Tensile stress, biaxial

During the ignition phase, as the pressure increases, the propellant is loaded by hydrostatic pressure imposed on a biaxial tensile stress field. Because the propellant is incompressible in the ignition condition, the pressure is transmitted entirely to the case, which, being thin because of the weight requirement, presents significant hoop deformations. Therefore, a tensile strain... 

To investigate the effect of the porous layer on the state of strain in the epitaxial film, the radius of curvature Rc of the GaN/SiC and GaN/PSC samples using XRD was measured [55,56]. The measurements showed that GaN films grown on nonporous SiC experienced biaxial tensile stress, which resulted from film/substrate mismatches. In contrast, the films grown on PSC were compressed. The Rc measurements also revealed that with increase of the thickness of the PSC layer the value of the compressive stress increased. 

The Mohr circle representation (Fig. 9.6c) is a graphical method of relating stress components in different sets of axes. When the axes in the material rotate by an angle B, the diameter of the circle rotates by an angle 2 B. If the material yields, the circle has radius k, the constant in the Tresca yield criterion. The axes of the Mohr diagram are the tensile and shear stress components. Thus, in the left-hand circle, representing the stresses at A in Fig. 9.6b, the ends of the horizontal diameter are the principal stresses. The principal axes are parallel and perpendicular to the notch-free surface. There is a tensile principal stress Ik parallel to the surface, and a zero stress perpendicular to the surface. The points at the ends of the vertical diameter represent the stress components in the a)3 axes, rotated by 45° from the principal axes. In the a/3 axes, the shear stresses have a maximum value k, and there are equal biaxial tensile stresses of magnitude = k (the coordinate of the centre of the circle). 

Chapter 6 dealt with residual stresses that occur when products are cooled rapidly from both the sides. There are biaxial compressive stresses in the surface layers and biaxial tensile stresses in the interior. If a hole is drilled through such a product, it cuts through the tensile stress region, and acts as a stress-concentrating feature with a q value of 2. If there is ingress of a stress cracking fluid, radial cracks may form from the bore of the hole, perpendicular to the residual circumferential stresses. These cracks will be at the mid-thickness of the product. 

The lower surface of the sheet is subjected to a balanced biaxial tensile stress, which is maximum at the centre of the sheet. If a central force F is applied as a vmiform pressure to a disc of radius a, on a sheet of thickness t supported at a radius R, the central biaxial tensile stress is... 

A balanced biaxial tensile stress is equivalent to uniaxial compression. Inflation of a rubber balloon is a specifie example of this type of stress. The pressure required to inflate a balloon passes through a maximum. This is intuitively obvious to anyone who has ever tried to inflate a balloon using only limgpower. One s lungs are usually strained almost to the bursting point before the balloon starts to expand. The mathematics for this situation can be given in a few steps. 

Films deposited on a rigid substrate experience biaxial tensile stresses during drying because they cannot shrink in the plane of the film. The biaxial tensile stress develops during drying as a result of the capillary tension in the pore liquid as it stretches to cover the dried surface exposed by the evaporation of the liquid (see Chapter 5). The capillary tension in the liquid would cause the film to shrink except the rigid substrate prevents the shrinkage in the plane of the film. Films... 

Fig. 4.37. Steady advance of a crack in the a —direction through a thin film. Crack growth is driven by the residual biaxial tensile stress (Tm existing prior to cracking.

In deriving a relationship between midpoint deflection of a pressurized membrane bulge and the applied pressure given in (5.92), the influence of initial stress was neglected. Determine how the relationship with the modified to account for an initial equi-biaxial tensile stress in the film. 

For which polymers and under which conditions do crazes occur Crazes form primarily in amorphous polymers, for molecular weights above the entanglement limit. There is no craze formation under compression or under pure shear. The typical situation leading to craze initiation is the imposition of an uniaxial or biaxial tensile stress. If such stresses are applied and fulfill certain threshold conditions, crazes form statistically, preferentially at first at the sample surface. The initiation rate depends on the applied stress, as is shown in Fig. 8.22. The higher the stress imposed, the shorter is the time for the observation of the first crazes. After the initial increase with time, the craze density saturates. Removing the stress, the crazes close their openings somewhat, but survive. They disappear only if the sample is annealed at temperatures above the glass transition. 

Residual stresses are also very important in many adhesive bonds. When adherends with similar coefficients of thermal expansion are bonded with an adhesive, a biaxial tensile stress often results within the adhesive layer. Interfacial stresses, obeying shear lag distributions, are limited to the edges and around holes and defects where free edges are present. When dissimilar adherends are bonded together, significant stresses can result in both the adherends and the adhesive, as can curvatures of the bonded system. These residual stresses can often be very significant when compared with mechanically induced stresses. 

Frequent changes in humidity can initiate mechanical effects caused by water. Cyclical shrinking and swelling can lead to crack formation. During a period of water absorption, the surface of the plastics part is wetter than its center. The surface tends to swell due to water absorption, but swelling is prevented by the dry core. Compression stresses arise at the surface while tensile stresses are present In the core. The conditions are reversed when a previously soaked part comes into a dry environment. Here, biaxial tensile stresses arise in the surface and corresponding compression stresses in the core [36]. 

R.E. Robertson (University of Michigan, Ann Arbor, Michigan) In this instance, couldn t you say that you do have deformation sideways, but, in effect, it s like an increasing hydrostatic pressure and superimposed on that is a biaxial tensile stress ... 

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