Stress-Related Dimensioning

The basic equation for conventionai dimensioning states that  

For example, the specification of admissible stress for a swimming pool pump takes the following form  

The number of reduction factors can be expanded according to load analysis. Table 1.25 shows the influence of injection molding orientation on drill holes and weld lines made from ABS [105]. 

The R factors listed in Table 1.25 are suitable for a general evaluation of reduction factors for semi-crystalline, amorphous, and glass fiber-reinforced thermoplastics. 

If dimensioning is performed consistently and systematically, only the characteristic data acquired during short-term tests are suitable as characteristic measurement data (K values). They include yield point Oy, ultimate strength Of for brittle material behavior, and the threshold for a particular non-elastic deformation Ogg. 

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The manner in which the shear strain responds to the shear stress (or vice versa) in this situation defines the mechanical or rheological classification of the material. The parameters in any quantitative functional relation between the stress and strain are the rheological properties of the material. It is noted that the shear stress has dimensions of force per unit area (with units of, e.g., Pa, dyn/cm2, lbf/ft2) and that shear strain is dimensionless (it has no units). 

For time reiated resistance factors larger than 1, fen, = 1 was used (as recommended for dimensioning) and the measured vaiue was added in brackets stress related resistance factors... 

Derive the thermoelastic stress-strain relations for an orthotropic lamina under plane stress, Equation (4.102), from the anisotropic thermoelastic stress-strain relations in three dimensions. Equation (4.101) [or from Equation (4.100)]. 

It is the prediction of performance in its broadest sense, including all the characteristics and properties of materials that are essential and relate to the processing of the plastic. To the designer, an example of a strict definition of a design property could be one that permits calculating product dimensions from a stress analysis. Such properties obviously are the most desirable upon which to base material selections. 

For reactors with free turbulent flow without dominant boundary layer flows or gas/hquid interfaces (due to rising gas bubbles) such as stirred reactors with bafQes, all used model particle systems and also many biological systems produce similar results, and it may therefore be assumed that these results are also applicable to other particle systems. For stirred tanks in particular, the stress produced by impellers of various types can be predicted with the aid of a geometrical function (Eq. (20)) derived from the results of the measurements. Impellers with a large blade area in relation to the tank dimensions produce less shear, because of their uniform power input, in contrast to small and especially axial-flow impellers, such as propellers, and all kinds of inclined-blade impellers. 

The ratios of mean-squared dimensions appearing in Equation (13) are microscopic quantities. To express the elastic free energy of a network in terms of the macroscopic (laboratory) state of deformation, an assumption has to be made to relate microscopic chain dimensions to macroscopic deformation. Their relation to macroscopic deformations imposed on the network has been a main area of research in the area of rubber-like elasticity. Several models have been proposed for this purpose, which are discussed in the following sections. Before that, however, we describe the macroscopic deformation, stress, and the modulus of a network. 

In textbooks, plastic deformation is often described as a two-dimensional process. However, it is intrinsically three-dimensional, and cannot be adequately described in terms of two-dimensions. Hardness indentation is a case in point. For many years this process was described in terms of two-dimensional slip-line fields (Tabor, 1951). This approach, developed by Hill (1950) and others, indicated that the hardness number should be about three times the yield stress. Various shortcomings of this theory were discussed by Shaw (1973). He showed that the experimental flow pattern under a spherical indenter bears little resemblance to the prediction of slip-line theory. He attributes this discrepancy to the neglect of elastic strains in slip-line theory. However, the cause of the discrepancy has a different source as will be discussed here. Slip-lines arise from deformation-softening which is related to the principal mechanism of dislocation multiplication a three-dimensional process. The plastic zone determined by Shaw, and his colleagues is determined by strain-hardening. This is a good example of the confusion that results from inadequate understanding of the physics of a process such as plasticity. 

Ctjki is a fourth order tensor that linearly relates a and e. It is sometimes called the elastic rigidity tensor and contains 81 elements that completely describe the elastic characteristics of the medium. Because of the symmetry of a and e, only 36 elements of Cyu are independent in general cases. Moreover only 2 independent rigidity constants are present in Cyti for linear homogeneous isotropic purely elastic medium Lame coefficient A and /r have a stress dimension, A is related to longitudinal strain and n to shear strain. For the purpose of clarity, a condensed notation is often used... 

When lamellar structures are formed, it is necessary to ensure that the dimensions of the simulation cell are commensurate with the intrinsic periodicity of the lamellae. This process prevents unintentionally subjecting the system to artificial pressure as a result of the geometric constraints. Subjecting the system to a predetermined pressure, or stress, in a controlled manner can be achieved by allowing the system to fluctuate parallel to solid directions, which are introduced in Figure 14. For these directions, it would be appropriate to employ the usual techniques related to constant stress simulations.52,53... 

A monomolecular film is resistant to shear stress in the plane of the surface, as is also the case in the bulk phase a liquid is retarded in its flow by viscous forces. The viscosity of the monolayer may indeed be measured in two dimensions by flow through a canal on a surface or by its drag on a ring in the surface, corresponding to the Ostwald and Couette instruments for the study of bulk viscosities. The surface viscosity, r s, is defined by the relation... 

A proper choice of the parameters for the extension springs can provide the desired stiffness, endurance, and to minimize the dimension of the instrument. A simple theory of the deflection and maximum stress of springs is presented in Appendix F. The relation between the axial load P and the deflection F of a spring with coil diameter D, number of coils n, and wire diameter d is ... 

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