Biaxial shear testers

A tester in which both methods of consolidation - either steady state flow (Fig. 1 and 2) or uniaxial compression (Fig, 3) - can be realized, is the true biaxial shear tester [2,3,4,5] (Fig. 

The sample is constrained in lateral x - and y-direction by four steel plates. Vertical deformations of the sample are restricted by rigid top and bottom plates. The sample can be loaded by the four lateral plates, which are linked by guides so that the horizontal cross-section of the sample may lake different rectangular shapes. In deforming the sample, the stresses Ox and Oy can be applied independently of each other in x- and y-direction. To avoid friction between the plates and the sample the plates are covered with a thin rubber membrane. Silicone grease is applied between the steel-plates and the rubber membrane. Since there are no shear stresses on the boundary surfaces of the sample Ox and Oy are principal stresses. With the true biaxial shear tester the measurement of both stresses and strains is possible. 

The Flow Function as the dependence of the unconfmed yield strength Oc on the major consolidation stress oi (at steady state flow) can ordy be determined using testers where both stress states can be realized. Steady state flow can be realized in Jenike s tester, in annular shear cells, in a torsional shear cell, in the true biaxial shear tester and in a very specialized triaxial cell [2]. The unconfined yield strength Oe can be determined by running tests in Jenike s tester, in an annular shear cell [10], in uniaxial testers and in the true biaxial shear tester. Therefore, only Jenike s tester, annular shear cells and the true biaxial shear tester can guarantee the measurement of Flow Functions Oc (cf ) without further assumptions. 

Eibl and others have shown that the Finite Element Method can be used with success to model pressures in silos [20]. To apply this method a constitutive model has to be used. The models of Lade [21] and Kolymbas [22] may be mentioned as examples. Each constitutive model contains parameters, which have to be identified from calibration tests. The most important demand for this calibration test is that the complete state of stress and the complete state of strain can be measured in the equivalent testers. From the mentioned testers this requirement can only be fulfilled by the true biaxial shear tester and by very special triaxial cells [2]. Lade himself and also Eibl used results from triaxial tests for calibration. Feise [5,23] could show the advantages of using the true biaxial shear tester. 

Because neither the state of stress nor the state of strain are fully determined in the Jenike and Ring Shear Tester, in this paper a Biaxial Shear Tester has been used. Due to the design of this tester the complete state of strain and complete state of stress are fully determined. 

Three five component load cells (LCl-3) measure normal and shear stresses at the sample boundary. Due to the design of the biaxial shear tester and the test preparation all measured... 

Investigation on Pure Shearing of Cohesive Limestone with True Biaxial Shear Tester Chem. Eng. Technol. 15 (1992), 295-299 Zetzener, H., Schwedes, J. 

Behaviour of bulk solids during relaxation in the Biaxial Shear Tester International Symposium Reliable Flow of Particulate Solids III, ll.-13.August 1999,... 

In order to develop the proper dow pattern, knowledge of a material s dow properties is essential. Standard test equipment and procedures for evaluating sohds dow properties are available (6). Direct shear tests, mn to measure a material s friction and cohesive properties, allow determination of hopper wall angles for mass dow and the opening size required to prevent arching. Other devices available to evaluate sohds dowabiUty include biaxial and rotary shear testers. 

One way which relies upon the fundamental knowledge of the stress-strain-volume behaviour of bulk solids is dependent upon the development of testers such as the biaxial and triaxial shear testers as well as the now universally accepted Jenike shear cell, or the standard shear test tester. Other instruments, such as the annular shear cells and the cross-sectional Peschl and Colijn (1977) tester, use the same stress-strain-volume principle. These annular shear cells may also be used to evaluate a bulk powder flow function. The powder flow function, having been discussed previously, still requires a family of yield loci before cohesion can be evaluated. 

Figure 1.35 Difference between direct and indirect shear testers. (Jenike direct shear tester inside square and biaxial tester solid rectangle.)...

All of the shear testers previously discussed are biaxial, which means there are forces applied or measured in two different planes (horizontal and vertical). The design of a testing machine can be simplified if all of the measurements and motions can be made in one plane, i.e. in a uniaxial tester. 

The principle of these testers is that the specimen can be subjected to controlled stresses in two orthogonal directions (biaxial testers) or three orthogonal directions (triaxial testers). In the case of the triaxial testers, two of the orthogonal stresses are usually equal, normally generated by liquid pressure in a pressure chamber. The specimen is placed in a cylindrical rubber membrane and enclosed by rigid end cups. The specimen is consolidated isotropically, i.e. by the same pressure in all three directions which leads to volumetric strain but little or no shear strain. This is followed by anisotropic stress conditions, whereby a greater axial stress is imparted on the specimen by mechanical force through the end cups. In the evaluation of results it is assumed that the principal stresses act on horizontal and vertical planes, and Mohr circles can be easily drawn for the failure conditions. 

The failure function can be measured directly in a number of ways. Some are rather complex and still under development, like the new plane strain biaxial tester with flexible boundaries30, but the simplest method so far is the uniaxial compression test. Only the version developed by Williams et al,24 gives results close to those obtained indirectly with the Jenike shear cell, the other versions yield relative measurements only. 

POSTEC - unaxial research tester In the POSTEC - uniaxial tester, discussed by Maltby and Enstad (1993), the sample is confined in a cylindrical die and wrapped in a flexible membrane which is stretched between the outer periphery of the piston and the inner perimeter of the lower part of the die. Since the membrane is stretched and in contact with the wall and powder, the sample is compacted homogeneously thus the wall friction between the specimen and the die is reduced. Comparison of the POSTEC uniaxial tester with a biaxial and Jenike-type shear eell testers, with the standardised CRM-116 limestone powder, indicated that the fc values obtained with the POSTEC are slightly less than those obtained with Jenike-type shear cells and a biaxial tester. Since the total time for... 

Biaxial testers measure shear stresses related to normal stresses. However, the flow-function graph and its interpretation for silo design requires the calculation of principal stresses (fc and aO from the normal and shear stress data by the use of yield loci and Mohr s circles (a mathematical tool). In concept, a perfect imiaxial tester can directly apply and measure principal stresses, making the construction of yield loci and use of Mohr circles unnecessary. This would expedite the completion of flow functions and reduce testing time. 

The Hang-Up Indicizer was found to be highly reproducible in our tests [4], but the reported values of unconfined yield strength tend to lie below those obtained with biaxial testers. One reason is probably that the test specimen is fully confined during the consolidation step, and it may not reach the state of steady state flow in which the bulk density and shear stress remain constant as with the biaxial testers. Despite the deviation... 

The purpose of this paper is to use the Flexible Wall Biaxial Tester to get more insight in powder flow behavior. This has been done by preparing powder samples and shearing them with constant volume and with eight different types of deformation. Anisotropy is occurring in these samples due to the structure in the powder. It was seen that stresses on opposite walls differ which means that there are shear stresses. It is thought that these are at least partially caused by the powder and not by the tester. This would mean that the principal axes of stress are not in the same direction as the principal axes of strain. 

Fig. 3. The eight different shear steps which are possible with the Flexible Wall Biaxial Tester. The volume is the same for all types. The dotted lines represent the starting position.

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