A Material Properties

The identity tensor by is zero for i J and unity for i =J. The coefficient X is a material property related to the bulk viscosity, K = X + 2 l/3. There is considerable uncertainty about the value of K. Traditionally, Stokes hypothesis, K = 0, has been invoked, but the vahdity of this hypothesis is doubtful (Slattery, ibid.). For incompressible flow, the value of bulk viscosity is immaterial as Eq. (6-23) reduces to... 

The relative shock velocity t/ = (7 — Uj is the Eulerian shock velocity often used because it is a material property and is independent of the motion of the... 

Here M is the moment and Mp the fully-plastic moment of, for instance, a beam P/A is the indentation pressure and H the hardness of, for example, armour plating.) The left-hand side of each of these equations describes the loading conditions the right-hand side is a material property. When the left-hand side (which increases with load) equals the right-hand side (which is fixed), failure occurs. 

There are further ramifications of this observation. In essence if the value of a material property changes with temperature and this change arises from changes in the viscosity of the system then it may well be possible to apply the WLF equation. 

Gc is a material property which is referred to as the toughness, critical strain energy release rate or crack extension force. It is effectively the energy required to increase the crack length by unit length in a piece of material of unit width. It has units of J/m. ... 

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... 

A more universal fracture characteristic for use with ductile materials is the J integral . This is similar to CTOD but relates a volume integral to a surface integral and is independent of the path of the integral it can be classed as a material property. The J integral can also be used to predict critical stress levels for known crack lengths or vice versa. 

Observe that this is a geometric property, not to be confused with the modulus of the material, which is a material property. I, c, Z, and the cross-sectional areas of some common cross-sections are given in Fig. 3-1, and the mechanical engineering handbooks provide many more. The maximum stress and defection equations for some common beamloading and support geometries are given in Fig. 3-2. Note that for the T- and U-shaped sections in Fig. 3-1 the distance from the neutral surface is not the same for the top and bottom of the beam. It may occasionally be desirable to determine the maximum stress on the other nonneutral surface, particularly if it is in tension. For this reason, Z is provided for these two sections. 

Consequently the absolute potential is a material property which can be used to characterize solid electrolyte materials, several of which, as discussed in Chapter 11, are used increasingly in recent years as high surface area catalyst supports. This in turn implies that the Fermi level of dispersed metal catalysts supported on such carriers will be pinned to the Fermi level (or absolute potential) of the carrier (support). As discussed in Chapter 11 this is intimately related to the effect of metal-support interactions, which is of central importance in heterogeneous catalysis. 

The variation in the mode of failure makes comparison of different types of cement quite impossible. As Darvell (1990) has pointed out, compressive strength is not a material property under any condition, but can only be used to compare materials of a very similar nature. 

Physical characterization of polymers is a common activity that research and development technologists at the Dow Chemical Company perform. A material property evaluation that is critical for most polymer systems is a tensile test. Many instruments such as an Instron test frame can perform a tensile test and, by using specialized software, can acquire and process data. Use of an extensometer eliminates calibration errors and allows the console to display strain and deformation in engineering units. Some common results from a tensile test are modulus, percent elongation, stress at break, and strain at yield. These data are then used to better understand the capabilities of the polymer system and in what end-use applications it may be used. 

Creep-rupture is measured using the same methods as creep except that the tests are continued until the specimen ruptures. Gripping and specimen alignment become increasingly important if rupture is to be seen as a material property independent of the... 

Orimo, S. Nakamori, Y. Zuttel, A., Material properties of MBH4 (M=Li,Na,and K). Materials Science and Engineering B... 

In this chapter, we will focus mostly on the constant in Eq. (4.1), and not the flux or driving force, since these are specific to a process. The proportionality constant is a material property, however, which we can measure, correlate with process parameters, and hopefully predict. The term constant is in quotations, becanse we will see that in some instances, it is really a fnnction of the driving force. It is important to understand (a) the driving forces nnder which this proportionality constant operates and (b) the effect the constant has on transport phenomena. 

The ratio of permittivity with the dielectric to the permittivity in vacuum, e/eo, is called the relative permittivity, s, or dielectric constant. The dielectric constant is a material property. Some values of dielectric constants for common ceramic and glass insulators are given in Table 6.3. Since a polarizable material causes an increase in charge per unit area on the plates of a capacitor, the capacitance also increases, and it can be shown that the dielectric constant is related to the capacitance and displacement in vacuum and with the dielectric material as follows ... 

The quantity (1 + /) is called the relative magnetic permeability (also dimensionless), which is also a material property. 

The absorption coefficient is a material property and is a fnnction of the wavelength... 

Of the three physical properties covered in this chapter, optical properties have the least importance in composite and biological applications. This is not to say that there are no applications of optical properties in composites or biological materials. There are indeed, such as the use of birefringence in the analysis of stress distribution and fiber breakage in fiber-matrix composites [14] and in the development of materials for ophthalmic implants such as intraocular devices [15]. These topics are beyond the scope of this text, however, even as optional information, and introduce no new concepts from a material property standpoint. There are many interesting articles and... 

The dispersed particles also attract each other through van der Waals forces (Chapter 10), which decrease with increasing interparticle separation. A material property known as the Ha-maker constant, A, can be used as a measure of the strength of the van der Waals attraction. 

We have already seen from Example 10.1 that van der Waals forces play a major role in the heat of vaporization of liquids, and it is not surprising, in view of our discussion in Section 10.2 about colloid stability, that they also play a significant part in (or at least influence) a number of macroscopic phenomena such as adhesion, cohesion, self-assembly of surfactants, conformation of biological macromolecules, and formation of biological cells. We see below in this chapter (Section 10.7) some additional examples of the relation between van der Waals forces and macroscopic properties of materials and investigate how, as a consequence, measurements of macroscopic properties could be used to determine the Hamaker constant, a material property that represents the strength of van der Waals attraction (or repulsion see Section 10.8b) between macroscopic bodies. In this section, we present one illustration of the macroscopic implications of van der Waals forces in thermodynamics, namely, the relation between the interaction forces discussed in the previous section and the van der Waals equation of state. In particular, our objective is to relate the molecular van der Waals parameter (e.g., 0n in Equation (33)) to the parameter a that appears in the van der Waals equation of state ... 

Fourier s law states that heat flux (W/m2 or J/s-m2) is proportional to the negative gradient of the temperature field, with the constant of proportionality being a material property called the thermal conductivity A.,... 

Secondly, Irwin 6) found that the stress field around a sharp crack in a linear elastic material could be uniquely defined by a parameter named the stress-intensity factor, K and stated that fracture occurs when the value of K, exceeds some critical value, K C. Thus, K, is a stress field parameter independent of the material whereas Klc, often referred to as the fracture toughness, is a measure of a material property. Again the subscript I is used to denote the tensile-opening mode. 

To understand the significance of material properties, one only has to think of density, which is also a material property. The density of a substance defines how much volume, let s say, of water, that the substance will displace on immersion. Instead of measuring the volume of water each time one drops this substance in any container of water, one measures its density and calculates how much water it will displace on immersion. Clearly, the material property concept leads to predictive abilities. It is now known that the relative ordering of the molecules in a simple bodymatter defines its density and that by altering the ordering of the molecules, one... 

Brittle Liable to break Sharp crack with small amounts of deformation around the crack tip. Brittleness is a behavior, not a material property. 

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