Yield stress in tension

When a fibre is bent, stresses develop in the fibre. When the tension stresses on the outside of the bend exceed the yield stress in tension, the fibre will break. This happens when the bending radius becomes smaller than a critical value ... 

As explained earlier, most authors quote nominal mbber contents rather than mbber phase volumes, and there is therefore very little information in the literature on the relationship between Oyc and 0 for mbber-modified plastics. A rare exception occurs in the work of Oxborough and Bowden vdio measured yield stresses in tension and compression for a series of HIPS polymers ccmtaining composite rubber particles. Their results are presented in Fig. 7. Equation (9) underestimates the yield stresses both in tension and compression, and it must be concluded fiiat the effective area model does not provide a satisfactory basis for correlating yield data in this class of material. Either the model itself must be modified in some way, or some allowance must be made for load sharing with the mbber particles, if the effective area apprcrach is to be retained. 

The results of both studies are summarized in Fig. 26 and it is clear from the data that the PP-blend system has a higher fracture toughness than the pure PP system for all values of X. If one now plots on Fig. 26b the value of oyl7,n- /ac for both systems [using Eq. (24) and the value of <5 obtained from fitting the PP/PA-6 interface data to Eq. (19)],both data sets fall on the same fine as one would expect for two systems which have the same interfacial structure but different values of ocmze. The precise values of the crazing stress in a plastic zone are not directly known for PP and for the blend but the yield stress in tension was meas-... 

Ty() Yield stress in pure shear (Ty, Yield stress in tension... 

PresSUrG-ModiflGd CritGria. One major shortcoming of the criteria described above is that they predict that the yield stresses in tension and compression are the same. However, in practice it is generally found for polymers that the yield stress in compression is higher than that in tension. This effect is usually considered to be a consequence of the fact that the yield stress depends on the hydrostatic pressure that develops imder load. The hydrostatic pressure component... 

According to Equation 8.17, the meridional stress <7 decreases along the inclined wall of the sheet, being higher at the transition point C and smaller at point D. Because the meridional stress at point C must be kept below the yield stress in tension (for a perfectly plastic material), it follows that the inclined wall surface of the sheet adjacent to the forming tool is elastic. This result, together with the stress field in the small localised plastic zone that is summarised in Table 8.2, results in the schematic distribution of the principal stresses that is depicted in Figure 8.4. 

As can be seen in Fig. 2, the adhesive behaviour is non-linear and also varies with temperature. A Poisson s ratio of 0.38 was used, as given by the manufacturer and a ratio of yield stress in compression to yield stress in tension of 1.3 was assumed. Poisson s ratio, and the yield stress ratio were assumed to be independent of temperature. The measured elastic moduli at the four different temperatures are given in Table 2. 

Table 1 The material constants of the SiC particle and the Si3N4 matrix [19]-[21] the Young s modulus, E the Poisson s number, p, the thermal expansion coefficient, a the yield stress in tension and compression, <3yt and o c, respectively the fracture toughness, Kic the SiC particle radius and volume fraction, R and v, respectively.

Along the region of the curve ABD the stress increases with the total strain, which indicates that the material becomes progressively harder (though not usually at a constant rate) as it is deformed plastically, a phenomenon known as w ork hardening. If the test specimen is a suitably squat cylinder the behaviour observed in a compression test is very similar to that obse/ved in tension over the range of strain represented by the curve ABD there is a range of purely elastic deformation and, at a stress closely equal to the yield stress in tension, plastic deformation occurs and the material work hardens. 

To utilise hiUy the strength of the inner member it should be stressed from the yield point in compression to the yield point in tension. From Figure 9 it is seen that if the members are initially stress-free at least three must be employed to make this possible. 

This table is split into two tables by usage Table IX-l A, Basic Allowable Stresses in Tension for Metal Piping Materials and Table IX-1B, Specified Minimum Yield Strength for Steel Pipe Commonly Used in Pipeline Systems. 

The yield stress in uniaxial tension is roughly proportional to Young s modulus. Equation 11.31 (with a relative standard deviation of 22% at T=298K, see Figure 11.11 for an illustration) is a slight modification of the original equation by Seitz [16], who used a proportionality constant of 0.025 instead of 0.028 based on the analysis of the data listed in Table 11.6. 

In using this equation, check to assure that the combined compressive stress does not exceed that allowed for simple compression (taken as 1/3 the yield point in tension) and that it is within the safe limits of elastic stability (taken as 1.5 times 10 t/r). 

The allowable yield stress Ty of the shaft material under pure tensional loading is obtained from the yield stress in simple tension a-y since from the shear strain energy theory of failure ... 

Figure 8.3 shows, for PC, that there is a substantial difference between the yield stress in compression and that in tension. As discussed in Chapter 7, for metallic glasses, and as outlined here in Section 8.6.1, this difference is a consequence of the quite considerable activation dilatation, e, kinematically coupled to the transformation shear strain. It arises from the transitory expansion of the transformation volume Qf of the ST due to the internal random rearrangement of molecular segments occuring during the relaxation event. 

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