Principles of Shear Testing -

BHG Doc No. Peschl-003 Rev A

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Bulk Handling Global Pty Ltd Bulk solids and powder flow properties testing, silo and hopper design, discharge and conveying technology Principles of shear testing Paper by:- Dr. Ivan Peschl IPT. Seminar – MIT Boston 14th May 1999

Peschl – Bulk solids and powders flow property testing



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Principals of shear testing for bulk solids.

The shear testing technique should measure the resistance of a soil/powder against plastic deformation in relation to the pressure working in the shear plain.

An idealized shear test is shown in fig. 1. - An infinite plain representing the test sample. The upper portion moves relative to the lower portion, creating a uniform shear plane in between the moving spaces. Ideally, the shear testing device should reach this idealized situation as soon as possible. For practical consideration, the shear tester should have limited dimensions.

The basis of shear testing of products has derived from soil mechanics. Of original design by

Casagrande, the shear testing device was rectangular because with limited knowledge at that time, soil samples were easily prepared as rectangular as compared to other forms. The rectangular cell was composed from a cell base, and a top-loading cover. The intention was a linear movement of the “loading cover” against the cell base, and the soil-sample shears in-between the cell base and the loading cover. For soil samples, this method of shear test by Casagrande delivered acceptable results.

As knowledge and experience was gained, the Casagrande tester was introduced to bulk solids powders. However, unlike soil samples which have been consolidated for thousands of years, it was found that the samples of industrial powders required to be consolidated in the shear cell, and the rectangular format was found to be less than ideal. Industrial powders were found to be more or less loose powders, as compared to soils.

Experimentation and process requirements lead to a device where powders can be more efficiently filled and consolidated. Early pioneer Jenike altered the square cell design of Casagrande, having a cell base cell ring and a loading cover. Operation of the shear cell remained a linear movement. In this revised design, the consolidation process occurred during the shearing process, until a stable shear stress was established. By experimentation, some powders too small in particle size were unable to reach a stable shear stress, making this design limited in effectiveness.

This lead to a need for shear tester design which would allow a longer shear strain until the shear

stresses reaches a stable value.

In order to reach a longer shear strain, Walker developed the ring shear tester. The Walker ring shear tester was based on an inner and outer annulus, with the loading lid located in between the inner and outer ring. The inner ring is introduced because the idea that the shear stress is dependent of the radius. Approximate uniform shear stresses have been supposed in the ring formed sample. The assumption of a linear function of the stresses versus the radius was more realistic compared to previous shear tester designs. The linear function of stress would only be valid during the elastic deformation of the sample.

However, for true testing of shear requirements, the function of plastic deformation is of more important value rather than the values of elastic deformation.

In the Walker design shear cell, the shear plane was localized directly under the top cover, where the shear stress is a combination of wall friction of top cover and internal friction of the powder. As the shear plane occurs in this localized region, it is established that it is a limitation of the ring shear cell tester. The Walker (annulus) shear cell design, does allow the measurement of the plastic deformation, however, the measured shear stress during deformation, is equal at any radius of the sample. Therefore, the introduction of the inner ring of the shear cell is not necessary. Continued.



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Principals of shear testing for bulk solids. – Continued.

Extensive development has lead to the Peschl full area rotational split ring shear cell - without an inner ring. The Peschl rotational shear cell combines the advantages of Jenike shear cell and Walker ring shear cell. In the rotational shear cell, the shear plane is located in the middle of the sample tested – well away from the surfaces of the upper and lower cells, with the ability to apply unlimited shear strain due to rotational movement. This shear tester approaches the most the idealized infinite powder sample as shown in fig. 1.

Jenike shear tester.

The Jenike shear tester consists from a cell bottom, cell ring and top loading cover as shown in fig. 2. Shearing is introduced by translation of the top loading cover and cell ring against the cell base. The shear force is externally introduced (rather than within the sample) by movement of the cell ring. As a result of the linear ring movement, the internal pressure is higher on the trailing side of the upper cell, and lower on the leading side. This leads to a consequential inclination of the top lid.

The shear force is partially introduced by movement of the cell ring. This effect has as result a non- uniform development of the consolidation pressure and the shear stress over the cross section of the shear cell.

Because of translation movement, the shear strain is limited to few millimeters, whereby the ring moves over the cell base. For some elastic powders, the allowed shear strain is already reached before the plastic shear stress is established. As the Jenike shear cell relies on a linear operation of the cells to achieve shear, the function of pressure applied to the sample area is varying due to uneven displacement of sample particles during the linear movement. These issues place a limitation on the intension to measure the true shear stress as function of pressure. Ring shear tester and similar designs.

Following the Walker development of the ring shear tester, various reputable institutes have designed shear testers with minor differences in size or design. These variations have some common characteristics in design where the cell base and the loading top cover is ring formed. The top cover, which is provided with vertical wings, presses on the surface of the powder in the ring formed space as shown in fig. 3.

A number of influences from these designs are described as follows:

a. Variation of consolidation pressure in the tangential direction is introduced by wings on the top cover.

b. Variation of pressure in the radial direction is introduced trough the ring-orifices on the outer and inner radius of the cell. The powder tends to leak through the ring formed orifice between the cell wall and the loading cover. Consequently, pressure drops to zero at the place of orifices because of loss of material during the shearing.

c. The shear plane is directly under the loading ring. Because of this, the shear plane consists of areas where wall friction is measured and areas where internal friction is measured. Consequently, a mixture between wall friction and internal friction will be measured depending on the geometry of construction and the powder properties.

Continued.



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Ring shear tester and similar designs. – Continued.

d. Difference of shear stress occurs at the place of the wings - passive on the pressure side and active on opposite side. Consequently, the sample tends to compress on the side of high passive pressure and expand on the side of the low active pressure – also we receive a variation of compaction in the shear cell and as result a non-uniform shear stress.

e. Difficulties during the course of measurement of wall friction. Problems: The wall

sample has to be machined to a ring form and has to be fixed to the bottom. The measurement of friction is accompanied with measurement of forces along the sidewalls of the cell. The result is a measurement of to high wall friction.

f. Measurement of Time Consolidation is difficult with alternative ring shear testers. Ideally, time consolidation should be measured without the removal of shear cell covers. The first movement of upper cells should be during measurement of shear stress after time consolidation. This is not ensured because of following reasons: • A guided loading cover originally designed by Walker, required the lifting of the

load cover during the ongoing measuring process. This also increases the duration of testing time.

• Using a free load-cover, the positioning and concentricity of cover and cell is

difficult to establish, and requires re-setting to allow clearance and freedom of the cell torque arm. By this process the shear plain is partially disturbed and the measured time consolidation shear stress is generally lower.

g. Ultimately, the design of a ring shear cell tester should include features that allow the

shear stress as a linear function of the radius of the shear cell. Experimentation shows that these values are only achieved after elastic deformation limits are reached, and plastic deformation is established to the further shear process. By this plastic deformation, the plastic shear stress is constant across the entire volume of the shear cell – from the outer radius of the shear cell right to the middle of the shear cell. That means that the inner ring of a ring shear cell is not necessary.

Peschl rotational split level shear cell.

Peschl has developed a rotational shear cell whereby the shear plain occurs in the middle of the

sample, exactly between the end of the cell base and the beginning of the rotational ring. The location of the shear plane is located in this region, due to the design of the surfaces of the upper and lower cell surfaces which entraps the particles and shear occurs directly within the body of the sample. The increased holding friction prevents the sample from shearing on the surfaces of the upper and lower cells. The shear plane occurs in the split level between bottom and the loading cover.

Consequently, the Peschl shear tester, shown in fig. 4, is a true full area shear tester which directly measures the internal friction of powder against powder, without disturbing effects. The Peschl split cell shear tester allows sufficient shear strain to reach the stable value of the shear stress by plastic deformation. Thus peak initial shear stress is accurately measured, and used in determining the Mohr’s values. Continued.



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Peschl rotational split level shear cell. – Continued.

In fig.5 is the development of the shear stress and density versus shear strain as function of the radius for significant stages shown.

a. In begin of the shearing, fig. a, by strain between 0 and K1, is elastic deformation in which period the shear stress. T is in linear relation to the radius R.

b. The next stage, fig b shows that by further shearing, the shear stress is lower in value

at the minor radius, to the maximum T1.

c. By further shearing, the maximum shear stress T1, is achieved in the middle region of the shear cell at the strain K2. With additional shearing, the shear stress stays constant over the entire surface of the shear cell.

d. By discontinuing shearing, and unload the shear stress by allowing the shear cell to

move free, the shear cell rotates backwards as the shear stresses at strain K3 are not in equilibrium. The shear cell rotates backwards until the shear stresses across the radius are in equilibrium. This deformation can only happen by elastic deformation. Consequently, the shear stresses in the middle of the shear cell are not altered, and remain at T1values. By shearing under decreased consolidation pressure, the shear stress reduce in value according to the yield locus and reach a value of T2.

e. During the next stages of shearing K4-K5, the sample deforms elastically, whereby two processes are simultaneously changing – the shear stress and the density. By stopping the shearing at K3, the sample compacts as the particles find the line of least resistance in the inter-particular spaces, which leads to higher consolidated density. When we start to shear again, we shear at the higher density and consequently with higher shear stress T2. In the graphic for development of shear stress versus the strain the value T2, is represented as a peek at strain K5

f. By continuing the shearing, the density decreases because of the shearing action. At

is reduced density, lower shear stress T3 – the plastic shear stress K6 corresponds to the consolidation pressure.

Conclusion.

Shearing is always a process of altering density by varying consolidation pressure, as well as altering shear from static to dynamic conditions. The maximized/peek shear stress development can also be attained by constant consolidation pressure due to plastic and non plastic deformation, as well as fluctuations in density created by dynamic and static movement of particles.

The maximized/peek shear stress is attributed to, and attained purely by the normal shear process. The recording of these values is easily attained, and of importance to measuring true material properties. Hence, techniques such as altering sample preparation, varying consolidation load midstream of a test, or altering the movement path of cells have a major impact on results. The Peschl rotational shear tester avoids all these pitfalls currently experienced by previous design shear testing equipment.

Continued.



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Fig 1. Idealized shear test –

a. Infinite shear plain. b. Constant volume - Mohr diagram for plastic deformation. Shear stress on the top of the Mohr circle. c. Compacting volume – Shear stress right from the top of the Mohr circle. d. Expanding sample – Shear stress left of the top of the Mohr circle e. Idealized shear test – Angle of expansion vector = AL is equal to the internal angle of friction = F.

Continued.



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Fig 2. Jenike shear tester S – Vertical pressure in the shear plane N – Shear force – S1P – Passive – High pressure on the ring wall S2P – Active – Low pressure on the ring wall T – Shear stress TPP – High shear stress on the passive pressure side TPA – Low shear stress on the active pressure side

Continued.



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Fig 3. Ring shear tester Fig 3A General view of the ring shear tester Sn – consolidation load T – shear force - moment

Fig 3B View on the top cover with wings and cell base ring shear tester

Continued.



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Fig 3B. Forces and pressures over the cross section of a ring shear tester

A. Vertical pressure distribution because of wings on the top loading lid B. Horizontal active and passive pressures on the wings C. Non uniform distribution of the shear stress because of non uniform vertical consolidation

pressure, as well as non uniform horizontal stress as a result of the wings

Continued.



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Fig 4. Peschl shear tester consists of a base cell ring and top consolidation cover S – Consolidation pressure S1 - Major main stress S2 – Minor main stress T – Shear stress

A. Uniform distribution of vertical consolidation pressure over the entire cross section of the shear cell

B. Shear plane in between the cell base and cell ring C. Uniform distribution of the shear stress over the entire cross section of the shear cell

Continued.



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Fig 4A Peschl shear tester

A. Raw materials shear cell B. Standard shear cell C. Pharmaceutical shear cell

A B C

Continued.



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Fig 5. Development of shear stress during a shear stress

Fig 6 Development of shear stress during a shear test measured with a scientific shear cell

1. Few starting tests by increasing the shear stress 2. Development of the shear stress by continuation of the shear process 3. Backwards of the strain as a result of establishing equilibrium of the shear

stresses over the cross section of the shear cell

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Principles of Shear Testing -