Variability of Material Properties

Modulus of elasticity E Stiffness—resistance to elastic deformation 

Tensile strength TS Maximum load-bearing capacity 

Modulus of resilience Ur Energy absorption—elastic deformation 

Toughness (static) — Energy absorption—plastic deformation 

It should also be mentioned that scatter exists for other measured material properties, such as density, electrical conductivity, and coefficient of thermal expansion. 

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Fluorescence spectroscopy as a means of judging process conditions in a polymerization reaction has been reported [48]. The authors optimized parameters such as the reactant ratio and catalyst amount to reach the smallest variability of material properties. The samples were deposited on a 96-micro reactor array and examined with a spectro-fluorometer during the reaction. 

A deterministic approach (i.e. all types of loading, dimensions and material parameters etc. are constant) provides an older but simple way to simulate mechanical systems. However, a deterministic approach cannot truly include the variability of all inputs (i.e. variability of material properties of the ore), because nature and the world are stochastic. Solution of the ore disintegration process via deterministic approach (i.e. basic simple solution) is shown in reference Frydrysek Gondek 2008. However, this problem is solved via probabihstic approaches which are based on statistics. 

One of the major reasons why design should be based on statisties is that material properties vary so widely, and any general theory of reliability must take this into aeeount (Haugen and Wirsehing, 1975). Material properties exhibit variability beeause of anisotropy and inhomogeneity, imperfeetion, impurities and defeets (Bury, 1975). All materials are, of eourse, proeessed in some way so that they are in some useful fabrieation eondition. The level of variability in material properties assoeiated with the level of proeessing ean also be a major eontribution. There are three main kinds of randomness in material properties that are observed (Bolotin, 1994) ... 

A more common use of informatics for data analysis is the development of (quantitative) structure-property relationships (QSPR) for the prediction of materials properties and thus ultimately the design of polymers. Quantitative structure-property relationships are multivariate statistical correlations between the property of a polymer and a number of variables, which are either physical properties themselves or descriptors, which hold information about a polymer in a more abstract way. The simplest QSPR models are usually linear regression-type models but complex neural networks and numerous other machine-learning techniques have also been used. 

The variability of physical properties widens both the dimensional x- and the dimensionless pi-space. The process is not determined by the original material quantity x, but by its dimensionless reproduction. (Pawlowski [27] has clearly demonstrated this situation by the mathematical formulation of the steady-state heat transfer in an concentric cylinder viscometer exhibiting Couette flow). It is therefore important to carry out the dimensional-analytical reproduction of the material function uniformly in order to discover possibly existing, but under circumstances concealed, similarity in the behavior of different substances. This can be achieved only by the standard representation of the material function [5, 27]. 

Now we have three equations for the five variables. In order to solve shock problems, we need two more relationships. We will see in the next chapter that these are derived from experimental data of material properties and from specification of boundary conditions. 

In the previous section we noted that, in the abstract, A1 (or any other material) may be characterized by a series of numbers, its material parameters, to be found in a databook. However, as we already hinted at, because of the history dependence of material properties, the description of such properties is entirely more subtle. There is no one aluminum, nor one steel, nor one zirconia. Depending upon the thermomechanical history of a material, properties ranging from the yield strength to the thermal and electrical conductivity can be completely altered. The simplest explanation for this variability is the fact that different thermomechanical histories result in different internal structures. 

For dealing with variability of soil properties at the larger scale, a continuum approach is implemented. Thereby a representative elementary volume (REV) is considered to exist and material properties related to flow and transport are defined at the centre of this REV. Thermodynamic principles related to conservation of mass and momentum are further applied on the REV to obtain governing flow and transport equations. The... 

The time-temperature superimposition technique allows the prediction of material properties that normally would require measurements over many months or years. To collect the necessary data, measurements of a time-dependent variable are made at a number of temperatures. The curves are shifted mathematically along the time axis until some overlap occurs and a continuous curve is formed covering several decades of time this curve is called a master curve. A master curve can be used to determine the time-dependent property as a function of time. Figure 10.30c shows total strain as a function of time and temperature for PTFE. 

Materials manufacturing can also benefit from combinatorial methods. Libraries to optimize recipes and process conditions can be studied using many of the methods and assays developed for materials discovery. The ability to correlate the synthesis variables with materials properties is valuable in determining manufacturing specifications for a given... 

The compounds formed by the Group IIIA elements of the periodic table, Al, Ga and In, with the group VA elements, P, As and Sb, have the potential to be extremely important semiconductor materials. The attractiveness of Group III-V compounds as electronic materials lies in the variability of electrical properties among the different compounds and the fact that these properties are often superior to those found in Si. 

Synthetic polymeric materials possess enormous variability of utility properties, which depend ... 

Part of any quality control system is the keeping of adequate records, which should be available to all parties. These are particularly valuable when the manufacturer makes standard products, as they record the variability of the properties over a period of time. They also give confidence when a standard product is to be adapted for a particular application, by changing the shape, the materials or otherwise, that the properties will be as predicted. 

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