Pure shear stress

This test has an inherent problem associated with the stress concentration and the non-linear plastic deformation induced by the loading nose of small diameter. This is schematically illustrated in Fig 3.17, where the effects of stress concentration in a thin specimen are compared with those in a thick specimen. Both specimens have the same span-to-depth ratio (SDR). The stress state is much more complex than the pure shear stress state predicted by the simple beam theory (Berg et al., 1972 ... 

Note 5 The stress tensor resulting from a pure shear deformation or flow is called a pure shear stress. 

In diffusion specimens that have a relatively narrow diffusion zone compared to the extent of the specimen in the diffusion direction, compatibility stresses are pure shear stresses, and if the stresses exceed the crystal s yield stress, the onset of plastic flow enables the cross section of the diffusion specimen to remain constant.4... 

One main difference between both criteria is the value of the pure shear stress [Pg.370]

Shear strain is measured by the magnitude of the angle representing the displacement of a certain plane relative to the other, due to the application of a pure shear stress, such as a in Figure 3.1c. The corresponding shear strain y may be taken equal to the ratio aa /ab ( = tan a). A shear strain is produced in torsion, when, for example, a circular rod is twisted by tangential forces, as shown in... 

Pure shear stresses are those which are imposed parallel to the bond and in its plane (Figure 11.1). Single-lap shear specimens do not represent pure shear, but are practical and relatively simple to prepare. They also provide reproducible, usable results. The preparation of this specimen and method of testing are described fully in ASTM D1002-01. Two types of panels for preparing multiple specimens are described. ... 

Markolf, in 1970, demonstrated that the sheer stiffness in the horizontal plane of the disc was 150 N. This was considered to be a high value and was thought to be clinically significant, showing that a large force was required to cause abnormal horizontal displacement of an intact vertebral disc unit. It showed that it should be relatively rare for the annulus to fail under pure shear stress. Clinical evidence suggested that annular disruption was more frequent, as the disc does not fail under shear stress alone it fails under a combination of bending, sheer, torsion and tension stresses. Dr. Farfan, in 1970, demonstrated that it took only a force of 31 N to cause failure of the disc under axial rotation. 

An adhesively bonded structure is considered in shear when the applied loads act in the plane of the adhesive layer. The loads tend to produce sliding of the adherends and this results in sliding or shearing of the adhesive. These shear stresses should not be confused with pure shear stresses, which are typical of uniform blocks of a homogeneous material. Interactions between adhesive thickness, adherend thickness and yield strength, and bond geometry produce nonuniform stresses. When this occurs, the shear bond may actually be dominated by tensile stresses rather than shear stresses. However, in service, adhesive structures rarely encounter these pure shear conditions. Therefore, standard shear tests provide adequate duplication of conditions which may exist in an actual structural adhesive application. 

Similarly, if the cubic crystal is subjected only to a pure shear stress <74, it is apparent from (3.3) and (3.6) that... 

Here, Wo is a characteristic level of back stress that primarily affects the initial slope of the uniaxial stress versus remanent strain curve, and m is another hardening parameter that controls how abruptly the strain saturation conditions are reached. Figure 2a illustrates the predictions of the effective stress versus the effective remanent strain from the constitutive law for uniaxial compression, pure shear strain, pure shear stress and uniaxial tension. It is interesting to note that the shear strain and shear stress curves do not coincide. This feature is due to the fact that the material can strain more in tension than in compression, and has been confirmed in micromechanical simulations. Figure 2b illustrates the uniaxial stress versus remanent strain hysteresis curves for two sets of the material parameters Wq and m. 

Figure 2. (a) Effective stress versus effective remanent strain curves for the model material described in Section 2 in uniaxial compression, pure shear strain, pure shear stress and uniaxial tension tests, (b) Uniaxial stress versus remanent strain hysteresis loops for the model material illustrating the effect of the hardening parameter In both cases notice the asymmetry in the remanent strains that can be achieved in tension versus compression. 

Herein, L is the length of the cylinder, T is the appUed torque, r is the radial distance, J is the polar second moment of area and G is the shear modulus. These equations are developed assuming a linear relation between shear stress and strain as well as homogeneity and isotropy. With these assumptions, the shear stress and strain vary linearly with the radius and a pure shear stress state exists on any circumferential plane as shown on the surface at point A in Fig. 2,2. The shear modulus, G, is the slope of the shear stress-strain curve and may be found from. 

A general state of stress at a point or the stress tensor at a point can be separated into two components, one of which results in a change of shape (deviatoric) and one which results in a change of volume (dilatational). Shape changes due to a pure shear stress such as that of a bar in torsion given in Fig. 2,2 are easy to visualize and are shown by the dashed lines in Fig. 2.16(a) (assuming only a horizontal motion takes place). 

Let us apply a stress to a general medium and ask under what conditions it could cause an electric displacement. The basic problem we then have to sort out is the proper description of the symmetry of stress. Clearly a stress cannot be described by a polar vector - there must be at least two. A simple illustration of this is given in Fig. 26. We see that in two dimensions a homogeneous tensile stress as well as a pure shear stress has two perpendicular mirror planes, one twofold rotation axis, and one center of symmetry (center of inversion). In three dimensions we have analogously three mirror planes, three twofold axes, and the center of symmetry, which we may enumerate as m, m, m, 2,2, 2, Z (see Fig. 27). These are the symmetry elements of the point group mmm (or D2/,). This is the orthorombic point... 

Figure 26. The symmetry of stress (a) pure tensile stress, (b) pure shear stress.

Fig. 3.48 a Stress distribution on a circular section subjected to a pure torsional moment T. b elemental free body taken at any point in the bar which shows the biaxial stress state generated by pure shearing-stress... 

Cracks at, or near, interfaces - The above has considered the aspect of cracks located in bulk material, but a second important case is that of cracks at, or very close to, a bimaterial interface. However, an immediate problem arises namely, that when the joint is subjected to solely tensile loads applied normal to the crack, which is located along or parallel to the interface, then these will induce both tensile and shear stresses around the crack tip. Therefore, both Ku and terms are needed to describe the stress field the subscript i indicating a crack at, or near, the interface. Similarly, an applied pure shear stress will also induce both such terms. However, these Kn and Km terms no longer have the clearly defined physical significance, as for the bulk material case and illustrated in Fig. 7.3. Mathematical modelling has shown [21-27] that, for linear-elastic materials, the local stresses ahead of the crack tip at a bimaterial interface are proportional to ... 

A similar analysis may be applied to the other three prisms of material with cross-sections ABE, CDG and ADH. Then, the stresses acting on the material contained in the section ABCD are shown in Fig. 2.5(c). Only equal shear stresses act on the surface of this section, giving a state of affairs known as a pure shear stress. There is no associated change in volume for small strains, only a change in shape. 

N. Hisabe, I. Yoshitake, H. Tanaka and S. Hamada, Mechanical behavior of fiber reinforced concrete elements subjected to pure shearing stress , in International Workshop on High Perfromance Fiber Reinforced Cementitious Composites in Structural Applications, Honolulu, 2005, CD-ROM. 

When direct measurement of the shear properties are desired, a round, cylindrical specimen with a circular cross section is used and a torque is applied to produce a pure shear stress state. The curve of x as a function of y yield the desired properties. 

In practice, the major Poisson s ratio is measured using a longitudinal tensile specimen (Equation 8.45), and the minor Poisson s ratio is computed using Equation 8.49. Finally, a pure shear stress is applied to a 0° test specimen, such that... 

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