Strain unload

Therefore the hnal point A of the loading ramp has coordinates = 0.01 and = 403 MPa, Fig. 6.30b. The next step is to build the unloading ramp. To this purpose Eq. (6.6) will be used with the starting point A = (0.01 403). The quation will be solved by iteration with a step-by-step procedure using, as before, a strain unloading step As = 0.002. For the hrst step it is... 

Figure 2.2c shows a hysteresis loop if the acetal copolymer is cycled to 5% strain, unloaded, and cycled to 10% strain. The strain rate was 0.2 min. in Figure 2.2b and c. There was a 0.1-min hold time at 5% and 10% strain, and it is evident that there was some small immediate relaxation of stress before the unloading at 0.2/min. occurred. (Modeling of this behavior is discussed in Chapter 3, where mechanical models and the dynamic modulus are described.)... 

Figure C2.1.17. Stress-strain curve measured from plane-strain compression of bisphenol-A polycarbonate at 25 ° C. The sample was loaded to a maximum strain and then rapidly unloaded. After unloading, most of the defonnation remains.

An important aspect of the mechanical properties of fibers concerns their response to time dependent deformations. Fibers are frequently subjected to conditions of loading and unloading at various frequencies and strains, and it is important to know their response to these dynamic conditions. In this connection the fatigue properties of textile fibers are of particular importance, and have been studied extensively in cycHc tension (23). The results have been interpreted in terms of molecular processes. The mechanical and other properties of fibers have been reviewed extensively (20,24—27). 

Unloading. The strain lies on the elastic limit surface = 0, but the tangent to the strain history points inward into the elastic region < 0. It is assumed that k — 0. The material is said to be unloading and the elastic limit surface is stationary. 

Samples are most frequently shock deformed under laboratory conditions utilizing either explosive or gun-launched flyer (driver) plates. Given sufficient lateral extent and assembly thickness, a sample may be shocked in a onedimensional strain manner such that the sample experiences concurrently uniaxial-strain loading and unloading. Based on the reproducibility of projectile launch velocity and impact planarity, convenience of use, and ability to perform controlled oblique impact (such as for pressure-shear studies) guns have become the method of choice for many material equation-of-state and shock-recovery studies [21], [22]. 

Collectively, the shock/release sequence amounts to a single cycle stress/ strain path change excursion with elastic and plastic deformation operative during both loading and unloading. 

This phenomenon is still under investigation as is the substantial departure of calculated from that measured at volume strains below 0.15 as shown in Fig. 7.13. Details of these calculations are presented in the work of Johnson et al. [47]. The important consideration is that the unloading wave also contains micromechanical information if we only can be clever enough to apply proper interpretation to macroscale measurements. 

Figure 8.2 shows a non-linear elastic solid. Rubbers have a stress-strain curve like this, extending to very large strains (of order 5). The material is still elastic if unloaded, it follows the same path down as it did up, and all the energy stored, per unit volume, during loading is recovered on unloading - that is why catapults can be as lethal as they are. 

Tests have shown that when total strain is plotted against the logarithm of the total creep time (ie NT or total experimental time minus the recovery time) there is a linear relationship. This straight line includes the strain at the end of the first creep period and thus one calculation, for say the 10th cycle allows the line to be drawn. The total creep strain under intermittent loading can then be estimated for any combinations of loading/unloading times. 

A cylindrical polypropylene pressure vessel of 150 mm outside diameter is to be pressurised to 0.5 MN/m for 6 hours each day for a projected service life of 1 year. If the material can be described by an equation of the form s(t) = At" where A and n are constants and the maximum strain in the material is not to exceed 1.5% estimate a suitable wall thickness for the vessel on the assumption that it is loaded for 6 hours and unloaded for 18 hours each day. Estimate the material saved compared with a design in which it is assumed that the pressure is constant at 0.5 MN/m throughout the service life. The creep curves in Fig. 2.5 may be used. 

The elastic-shock region is characterized by a single, narrow shock front that carries the material from an initial state to a stress less than the elastic limit. After a quiescent period controlled by the loading and material properties, the unloading wave smoothly reduces the stress to atmospheric pressure over a time controlled by the speeds of release waves at the finite strains of the loading. Even though experiments in shock-compression science are typically... 

Given limits to the time resolution with which wave profiles can be detected and the existence of rate-dependent phenomena, finite sample thicknesses are required. To maintain a state of uniaxial strain, measurements must be completed before unloading waves arrive from lateral surfaces. Accordingly, larger loading diameters permit the use of thicker samples, and smaller loading diameters require the use of measurement devices with short time resolution. 

Fig. 3-7 Examples are shown of elasticity changes for engineering TPs involving one cycle of loading and unloading. The curves show effects of stress and time under load and strain recovery after loading.

The inability of the strain softened molecules to recover their random coil conformation when unloaded. 

However, not all properties are improved by filler. One notable feature of the mechanical behaviour of filled elastomers is the phenomenon of stresssoftening. This manifests itself as a loss of stiffness when the composite material is stretched and then unloaded. In a regime of repeated loading and unloading, it is found that part of the second stress-strain curve falls below the original curve (see Figure 7.13). This is the direct opposite of what happens to metals, and the underlying reasons for it are not yet fully understood. 

Suk, M. and GUIs, D. R., Comparison of Friction Measurement Between Load/Unload Ramps and Suspension Lift Tabs Using Strain Gage and Actuator Current, IEEE Trans. Magn., Vol. 36,2000, pp. 2721-2723. 

The plastic deformation of a member terminates with its rupture which normally occurs at the smallest section of the neck formed due to plastic instability. After being loaded into the plastic range, if the member is unloaded before plastic instability occurs then the elastic component of the strain can be recovered. This is a consequence of the atoms returning to... 

Equation 32 gives the total strain energy stored in a domain of a fibre with an orientation angle 0 in the unloaded state after the stress has been increased from 0 to o. The first term on the right-hand side is the strain energy of the chain extension, and the second term is the shear strain energy. The continu-... 

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