Material properties variability

The effect of ground loads on pipes can be described by equations that involve the primary geometric and material property variables. Various analytical approaches have been adopted and there has been some disagreement between different national codes. The analyses are usually based on techniques first described by Spangler to calculate deflection of highway culverts. In the UK equations devised by the Transport and Road Research Laboratory (TRRL) [4] have been used. The German and Scandinavian codes have become widely used in Europe but in future it is likely that computer-interpreted... 

Eq. 2.2 is a relationship among k — r independent dimensionless products, where r is the minimum number of reference dimensions required to describe the variables. While the Buckingham If theorem itself is straightforward, development of a dimensionless expression for a process or a phenomenon requires a systematic dimensional analysis [Ref. 4 for more details]. For most engineering problems, variables can be divided into three groups (1) geometric variables, (2) material property variables, and (3) process variables. The reference dimensions are normally the basic dimensions such as mass M), length (L), and time (7). 

Some researchers classify the different types of uncertainty into aleatory and epistemic (Der Kiureghian and Ditlevsen 2009). Aleatory uncertainty refers to those types of uncertainty that are inherent in nature and, therefore, irreducible by definition. For example, the variability in material properties, variability in earthquake loading, etc. are all irreducible in nature. Epistemic uncertainty refers to those types of uncertainty that may be reduced when more information is available. For example, when an improved model can be used to predict the response of a structure, then the uncertainty regarding the model prediction would decrease, thereby decreasing the overall uncertainty. 

The performance characteristics of ceramic sensors are defined by one or more of the foUowing material properties bulk, grain boundary, interface, or surface. Sensor response arises from the nonelectrical input because the environmental variable effects charge generation and transport in the sensor material. 

As with any constitutive theory, the particular forms of the constitutive functions must be constructed, and their parameters (material properties) must be evaluated for the particular materials whose response is to be predicted. In principle, they are to be evaluated from experimental data. Even when experimental data are available, it is often difficult to determine the functional forms of the constitutive functions, because data may be sparse or unavailable in important portions of the parameter space of interest. Micromechanical models of material deformation may be helpful in suggesting functional forms. Internal state variables are particularly useful in this regard, since they may often be connected directly to averages of micromechanical quantities. Often, forms of the constitutive functions are chosen for their mathematical or computational simplicity. When deformations are large, extrapolation of functions borrowed from small deformation theories can produce surprising and sometimes unfortunate results, due to the strong nonlinearities inherent in the kinematics of large deformations. The construction of adequate constitutive functions and their evaluation for particular... 

Clearly, the only variables left on the right-hand side of eqn. (7.3) are the material properties p and E. To minimise M, we must choose a material having the smallest possible value of... 

Variations in a produet s material properties, serviee loads, environment and use typieally lead to random failures over the most protraeted period of the produet s expeeted life-eyele. During the eonditions of use, environmental and serviee variations give rise to temporary overloads or transients eausing failures, although some failures are also eaused by human related events sueh as installation and operation errors rather than by any intrinsie property of the produet s eomponents (Klit et al., 1993). Variability, therefore, is also the souree of unreliability in a produet (Carter, 1997). However, it is evident that if produet reliability is determined during the design proeess, subsequent manufaeturing, assembly and delivery of the system will eertainly not improve upon this inherent reliability level (Kapur and Lamberson, 1977). 

The data used to generate the maps is taken from a simple statistical analysis of the manufacturing process and is based on an assumption that the result will follow a Normal distribution. A number of component characteristics (for example, a length or diameter) are measured and the achievable tolerance at different conformance levels is calculated. This is repeated at different characteristic sizes to build up a relationship between the characteristic dimension and achievable tolerance for the manufacture process. Both the material and geometry of the component to be manufactured are considered to be ideal, that is, the material properties are in specification, and there are no geometric features that create excessive variability or which are on the limit of processing feasibility. Standard practices should be used when manufacturing the test components and it is recommended that a number of different operators contribute to the results. 

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) ... 

Theoretically, the effects of the manufacturing process on the material property distribution can be determined, shown here for the case when Normal distribution applies. For an additive case of a residual stress, it follows that from the algebra of random variables (Carter, 1997) ... 

Virtually all design parameters such as tolerances, material properties and service loads exhibit some statistical variability and uncertainty that influence the adequacy of the design. A key requirement in the probabilistic approach is detailed knowledge... 

The term nonlinear in nonlinear programming does not refer to a material or geometric nonlinearity but instead refers to the nonlinearity in the mathematical optimization problem itself. The first step in the optimization process involves answering questions such as what is the buckling response, what is the vibration response, what is the deflection response, and what is the stress response Requirements usually exist for every one of those response variables. Putting those response characteristics and constraints together leads to an equation set that is inherently nonlinear, irrespective of whether the material properties themselves are linear or nonlinear, and that nonlinear equation set is where the term nonlinear programming comes from. 

Unlike incompatible heterogeneous blends of elastomer-elastomer, elastomer-plastic, and plastic-plastic, the reactively processed heterogeneous blends are expected to develop a variable extent of chemical interaction. For this reason the material properties, interfacial properties, and phase morphology of reactively processed blends would differ significantly from heterogeneous mixtures. 

The early development of modern plastic materials (over a century) can be related to the electrical industry. The electronic and electrical industry continues to be not only one of the major areas for plastic applications, they are a necessity in many applications worldwide (2,190). The main reasons is that plastic designed products are generally basically inexpensive, easily shaped, fast production dielectric materials with variable but controllable electrical properties, and jn most cases the plastics are used because they are good insulators (Chapter 5, ELECTRICAL PROPERTY). 

The basics observed in molded products are always the same only the extent of the features varies depending on the process variables, material properties, and cavity contour. That is the inherent hydrodynamic skin-core structure characteristic of all IM products. However, the ratio of skin thickness to core thickness will vary basically with process conditions and material characteristics, flow rate, and melt-mold temperature difference. These inherent features have given rise to an increase in novel commercial products and applications via coinjection, gas-assisted, low pressure, fusible-core, in-mold decorating, etc. 

An understanding of the influence of the various forms on the material properties of PMMA is important and variable temperature infrared and Raman... 

The approach taken here is to employ standard materials characterization tests to measure the materials properties of the granulated product. With this information, the mechanism of attrition, i.e., breakage versus erosion, is determined. The rate of attrition can then be related, semi-empirically, to material properties of the formulation and the operating variables of the process, such as bed depth and fluidizing velocity. 

The large amount of variables affecting attrition can be classified into two major groups, i.e., the various factors related to material properties and factors related to process conditions. 

Fig. 3 Dual-side catalyst for variable material properties...

While the various strategies described above have proven promising, SOFC electrodes remain largely empirically understood and far from optimized and suffer from numerous short- and long-term degradation problems. Reported performances vary tremendously with many unknown variables at work and limited understanding as to how materials properties and microstructure relate to performance and long-term stability. ... 

Raman spectroscopy s sensitivity to the local molecular enviromnent means that it can be correlated to other material properties besides concentration, such as polymorph form, particle size, or polymer crystallinity. This is a powerful advantage, but it can complicate the development and interpretation of calibration models. For example, if a model is built to predict composition, it can appear to fail if the sample particle size distribution does not match what was used in the calibration set. Some models that appear to fail in the field may actually reflect a change in some aspect of the sample that was not sufficiently varied or represented in the calibration set. It is important to identify any differences between laboratory and plant conditions and perform a series of experiments to test the impact of those factors on the spectra and thus the field robustness of any models. This applies not only to physical parameters like flow rate, turbulence, particulates, temperature, crystal size and shape, and pressure, but also to the presence and concentration of minor constituents and expected contaminants. The significance of some of these parameters may be related to the volume of material probed, so factors that are significant in a microspectroscopy mode may not be when using a WAl probe or transmission mode. Regardless, the large calibration data sets required to address these variables can be burdensome. 

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