Upper yield stress

Thermosets, like other amorphous polymers, can exhibit physical aging when kept at temperatures below Tg (Chapter 10). The upper yield stress measured at room temperature (below Tg) increases with prolonged aging time (Cook et al., 1999), like the modulus or the specific density. 

The macroscopic upper yield stress is lineary related to Tg — T for a given strain rate, and can be adjusted with Argon s, Bowden s, and Kitagawa s models. The influence of strain rate is well represented by the phenomenological Eyring s equation. 

As for the neat PA6, it experiences a characteristic double yield (probably due to residual humidity) and starts its steady-state plastic regime at an upper yield stress of about 50 MPa. 

For some metals, notably steels, there is an abrupt break in the stress-strain plot at the upper yield point (Figure 10.18). This is followed by continued deformation at a lower yield stress, at the lower yield point, before the curve rises again. Between the upper and lower yield points, deformation occurs in localised regions that have the form of bands, rather than across the specimen in a uniform manner. The reason for this is that the dislocations, which would move during plastic deformation, are pinned in the steel, mainly by the interstitial carbon atoms present. At the upper yield stress, these become mobile and, once released, they can move and multiply at a lower stress value. This is analogous to sticking and slipping when a body over-... 

Figure 13.11 shows the tensile test results of (a) the disassembled and reconstituted original HIPS with the wide particle-size distribution having a craze-flow stress of = 19.0 MPa as a standard for comparison (b) the special blend containing only the large particles with a flow stress (Tco = 18.17 MPa (c) the special blend containing only the small particles with a flow stress of around CTco = 20.46 MPa, but a substantial upper yield stress of 24.0 MPa. Clearly, the two special blends with narrow particle-size distributions have substantially different behaviors and bracket the behavior of the reassembled original HIPS. 

We note further from Fig. 13.12 that fully 40% of the small-particle size distribution falls below the critical particle-size estimate of Dc = 0.93 pm, reducing the effective fraction of the particle volume fraction from 0.22 to 0.13. This results in a substantial upper yield stress of 24 MPa, as Fig. 13.11(c) shows. However, once an effective craze network has developed the actual craze-flow stress of this blend drops to 20.5 MPa, in keeping with expectations. 

Fi ire t0.16 Stress-strain diagram for a mild steel sample (ksi = 1000 IbAn, elastic stress, (o-r), = upper-yield stress, (o-r)/ = loaer-yleld stress, a, = ultimate stress, and a, = fracture stress). 

Fig. 9. Dislocation microstructures in silicon crystals after high-stress deformation, (a) <123> crystal deformed up to the upper yield stress (t = 800 MPa) at T = 425 °C under a strain rate of 2 x 10 s and a confining pressure of 700 MPa (after Demenet [55]). (b) < 10 0 > crystal deformed at T = 450 "C under a strain rate of 2 x 10 s and a confining pressure of 1.5 GPa (after Castaing et al. [54]).

Some materials, notably annealed mild steel, show a rather different yielding behaviour, indicated schematically in Fig. 3.2(b). Starting at 0, a long elastic range is sharply terminated at A, when the stress reaches a value known as the upper yield stress. There is an abrupt partial unloading and macroscopic plastic deformation... 

Mild Steel ( 1% carbon) 400 (upper yield stress) 300 (lower yield stress) 460... 

Concerning the effect of the hydrostatic pressure on the mechanical properties of metals, it was found that the hydrostatic pressure had no effect on the lower yield stress for mild steel nor on the stress-strain curve for silicon-aluminium alloy. However, a small reduction in the upper yield stress was observed on mild steel [16]. For more strain hardened specimens the decrease in yield stress was much higher. In unanimous option of all researchers the deformability increases under effect of superimposed hydrostatic pressure [16]. 

---