Stresses, normal, tangential

Huh and Scriven add, to all constraints already taken into account, that the 1/v interface is a material surface, that is not crossed by any matter flux. This adds two conditions, namely, the vanishing of the normal velocity on both sides of the interface. This results in four additional boundary conditions along the 1/v interface continuity of tangential stress, of tangential speed and one condition for the normal speed on each side. Now there are eight conditions in all. 

For a thin multilayered disc, the stress normal to the disc can be ignored and the radial and the tangential stresses, Or and oe, are related to the radial and the tangential strains, Sr and se, by... 

As previously observed, one of the most important tests in designing a reinforcement system with composite materials is the verification of safety following degradation due to debonding. This test requires the measurement of the ultimate strength transferrable from the concrete to the reinforcement, along with the measurement of the stresses, both tangential and normal, exerted on the concrete-FRP interface. The first measurement is required in order to verify the ultimate limit state, and the second for the serviceability sfiess state. 

A plot of the a-yy component of the tangential stress, normalized by the hardness, against distance in the x direction shows pictorially in Figure 1.5 the small effect on surface stress different-sized indents have and the tensile nature of the stress with residual values exceeding load stresses. 

The total stress normal to the surface must be balanced by atmospheric pressure plus the surface tension contribution across the curved interface. We can usually neglect surface tension effects for melts, and we can always take atmospheric pressure to be zero. The tangential stress at the surface is finite because of aerodynamic drag it is conventional to represent the stress from air drag as jPaV co, where pa is the density of the air, v is the magnitude of the relative velocity between the surface and the air, and cd is a dimensionless drag coefficient that depends on shape and on... 

In view of the experimental errors normally affecting shear cell measurements and the amount of personal judgement required to draw Mohr stress circles tangential to a curved yield locus, there is always some uncertainty in the flow function derived from the Jenike-type shear yield loci method. A direct measurement therefore offers considerable advantage and, besides possibly giving better accuracy, may prove to be more rapid and reproducible. 

Other dimensional systems have been developed for special appHcations which can be found in the technical Hterature. In fact, to increase the power of dimensional analysis, it is advantageous to differentiate between the lengths in radial and tangential directions (13). In doing so, ambiguities for the concepts of energy and torque, as well as for normal stress and shear stress, are eliminated (see Ref. 13). 

These important results can be combined by superposition to compute the displacement for any arbitrary normal stress distribution applied to the free surface. Similar approaches can be taken for arbitrary tangential stress distributions. 

There are two possible kinds of force acting on a fluid cell internal stresses, by which an element of fluid is acted on by forces across its surface by the rest of the fluid, and external forces, such as gravity, that exert a force per unit volume on the entire volume of fluid. We define an ideal fluid to be a fluid such that for any motion of the fluid there exists a pressure p(x, t) such that if 5 is a surface in the fluid with unit normal vector n, the stress force that is exerted across S per unit area at x at time t is equal to —p x,t)h. An ideal fluid is therefore one for which the only forces are internal ones, and are orthogonal to 5 i.e. there are no tangential forces. ... 

Elastic Strength Pressure (ESP). Computed true internal gas pressure in a gun at any given cross section thereof that will stress the metal at the inner layer of the wall at that section tangentially up to the max elastic limit of the metal from which the inner layer is made. Normally required to be at least 1.5 times the computed max pressure... 

Independent of the sign convention used, the stress components can be classified into two types those that act tangentially to the face of the element and those that act normal to the face. Tangential components such as rxy, ryx, Tyz tend to cause shearing and are called shear stress components (or simply shear stresses). In contrast, the stress components rxx, Tyy, jzz act normal to the face of the element and are therefore called normal stress components (or normal stresses). Although there are six shear stress components, it is easily shown that ri = t, for t = j for example, ryx = rxy. Thus there are three independent shear stress components and three independent normal stress components. 

The boundary conditions are the same as for steady motion considered in Chapters 1, 3, and 4, i.e., uniform flow remote from the particle, no slip and no normal flow at the particle boundary, and, for fluid particles, continuity of tangential stress at the interface. For a sphere the normal stress condition at the interface is again formally redundant, but indicates whether a fluid particle will remain spherical. 

The forces and stresses applied to a body may be resolved in three vectors, one normal to an arbitrarily selected element of area and two tangential. For the yz plane, the stress vectors are a, and on, a, respectively. Six analogous stresses exist for tile other orthogonal orientations, giving a total of nine quantities, of which three exist as commutative pairs (arl = crSr). The state of stress, therefore, is defined by three tensiic or normal components (pxx,oyy. o--f) and three shear or tangential components (crIy,cr.I ,CTy,), The shear components are most readily applicable to the determination of jj and G,... 

Both the normal and tangential components of stress must balance, and the kinematics of the surface and flow field must be consistent along a melt-fluid interface. For the meniscus shown in Figure 6 and described by the normal and tangent vectors (n, t), these conditions dictate that... 

Plastic deformation. If normal or tangential stresses become too high, plastic deformation of the contact area will occur. Under certain circumstances, this can lead to plastic shearing, parallel to the surface, without plastic penetration normal to the surface. 

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