Yield stress calculation

The table shows the force needed to fracture single-edge bars of several polymers at room temperature in a three-point bending test. Bar dimensions are IT = 10 mm, B = 6 mm, a = 5 mm the test span S is 80 mm. The second column in the table gives the corresponding yield stress. Calculate Kic for each polymer, and indicate in which cases valid plane strain conditions exist. 

Fig. 4. Left Elasto-plastic (un-)loading including a non-imiqueness regime. Right Illustration of the ID-stress-strain-curve interpolation, the yield stress calculation and Drucker s postulate.

The errors associated with the yield stress calculated by a given method should not exceed 5%. The relative values returned by the different calculation methods applied to a single sample will depend upon the calculation parameters chosen. In general, the value calculated from the yield maximum will be the largest. 

The outlined scheme is shown to yield stable solutions for non-zero Weissenberg number flows in a number of benchmark problems (Swarbric and Nassehi, 1992b). However, the extension of this scheme to more complex problems may involve modifications such as increasing of elemental subdivisions for stress calculations from 3 x 3 to 9 x 9 and/or the discretization of the stress field by biquadratic rather than bi-linear sub-elements. It should also be noted that satisfaction of the BB condition in viscoelastic flow simulations that use mixed formulations is not as clear as the case of purely viscous regimes. 

A powder s strength increases significantly with increasing previous compaction. The relationship between the unconfined yield stress/, or a powder s strength, and compaction pressure is described by the powder s flow function FE The flow function is the paramount characterization of powder strength and flow properties, and it is calculated from the yield loci determined from shear cell measurements. [Jenike, Storage and Flow of Solids, Univ. of Utah, Eng. Exp. Station Bulletin, no. 123, November (1964). See also Sec. 21 on storage bins, silos, and hoppers.]... 

The closer one approaches to the tip of the crack, the higher the local stress becomes, until at some distance r from the tip of the crack the stress reaches the yield stress, o,, of the material, and plastic flow occurs (Fig. 14.2). The distance r is easily calculated by setting crio ai = o y in eqn. (14.1). Assuming r to be small compared to the crack length, a, the result is... 

Example 2.10 The polypropylene snap fit shown in Fig. 2.22 is to have a length of 10-30 mm. If the insertion force is not to exceed 4 N and the yield stress of the plastic is 30 MN/m, calculate suitable cross-sectional dimensions for the snap fit. The short-term modulus of the polypropylene is 900 MN/m and the coefficient of friction is 0.3. The safety factor on stress is to be 2. 

If the extruder is to be used to process polymer melts with a maximum melt viscosity of 500 Ns/m, calculate a suitable wall thickness for the extruder barrel based on the von Mises yield criterion. The tensile yield stress for the barrel metal is 925 MN/m and a factor of safety of 2.5 should be used. 

We wish to calculate the relationship between the fluid pressure and the yield stress. 

Yield Strength Collapse Pressure Formula. The yield strength collapse pressure is not a true collapse pressure but rather the external pressure p that generates minimum yield stress on the inside wall of a tube as calculated by... 

Concrete calculations carried out via formula (10) for different values of constant have shown that it reflects the behavior of flow curves quite really. However, a series doubt remains for such a system (with a yield stress) it is not obvious how to determine the initial Newtonian viscosity (is it necessary to determine it and does it exist ). 

Interpretation of data obtained under the conditions of uniaxial extension of filled polymers presents a severe methodical problem. Calculation of viscosity of viscoelastic media during extension in general is related to certain problems caused by the necessity to separate the total deformation into elastic and plastic components [1]. The difficulties increase upon a transition to filled polymers which have a yield stress. The problem on the role and value of a yield stress, measured at uniaxial extension, was discussed above. Here we briefly regard the data concerning longitudinal viscosity. 

It has been found that with many plastics the calculated flexing stress can far exceed the yield point stress, if the assembly occurs too rapidly. In other words, the flexing finger will just momentarily pass through its condition of maximum deflection or strain, and the material will not respond as if the yield stress had been greatly exceeded. 

The deformation zones were calculated for the polymers of Table 5.1 and Table 6.1 according to the Dugdale-Barenblatt-model. Yield stress ay from tensile tests was used instead of the cohesive stress ctc since a reasonable agreement of ay and ctc... 

A fluid with a finite yield. stress is sheared between two concentric cylinders, 50 mm long. The inner cylinder is 30 mm diameter and the gap is 20 mm. The outer cylinder is held stationary while a torque is applied to the inner. The moment required just to produce motion was 0.01 N m. Calculate the force needed to ensure all the fluid is flowing under shear if the plastic viscosity is 0.1 Ns/ni2. 

The primary FML must be able to support its own weight on the side slopes. In order to calculate self-weight, the FML-specific gravity, friction angle, FML thickness, and FML yield stress must be known. 

The slurry behaves as a non-Newtonian fluid, which can be described as a Bingham plastic with a yield stress of 40 dyn/cm2 and a limiting viscosity of 100 cP. Calculate the pressure gradient (in psi/ft) for this slurry flowing at a velocity of 8 ft/s in a 10 in. ID pipe. 

As for the derivation of Eqs. 122,123 and 124 only the transitions 1—>2 have been counted, these equations do not describe recovery processes, where the transitions 2 —>1 are important as well. These approximations have been made for convenience s sake, but neither imply a limitation for the model, nor are they essential to the results of the calculations. Equation 124 is the well-known formula for the relaxation time of an Eyring process. In Fig. 65 the relaxation time for this plastic shear transition has been plotted versus the stress for two temperature values. It can be observed from this figure that in the limit of low temperatures, the relaxation time changes very abruptly at the shear yield stress Ty = U0/Q.. Below this stress the relaxation time is very long, which corresponds with an approximation of elastic behaviour. 

When mixing a liquid exhibiting a yield stress, it is clear that material near the impeller will be fluid while that further away, where the shear stress has fallen below the yield stress ry, will be stagnant. Mixing therefore occurs only in a cavern around the impeller. The cavern diameter Dc for a flat blade single impeller can be calculated from the equation... 

Sm is the maximum allowable operating stress, calculated as specified minimum yield strength x Hf, where Hf is the material performance factor from Mandatory Appendix IX, Table IX-5A or IX-5B. Material performance factors account for the adverse effects of hydrogen gas on the mechanical properties of carbon steels used in the construction of pipelines. 

Here the yield stress is the Bingham yield value and the value of rj(co) is the linear value reached at high shear, often referred to as the plastic viscosity. The calculation of the material behaviour follows the same route as with the Newtonian case so ... 

Princen [57, 64, 82] and others [84] also noted the presence of wall-slip in rheological experiments on HIPEs and foams. However, instead of attempting to eliminate this phenomenon, Princen [64] employed it to examine the flow properties of the boundary layer between the bulk emulsion and the container walls, and demonstrated the existence of a wall-slip yield stress, below that of the bulk emulsion. This was attributed to roughness of the viscometer walls. Princen and Kiss [57], and others [85], have also showed that wall-slip could be eliminated, up to a certain finite stress value, by roughening the walls of the viscometer. Alternatively [82, 86], it was demonstrated that wall-slip can be corrected for and effectively removed from calculations. Thus, viscometers with smooth walls can be used. This is preferable, as the degree of roughness required to completely eradicate wall-slip is difficult to determine. 

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