Transverse direct stress

Fig. 16. (a) Transverse direct stress per unit load (or JF) in the adherend plotted against z for a 1 in x 1 in single-lap joint... 

The manufacturers stress ease of processing as a particular feature of the material. Recommended melt temperatures are in the range 320-340°C and mould temperatures are 135-165°C. Mould shrinkage of glass-filled grades is usually of the order of 0.2-0.4% in the flow direction and up to twice this value in the transverse direction. The materials are notable for their ability to withstand vapour phase and infrared soldering processes. 

The properties of a unidirectional fibre will not be nearly so good in the transverse direction compared with the longitudinal direction. As a material in service is likely to be subjected to stresses and strains in all directions it is important to be aware of the properties in all directions. The transverse direction will, of course, be the weakest direction and so it is necessary to pay particular attention to this. 

Consider the situation of a thin unidirectional lamina under a state of plane stress as shown in Fig. 3.9. The properties of the lamina are anisotropic so it will have modulus values of E and Ei in the fibre and transverse directions, respectively. The values of these parameters may be determined as illustrated above. 

Any deformation of the matrix material in the x-direction is ignored. Thus, the change in strain energy is presumed to be dominated by the energy of transverse (extensional) stresses. Thus, for the matrix. 

Composite materials typically have a low matrix Young s modulus in comparison to the fiber modulus and even in comparison to the overall laminae moduli. Because the matrix material is the bonding agent between laminae, the shearing effect on the entire laminate is built up by summation of the contributions of each interlaminar zone of matrix material. This summation effect cannot be ignored because laminates can have 100 or more layersi The point is that the composite material shear moduli and G are much lower relative to the direct modulus than for isotropic materials. Thus, the effect of transverse shearing stresses. 

The treatment of transverse shear stress effects in plates made of isotropic materials stems from the classical papers by Reissner [6-26] and Mindlin [6-27. Extension of Reissner s theory to plates made of orthotropic materials is due to Girkmann and Beer [6-28], Ambartsumyan [6-29] treated symmetrically laminated plates with orthotropic laminae having their principal material directions aligned with the plate axes. Whitney [6-30] extended Ambartsumyan s analysis to symmetrically laminated plates with orthotropic laminae of arbitrary orientation. 

The curves for 3M XP251S fiberglass-epoxy are shown in Figures C-1 through C-5 [C-1]. Curves are given for both tensile and compressive behavior of the direct stresses. Note that the behavior in the fiber direction is essentially linear in both tension and compression. Transverse to the fiber direction, the behavior is nearly linear in tension, but very nonlinear in compression. The shear stress-strain curve is highly nonlinear. The Poisson s ratios (not shown) are essentially constant with values v.,2 =. 25 and V21 =. 09. 

Now recognize an apparent contradiction in classical plate theory. First, from force equilibrium in the z-direction, we saw transverse shear forces and Qy must exist to equilibrate the lateral pressure, p. However, these shear forces can only be the resultant of certain transverse shearing stresses, i.e.. 

The importance of grain shape and the orientation of the applied stress to the short transverse direction has already been pointed out. Overageing also generally lowers strength and stress-corrosion susceptibility. Both the design and manufacture of components are important. Quenched components often have high internal tensile stresses and subsequent machining of such... 

Although nearly all creep and stress-relaxation tests are made in uniaxial tension, it is possible to make biaxial tests in which two stresses are applied at 90° to one another, as discussed in Section VI. In a uniaxial test there is a contraction in the transverse direction, but in a biaxial test the transverse contraction is reduced or even prevented. As a result, biaxial creep is less than uniaxial creep--in cquihiaxial loading it is roughly hall as much for equivalent loading conditions. In the linear region the biaxial strain 2 in each direction is (255.256)... 

In the [ 45]j tensile test (ASTM D 3518,1991) shown in Fig 3.22, a uniaxial tension is applied to a ( 45°) laminate symmetric about the mid-plane to measure the strains in the longitudinal and transverse directions, and Ey. This can be accomplished by instrumenting the specimen with longitudinal and transverse element strain gauges. Therefore, the shear stress-strain relationships can be calculated from the tabulated values of and Ey, corresponding to particular values of longitudinal load, (or stress relations derived from laminated plate theory (Petit, 1969 Rosen, 1972) ... 

Fig. 6.15, Stress distributions ahead of crack tip in the transverse direction of orthotropic laminate in...

Ki = a y/a is the stress intensity factor, and F, the material constant, both of which depend on the degree of anisotropy of the composite controlled by the composite elastic moduli in the longitudinal and transverse directions, El and Ej, in-plane Poisson ratio, vlt, and Glj. For a perfectly isotropic material, jr/8(l + Vlt) 0.3. Also, the material parameters, i and < 2 are given by ... 

The microductile/compliant layer concept stems from the early work on composite models containing spherical particles and oriented fibers (Broutman and Agarwal, 1974) in that the stress around the inclusions are functions of the shear modulus and Poisson ratio of the interlayer. A photoelastic study (Marom and Arridge, 1976) has proven that the stress concentration in the radial and transverse directions when subjected to transverse loading was substantially reduced when there was a soft interlayer introduced at the fiber-matrix interface. The soft/ductile interlayer allowed the fiber to distribute the local stresses acting on the fibers more evenly, which, in turn, enhanced the energy absorption capability of the composite (Shelton and Marks, 1988). 

The propagation of linear acoustic waves in solids depends on two laws discovered by two of the most illustrious physicists of the seventeenth century, one from Cambridge and the other from Oxford. Consider a volume element of an isotropic solid subjected to shear, as shown in Fig. 6.1. If the displacement in the transverse direction is , and the component of shear stress in that direction is os, then Newton s second law may be written... 

Er = modulus in the longitudinal direction relative to the direction of orientation Et — modulus in the transverse direction — angle between the applied stress and the orientation axis... 

Figure 2 shows both longitudinal and transversal magnetoelastic stresses in manganite Lao.67Cao.33Mn03 films, with respect to the direction of the magnetic field. 

Other examples of tissues exhibiting active and passive tension include cornea, cardiovascular tissue, and cartilage. When a corneal transplant is trephined out from a cadaver eye, the corneal material to be transplanted shrinks from about 8.5 mm to about 8.0 mm as a result of unloading of the passive and active tensions that exist. In the cardiovascular system, passive and active stresses along the longitudinal and transverse directions of the vessel wall provide in situ strains that are as high as 50% in the carotid artery. 

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