# A Novel Solution for Uniaxial Powder Testing

By AZoM Editors

Introduction
Uniaxial Testing Process
Uniaxial Testing Versus Shear Testing
Calculations in Uniaxial Testing
Calculations in Shear Testing
Comparison of Data
Conclusion

## Introduction

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 σ1c, is the factor used to categorise the powders as cohesive, with FF approximately equal to 1, and free flowing, with FF greater than 10.

## 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 confined sample

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 0.6.

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 testing.

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 limestone sample

## Conclusion

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 testing.

Freeman 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.

The FT4 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 Innovation.

This information has been sourced, reviewed and adapted from materials provided by Freeman Technology.