Material properties stiffness

Studies of local material properties stiffness, hardness, friction, elasticity, adhesion, magnetic and electrostatic forces, hydrophilicity/hydrophobicity, thermal behaviour, etc. 

Commonly used materials for cable insulation are poly(vinyl chloride) (PVC) compounds, polyamides, polyethylenes, polypropylenes, polyurethanes, and fluoropolymers. PVC compounds possess high dielectric and mechanical strength, flexibiUty, and resistance to flame, water, and abrasion. Polyethylene and polypropylene are used for high speed appHcations that require a low dielectric constant and low loss tangent. At low temperatures, these materials are stiff but bendable without breaking. They are also resistant to moisture, chemical attack, heat, and abrasion. Table 14 gives the mechanical and electrical properties of materials used for cable insulation. 

If there is an infinite numtser of planes of material property symmetry, then the foregoing relations simplify to the isotropic material relations with only two independent constants in the stiffness matrix ... 

Sometimes the stiffness matrix for a lamina, [Q j], Is not constant through the thickness of the lamina. For example, if a temperature gradient or moisture gradient exists in the lamina and the lamina material properties are temperature dependent and/or moisture dependent, then [Qij]i( is a function of z and must be left inside the integral. In such cases,... 

Verify for a single layer of isotropic material with material properties E and v and thickness t that the extensional and bending stiffnesses are... 

This section is devoted to those special cases of laminates for which the stiffnesses take on certain simplified values as opposed to the general form in Equation (4.24). The general force-moment-strain-curvature relations in Equations (4.22) and (4,23) are far too comprehensive to easily understand. Thus, we build up our understanding of laminate behavior from the simplest cases to more complicated cases. Some of the cases are almost trivial, others are more specialized, some do not occur often in practice, but the point is that all are contributions to the understanding of the concept of laminate stiffnesses. Many of the cases result from the common practice of constructing laminates from laminae that have the same material properties and thickness, but have different orientations of the principal material directions relative to one another and relative to the laminate axes. Other more general cases are examined as well. 

For a single isotropic layer with material properties, E and v, and thickness, t, the laminate stiffnesses of Equation (4.24) reduce to... 

For laminates that are symmetric in both geometry and material properties about the middle surface, the general stiffness equations. Equation (4.24), simplify considerably. That symmetry has the form such that for each pair of equal-thickness laminae (1) both laminae are of the same material properties and principal material direction orientations, i.e., both laminae have the same (Qjjlk and (2) if one lamina is a certain distance above the middle surface, then the other lamina is the same distance below the middle surface. A single layer that straddles the middle surface can be considered a pair of half-thickness laminae that satisfies the symmetry requirement (note that such a lamina is inherently symmetric about the middle surface). ... 

Because of the analytical complications involving the stiffnesses Ai6, A26, D g, and D26, a laminate is sometimes desired that does not have these stiffnesses. Laminates can be made with orthotropic layers that have principal material directions aligned with the laminate axes. If the thicknesses, locations, and material properties of the laminae are symmetric about the middle surface of the laminate, there is no coupling between bending and extension. A general example is shown in Table 4-2. Note that the material property symmetry requires equal [Q j], of the two layers that are placed at the same distance above and below the middle surface. Thus, both the orthotropic material properties, [Qjjlk. of the layers and the angle of the principal material directions to the laminate axes (i.e., the orientation of each layer) must be identical. 

The stiffnesses of an antisymmetric laminate of anisotropic laminae do not simplify from those presented in Equations (4.22) and (4.23). However, as a consequence of antisymmetry of material properties of generally orthotropic laminae, but symmetry of their thicknesses, the shear-extension coupling stiffness A.,6,... 

For the general case of multiple isotropic layers of thickness t and material properties E( and V, the extensional, bending-extension coupling, and bending stiffnesses are given by Equation (4.24) wherein... 

The term quasi-isotropic iaminate is used to describe laminates that have isotropic extensionai stiffnesses (the same in all directions in the plane of the laminate). As background to the definition, recall that the term isotropy is a material property whereas laminate stiffnesses are a function of both material properties and geometry. Note also that the prefix quasi means in a sense or manner. Thus, a quasi-isotropic laminate must mean a laminate that, in some sense, appears isotropic, but is not actually isotropic in all senses. In this case, a quasi-isotropic... 

Prove that the bending-extenslon coupling stiffnesses. By, are zero for laminates that are symmetric in both material properties and geometry about the middle surface. 

Shaft stiffness Most machine-trains used in industry have flexible shafts and relatively long spans between bearing-support points. As a result, these shafts tend to flex in normal operation. Three factors determine the amount of flex and mode shape that these shafts have in normal operation shaft diameter, shaft material properties, and span length. A small-diameter shaft with a long span will obviously flex more than one with a larger diameter or shorter span. 

Also, it appears from the data that these metals are much stiffer and significantly stronger than the plastics. This approach to evaluation could eliminate the use of plastics in many potential applications, but in practice it is recognized by those familiar with the behavior of plastics that it is the stiffness and strength of the product that is important, not its material properties. 

To illustrate the correct approach, consider applications in which a material is used in sheet form, as in automotive body panels, and suppose that the service requirements are for stiffness and strength in flexure. First imagine four panels with identical dimensions that were manufactured from the four materials given in Table 3-1. Their flexural stiffnesses and strengths depend directly on the respective material s modulus and strength. All the other factors are shared in common with the other materials, there being no significantly different Poisson ratios. Thus, the relative panel properties are identical with the relative material properties illustrated in Fig. 3-3. Obviously, the metal panels will be stiffer and... 

The contact force between two particles is now determined by only five parameters normal and tangential spring stiffness kn and kt, the coefficient of normal and tangential restitution e and et, and the friction coefficient /if. In principle, kn and k, are related to the Young modulus and Poisson ratio of the solid material however, in practice their value must be chosen much smaller, otherwise the time step of the integration needs to become unpractically small. The values for kn and k, are thus mainly determined by computational efficiency and not by the material properties. More on this point is given in the Section III.B.7 on efficiency issues. So, finally we are left with three collision parameters e, et, and which are typical for the type of particle to be modeled. 

The overall objective of a dynamic blast analysis is to assess the capability of a structure to resist a specified blast load. To accomplish this goal, the analysis should be able to predict, with a fair degree of accuracy, the dynamic response of the structure. The analysis of a typical member begins with a given structural configuration, which includes the type of material, span length, support conditions and applied loading. Material properties are then used to estimate member stiffness,... 

Eigure 6 shows the stiffness of Ecoflex /PLA blends depending on the PLA amount. PLA today is a thermoplastic polymer made from renewable raw materials and is available on industrial scale. Blending the completely different thermoplastic polyesters - stiff and brittle PLA with soft and flexible Ecoflex - a whole range of different material properties can be accessed, depending on the ratio of both polymers. 

One of the most desirable aspects of plastics and composites is the ability to make net-shaped parts. The same process that creates the material also creates the structure. The penalty for this advantage is that the process of curing a thermosetting plastic or composite part is irreversible. Any part that is not properly processed represents a loss of part, material and the money and time required to make that part, although larger parts are usually repaired if possible. Proper shape becomes a controlled property in addition to the bulk material properties, such as mechanical (stiffness or strength), physical (density, void content, etc.), chemical (degree of cure or carbonization, chemical resistance), electrical (resistivity, conductivity), or any combination of these. 

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