The standard measurement of the yield locus is taken over from the classic soil mechanics. This yield locus contains a number of points consolidated with the same pressure and sheared under different load. That means that such yield locus represents the shear resistance for different over consolidation. This test fits all processes where the powder passes different pressure regions like silos and similar machines. However, we have to realize that other circumstances could require other configuration of the shear test.
The first steps are conditioning a step which has to provide a sample of comparable conditions regarding density, cohesive forces and other properties influencing the yield locus. We call this step CONSOLIDATION STEP. This preparatory step has to be repeated, by constant vertical load, until the maximal top value τm is reached and the stationary value is maximum and constant. After certain strain the shear stress is constant over the entire cross-section of the shear cell because shear stress must reach the maximal value according to the value for plastic deformation. This occur in translational, rotational full area and ring shear cell.
The vertical sample pressure of the shear step changes from "consolidation load" down to the the selected shear steps. The sample will be sheared under this lower pressure until the the PEAK is reached. The shear values Τm represent the points on the STATIC YIELD LOCUS corresponding with the STATIC DENSITY valid for the change from static state to steady-state shearing.
For scientific studies or other reasons, the development of the stationary conditions can be chosen where by the shearing is continued over full step time. In this case the stationary conditions represent the DYNAMIC YIELD LOCUS, which will cross the origin. The shear values Τs represent then points on the DYNAMIC YIELD LOCUS corresponding with the DYNAMIC DENSITY during shearing under the load σN valid for a steady state shearing.
Before the measurement of another point on the yield locus can be executed, a repeat of the consolidation stage is to be carried out. Theoretically, the steady-state shear value of the consolidation steps is expected to be constant. Because of changing shear plane during the shear test, the stationary value cam vary a little. The average of this value can be used for correction of the top shear stress values Τm (Pro Rating).
There are a number of influences which can be followed during the shear test.
Generally, the deformation of a powder can be described in three areas:
During the elastic deformation, there are only changes of density according to the new pressure. Other changes can not occur because there are no displacement of the particles to each other.
During the transition period whereby the powder shears, a number of processes will be fulfilled. Because of shearing the particles can rearrange their position to each other and the density will be adopt to new conditions. Small irregularities because of not ideal preparation of the sample will be eliminated. The powder sample is deformed under the consolidation load PC, until THE STEADY-STATE SHEAR STRESS Τs has been reached.
Some repeated steps under normal load σN are necessary in order to obtain THE MAXIMUM SHEAR STRESS Τm. This peak TM is not a real over-consolidation, but is an result of different particle-packing during the shearing and static stage. During the shearing (plastic deformation) the particles need room to move over each other and consequently the packing must be lower then by static stage. That means that we have an static and an dynamic density. During the begin of shearing the density is the higher (static density) and the shear stress is consequently higher. After certain strain, the density changes to the lower dynamic density and the shear stress is consequently lower. This process is repeatable, by repeating shearing followed by an static period.
In the flat tension condition there always are two main tensions proceeding to each other vertically(σ1,σ2), the normal tensions wanting to extremely for these while the shear stresses are disappearing at the same time. These touch the tension circle point in these where are the break tensions(σ,τ) appear in the gliding area. This one forms with the level of the main tensions the angle a. Therefore the situation of the gliding area is determines by the angle of the internal friction(φ).
Each (σ,τ) combination, lies on the straights, lead to the flowing of the powder, tension conditions below the straights are stable, above is physically not possible.
The circle of Mohr describes all stresses at an point of the powder mass. The minor an mayor principal stress are on the σ-axes. The midpoint of the Mohr circle represents the average stress between mayor and minor principal stress. The stresses can only grow only until the shear stress reaches the value of plastic deformation. Stresses above this value are not possible.
For determination of the Mohr diagram we use only the top values of the shear stress by different loading of the sample. This represents the transition stage between the elastic and plastic deformation – the highest resistance to change from static stage to dynamic movement.
STATIC YIELD LOCUS - The line passing through the peak values, at the transition between the elastic and plastic deformation of all measured points, forms the static yield locus. The highest point on the yield locus is the peak measured at consolidation normal stress. The consolidation Mohr circle is tangent to the yield locus and passes trough the measured shear stress for the consolidation normal stress. Points to the left of the tangent point of the Mohr circle through the origin result in a non linear curve and, these points should be not used for linear approximation of the yield locus.
σ1 = σn + Τn * ( tan(φ) + 1 / cos(φ) )
σ2 = σ1 - 2 * Τn / cos(φ)
σd = 2 * (Τn - Sn * tan(φ)) * tan( Pi / 4 + φ / 2)
The unconfined compressive strength is calculated from the static and time consolidation yield loci and is the mayor principal stress of the Mohr circle passing trough the origin and tangent to the respective loci.
DYNAMIC YIELD LOCUS contains the measured steady state shear points - the shear stresses during the movement. The dynamic yield locus crosses the τ/σ axes at the origin or slightly above the origin. Consequently, the cohesion is very small.
After short consolidation time, the most powders can be measured unmediated. The test results are reproducible at any time. Only the consolidation stress is a measure for the behavior of the powder. This type of measurement is the basic measurement for all powders. The results of the tests under other circumstances are always related to the instantaneous test.
Powders can by storage (if they aren't shear) get a time consolidation. Time consolidation can be caused by crystallization or sinter events and cause technological problems if they aren't recognized because the values of the compressive strength rise. The time consolidation also can be measured also with knowing that the measured values of the shear stresses are higher as without time consolidation.
The points passing trough the non repeatable peak values form the time-consolidation yield locus. The time- consolidation yield loci are most often parallel to the instantaneous static yield locus, but in a higher position. The position of the time- consolidation yield loci are higher for longer consolidation time. In practice its for the most part quite enough to pass a one point measurement and the instantaneous static yield locos will be shifted.
For all powders, the yield locus can be described with two characteristic properties: The angle of internal friction (φ) and cohesion (Τc). The equation for calculating of the shear stresses is: Τ = Τc + σ * tan(φ)
With these characteristics we can describe any powder:
|Cohesion less||φ>0||Τc = 0|
|Cohesive||φ>0||Τc > 0|
|Plastic||φ=0||Τc > 0|
|Fluidized||φ=0||Τc = 0|
For free flowing materials only frictional forces between particles can exist. The number of contacts can be changed by changing the pressure in which case we obtain higher number of contacts for higher pressure. Because of no cohesion an completely rearrangement of the particles is possible. Because of rearrangement of particlesaccording to the actual value of the pressure the shear value is independent from the history of powder. The arrangement of the particles, the packing, is only dependent of pressure and dynamic condition. For powder in rest, the density is higher than for a powder in move (shear). Therefore, for cohesionles powders, the shear value (peaks) at the begin of flow is higher than the during steady state deformation (stationary value).
Ideal plastic powders are mostly saturated and have very high cohesion. The individual particles can not change their position and because of saturation the powder mass is incompressible. That means the shear stresses for begin of flow and for steady state stage are the same. Consequently, because of incompressibility, the change of pressure can not lead to change of number of contacts and the shear stresses are only dependent of the cohesion. The normal stress has no influence. The angle of internal friction is zero and the shear/strain diagrams don’t show any peaks.
By cohesive powders the inter-particular forces are frictional forces and cohesive forces. Changing the pressure, the rearrangement of individual particles is almost restricted because of cohesive forces. The process of compression is in static situation mot reversible. Therefore the cohesive powders are influenced by history, the previous normal stress, shear and the time. By shearing, whereby the particles move, the contact between particles changes all the time and the cohesive forces loss the influence. Consequently during the shearing the rearrangement of the particles is possible. The movement of particles leads to an decrease of cohesion and the value of the steady state points shows a line going trough zero or near to zero. The peak values at begin of flow, forms a line above the origin.
The cohesive powder have a stationary value which is independent of the previous normal stress. The line through the stationary points is the same for all measured points of all different yield loci for different consolidation stress. From this, we can conclude rearrangement of particles is possible through shearing – the powder is in flowing condition nearly cohesionless. The practice approve this – keep the powder flowing in the silo and you will prevent bridging.
In soil mechanic this type of powders are not handled. In industrial practice, many powders are brought in fluidized stage because of mechanical or process advantages. Some fine powders, fluidize non expected, by example when mixed with air. This can happen by filling of silos or by collapsing of a bridge or rate hole. In such cases it coarse many problems like flooding out of a silo, or have problems by pressing tablets. The characteristic of the fluidized powder is that they lose the contact between particles. The internal friction become zero and the powder behave like a liquid. Fluidized powders can not be measured with our recent shear testers.
Each yield locus is also completely described by two Mohr circles. One, passing through the end-point of the yield locus containing maximal major (σ1) and minor (σ2) principal stresses. The other is at the beginning of the yield locus, where the minor principal stress passes through the origin and the major principal stress represents the unconfined compressive strength (σd). This are the parameters which we receive from a shear test and they are very useful for developing an ONE NUMBER IDENTIFICATION of the powders – the FLOWABILITY. FL = σ1 / σc
|25 >||FL||> 15||slight cohesive|
|15 >||FL||> 5||cohesive|
|5 >||FL||> 2||very cohesive|
|2 >||FL||> 1||plastic|