Measurement of stiffness

Hardness is essentially a measure of stiffness and in principle can be related to modulus. For plastics, the term hardness refers to resistance to indentation but depending on the test method the measurement is made either with the indentation load applied or after its removal when elastic recovery has taken place. The standard methods are given in ISO 868 (Shore) [6] and ISO 2039 (Ball indentation and Rockwell) [7]. However, Vickers microhardness is more satisfactory for monitoring degradation of rigid materials. 

CNTs are among the world s strongest materials. The mechanical characteristics of CNTs stand out due to their very high stiffness and tensile strength. The Young s modulus, i.e. a measure of stiffness and thus of how much a given material deforms upon application of mechanical stress, is about 1 TPa, which is comparable to in-plane graphite [40]. 

Dinelli, F., Biswas, S. K., Briggs, G. A. D., and Kolosov, O. V. (2000a). Measurements of stiff-material compliance on the nanoscale using ultrasonic force microscopy. Phys. Rev. 5 61(20), 13995-14006. [300]... 

There are two reasons for using a tensile stress/strain test other than the standard method as typified by ISO 37. First, it can be sensibly argued that a more useful measure of stiffness is the so-called relaxed modulus, i.e. the stress at a given elongation after a fixed time of relaxation this is essentially a short term stress relaxation test. Secondly, it may be more convenient for quality control purposes to have a simple test in which only one parameter is measured. 

The most obvious simple measure of stiffness, hardness, has in the past not often been used at low temperatures because of experimental difficulties due to icing up of the moving parts of the apparatus. There were no real fundamental reasons why this problem could not be overcome and suitable apparatus is now available, although low temperature hardness tests seem to be mostly restricted to the detection of crystallisation (see Section 3.5). 

Kojima, H., Ishijima, A., and Yanagida, T. (1994). Direct measurement of stiffness of single actin filaments with and without tropomyosin by in vitro nanomanipulation. 

As a measure of stiffness, the Young s modulus is important in the predictive behavior of the material being used. For linear analysis, E = stress/strain. For automotive applications, some common materials are steel (E 200 GPa), aluminum (E 70 GPa), and nylon (E 8.5 GPa). As stated earlier, Hook s law is force = spring constant spring displacement (F = KU). The generalized Hook s... 

As we saw in the preceding discussion, several mechanical parameters can be derived from stress-strain tests. Two of these parameters are of particular significance from a design viewpoint. These are strength and stiffness. For some applications, the ultimate tensile strength is the useful parameter, but most polymer products are loaded well below their breaking points. Indeed, some polymers deform excessively before rupture and this makes them unsuitable for use. Therefore, for most polymer applications, stiffness (resistance to deformation under applied load) is the parameter of prime importance. Modulus is a measure of stiffness. We will now consider how various structural and environmental factors affect modulus in particular and other mechanical properties in general. 

For all materials (other than fabrics, for which the concept is not relevant) the basic parameter is a measure of stiffness or modulus derived from the stress-strain curve. As with tensile tests, because the stress -strain relation is generally not linear, care must be taken to compare only measures of stiffness defined in the same way. With rigid foams and plastics there are additionally measures of yield or strength. 

Mechanical performance of the heart, more specifically the left ventricle, is typically characterized by estimates of ventricular elastance. The heart is an elastic bag that stiffens and relaxes with each heartbeat. Elastance is a measure of stiffness, classically defined as the differential relation between pressure and volume ... 

As a measurement of stiffness. Young s modulus is used, defined in the usual way. 

Fkf. 16.(a) Polymethylmethacrylate (Perspex) ami (h) polystyrene. Room temperature measurements of stiffness constants for uniaxially drawn specimens. (From... 

By combining static-creep and dynamic tests, a range of stiffness modulus can be obtained. When measurements of stiffness modulus as a function at time, at various temperatures, are carried out and the results are plotted in logarithmic scales, a graph of the type shown in Figure 4.16 is obtained. 

According to IAN 73/06 (Highways Agency 2009a), foundation surface modulus is defined as a measure of stiffness modulus on the basis of the application of a known load at the top of the foundation it is a composite value with contributions from all underlying layers. 

Layer modulus is defined as a measure of stiffness modulus assigned to a given foundation layer usually, this is a long-term estimate that takes account of degradation caused by factors such as cracking. 

When r < He, the solution approach discussed above for is tqrpropriate for a simulation in which only the motion of the mechanism is desired, and the exact magnitudes of the constraint forces are not required. If an exact solution is desired for h , then a more detailed model of the system will be needed which includes some measures of stiffness. 

The modulus 5 is a measure of stiffness or hardness of an object. The compliance T is a measure of its softness. In regions far from transitions, the elongation compliance J is defined as in Eq. 22 ... 

Modulus the ratio of stress to strain, which is a measure of stiffness of a polymer. A high modulus polymer is stiff and has very low elongation. Some systems, especially solutions of high molecular weight or cross-linked polymers, show complex behavior under stress. They posses an elastic modulus, G, and a loss modulus, G", representing the recoverable and irrecoverable strain, respectively. 

Figure 1.6 Idealized modulus-temperature behavior of an amorphous polymer. Young s modulus, stress/strain, Is a measure of stiffness.

Probability of Avrami crystal fronts crossing 1/p = measure of stiffness Pi = probability of finding a molecule Pi, Q2 = heat absorbed and released Racmic-opposite side End-to-end distance... 

Another model is the wormlike chain model [2], Its measure of stiffness is the persistence length, which is half the Kuhn length. The persistence and Kuhn lengths characterize the number of bonds over which orientational correlations decay to zero along the chain. These are simplified models of bond correlations. A better treatment, which we won t explore here, is the rotational isomeric state model [1, 3], which accounts not only for the angles and lengths of chemical bonds, but also for the different statistical weights of the various possible bond conformations. 

A large number of biomaterials are made up of intermediate filaments and therefore their mechanical properties are of great interests. Elastic moduli of these filaments depend upon the particular composition of the filament and the state of hydration. Bending modulus of hydrated intermediate filaments is found to be much less compared to the dry filament. E.g., Young s modulus of horsehair keratin is 6.8 GPa and 2.4 GPa respectively. For most of the cases, in vitro measurement of stiffness parameters agree quite well with the in vivo data and therefore can be directly implemented in the model. 

The elastic modulus ( modulus of elasticity , Young s modulus or tensile modulus ) is the ratio of the applied stress to the strain it produces in the region where strain is proportional to stress, i.e. in the initial straight-line portion of the stress-strain curve. Modulus is primarily a measure of stiffness, and plastic parts should be designed such that service behaviour normally falls in this linear region. 

Figure 10.7 Schematic presentation of the Perkin-Elmer thermal mechanical analyser (top). Bottom left expansion probe for measurement of linear thermal expansion coefficient. Bottom right penetration probe for measurement of stiffness.

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