Tensile analysis

W.F. Cowan, E.J.K. Cowdrey, Evaluation of paper strength components by short span tensile analysis, Tappi J 57 (2) (1973) 90. 

By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

Division 2. With the advent of higher design pressures the ASME recognized the need for alternative rules permitting thinner walls with adequate safety factors. Division 2 provides for these alternative rules it is more restrictive in both materials and methods of analysis, but it makes use of higher allowable stresses than does Division 1. The maximum allowable stresses were increased from one-fourth to one-third of the ultimate tensile stress or two-thkds of the yield stress, whichever is least for materials at any temperature. Division 2 requkes an analysis of combined stress, stress concentration factors, fatigue stresses, and thermal stress. The same type of materials are covered as in Division 1. 

Forming Limit Analysis. The ductihty of sheet and strip can be predicted from an analysis that produces a forming limit diagram (ELD), which defines critical plastic strains at fracture over a range of forming conditions. The ELD encompasses the simpler, but limited measures of ductihty represented by the percentage elongation from tensile tests and the minimum bend radius from bend tests. 

Base-metal P numberf Weld-metal analysis A numberf Material group Nominal waU thickness Minimum specified tensile strength, base metal Metal temperature range h/in, nominal wall Minimum time, b Brinell hardness, maximum... 

An account of the mechanism for creep in solids placed under a compressive hydrostatic suess which involves atom-vacancy diffusion only is considered in Nabano and Hemirg s (1950) volume diffusion model. The counter-movement of atoms and vacancies tends to relieve the effects of applied pressure, causing extension normal to the applied sU ess, and sluinkage in the direction of the applied sU ess, as might be anticipated from Le Chatelier s principle. The opposite movement occurs in the case of a tensile sU ess. The analysis yields the relationship... 

Attenuation occurs because the tensile release, which is traveling at an elastic longitudinal wave speed, Q, overtakes the tensile front traveling at a plastic wave speed Cp < Q. Assuming a pulse as shown in Fig. 8.10 with a stress rate in the tensile front and tensile release of a and b, respectively, an approximate analysis shows that the peak will decay by an amount... 

Consider the design of a glass window for a vacuum chamber (Fig. 18.6). It is a circular glass disc of radius R and thickness f, freely supported in a rubber seal around its periphery and subjected to a uniform pressure difference Ap = 0.1 MPa (1 atmosphere). The pressure bends the disc. We shall simply quote the result of the stress analysis of such a disc it is that the peak tensile stress is on the low-pressure face of... 

For example, suppose we are interested in knowing the distribution of stress assoeiated with the tensile statie loading on a reetangular bar (see Figure 4.23). It is known from a statistieal analysis of the load data that the load, F, has a eoeffieient of variation Q = 0.1. The stress, L, in the bar is given by ... 

Macrostrain is often observed in modified surfaces such as deposited thin films or corrosion layers. This results from compressive or tensile stress in the plane of the sample surface and causes shifts in diffraction peak positions. Such stresses can easily be analyzed by standard techniques if the surface layer is thick enough to detect a few diffraction peaks at high angles of incidence. If the film is too thin these techniques cannot be used and analysis can only be performed by assuming an un-... 

In the above analysis, Johnson et al. [6] assume that the interfacial forces act only when the surfaces are in contact, i.e. the attractive forces are considered to be of infinitesimally short range. This analysis ignores the forces acting just outside the edge of the contact circle. Because of this, the theory predicts an infinite tensile stress at the edge of the contact. If the attractive force between the surfaces is allowed to have a finite range, the infinity in the tensile stress disappears. The stress at the edge of the contact circle is still tensile, but it remains finite. 

Fig. 12. Tensile strength a, vs. number of backbone bonds per monomer 1 /a, reported for a range of polymers by Vincent [75]. The solid line is the theoretical line for vector percolation analysis of strength discussed herein.

Only a small amount of work has been done up to now concerning the prediction of bond strengths and other properties based on the results of the analysis of the resin. Ferg et al. [59] worked out correlation equations evaluating the chemical structures in various UF-resins with different F/U molar ratios and different types of preparation on the one hand and the achievable internal bond as well as the subsequent formaldehyde emission on the other hand. These equations are valid only for well defined series of resins. The basic aim of such experiments is the prediction of the properties of the wood-based panels based on the composition and the properties of the resins used. For this purpose various structural components are determined by means of - C NMR and their ratios related to board results. Various papers in the chemical literature describe examples of such correlations, in particular for UF, MF, MUF and PF resins [59-62]. For example one type of equation correlating the dry internal bond (IB) strength (tensile strength perpendicular to the plane of the panel) of a particleboard bonded with PF adhesive resins is as follows [17]... 

As in the case of the transverse tensile modulus, 2. the above analysis tends to underestimate the in-plane shear modulus. Therefore, once again it is common to resort to empirical relationships and the most popular is the Halpin-Tsai equation... 

Dynamic tensile failure, called spall, is frequently encountered in shockloading events. Tension is created as compression waves reflect from stress-free surfaces and interact with other unloading waves or release-wave profiles. Spall has been widely studied by authors such as Curran, Ivanov, Dremin, and Davison and there is considerable data. As shown in Fig. 2.19, the wave profiles resulting from spall are characterized by an additional loading pulse after release of pressure. The late pulse is caused by wave reflection from the internal void of the tensile fracture. Analysis of such wave profiles yields appropriate spall stress values. 

Alternately, samples subjected to controlled tensile loading are preserved for post-shock analysis, and sectioned so that internal cracks, their morphol-... 

An analysis of loading mode effects has also provided evidence of the critical role of hydrogen. A stress-intensity factor (K) can be achieved in either a tensile loading mode (mode I) or a shearing mode (mode III) (Section 8.9). Under mode I conditions the volume of metal immediately in... 

The design of the threads requires control, to prevent excessive shear, resulting in stripping the threads when torqued, and also to limit hoop stresses that can result in tensile failure. Although the mechanics of stress analysis for screw threads are readily available, the equations for them can be rather complicated. 

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