By AZoM Editors
Table of ContentsIntroductionUniaxial
Testing ProcessUniaxial Testing Versus Shear
Testing Calculations in
Uniaxial Testing Calculations
in Shear Testing Comparison of
The procedure followed in Uniaxial Testing is to measure the magnitude of
force that is required to break or fracture a column of the consolidated powder.
Based on the relative binding force between particles, the powders are
classified as free -flowing or cohesive. The new technique developed by Freeman
Technology to enhance the capability of the FT4 Powder
Rheometer and comparison of the data with rotational shear testing is discussed
in the subsequent sections.
Uniaxial Testing Process
The first step in the testing procedure is to load the sample into a hollow
cylinder and compress it by applying stress of known value to form a
consolidated powder stack. The stress is then removed followed by the removal of
the cylinder. This leaves a compressed standing stack of the powder sample. Then
the stress applied on the top of the stack is gradually increased until the
break point is reached. During the process the values of breaking stress
(σc) and consolidating stress (σ1) are noted.
Figure 1. Uniaxial testing (a) producing a consolidated
column, (b) removing the piston and cylinder, (c) re-applying the piston and
increasing the normal stress to the point of column failure.
Uniaxial testing is not favourable for free-flowing samples, in which case
rotational shear testing proves more effective. Uniaxial testing is faced with
the challenge of producing a repeatable and uniform compression state. The new
accessory from Freeman proves to be of great help in preparing a uniform
consolidated column. The flow function (FF), which is equal to
σ1/σc, is the factor used to categorise the powders as
cohesive, with FF approximately equal to 1, and free flowing, with FF greater
Uniaxial Testing Versus Shear Testing
Calculations in Uniaxial Testing
Let us consider that vertical consolidating stress (σv) is being
applied on a powder sample that is enclosed within vertical walls.
Figure 2. Applying a vertical consolidating stress to a
If the sample were a liquid, the vertical stress leads to horizontal stress
σh of equal value. However, horizontal stress is not developed in
solid samples (e.g. concrete) due to application of a vertical force. In case of
powders, the ratio of σh to σv (λ) ranges between 0.3 and
Figure 3. Defining the stresses acting on a triangular
slice through the consolidated column prepared for uniaxial testing
The vertical stress transforms into shear stress t having values greater than
0 except 0° and 90° angles. The stresses at these two angles are referred to as major and
minor stresses. In uniaxial testing these stresses are the consolidation stress
and horizontal stress, respectively. The stresses are depicted in the form of a
Mohr’s stress circle in Figure 4. At the breaking point of the powder, the value
of horizontal stress is 0, which is represented by another Mohr’s Circle.
Figure 4. Mohr’s circles representing the stresses acting
on the uniaxial column when consolidated and at the point of fracture
Calculations in Shear Testing
In the case of rotational shear testing process, the value of shear stress is
noted for a range of applied normal stress and the values are plotted as a yield
locus as shown in Figure 5.
Figure 5. Shear test data derived from rotational shear
The value of breaking stress is calculated by drawing a Mohr’s circle that is
tangential to the yield locus and cuts through the origin of the shear stress
versus normal stress plot.
Comparison of Data
The analysis of data from both the methods is done by Mohr’s circles. The
data for uniaxial testing is obtained from the intercepts of the Mohr’s circle
whereas for shear stress the Mohr’s circle is fitted within the yield locus to
arrive at the data. In Figure 5, it is observed that if the yield locus cuts the
shear stress axis at a point close to the origin, small changes in the
consolidated stress can cause large changes in value of breaking stress.
Therefore, with shear testing we see that minute errors are magnified through
the extrapolation, which affects the repeatability of the data. Figure 6, which
gives the data comparison, shows that the uniaxial method produces more
repeatable results and shows more noise resistance.
Figure 6. Comparing shear and uniaxial test data for a
On the basis of the explanations in the above sections, we can conclude that
uniaxial testing yields a more reliable, accurate and straightforward
measurement of breaking stress when compared to shear testing. However, when it
comes to simplicity of the method, shear testing scores better than uniaxial
About Freeman Technology
Technology is a specialist company pioneering the measurement and
understanding of powders and their flow properties. Founded in 1989, the company
developed the novel, patented technology that forms the core of its Powder
Rheometer system at its design and manufacturing centre in Worcestershire,
UK where all manufacturing takes place in an ISO 9001:2008 accredited
environment. Research into understanding powder behaviour is central to the
company's business strategy.
Powder Rheometer is a universal powder tester that provides three
complementary approaches in a single instrument: measurement of bulk properties
including permeability, bulk density and shear property determination with
automated shear cells; and dynamic flowability using patented methodology. In
April 2007, the company received the Queen’s Award for Enterprise in
This information has been sourced, reviewed and adapted from
materials provided by Freeman Technology.
For more information on this source, please visit Freeman