Longitudinal stiffness

Considering that for our substrates the maximum indentation depth is 89 nm (Table 3.3), we have decided to perform constant nano-indentation depth experiments up to 80 nm. Moreover, considering the longitudinal stiffness of the can-... 

Maximum strain theory may be modified to predict the strength of randomly oriented short-fiber composites (22). llie Halpin-Tsai equations (14) have established relations for the stiffness of an oriented short-fiber ply from the matrix and fiber properties. These nations show that the longitudinal stiffness of an oriented short-fiber composite is a s itive function of the aspect ratio. 

Component stiffnesses using springs iih = horizontal stiffness E, = vertical stiffness E( = longitudinal stiffness... 

The Halpin-Tsai equations and the Mori-Tanaka model are the most used to predict mechanical properties of composites. The Halpin-Tsai equations predict stiffness of the unidirectional composites as a function of aspect ratio. In this model, the longitudinal stiffness and transverse engineering moduli are expressed in the following general form ... 

The use of dissimilar adherends decreases the joint strength due to a nonuniform stress distribution (see Fig. 27.5b). To reduce this problem, the joint should be designed so that the longitudinal stiffness of the adherends to be bonded are equal, i.e., Eiti = 2<2. where E is the longitudinal modulus, t the thickness, and the subscripts (1, 2) refer to adherend 1 and adherend 2. 

Adhesive shear stresses in a metal/composite double-lap joint for the case where the composite has a lower longitudinal stiffness than the metal (E c tc < fm) under a tensile load and a thermal load, at adhesive yielding (ry) (Adapted from Hart-Smith [1973])... 

Reinforcement layers. Fiber-reinfo-ced composites that normally use glass fibers. A variety of weaves and weights of reinforcement are possible to provide longitudinal stiffness. 

The local friction image (Figure 4.a), shows the initial situation turns to high friction with some stick-slip phenomena, inducing contact vibration, due to the low longitudinal stiffness of the test machine. The low fnction effect of the tribofilm is found to last about 25 cycles. 

Adding 40% by volume of reinforcing fibers to the matrix for the cases plotted would result in only about 50% increase in transverse stiffness of the composite, but would increase longitudinal stiffness by 400% (Figure 8.6). Hence, the addition of fiber reinforcement to a polymer matrix can have a very pronounced effect on its stiffness and directional properties, particularly in the liber direction. 

Mechanical Properties. Although wool has a compHcated hierarchical stmcture (see Fig. 1), the mechanical properties of the fiber are largely understood in terms of a two-phase composite model (27—29). In these models, water-impenetrable crystalline regions (generally associated with the intermediate filaments) oriented parallel to the fiber axis are embedded in a water-sensitive matrix to form a semicrystalline biopolymer. The parallel arrangement of these filaments produces a fiber that is highly anisotropic. Whereas the longitudinal modulus of the fiber decreases by a factor of 3 from dry to wet, the torsional modulus, a measure of the matrix stiffness, decreases by a factor of 10 (30). 

Laboratory measurements are primarily concerned with tread compound traction properties. Tread pattern and other tire parameters like cornering and longitudinal slip stiffness require still tests with tires on either large indoor machines or direct proving ground measurements. 

The tire constmction influences both cornering and longitudinal slip stiffness. These include the tire carcass, breaker construction, inflation pressure, and tread pattern design. However, since the two stiffness components can be measured, knowledge of the construction details is not necessary. The vehicle geometry influences the tire wear through the air resistance, which it creates, and through the load distribution between front and rear axles. 

As the laser beam can be focused to a small diameter, the Raman technique can be used to analyze materials as small as one micron in diameter. This technique has been often used with high performance fibers for composite applications in recent years. This technique is proven to be a powerful tool to probe the deformation behavior of high molecular polymer fibers (e.g. aramid and polyphenylene benzobisthiazole (PBT) fibers) at the molecular level (Robinson et al., 1986 Day et al., 1987). This work stems from the principle established earlier by Tuinstra and Koenig (1970) that the peak frequencies of the Raman-active bands of certain fibers are sensitive to the level of applied stress or strain. The rate of frequency shift is found to be proportional to the fiber modulus, which is a direct reflection of the high degree of stress experienced by the longitudinally oriented polymer chains in the stiff fibers. 

Extensive experimental testing was performed on IM6/3100 to obtain longitudinal and transverse stiffnesses and major Poisson s ratio as a function of degree of cure. A detailed explanation of the test procedure can be found in [5], The model predictions and experimental results for this material system are shown in Figures 8.11-8.13. From these relations the lamina stiffnesses Qy can be obtained from... 

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