are dealt with. One is the longitudinal wave which induces the change of stress and strain but no change of the string shape. Another is the transverse wave which induces the change of string shape but no change of the stress and strain; however, they influence each other. Historically, the studies on elasto-plastic dynamics of strings probably began in the period of World War II, although the research results were published only after the war. The stress wave propagation in strings can be studied either by Lagrange or Euler variables, or a mix of both. The study in this chapter is limited to flexible strings. “Flexible” means that the stretch force at any point on the string is always acting in the tangential direction of the instantaneous profile of the string.

CHAPTER 4 – Interaction of Elastic–Plastic Longitudinal Waves in Bars

This chapter discusses the interaction of elasto-plastic loading and unloading waves in bars. While discussing the interaction between elastic–plastic waves, it is important to figure out whether such a wave interaction is a loading process or an unloading process. This is not the case with linear waves, because for linear elastic material, the stress–strain relationship is linear and identical for both the loading and unloading cases. However, for the elasto-plastic waves the stress–strain curves are not linear, thus the superimposition principle is no longer held good. The stress–strain curves of an elastic–plastic material are different in the loading and unloading cases, representing irreversible thermal–mechanical processes. Thus, it is necessary to distinguish whether the stress wave interaction is a loading case or an unloading case, and then to treat the respective case differently. The chapter discusses the loading cases of two elastic–plastic wave interaction, and then the unloading cases. It also describes in detail the governing equations and characteristic lines of both unloading and loading waves. Additionally, the general properties of the loading-unloading boundary propagation are outlined along with relevant equations.

CHAPTER 3 – Interaction of Elastic Longitudinal Waves

This chapter discusses the interaction of elastic longitudinal waves and outlines the longitudinal coaxial collision of two elastic bars. It describes the reflection of elastic longitudinal waves at fixed end and free end. When a stress wave propagating in a bar arrives at the other end of the bar, a wave reflection occurs. The reflective wave varies depending on the actual boundary condition. The chapter explains what happens during a coaxial collision of two elastic bars with finite length. Further, it outlines the reflection and transmission of elastic longitudinal waves in different conditions. An elucidation on the Hopkinson pressure bar and flying piece is provided. Utilizing the property that the compressive pulse is reflected as a tension pulse at the free end of a bar, Hopkinson presented a crafty test to measure the pressure–time waveform in a bar. This test was followed by Kolskys experiment in history. It is known as the split Hopkinson pressure bar.. The chapter concludes by presenting information on dynamic fracture induced by reflective unloading waves.

CHAPTER 11 – General Theory for Linear Elastic Waves

This chapter discusses the general theory for linear elastic waves in infinite homogeneous media. It provides elementary knowledge of the general three-dimensional theory of stress wave propagation. It also describes the wave reflection and transmission under oblique incidence and the Rayleigh surface waves. The discussion leads to the conclusion that in homogeneous, isotropic, and linearly elastic media, the propagation of an arbitrary displacement disturbance can generally be divided into an irrotational wave and an isometric wave. An arbitrary displacement can be divided into two parts, an irrotational part and an isometric part. Oblique-incidence, reflection, and transmission of elastic plane waves are described here. Although irrotational waves and isometric waves are unrelated during their propagation, they are often correlated when they are reflected or refracted at the body surface. The complexities of 3D elastic wave problems mainly lie on the conversion of wave mode and the generation of new non uniform waves during the reflection of waves arriving at the interface. The 3D problems involving elastic–plastic waves, visco-elastic waves, or elastic-visco-plastic waves, etc., are much more complicated.