Flow stress temperature dependence

FIGURE 17.7 (a) Stress-strain curve for a crystal suitably oriented for plastic flow, (b) Temperature dependence of the normalized critical resolved shear stress for two strain rates, where y, >... 

Most polymer processes are dominated by the shear strain rate. Consequently, the viscosity used to characterize the fluid is based on shear deformation measurement devices. The rheological models that are used for these types of flows are usually termed Generalized Newtonian Fluids (GNF). In a GNF model, the stress in a fluid is dependent on the second invariant of the stain rate tensor, which is approximated by the shear rate in most shear dominated flows. The temperature dependence of GNF fluids is generally included in the coefficients of the viscosity model. Various models are currently being used to represent the temperature and strain rate dependence of the viscosity. 

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. 

Metals Successful applications of metals in high-temperature process service depend on an appreciation of certain engineering factors. The important alloys for service up to I,I00°C (2,000°F) are shown in Table 28-35. Among the most important properties are creep, rupture, and short-time strengths (see Figs. 28-23 and 28-24). Creep relates initially applied stress to rate of plastic flow. Stress... 

In (8.35) Y is the flow stress in simple tension (and may itself be a function of the temperature and strain rate) and is the critical volumetric strain at void coalescence (calculated within the model to equal 0.15 independent of material). Note that the ductile fragmentation energy depends directly on the fragment size s. With (8.35), (8.30) through (8.32) become, for ideal ductile spall fragmentation,... 

Figure 9.6. (a) The temperature dependence of the flow stress for a Ni-Cr-AI superalloy containing different volume fractions of y (after Beardmore et al. 1969). (b) Influence of lattice parameter mismatch, in kX (eflectively equivalent to A) on creep rupture life (after Mirkin and Kancheev... 

Fig.4. The dependence of flow stress on deformation temperature in tension test (left) and in compression test (right) of the A12n78 alloy after heat treatment.

The hydrogen effect on ductility and the flow stress will be considered first on the example of non-alloyed titanium. The Ti - H phase diagram is given in Fig. 1, and Fig. 2 shows the temperature dependence of ductility of Ti-a H alloys, A , for several X values. Tensile tests were run at a rate e 10" s . Ductility of the commercial... 

Fig. 10 shows that the flow stress of the hydrogen-alloyed compacts is essentially less than that of the outgassed ones at all test temperatuics. The flow stress relation between the hydrogen-alloyed and outgassed compacts depended on the strain. At equal strains at test temperatures, this ratio could achieve 2 or more. Thus, the effect of hydrogen on the properties of compacted powders is much similar to that observed on bulk titanium. 

P. R. Thornton, R. G. Davies, and T. L. Johnston, The Temperature Dependence of the Flow Stress of the j Phase Based on Ni3Al, Metall. Trans, AIME, 1,207 (1970). 

The attained value of crinax at y = const (Fig. 3 presents the data for y = 11s- ) and the rise time of the stationary flow ts, are dependent upon the break time tbr between experiments points 1-4 in Fig. 3 correspond to the break times of 1200, 600, 60, and 24 s, respectively. Upon the break time increase, the values of crmax and tsl also increase however, at times periods of longer than 15 min (experiments were performed up to 1 h) they become independent of time. The behaviour is qualitatively the same at fixed break times and temperatures but for various y. Moreover, the ratio of deformation rate (see Fig. 4). For the same tbr and different T the functions cr(t) differ one from another by a constant number. Therefore, temperature (just as y) has no influence on the ratio a/crsl as a function of t, which implies that the influence of T on qualitatively studied in stationary flows. 

The results of the calculations shown in Fig. 2.32 represent a complete quantitative solution of the problem, because they show the decrease in the induction period in non-isothermal curing when there is a temperature increase due to heat dissipation in the flow of the reactive mass. The case where = 0 is of particular interest. It is related to the experimental observation that shear stress is almost constant in the range t < t. In this situation the temperature dependence of the viscosity of the reactive mass can be neglected because of low values of the apparent activation energy of viscous flow E, and Eq. (2.73) leads to a linear time dependence of temperature ... 

Indeed, as above discussed, plastic flow stress serves as a reference for describing the temperature dependence observed with a given polymer. 

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 plastic flow stress, crpf, of PMMA is shown in Fig. 18. At high temperatures (T > 50 °C) the crpf curve is parallel to that of cry, but at lower temperatures it is gradually lower and lower, the decrease being particularly pronounced below 0 °C. 

Fig. 20 Strain rate dependence of yield stress, ay, and plastic flow stress, apf, of PMMA at the indicated temperatures (From [33])...

First, let us examine the temperature dependence of the plastic flow, apf, shown in Fig. 18. As already mentioned in Sect. 2.2.2, the plastic flow requires whole chain motions like those occurring above the a transition, whatever the considered temperature. This feature is reflected in the large activation volume associated with crpf and in the independence to temperature. Consequently, one can consider the plastic flow stress as a reference behaviour in the molecular analysis of plastic deformation. 

The temperature dependence of the plastic flow stress, higher temperatures an increase of crpf with increasing CMI content is observed, similar to that seen for oy. 

The temperature dependence of the yield stress and the plastic flow stress for PMMA and a large series of MGIMx copolymers [35] is shown in Fig. 44. For comparison purpose, the yield stress of PMMA and various MGIMx are presented together in Fig. 45. 

Figure 46 presents the temperature dependence of the plastic flow stress for PMMA and the various MGIMx copolymers. As it could be expected from Fig. 44, the behaviour of apf is quite similar to that of ay. 

The temperature dependence of the yield stress, cry, and the plastic flow stress, cTpf, for the various xTy -y copolyamides is shown in Fig. 87. For comparison, the yield stresses of the various copolyamides [61] are shown in Fig. 88. 

Figure 90 shows the temperature dependence of the plastic flow stress for the various xTy -y copolyamides. As can be seen also from Fig. 87, the general shape of crpf curves is similar to that of cry. 

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