Strain average

Substitution of Eqs. (9) into Eqs. (8) and subsequent differentiation with respect to lead to the equilibrium equations in terms of microstresses and microstrains (i.e. strains averaged across the layer thickness). To exclude the latter, constitutive equations for the damaged layer and the outer sublaminate, equations of the global equilibrium of the laminate as well as generalised plane strain conditions are employed. Finally, a system of coupled second order non-homogeneous ordinary differential equations is obtained... 

Here, Pcz>/ P>gd/ o are constant for the whole pattern (taken at zero value of the wave vector Sq of the first peak). The integral breaths found from the experimental diffraction profiles allow calculation of the surface-weighted (Ds) and volume-weighted (Dy) domain size and a mean-square (Gaussian) strain, s, which is the total strain averaged over infinite distance ... 

Hashin and Shtrikman have determined bounds using basic elasticity energy theorems rather than stress and strain averaging and their predictions can be written in the form... 

Feather fiber Maximum length (cm) Average denier [Pg.172]

Temperature ( C) Mo(dulus Average St.Deviation (GPai Ultimate Tensile Strength Average St,Deviation (MPa) Failure Strain Average St,Deviation ... 

Finally, due to the stress—strain cycle asymmetry induced by creep strain, average stresses develop positive for holding in compression and negative for holding in tension. The measured mean stresses range between —25 and 4-25 MPa, which can affect life in the case of cyclic loadings at low amplimde. 

During the optical coat work stress examination method the upper plate of the head of some of the bolts was covered with an optical coat work (Fig. 4). On the head of some other bolts strain gauges were stuck which measured the plain biaxial stress state in the middle of the top surface of the head of the bolt (3.5 x 3 mm). The magnetic probe detected average stresses up to 0.1 mm depth in an area of 14 mm diameter in the middle of the head of the bolt. 

Phonons are nomial modes of vibration of a low-temperatnre solid, where the atomic motions around the equilibrium lattice can be approximated by hannonic vibrations. The coupled atomic vibrations can be diagonalized into uncoupled nonnal modes (phonons) if a hannonic approximation is made. In the simplest analysis of the contribution of phonons to the average internal energy and heat capacity one makes two assumptions (i) the frequency of an elastic wave is independent of the strain amplitude and (ii) the velocities of all elastic waves are equal and independent of the frequency, direction of propagation and the direction of polarization. These two assumptions are used below for all the modes and leads to the famous Debye model. 

Nujol . To measure the CD speetnim, they had to overeome the birefringenee of the strained diamond windows of the high-pressure eell. They did this by reeording and averaging speetra of the sample—and of a... 

The breadth of the peaks in an x-ray diffractogram provide a detennination of the average crystallite domain size, assuming no lattice strain or defects, tlirough the Debye-Scherr fonnula ... 

Plasmodium vivax, responsible for the most prevalent form of malaria (benign tertian), has an incubation period of 8—27 days (14 average). A variety seen in northern and northeastern Europe has an incubation period as long as 8—10 months. The disease can cause splenic mpture and anemia. Relapses (renewed manifestations of erythrocytic infection) can occur with this type of malaria. Overall, P. vivax is stiU susceptible to chloroquine however, resistant strains have been reported from Papua New Guinea and parts of Indonesia. Plasmodium malariae the cause of quartan malaria, has an incubation period of 15—30 days and its asexual cycle is 72 hours. This mildest form of malaria can cause nephritis in addition to the usual symptoms. It is a nonrelapsing type of malaria but the ted blood ceU infection can last for many years. No resistance to chloroquine by this plasmodium has been reported. Plasmodium ovale responsible for ovale tertian malaria, has an incubation period of 9—17 days (15 average). Relapses can occur in people infected with this plasmodium. No chloroquine resistance has been reported for this parasite. 

A minimum of 10 to 35 parts carbon black to 100 parts of mbber is required to obtain a resistivity in the order of 10 Q-cm. At that loading the carbon black particles, which have an average radius of 10 nm, form grapelike aggregates that provide continuous paths for the electrical current. Special purpose mbbers containing even more carbon black have resistances as low as 1 Q-cm (129). The electrical resistivity of mbber with carbon black is sensitive to strain history, probably because of temporary dismptions of the continuity of the carbon black aggregates. 

Plastic Stra.ln Ra.tlo. The plastic strain ratio is the ratio of strains measured in the width over the thickness directions in tensile tests. This ratio characterizes the abhity of materials to resist thinning during forming operations (13). In particular, it is a measure of the abhity of a sheet material to resist the thinning and failure at the base of a deep drawn cup. The plastic strain ratio is measured at 0°, 45°, and 90° relative to the rolling direction. These three plastic strain ratios Rq, R, and R q, are combined to obtain the average strain ratio, cahed the R or the R value, and its variation in strain ratio, cahed... 

Orowan [7] has shown that when disloeations move with average veloeity V under the influenee of a shear stress r, the rate at whieh plastie shear strain is aeeumulated is given by... 

Steady-propagating plastic waves [20]-[22] also give some useful information on the micromechanics of high-rate plastic deformation. Of particular interest is the universality of the dependence of total strain rate on peak longitudinal stress [21]. This can also be expressed in terms of a relationship between maximum shear stress and average plastic shear strain rate in the plastic wave... 

For example, a 10 GPa (total strain = 0.06) shock wave in copper has a maximum total strain rate 10 s [21] the risetime would thus be (eje) 0.6 ns. For uniaxial-strain compression, y averaged over the entire shock front. The resolution of the shock wave in a large-scale, multidimensional finite-difference code would be computationally expensive, but necessary to get the correct strength f behind the shock. An estimate of the error made in not resolving the shock wave can be obtained by calculating dt/dy)o with y 10 s (the actual plastic strain rate) and y 10 s (the plastic strain rate within the computed shock wave due to a time step of 0.06 qs). From (7.41) with y = 10 s (actual shock wave) and y = 10 s (computation) ... 

We first consider strain localization as discussed in Section 6.1. The material deformation action is assumed to be confined to planes that are thin in comparison to their spacing d. Let the thickness of the deformation region be given by h then the amount of local plastic shear strain in the deformation is approximately Ji djh)y, where y is the macroscale plastic shear strain in the shock process. In a planar shock wave in materials of low strength y e, where e = 1 — Po/P is the volumetric strain. On the micromechanical scale y, is accommodated by the motion of dislocations, or y, bN v(z). The average separation of mobile dislocations is simply L = Every time a disloca-... 

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