Elastic stress, experimental determination

The coefficients Cn are called elasticity constants and the coefficients Su elastic compliance constants (Azaroff, 1960). Generally, they are described jointly as elasticity constants and constitute a set of strictly defined, in the physical sense, quantities relating to crystal structure. Their experimental determination is impossible in principle, since Cu = (doildefei, where / i, and hence it would be necessary to keep all e constant, except et. It is easier to satisfy the necessary conditions for determining Young s modulus E, when all but one normal stresses are constant, since... 

Elastic and viscous stress-strain curves can be experimentally determined from incremental stress-strain curves measured on samples of different tendons. Typical elastic and viscous stress-strain curves for rat tail and turkey tendons are shown in Figures 7.4 and 7.5. For both types of tendons the curves at high strains are approximately linear. As we discuss in Chapter 8, the elastic modulus can be calculated for collagen, because most of the tendon is composed of collagen and water, by dividing the elastic slope by the collagen content of tendon. When this is done the value of the elastic modulus of collagen in tendon is somewhere between 7 and 9 GPA. 

Note that the residual stress aM — 0 on the elastic properties becomes homogeneous (Ef = Em = EL). While connections between the residual stresses and constituent properties are rigorous, experimental determination is still necessary, because ft is not readily predictable. In general, ft includes terms associated with the thermal expansion difference, ay— am, as well as volume changes that occur either upon crystallization or during phase transformations. For CVI systems, intrinsic stresses may also be present. 

The values of stress depression predicted by Equation 1 for hard elastic polypropylene, are, however, far lower than experimentally determined. 

Elastic fracture mechanics can be applied to rubbers provided that allowance is made for their non-linear stress-strain behaviour. The steps are (a) replacing experimentally determined strain energy density remote from the crack and (b) replacing uq, the crack length in the unstrained state, by u = >n... 

Young s modulus of elasticity quantifies the elasticity of the polymer. Like tensile strength, this is highly relevant in polymer applications involving physical properties of polymers. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke s law holds. This can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material. 

Surface stress There have been few experimental determinations of surface stress. Cammarata [6] has summarized most of these. The surface stress will induce a radial elastic strain (e) in small spheres, which can be measured by electron diffraction. This strain has been related to the surface stress using the Laplace equation (see Chapter 6) by... 

Fig. 7.19. Experimentally determined stress versus temperature hysteresis data for a 1 jjLm. thick A1 film deposited on a relatively thick elastic substrate. The specimen was first heated from room temperature to 300 °C (the data point set marked 1 ), held at that temperature for 30 min., and then subsequently cooled to a minimum temperature before being heated again to 300 °C. This minimum temperature was chosen to be 110, 50, 20 and —10 °C for the four thermal cycles, the heating portions of which are denoted by the numbers 2, 3, 4 and 5, respectively. The specimen was held at 300 °C for 30 min. during each thermal cycle. The as a function of temperature. The solid curves in Figure 7.19 show the response for elastic and plastic deformation implied by (7.75) and (7.76). To denotes the stress-free reference temperature. Experimental data provided by Y. J. Choi, Massachusetts Institute of Technology (2002).

In 1812, even before Maxwell, Kelvin and Boltzman, the Scottish scientist Sir David Brewster (1781-1868) discovered that certain transparent optically isotropic solids (e.g., glass) when loaded developed optical characteristics of natural crystals. That is, he found that such a solid when loaded exhibited birefringence or double refraction and thus behaved as a temporary crystal. His discovery was the beginning of the well-known photoelastic method by which it is possible to experimentally determine the state of stress or strain on the interior of a loaded elastic body using polarized light. Maxwell (as well as F. E. Neumann at an earlier date) also studied the technique and deduced the relationship between stress and the optic effect now known as the Maxwell-Neumann stress-optic law. The impor-... 

The experimental determination of the two latter influences on the elastic properties of a vulcanized elastomeric material is performed effectively with the aid of stress relaxation tests [242]. Relaxation effects depend on temperature and loading time. Here, a distinction must be made between physical and chemical relaxation [242]. 

In AD2000 code [9], there is the possibility to evaluate the results of an FE analysis based on Chapter S4 Estimation of stresses based on computed and experimental strength analysis. Chapter S4 describes basically the elastic stress analysis method Stresses are determined using an elastic analysis, classified into categories, and limited to allowable values that have been conservatively established so that a plastic collapse will not occur for thick-walled components, the plastic analysis methods are more adequate. In Chapter S4 [9], there is no guideline for such an analysis, but the application is not forbidden. 

More than 40 years qfter Weissenberg s pioneering proposal [Figures 4.1.1 and 8.1.1] for die measurement of shear and normal stresses during shear flow of elastic Uquids, the determination of the rheological material functions of polymers in simple shear flow is still a nightmareforthe experimenter. J. Meissner et al. (1989)... 

Before going further, I think it will be helpful if we examine closely one of the fundamental underlying aspects of the theory which gives rise to many of the important kinetic features I have sketched previously. First, however, the general relationship between distribution functions and experimentally observed response functions must be understood. As an example in this case, I will briefly review the relationship between the distribution of elastic relaxation times H( ) and the experimentally determined stress relaxation modulus E(t). Mathematically these functions are related by the expression... 

Influence of the shape of pores on elastic properties was determined on the basis of the theory elaborated by Rossi for concentration of stresses on pores, C53. According to investigations published in C63, for sphericalpores slope of the curve E = fCPD is the least for a given medium and axial ratio a/c=l. Following deviation from spherical shape to prolate spheroid increases also the curve slope, what was confirmed experimentally. On their basis one can determine axial ratio a/c for pores and influence of technological... 

---