Stresses, static and dynamic

Irrespective of the analysis approach, the representative volume element must be carefully defined and used. In fact, the representative volume element is crucial to the analysis and is the micromechanics analog of the free-body diagram in statics and dynamics. The representative volume element is of higher order than the free-body diagram because deformations and stresses are addressed in addition to forces. 

As a plastic is subjected to a fixed stress or strain, the deformation versus time curve will show an initial rapid deformation followed by a continuous action. Examples of the standard type tests are included in Fig. 2-1. Details on using these type specimens under static and dynamic loads will be reviewed throughout this chapter. (Review also Fig. 8-9 that relates elasticity to strain under different conditions.)... 

Dynamic loading in the present context is taken to include deformation rates above those achieved on the standard laboratorytesting machine (commonly designated as static or quasi-static). These slower tests may encounter minimal time-dependent effects, such as creep and stress-relaxation, and therefore are in a sense dynamic. Thus the terms static and dynamic can be overlapping. 

It is well known that mechanical loads on a structure induce stresses within the material such as those shown in Fig. 2-4. It is also well known that the magnitudes of these static and dynamic stresses depends on many factors, including forces, angle of loads, rate and point... 

It is important to recognize that all materials will have problems in certain environments, whether they are plastics, metals, aluminum, or something else. For example, the chemical effect and/or corrosion of metal surfaces has a damaging effect on both the static and dynamic strength properties of metals because it ultimately creates a reduced cross-section that can lead to eventual failure. The combined effect of corrosion and stress on strength characteristics is called stress corrosion. When the load is variable, the com-... 

Make static and dynamic analyses of pipe systems to avoid excessive stresses or excessive vibrations. 

For steel, the modulus of elasticity is the same in the elastic region and yield plateau for static and dynamic response. In the strain hardening region the slope of the stress-strain curve is different for static and dynamic response, although this difference is not important for most structural design applications. 

Framework of load compensator on plane wings injection moulding of carbon fibre reinforced PEEK replaces the aluminium alloy previously used. This part plays a critical role in plane safety and must resist the static and dynamic stresses and hydraulic fluids. The grade selected after many tests has a high fluidity allowing the manufacture of parts with dimensions of 200 mm by 400 mm. With 30% carbon fibre reinforcement, this PEEK grade ... 

Mode coupling theory provides the following rationale for the known validity of the Stokes relation between the zero frequency friction and the viscosity. According to MCT, both these quantities are primarily determined by the static and dynamic structure factors of the solvent. Hence both vary similarly with density and temperature. This calls into question the justification of the use of the generalized hydrodynamics for molecular processes. The question gathers further relevance from the fact that the time (t) correlation function determining friction (the force-force) and that determining viscosity (the stress-stress) are microscopically different. 

SFM s can be also classified according to static and dynamic operating modes. Under quasi-static conditions, the microscope measures the instantaneous response of the cantilever when it interacts with the sample. Dynamic SFM enables separation of the elastic and inelastic component in the cantilever deflection when the sample surface is exposed to a periodically varying stress field. The dynamic modes are useful for investigation of viscoelastic materials such as polymers and results in additional improvements in the signal-to-noise ratio. 

A.M. Tishin, Yu.I. Spichkin and J. Bohr, Static and dynamic stresses 87... 

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

The derivation of fundamental linear viscoelastic properties from experimental data obtained in static and dynamic tests, and the relationships between these properties, are described by Barnes etal. (1989), Gunasekaran and Ak (2002) and Rao (1992). In the linear viscoelastic region, the moduli and viscosity coefficients from creep, stress relaxation and dynamic tests are interconvertible mathematically, and independent of the imposed stress or strain (Harnett, 1989). 

Clark [21] has measured the shear stress at static and dynamic state of a foam from hydrolysed keratin, and soap. The maximum static shear stress Toji was 35.0 Pa and the dynamic T0d was 23.0 Pa at 1% keratin concentration and 225.0 Pa and 110.0 Pa, respectively, at 10% concentration. According to Clark s data the To,, value is directly proportional to the surface viscosity. For a foam from 5% soap solution T0ii, and to,d coincided and were equal to 32 Pa. Being in qualitative agreement with Eqs. (8.14) - (8.16), this shear stress increased with diminishing foam bubble size. 

The crack opening can be determined (p = 1), if the fringe order n is known. This method has been used in investigations of stationary cracks to determine static and dynamic stress intensity factors, the latter being induced by a shock wave. 

Figure 3-12 Illustration of Static and Dynamic Yield Stress (Keentok, 1982).

The structure of the food sample would be disturbed considerably during the determination of Apminj so that the measured yield stress would be closer to the dynamic yield stress than the static yield stress (Figure 3-10). In contrast, in the vane method for determination of yield stress both the static and dynamic yield stresses can be determined. 

Foams usually possess a finite low-frequency elastic modulus, along with static and dynamic yield stresses. These and other aspects of foam flow and rheology can be captured qualitatively and even semiquantitatively by cellular foam models. 

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