Yield stress temperature dependence

The yield stress of the Ni-plated specimen was higher than the critical stress for the motion of edge dislocations. This fact is reflected in the yield stress-temperature relationship (Fig. 3). The observed temperature dependence would be larger than that of the edge dislocation motion. 

Foong et ai [23] showed that yield stress is dependent on temperature. Figure 14 shows the variation of yield stress with temperature for three carbonyl iron powder feedstocks. Feedstocks No. 2, 3 and 4 contained binder with EVA/beeswax ratio of 40/60, 60/40 and 70/30 respectively. It can be observed that yield stress decreases non-linearly with increasing temperature. This observation contrasted the views of Malkin [50]. He proposed that the yield stress of a filled polymer melt is independent of temperature. However, as there were neither actual experimental data nor references nuoted the nrono-sal was difficult to be verified. 

D) Method yielding the temperature dependence of ro. ST stress - temperature coefficient of undiluted or swollen samples. 

As a pipeline is heated, strains of such a magnitude are iaduced iato it as to accommodate the thermal expansion of the pipe caused by temperature. In the elastic range, these strains are proportional to the stresses. Above the yield stress, the internal strains stiU absorb the thermal expansions, but the stress, g computed from strain 2 by elastic theory, is a fictitious stress. The actual stress is and it depends on the shape of the stress-strain curve. Failure, however, does not occur until is reached which corresponds to a fictitious stress of many times the yield stress. 

Measurements of stress relaxation on tempering indicate that, in a plain carbon steel, residual stresses are significantly lowered by heating to temperatures as low as 150°C, but that temperatures of 480°C and above are required to reduce these stresses to adequately low values. The times and temperatures required for stress reUef depend on the high temperature yield strength of the steel, because stress reUef results from the localized plastic flow that occurs when the steel is heated to a temperature where its yield strength is less than the internal stress. This phenomenon may be affected markedly by composition, and particularly by alloy additions. 

Many properties are temperature dependent. For example up to 100°C the yield stress drops with temperature at a faster rate than does the yield stress of polypropylene however, it retains some strength up to 160°C. 

Figure 4. Yield stress of the Ti-6Al-4.5V alloy in dependence on hydrogen content st several temperatures. Temperature are 688 (curve 1), 745 (2), 735 (3), 806 (4), 867 (5) and 930 C (6).

The early study of brittle failures, notably those of the Liberty ships, indicated a temperature dependence. This can be illustrated by plotting both fracture stress (of) and yield stress (Oy) against temperature (Fig. 8.81). Below a certain temperature some materials exhibit a transition from ductile to brittle fracture mode. This temperature is known as the ductile-brittle transition temperature DBTT. 

Does yield stress depend on temperature Probably, not, and flow curves constructed at different temperatures look as is shown in Fig. 7, where the arrow indicates the direction of temperature increase. 

Proceeding from the nature of yield stress as a characteristic of strength of the structure formed by a filler, a situation can be imagined where the character of inter-molecular contacts will depend on temperature to a large extent, or at least, will sharply change at certain temperatures of transition. However, this is rather an exotic case, and although researchers have not observed it, it cannot be excluded. 

As shown in Sect. 2, the fracture envelope of polymer fibres can be explained not only by assuming a critical shear stress as a failure criterion, but also by a critical shear strain. In this section, a simple model for the creep failure is presented that is based on the logarithmic creep curve and on a critical shear strain as the failure criterion. In order to investigate the temperature dependence of the strength, a kinetic model for the formation and rupture of secondary bonds during the extension of the fibre is proposed. This so-called Eyring reduced time (ERT) model yields a relationship between the strength and the load rate as well as an improved lifetime equation. 

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

If up to 40% of ESI is blended with LDPE then foamed, the foam properties are closer to those of LDPE foams. Ankrah and co-workers (33) showed that the ESI/LDPE blends have slightly lower initial compressive yield strengths than the LDPE alone, allowing for the density of the foam. The temperature dependence of the yield stress is similar to that of LDPE foam (Figure 3). Although the yield stress is higher than EVA foam of the same density, the compression set values are lower. The ESI/LDPE foams have improved impact properties, compared with EVA foams of similar density. Analysis of creep tests shows that air diffuses from the cells at a similar rate to EVA foams of a greater density. 

An overview of the origins of yield stress and parameters which can lead to variations in behaviour with highly filled polymer dispersions is given by Malkin [1]. Much of the following literature, describing experimental work undertaken, demonstrates that yield phenomena can be correlated with the extent of interaction between the filler particles and the formation of a network structure. However, the actual behaviour observed during experimentation may also depend on the deformation history of the material, or the time and temperature of imposed deformation, especially if the material exhibits thixotropic properties. 

Yield stress values can depend strongly on filler concentration, the size and shape of the particles and the nature of the polymer medium. However, in filled polymer melts yield stress is generally considered to be independent of temperature and polymer molecular mass [1]. The method of determining yield stress from flow curves, for example from dynamic characterization undertaken at low frequency, or extrapolation of shear viscosity measurements to zero shear rate, may lead to differences in the magnitude of yield stress determined [35]. 

The flow behaviour of polymeric electrophotographic toner systems containing carbon black varying in surface area and concentration were determined using a cone and plate rheometer [51]. As the concentration of carbon black was increased, the viscosity at low shear rates become unbounded below a critical shear stress. The magnitude of this yield stress depended primarily on the concentration and surface area of the carbon black flller and was independent of the polymer (polystyrene and polybutyl methacrylate) and temperature. It was postulated that at low shear rates the carbon black formed an independent network within the polymer which prevented flow. 

Hence, the ratio Klc/Klcs may be directly and quantitatively related to the crack tip radius, g, at the onset of crack growth by assuming a failure criterion based upon the attainment of a critical stress acting at a certain distance ahead of the tip. A brief examination of Eq. (12) shows that it exhibits the same general trends with regard to rate and temperature dependence that were used successfully in the yield stress discussion to explain in a qualitative way the observed fracture behaviour. 

The transition metal carbides do have a notable drawback relative to engineering applications low ductility at room temperature. Below 1070 K, these materials fail in a brittle manner, while above this temperature they become ductile and deform plastically on multiple slip systems much like fee (face-centered-cubic) metals. This transition from brittle to ductile behavior is analogous to that of bee (body-centered-cubic) metals such as iron, and arises from the combination of the bee metals strongly temperature-dependent yield stress (oy) and relatively temperature-insensitive fracture stress.1 Brittle fracture is promoted below the ductile-to-brittle transition temperature because the stress required to fracture is lower than that required to move dislocations, oy. The opposite is true, however, above the transition temperature. 

Fig. 14 Temperature dependence of yield stress, cry, and plastic flow stress, crpf, for quenched and physically aged PMMA. Strain rate is 2 x 10-3 s-1 (From [32])...

The temperature dependence of the yield stress, ay, of PMMA obtained at a strain rate, s = 2 x 10-3 s-1, is shown in Fig. 18. A sigmoidal curve is observed, which looks like the temperature dependence of the Young s modulus, E. When increasing the strain rate a similar behaviour is observed. 

In order to check whether the temperature dependence of oy would reflect the change of modulus only, the ratio cry/E is plotted in Fig. 19. It is clear that the modulus does not normalise the yield stress behaviour, the latter decreasing more than the modulus when temperature increases. 

The strain rate dependence of the yield stress is shown at various temperatures in Fig. 20. To go further in the analysis, it is interesting to use the Eyring approach presented in Sect. 2.2.1.1. For this purpose, the ratio oy/T, K is plotted versus log( , s-1) at various temperatures in Fig. 21. A linear dependence is observed at each temperature, in agreement with the Eyring expression. However, the slopes show two different temperature regimes at low and high temperatures. Of course, the activation volume, Vo, directly related to the slope, reflects the change in behaviour, as shown in Fig. 22. At low temperature, the activation volume is small (around 0.1 nm3) and independent of temperature, whereas it increases rapidly above room temperature... 

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