Stress—Continue types

A unidirectional fibre composite consists of 60% by volume of continuous type-1 carbon fibres in a matrix of epoxy. Find the maximum tensile strength of the composite. You may assume that the matrix yields in tension at a stress of 40 MPa. 

Table I lists the mechanical properties of thermally hardened alloys of the duraluminum type (Al-Cu-Mg), as well as the Al-Zn-Mg-Cu alloys. A temperature decrease to 20 K increases the ultimate strength by 25 to 30%. The yield stress continuously increases as the temperature decreases. The relative elongation behaves in different ways in some alloys, it is practically constant, while in alloy V96 it is reduced by almost a factor of 5. Thus, hardening of alloys, such as V95 and V96, by thermal treatment produces materials with a sufficiently high level of strength, but losses in plasticity are inevitable. This is a significant limitation of their application in cryogenic equipment.

This effect has mostly been observed for lyotropic LCPs, sometimes also for thermotropic ones. The existence of region I in Figure 11.1 is explained by the formation of texture, a domain structure observed in many, mostly lyotropic LCPs. The texture occurs during relaxation when the stress levels are very low, that is, when approaching the rest state. Such a three-region flow curve was first observed in Ref. [50] and explained theoretically for lyotropic LCPs in Refs [51, 52] (see also Refs [4, 5, 53]). These theoretical descriptions are typically complementary to the more fundamental monodomain nematodynamic theories of both the molecular and the continuous types. 

A Hquid is a material that continues to deform as long as it is subjected to a tensile and/or shear stress. The latter is a force appHed tangentially to the material. In a Hquid, shear stress produces a sliding of one infinitesimal layer over another, resulting in a stack-of-cards type of flow (Fig. 1). 

Both time-related failure rates and demand-related failure rates can apply to and be reported for many pieces of equipment. Both types of rates are included in some of the data tables in Chapter 5. If a piece of equipment is in continuous service, such as a transformer, the failure rate is dominated by time-related stresses compared to demand-related stresses. Other failure rates may be dominated by demands. Take a piece of wire and repeatedly bend it. With each bend its probability of catastrophic failure increases. In a relatively short time, if the bending is continued, the wire will fail. On the other hand, the same wire could be installed in a manner that would prevent mechanical bending demands. In this case, the occurrence of catastrophic wire breakage would be remote. In the first instance, the failure rate is dominated by demand stresses and in the second by time-related stresses, such as corrosion. 

Products that are subjected to a load have to be analyzed carefully with respect to the type and duration of the load, the temperature conditions under which the load will be active, and the stress created by the load. A load can be defined as continuous when it remains constant for a period of 2 to 6 hours, whereas an intermittent load could be considered of up to two hours duration and is followed by an equal time for stress recovery. The temperature factor requires greater attention than would be the case with metals. The useful range of temperatures for plastic applications is relatively low and is of a magnitude that in metals is viewed as negligible. 

As a plastic is subjected to a fixed stress or strain, the deformation versus time curve will show an initial rapid deformation followed by a continuous action. Examples of the standard type tests are included in Fig. 2-1. Details on using these type specimens under static and dynamic loads will be reviewed throughout this chapter. (Review also Fig. 8-9 that relates elasticity to strain under different conditions.)... 

Long time dynamic load involves behaviors such as creep, fatigue, and impact. T vo of the most important types of long-term material behavior are more specifically viscoelastic creep and stress relaxation. Whereas stress-strain behavior usually occurs in less than one or two hours, creep and stress relaxation may continue over the entire life of the structure such as 100,000 hours or more. 

Creep modeling A stress-strain diagram is a significant source of data for a material. In metals, for example, most of the needed data for mechanical property considerations are obtained from a stress-strain diagram. In plastic, however, the viscoelasticity causes an initial deformation at a specific load and temperature and is followed by a continuous increase in strain under identical test conditions until the product is either dimensionally out of tolerance or fails in rupture as a result of excessive deformation. This type of an occurrence can be explained with the aid of the Maxwell model shown in Fig. 2-24. 

A creep test can be carried out with an imposed stress, then after a time have its stress suddenly changed to a new value and have the test continued. This type of change in loading allows the creep curve to be predicted. The simple law referred to earlier as the Boltzmann superposition principle, hold for most materials, so that their creep curves can thus be predicted. 

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