Stress maximum

Otnax = maximum stress level of the fatigue cycle... 

In Figure 5.24 the predicted direct stress distributions for a glass-filled epoxy resin under unconstrained conditions for both pha.ses are shown. The material parameters used in this calculation are elasticity modulus and Poisson s ratio of (3.01 GPa, 0.35) for the epoxy matrix and (76.0 GPa, 0.21) for glass spheres, respectively. According to this result the position of maximum stress concentration is almost directly above the pole of the spherical particle. Therefore for a... 

Machine components ate commonly subjected to loads, and hence stresses, which vary over time. The response of materials to such loading is usually examined by a fatigue test. The cylinder, loaded elastically to a level below that for plastic deformation, is rotated. Thus the axial stress at all locations on the surface alternates between a maximum tensile value and a maximum compressive value. The cylinder is rotated until fracture occurs, or until a large number of cycles is attained, eg, lO. The test is then repeated at a different maximum stress level. The results ate presented as a plot of maximum stress, C, versus number of cycles to fracture. For many steels, there is a maximum stress level below which fracture does not occur called the... 

The simplest method of reduciag stresses and reactions is to provide additional pipe ia the system ia the form of loops or offset-bonds. When physical limitations restrict the use of additional bends, a multiple arrangement of several small-size pipe mns may sometimes be used. Owiag to stress intensification, the maximum stress generally occurs at elbows, bends, and Ts. Thus, heavier-walled fittings may reduce the stress without significantly impairing flexibiUty. FiaaHy, effectively located restraints can reduce thermal effects on the equipment. 

In the large-diameter vertical cylindrical tanks, because hoop stress is proportional to diameter, the thickness is set by the hydrostatic hoop stresses. Although the hydrostatic forces increase proportionally with the depth of Hquid in the tank, the thickness must be based on the hydrostatic pressure at the point of greatest depth in the tank. At the bottom, however, the expansion of the shell owing to internal hydrostatic pressure is limited so that the actual point of maximum stress is slightly above the bottom. Assuming this point to be about 1 ft (0.305 m) above the tank bottom provides tank shells of adequate strength. The basic equation modified for this anomaly is... 

The strength of laminates is usually predicted from a combination of laminated plate theory and a failure criterion for the individual larnina. A general treatment of composite failure criteria is beyond the scope of the present discussion. Broadly, however, composite failure criteria are of two types noninteractive, such as maximum stress or maximum strain, in which the lamina is taken to fail when a critical value of stress or strain is reached parallel or transverse to the fibers in tension, compression, or shear or interactive, such as the Tsai-Hill or Tsai-Wu (1,7) type, in which failure is taken to be when some combination of stresses occurs. Generally, the ply materials do not have the same strengths in tension and compression, so that five-ply strengths must be deterrnined ... 

Expansion strains may be taken up in three ways by bending, by torsion, or by axial compression. In the first two cases maximum stress occurs at the extreme fibers of the cross section at the critical location. In the third case the entire cross-sectional area over the entire length is for practical purposes equally stressed. 

Subsection A This subsection contains the general requirements applicable to all materials and methods of construction. Design temperature and pressure are defined here, and the loadings to be considered in design are specified. For stress failure and yielding, this section of the code uses the maximum-stress theory of failure as its criterion. 

Ultimate tensile strength the maximum stress value as obtained on a stress-strain curve (Figure 30.1). 

Elastic limit the maximum stress a test specimen may be subjected to and which may return to its original length when the stress is released. 

Yield strength or tensile proof stress the maximum stress that can be applied without permanent deformation of the test specimen. For the materials that have an elastic limit (some materials may not have an elastic region) this may be expressed as the value of the stress on... 

In the case of most nonporous minerals at sufficiently low-shock stresses, two shock fronts form. The first wave is the elastic shock, a finite-amplitude essentially elastic wave as indicated in Fig. 4.11. The amplitude of this shock is often called the Hugoniot elastic limit Phel- This would correspond to state 1 of Fig. 4.10(a). The Hugoniot elastic limit is defined as the maximum stress sustainable by a solid in one-dimensional shock compression without irreversible deformation taking place at the shock front. The particle velocity associated with a Hugoniot elastic limit shock is often measured by observing the free-surface velocity profile as, for example, in Fig. 4.16. In the case of a polycrystalline and/or isotropic material at shock stresses at or below HEL> the lateral compressive stress in a plane perpendicular to the shock front... 

Now, to be successful, a spring must not undergo a permanent set during use it must always spring back. The condition for this is that the maximum stress (eqn. (12.3)) always be less than the yield stress ... 

In compression, of course, the strength is greater. Most ceramics are about fifteen times stronger in compression than in tension, for the reasons given in Chapter 17. For ice the factor is smaller, typically six, probably because the coefficient of friction across the crack faces (which rub together when the ceramic is loaded in compression) is exceptionally low. At stresses below 6 MPa, ice loaded in compression deforms by creep at 6 MPa it crushes, and this is the maximum stress it can carry. 

It is now easy to calculate the force on the narrow structure. If the pillar has a width w = 10 m where it passes through the ice sheet (thickness f = 2 m), it presents a section of roughly 20 m on which ice presses. The maximum stress the ice can take is 6 MPa, so the maximum force it can exert on the structure is... 

If we assume that the maximum stress applied is +3cr from the mean stress, where this loading stress value eovers 99.87% those applied in serviee ... 

The reliability, R/, as a funetion of the maximum stress value used is shown in... 

The stress, L, determined using the Modified Mohr method effeetively aeeounts for all the applied stresses and allows a direet eomparison to a materials strength property to be made (Norton, 1996), as was established for the Distortion Energy Theory for duetile materials. The set of expressions to determine the effeetive or maximum stress are shown below and involve all three prineipal stresses (Dowling, 1993) ... 

For fixed tubesheet design of shell and tube heat exchangers don t allow too high a temperature difference between tubeside and shellside without providing a shellside expansion joint. The author has seen 70 F (one company) and 100°F (another company) used as this limit. An easy way to calculate the maximum stress is as follows ... 

In the deflection temperature under load test (heat distortion temperature test) the temperature is noted at which a bar of material subjected to a three-point bending stress is deformed a specified amount. The load (F) applied to the sample will vary with the thickness (t) and width (tv) of the samples and is determined by the maximum stress specified at the mid-point of the beam (P) which may be either 0.45 MPa (661bf/in ) or 1.82 MPa (264Ibf/in ). 

If we take the nominal fracture toughness of IG-11 graphite to be 1 MPayin and the maximum stress in the process zone to be = 60.2 MPa according to the above analysis, we find that rj, = 88 pm. This value is virtually identical to r<, , = 90pm, the process zone dimension determined using Eq. 3. To summarize, the above analysis strongly supports a hypothesis that the maximum critical stress... 

Fig. 8. The dependence on contact angle of the magnitude and location of maximum stress concentration in a lap shear test. As the contact angle decreases, the stress concentration decreases, and its locus moves toward the center-plane of the adhesive phase. Redrawn from ref. [51].

In the traditional Dugdale model [56], a = Oy and the familiar result is obtained, Gic = cTySc- In the EPZ model, cr exceeds critical crack opening displacement <5c is proportional to the maximum stresses cr in the deformation zone... 

Corrosion Fatigue Limit—the maximum stress that a metal can endure without failure. This is determined in a stated number of stress applications under defined conditions of stressing and corrosion. 

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