Stress ratios

Rates of CF crack propagation generally are enhanced by increased stress ratio R, which is the ratio of minimum stress to maximum stress. 

Some other factors, namely, the metallurgical condition of the material such as composition and heat treatment, and the loading mode, such as uniaxial, affect fatigue crack propagation (4). 

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Fatigue tests were performed under load control mode on a Schenck horizontal fatigue testing machine with hydraulic grips and a maximum load capacity of 25 kN. Tension-tension constant amplitude fatigue tests were carried out at three stress levels 60% a , 70% Cu and 80% a at two different stress ratios R = 0.1 and R = 0.5. The test frequency was kept constant (f = 3 Hz) for all the tests. 

However, more experiments using a wider range of stress ratios will be required to achieve a more complete data set, in order to verify the validity of the model under a wide range of stress conditions. 

As demonstrated, Eq. (7) gives complete information on how the weight fraction influences the blend viscosity by taking into account the critical stress ratio A, the viscosity ratio 8, and a parameter K, which involves the influences of the phenomenological interface slip factor a or ao, the interlayer number m, and the d/Ro ratio. It was also assumed in introducing this function that (1) the TLCP phase is well dispersed, fibrillated, aligned, and just forms one interlayer (2) there is no elastic effect (3) there is no phase inversion of any kind (4) A < 1.0 and (5) a steady-state capillary flow under a constant pressure or a constant wall shear stress. 

TLCP viscosity or rjo viscosity of dispersed phase rjo = 171) critical stress ratio Poisson s ratio of matrix density... 

The best performance of the individual members of the drill string is obtained when the bending stress ratio of subsequent members is less than 5.5 [38]. Bending stress ratio (BSR) is defined as a ratio of the bending section moduli of two subsequent members, e.g., between the drill collar and the pipe right above it. 

Equation (3) is plotted with two different time scales in Figures 1 and 2 for values somewhat typical of an elastomer. All the initial deformation takes place in the spring at a later time the dashpot starts to relax and allows the spring to contract. Most of the relaxation takes place within one decade of time on both sides of the relaxation time, but this is shown clearly only in Figure 2. On the logarithmic time scale, the stress-relaxation curve has a maximum slope at the time / = T and the stress ratio cr/cr is 0.3679 ore. The stress relaxation may also be given in terms of a stress-relaxation modulus Er(t) ... 

Where the stress ratio defined in Fig. GR-2.1.2(b)B is less than one, Fig. GR-2.1.2(b)B provides a further basis for the use of carbon steels covered by (1) and (2) above, without impact testing. 

In this chapter the physical properties of resins related to processing will be described. The chapter and Appendix A4 include physical properties for many resins. These properties include bulk density and compaction, lateral stress ratio, stress at a sliding interface, melting flux, heat capacity, thermal conductivity, and melt density. Some of these properties are easy to measure by many laboratories while others such as the melting flux and stress at a sliding interface can be measured in only a few places using highly specialized equipment. 

The original solids-conveying model developed by Darnel and Mol [7] assumed that the pressure (or stress) in the solid bed is isotropic. This assumption was made to simplify the mathematics and because of the lack of stress data for solid bed compacts. Previous research, however, showed that stresses in solid compacts are not isotropic [8]. Anisotropic stresses can be represented by the lateral stress ratio. It is defined as the ratio of the compressive stress in the secondary direction to the compressive stress in the primary direction, as shown in Fig. 4.7 and Eq. 4.1. 

The lateral stress ratio depends on the resin type and shape, surface treatments such as additives, temperature, and pressure. The ratio is measured using a compaction cell [2], as shown in Fig. 4.8. This cell is very similar to one shown in Fig. 4.3 except the piston for the lateral stress ratio cell is octagonal in cross section and a pressure sensor is mounted in the cylinder wall. The stress ratio is calculated by dividing the pressure measured at the side of the cylinder by the calculated pressure in the axial direction at the height of the sensor. The calculation method can be found elsewhere [2j. The lateral stress ratio for select resins at 25°C and 2.5 MPa are provided in Table 4.1. 

Table 4.1 Lateral Stress Ratio at 25 °C and 2.5 MPa for Select Resins [2]...

The lateral stress ratio Is defined for particle systems that are consolidated under pressure, and thus the particles are essentially locked In place and unable to move relative to the neighboring particles. This type of consolidation occurs In the later... 

Kwade, A., Schulze, D., and Schwedes, ]., Determination of the Stress Ratio in Uniaxial Compression Tests - Part 2, Powder Handl. Process., 6, 2, 199 (1994)... 

Here, is the lateral stress ratio, and oy are the stresses in the x and y directions, and ff, in the case of the single-screw extruder, is assumed to be the local downstream pressure P. Lateral stress ratios were discussed in Section 4.2. 

Unlike the previous models by Darnell and Mol [14] and Tadmor and Klein [1], which are based upon the assumption of isotropic stress conditions, Campbell s model [20] considered anisotropic stress conditions, as suggested by Schneider [15], but it was assumed to be 1.0 due to the lack of published experimental data on the subject. Variations on the model set forth by Campbell and Dontula [20] include a modification to incorporate the lateral stress ratio [19, 22], and other modifications discussed by Hyun et al. [21, 23]. A modified Campbell-Dontula model with a homogeneous lateral stress is as follows ... 

Hyun et al. [21] evaluated both the original model by Darnell and Mol [14] and the model by Campbell and Dontula [19] for accuracy against experimental data, and determined that the Darnell-Mol model was less accurate than that of the Campbell-Dontula model. The incorporation of the lateral stress ratio in the calculations supported their conclusions even more. At the time of the work by Hyun et al, however, the physics for screw rotation was not well appreciated, and the evaluations for the Campbell models [23] were performed with coefficient of friction... 

An LDPE resin was used for this study. The resin had a melt index of 2.0 dg/min (2.16 kg, 190 °C) and a solid density of 0.922 g/cmT The shear viscosity was reported previously [37] thermal properties are provided in Chapter 4 bulk density as a function of temperature and pressure is provided in Fig. 4.4 and the coefficients of dynamic friction are provided in Appendix A5. The lateral stress ratio was measured at 0.7 [38] using the device shown in Fig. 4.8. 

The modified Campbell-Dontula model used a lateral stress ratio [5, 6] that is defined below ... 

Unfortunately, cannot be easily determined analytically, and is often either estimated using methods from the field of soil mechanics (from the normal stress ratio, K, or simply adjusted to a value which produces good fits for the experimental data. The forwarding force f, at the barrel wall is positioned in the plane of the barrel surface. This force is adjusted using as found in Eq. A5.1 and results in Eq. A5.2. This is because is the local pressure in the channel. Referring to Fig. A5.4, the forces are defined as follow ... 

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