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Über dieses Buch

The book describes behavior of materials (ductile, brittle and composites) under impact loadings and high strain rates. The three aspects: experimental, theoretical and numerical are in the focus of interest. Hopkinson bars are mainly used as experimental devices to describe dynamic behavior of materials. The precise description of experimental techniques and interpretation of wave interaction are carefully discussed. Theoretical background refers to rate dependent thermo viscoplastic formulation. This includes the discussion of well posedness of initial boundary value problems and the solution of the system of governing equations using numerical methods. Explicit time integration is used in computations to solve dynamic problems. In addition, many applications in aeronautic and automotive industries are exposed.



Testing With Bars From Dynamic to Quasi-static

The numerical calculation of the dynamic loading of a structure includes a great number of steps in which various fundamental or engineering problems are involved. Most of them are addressed in the present course at CISM. In this paper, we discuss the testing of materials in order to model their behaviour.
Because of waves induced in the testing device by impulse loadings and short time measurements, the data analysis has to deal with transient effects. Using bars makes easier such an analysis. For this reason, Hopkinson bars are a very commonly used dynamic testing device.
Using the word “dynamic” means that “time” is considered as an active parameter in the evolution process. When dynamically testing a structure (a cylindrical specimen is a common example of such a structure) the effects of time appears in different ways.
There is not static equilibrium in the machine so that measurements at specimen ends cannot be simply deduced from measurements with sensors incorporated in the machine, as it is the case with quasi-static testing. Furthermore, most sensors (like force cells) have a limited high passing band.
Transient effects in the specimen induce waves and the non-homogeneity of mechanical parameters. Consequently, average or global measurements cannot be right away related to local ones.
Stresses cannot be simply related to forces measurements as inertia effects are also involved – the most known effect is the confinement induced by lateral inertia, especially important when testing a big specimen of brittle material.
Short testing times do no allow for isothermal testing – a metallic specimen can have a temperature increase up to 100°C during a SHBP test.
The behaviour of an elementary volume of the material can depend on the rate of change of basic mechanical parameters strain and/or stress. This last effect (strain rate sensitivity) is the (only) one that is expected to be measured, in most cases.
In (dynamic) mechanical testing it is then suitable to consider separately the global measurements made on the specimen (forces applied at a part of the specimen border and displacement measured at another - or the same - part) and the analysis of its mechanical evolution.
This is commonly done in the quasi-static side but is not always, for historical reasons, done in dynamic testing.
The above discussion does not answer the basic question of the boarder between quasi-static and dynamic testing. Theoretically, indeed, waves in solids are still present in quasi-static testing. The common criterion to evaluate this limit is to compare the time τ e needed to reach equilibrium (say < 5% of non homogeneity of stresses and strains) to the measurement duration. Note that τ e mostly depends on the specimen size and on the elastic speed of waves in the material and not on the measurement duration. In the classical SHPB literature, this problem is related to the “impedance matching problem”, misunderstood in many publications, perfectly addressed in 1963 by Davies & Hunter. Based on this criterion, (too) many SHPB tests are considered as quasi-static ones.
Gérard Gary

Dynamic testing of materials: Selected topics

Dynamic testing of materials is a vast subject involving a large variety of techniques according to the investigated properties. Consequently, one cannot cover it extensively and the present chapter will address three selected topics that were discussed during the lecture series given at CISM. For those subjects, the main experimental tool is the Split Hopkinson Pressure Bar (SHPB, Kolsky apparatus), used in its two or one bar version. The SHPB is extensively covered in another chapter so that we will assume that the reader is reasonably familiar with this technique, and will focus here on selected applications, noting that the SHPB is, before anything else, an experimental setup that allows for determination of the boundary conditions (load, displacements) applied to a structure (a specimen being in that case a special case of structure). The following topics will be addressed:
Dynamic fracture of materials: Here we will present the one-point impact technique and its applications to both fracture mechanics testing, and also to dynamic tensile testing of quasi-brittle materials.
Pressure sensitivity of materials: We will describe the basic technique and its application to metallic and polymeric materials, with selected results.
Thermomechanical couplings: We will address here the effect itself, followed by various experimental techniques to measure transient temperature changes in impacted solids, followed by selected results.
As alluded before, such a chapter cannot be extensive, and is based mostly on the author’s experience. However, we will outline throughout the text relevant references that will allow the reader to expand his knowledge on the field.
Daniel Rittel

Dynamic Behavior of Materials. Constitutive Relations and Applications

In this chapter a particular attention has been directed on the dynamic behavior of materials and structures subjected to dynamic loading. Based on experimental observations, it is clear that the homogeneous material behavior of metals has several non linearities related for example to the strain rate and temperature sensitivity. Therefore, the material description and more precisely the constitutive relation used during numerical simulations for example must include all macroscopic observations. It has to be noticed that constitutive relations described in this chapter are defined in a macroscopic scale. Considering some examples, it is clear that the constitutive relation that was used is the key point to simulate a global problem allowing to avoid as frequently used some numerical tricks to obtain an agreement between experiments and numerical predictions. Following the concept described in this part, the reader will be available to propose new models to fit precisely their own materials for specific applications.
A. Rusinek, T. Jankowiak

Analysis of high-speed impact problems in the aircraft industry

The high cost of the energy needed to propel aircraft and ground vehicles has meant that reducing the weight in these systems is vital in order to reduce operational costs. This factor has a significant influence on the design of structures in the aeronautical industry and more recently in others such as high-speed rail networks and road haulage. This is a particularly sensitive issue for the civil aviation industry, given that the cost of fuel is one of the main expenses incurred by passenger airlines. Bearing in mind that fuel represents up to 40% of the total weight of an aircraft, a reduction of its weight results in a concurrent reduction in the amount of fuel needed as well as a significant reduction of the gross weight taken into account.
Ángel Arias, Jorge López-Puente, José Antonio Loya, David Varas, Ramón Zaera

Computer estimation of plastic strain localization and failure for large strain rates using viscoplasticity

The problem of modelling extreme dynamic events for metallic materials including strain rates over 107 s-1 and temperatures reaching melting point is still vivid in theoretical, applied and computational mechanics. Such thermomechanical processes are highly influenced by elasto-viscoplastic wave effects (their propagation and interaction) and varying initial anisotropy caused by existing defects in metals structure like microcracks, microvoids, mobile and immobile dislocations densities being together a cause of overall induced anisotropy during deformation (from the point of view of meso-macro continuum mechanics approach). It should be emphasised, that the most reliable way for estimation of such processes needs nowadays a complex phenomenological models due to limitations of current experimental techniques (it is still not possible to measure the evolution of crucial quantities e.g. temperature for extreme dynamic processes) and computational capabilities.
Within this document we consider recent achievements of Perzyna's type viscoplasticity theory for metallic materials accounting for anisotropic description of damage suitable for modelling plastic strain localization and failure for large strain rates.
Tomasz Łodygowski, Wojciech Sumelka

Inelastic Flow and Failure of Metallic Solids. Material Effort: Study Across Scales

The multiscale physical foundations of the concept of material effort in isotropic solid body are studied, in particular for solids revealing the strength differential effect. Various yield criteria result from this hypothesis: ellipsoid, paraboloid or hyperpoloid ones. The examples are discussed and visualized in the principal axes of stress or in the plane defined by coordinates: equivalent stress and mean stress. The numerical implementation of paraboloid yield surface forming plastic potential in an associated flow law is presented and an example of the identification of the strength differential effect ratio is discussed. Finally, some problems related with an account for the third invariant of stress deviator in failure criteria for isotropic solids and energy-based failure criteria for anisotropic solids are shortly discussed. Also the possibility for an account of two basic mechanisms responsible for inelastic flow: crystallographic slip and shear banding in modelling the inelastic flow law is outlined.
Ryszard B. Pęcherski, Kinga Nalepka, Teresa Frąś, Marcin Nowak
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