Shape stiffness-stress

Alloys are designed to meet specific needs. For example, the frames of racing bicycles can be made of a steel that contains manganese, molybdenum, and carbon to give them the stiffness needed to resist mechanical shock. Titanium frames are also used, but not the pure metal. Titanium metal stretches easily, so much so that it may not keep its shape under stress. However, when alloyed with metals such as tin and aluminum, titanium maintains its flexibility but keeps its shape. 

A reduction of the required energy could be reached by the incorporation of conductive fillers such as heat conductive ceramics, carbon black and carbon nanotubes [103-105] as these materials allowed a better heat distribution between the heat source and the shape-memory devices. At the same time the incorporation of particles influenced the mechanical properties increased stiffness and recoverable strain levels could be reached by the incorporation of microscale particles [106, 107], while the usage of nanoscale particles enhanced stiffness and recoverable strain levels even more [108, 109]. When nanoscale particles are used to improve the photothermal effect and to enhance the mechanical properties, the molecular structure of the particles has to be considered. An inconsistent behavior in mechanical properties was observed by the reinforcement of polyesterurethanes with carbon nanotubes or carbon black or silicon carbide of similar size [3, 110]. While carbon black reinforced materials showed limited Ri around 25-30%, in carbon-nanotube reinforced polymers shape-recovery stresses increased and R s of almost 100% could be determined [110]. A synergism between the anisotropic carbon nanotubes and the crystallizing polyurethane switching segments was proposed as a possible... 

What is the effect of shape on the diastolic LV pressure-volume relationship and on the quantitation of myocardial stiffness-stress relations ... 

Effect of ventricular shape on the myocardial stiffness-stress relations... 

Textile fibers must be flexible to be useful. The flexural rigidity or stiffness of a fiber is defined as the couple required to bend the fiber to unit curvature (3). The stiffness of an ideal cylindrical rod is proportional to the square of the linear density. Because the linear density is proportional to the square of the diameter, stiffness increases in proportion to the fourth power of the filament diameter. In addition, the shape of the filament cross-section must be considered also. For textile purposes and when flexibiUty is requisite, shear and torsional stresses are relatively minor factors compared to tensile stresses. Techniques for measuring flexural rigidity of fibers have been given in the Hterature (67—73). 

The S -shaped flexible elements were required to keep the stiffness and stresses low, due to the relatively heavy rotor weight as evident by the finite element stress analysis shown in Figure 6-30. The wire EDM teehnology allows the produetion of sueh a damper deviee, whieh ean be easily designed with an offset to eompensate for the defleetion due to rotor weight. 

Suppose we want to analyze the stresses in the two stiffeners. The geometry of the sandwich-blade stiffener is actually more complicated and less amenable to analysis than is the hat-shaped stiffener. Issues that arise in the analysis to determine the influence of the various portions of the stiffeners include the in-plane shear stiffness. In the plane of the vertical blade is a certain amount of shear stiffness. That is, the shear stiffness is necfessary to transfer load from the 0° fibers at the top of the stiffener down to the panel. In hat-shaped stiffeners, that shear stiffness is the only way that load is transferred from the 0° fibers at the top of the stiffener down to the panel. Thus, shear stiffness is the dominant issue in the design. And that is why we typically put 45° fibers in the web of the hat-shaped stiffener. 

MW fraction increases the melt flow, thus improving the processability but at the cost of toughness, stiffness, and stress crack resistance. In addition, the improvement in performance through narrowing the MWD is restricted by the catalyst, the process hardware, and the process control limitations. Dow has developed a reactor grade HDPE of optimized breadth, peak, and shape of MWD... 

The phenomenological ordering of polymers projected for use as constructing materials is not an easy matter. Sometimes the temperature stability is used as a criterion, i.e., the temperature up to which the mechanical properties remain more or less constant. Another attempt for classification, uses the E modulus or the shape of the curve of stress-strain measurements (see Sect. 2.3.5.1). In general one can say that semicrystalline thermoplastics are stiff, tough, and impact-resistant while amorphous thermoplastics tend to be brittle. Their E... 

The relationship between stress and strain in a test piece with bonded end pieces is very dependent on the shape factor of the test piece. This is usually defined as the ratio of the loaded cross-sectional area to the total force-free area (Figure 8.15). The larger the shape factor the more stiff the rubber appears and this property is much exploited in the design of rubber springs and mountings. 

The viscoelastic behaviour of rubbers is not linear stress is not proportional to strain, particularly at high strains. The non-linearity is more pronounced in tension or compression than in shear. The result in practice is that dynamic stiffness and moduli are strain dependent and the hysteresis loop will not be a perfect ellipse. If the strain in the test piece is not uniform, it is necessary to apply a shape factor in the same manner as for static tests. This is usually the case in compression and even in shear there may be bending in addition to pure shear. Relationships for shear, compression and tension taking these factors into account have been given by Payne3 and Davey and Payne4 but, because the relationships between dynamic stiffness and the basic moduli may be complex and only approximate, it may be preferable for many engineering applications to work in stiffness, particularly if products are tested. 

There was previously a separate ISO standard for adhesion in shear but this was withdrawn in favour of extending the standard for shear modulus to allow the test to be continued to the failure point, i.e. the two methods have been combined. The composite method is contained in ISO 182715 and uses the same quadruple element test piece as did the separate adhesion standard. The double sandwich construction is intended to provide a very stiff test piece which will remain in alignment under high stresses. The present standard quadruple test piece uses rubber elements 4 1 mm thick and 20 5 mm long and these tolerances are much less tight than previously. The measured adhesion strength in shear is less affected by the test piece shape factor then tension tests8 and the wider tolerances should be perfectly satisfactory. The test piece is strained at a rate of 50 mm/min, in line with the speed for most other adhesion to metal tests, and the result expressed as the maximum force divided by the total bonded area of one of the double sandwiches. The British equivalent BS 903 Part A 1416 is identical. 

There are a couple of things about this relationship. First of all it is only an approximation. We ll get back to that in a while. Second, we have only considered simple elongation so far. There is a modulus associated with shear and also a bulk modulus. The most important point, however, is that the modulus determined this way, dividing stress by strain, is a material property and independent of the shape of an object. It is what we mean when we talk about the stiffness of a material. Stiffness is crucial in many engineering applications. If a strain of just 1.6% were allowed in an aircraft s wing spar booms, for example, it would look something like Figure 13-8. 

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