Of the many techniques developed for. An introduction to uniaxial shear testing

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1 As appeared in December 215 PBE Copyright CSC Publishing An introduction to uniaxial shear testing Tim Freeman Freeman Technology While uniaxial shear testing provides many of the same fundamental parameters and is simpler than biaxial shear testing for characterizing powders, historical challenges have prevented its widespread adoption. This article describes uniaxial testing and compares it to biaxial testing. The article then explains the challenges of uniaxial testing and describes how those challenges can be overcome with advanced testing equipment and methodology. Uniaxial versus biaxial testing Uniaxial testing, as shown in Figure 1, involves measuring the stress required to fracture a consolidated powder column. First, an operator loads a material sample into a cylinder (not shown) and applies a known vertical preconsolidation stress to compress the material and form a stable column. The operator then removes the preconsolidation stress and cylinder, leaving a freestanding powder column (Figure 1a). Finally, the operator applies vertical compressive stress until the column fractures (Figure 1b). The stress at which the column fractures is the powder s unconfined yield strength (UYS) at that particular preconsolidation stress. Of the many techniques developed for characterizing powders, uniaxial testing is one of the easiest to understand. Uniaxial testing s intrinsic simplicity makes it highly appealing for industrial application, but the testing method has historically been inhibited by a lack of easy-to-use, practical testing equipment and an associated methodology. However, as the study discussed later in this article shows, by using modern testing equipment and methods, uniaxial testing has considerable potential as a repeatable, accurate, and cost-efficient test method for industrial powder characterization. Before looking at the study, it s important to understand how uniaxial testing works and how it differs from commonly used translational or rotational biaxial shear testing methods. [Editor s note: For more information about common shear test methods, see the For further reading section at the end of this article.] UYS ( c ) is one of the primary metrics derived by biaxial testing methods, so it s an already well-established parameter within the powder-testing community. A key attraction of uniaxial testing, however, is that it directly measures the material s UYS as a function of a preconsolidation stress, while biaxial testing extrapolates the UYS from a series of collected data points, as explained in the next section. Shear testing theory A basic understanding of the theory that underpins shear testing makes it easier to appreciate the link between uniaxial and biaxial shear test data. Both techniques begin by applying a normal (or perpendicular) preconsolidation stress to a powder sample in a vertically walled cylinder, as shown in Figure 2a. This vertical preconsolidation stress ( ) is transmitted through the sample in all directions, including in the horizontal plane, normal to the cylinder wall ( ). As shown in Figure 2b, the preconsolidation

2 stress also induces shear stress ( ) at all angular planes ( ) through the sample except at zero degrees (vertical) and 9 degrees (horizontal), where the shear stress equals zero (assuming the cylinder wall to be frictionless). Figure 1 Uniaxial testing a. Powder is consolidated to form a stable column The normal stresses acting in the vertical and horizontal planes are defined as the major and minor principal stresses, respectively. At the start of uniaxial testing, with the cylinder in place, the major principal stress ( 1 ) is equal to the vertical preconsolidation stress, and the minor principal stress is the horizontal stress induced as the powder pushes outward against the cylinder wall. However, with the cylinder removed and the compressive stress reapplied, at the point where the unconfined column fractures, the minor principal stress must be zero, and the vertical stress is, by definition, the powder s UYS ( c ) for that particular preconsolidation stress. The relationship between these stresses can be represented graphically using Mohr s stress circles, which plot shear stress as a function of normal stress. The Mohr s circle shown in the graph in Figure 3a represents the stresses acting on the powder column when confined and consolidated. The horizontal and vertical normal stresses are the left and right points, respectively, where the circle intersects the x-axis and the shear stress is zero. The shear stress at any angle is the point at which the angle 2 intersects the circle. Figure 2 How stress is transmitted through a powder sample under consolidation a. Normal stress acting vertically and horizontally b. Compressive stress is applied until column fractures Cylinder wall Powder sample b. Shear stress induced at all angular planes

3 Figure 3 Mohr s stress circles for uniaxial testing The Mohr s circle shown in the graph in Figure 3b shows the stresses acting on the unconfined powder column at the failure point, where the minor principal stress is zero and the vertical stress is the powder s UYS ( c ). a. Confined and consolidated powder column 2 In contrast, biaxial shear testing extrapolates the powder s UYS value by measuring shear stresses at a range of applied normal stresses and using the resulting data to plot a yield locus, as shown on the graph in Figure 4. The powder s UYS ( c ) is determined by drawing a Mohr s circle that s tangential to the yield locus and has a minor principal stress of zero. The major principal stress is determined by drawing another Mohr s circle through the preshear point (the steady-state shear stress measured at the preconsolidation stress) such that the circle is tangential to the yield locus. = 1 b. Unconfined powder column at failure point c Figure 4 Mohr s stress circles for biaxial testing Measured shear stress points Tangential points Yield locus Preshear point c 1 One challenge with this extrapolation process is that small changes in the data points can produce major variations in the UYS value. Testing has shown that an error of just 1 percent in measured shear stress with biaxial testing can translate to a variation in c of greater than 1 percent, particularly with less cohesive powders. 1 This amplification of relatively small measurement errors is a problem for all biaxial testing equipment, though advanced testing systems incorporate strategies to minimize such errors and provide more accurate and repeatable c values. Uniaxial testing addresses the root cause of these inaccuracies by eliminating the need for extrapolation and modeling. Uniaxial testing challenges With its simplicity and direct nature, you might think that uniaxial testing would be widely adopted, but the challenge of building a free-standing and uniformly consolidated powder column and developing a practical, easy-to-use tester that s applicable to a range of sample types have historically inhibited the method s use. Forming a stable powder column is difficult, particularly with a free-flowing material, and often requires high consolidation stresses. But using consolidation stresses that are much higher than the consolidation pressure in a typical industrial application can compromise the resulting data s relevance and create considerable uncertainty when trying to determine how a material might behave within an actual process. Ensuring that the consolidation stress is uniform throughout the powder column during uniaxial testing requires careful consideration of the effect of wall friction. Wall friction can create heterogeneity in the sample s bulk density and cause the c to be substantially underestimated. 2, 3, 4 Strategies to address this issue include layer-by-layer consolidation and using a flexible cylinder membrane with added lubricants. 5, 6 Though these methods

4 successfully generate data that are closely similar to data generated by a biaxial shear tester, neither method addresses the need for an easy-to-use solution for routine application. Modern uniaxial testing In recent years, powder testing devices have become progressively more precise and automated, allowing for the development of effective uniaxial testing protocols. Research at the University of Edinburgh, in particular, 2 has provided a platform for the latest commercial uniaxial testers. These testers incorporate double-ended compression to ensure more uniform consolidation throughout the powder column. The testers also use refined split-ring cylinder sleeves that easily slide against the consolidated material, minimizing disturbance to the powder column when removing the sleeve during the test. In the following study, a modern uniaxial tester analyzed six different powder samples. The materials tested included: CRM116 limestone (Commission of the European Communities, 4 microns, angular) Microcrystalline cellulose (MCC) (Avicel PH11 FMC Europe N.V., Belgium, 5 microns, irregular) Commercial talc powder (2 microns, platelets) Methyl cellulose (Metolose 9H, Shin Etsu, Japan, 83.4 microns, fibrous) Lactose 1 (Lactohale LH2, DFE Pharma, Germany, 5 to 16 microns, tomahawk ) Lactose 2 (Respitose ML6, DFE Pharma, Germany, 2 to 45 microns, tomahawk ) These materials range from cohesive to easy flowing and are commonly used in industry. MCC and lactose, for example, are routinely used as excipients in the pharmaceutical industry, and talc is a major ingredient of many personal-care products. The tester in the study used a split-ring sleeve and applied double-ended compaction to the samples. As shown in Figure 5, the study successfully generated c values for all six powders, including the relatively freeflowing MCC and lactose, which typically present a challenge for uniaxial testing. In absolute terms, the c values were lower and the associated flow function (a parameter routinely used to rank powder flowability) values were higher than analogous values measured with a biaxial shear tester, as shown in Figure 6. This is to be expected given that uniaxial testing doesn t include rotation along with the vertical consolidation, so a uniaxial tester generates a different packing structure in the column than a biaxial tester. Critically, however, the study s results indicate that uniaxial testing is able to rank the flowability of a broad range of powders, using a simple, direct, and highly repeatable test. This study s results, along with the results of previously published uniaxial testing studies 5, 6 suggest that testing success depends on compacting the sample from both ends, removing the cylinder without disturbing the consolidated sample, and setting up and performing the Figure 5 Uniaxial UYS data for six tested materials 12 Unconfined yield strength (kilopascals) Limestone Talc MCC Methyl cellulose Material Lactose 1 Lactose 2

5 Figure 6 Comparison of uniaxial and biaxial flow function data for MCC and talc Unconfined yield strength (kilopascals) MCC Biaxial tester MCC Uniaxial tester Talc Biaxial tester Talc Uniaxial tester Major principal stress (kilopascals) test to ensure good alignment and load application. With a well-designed tester that addresses these issues, uniaxial testing can be applied to a wide range of materials, including fairly free-flowing powders, which can be problematic for uniaxial and biaxial shear testing alike. References 1. M. Delancy, M. T. Freeman, K. Brockbank, and D. Millington-Smith, Accurately quantifying process-relevant powder properties for AM applications, Proceedings of AM/PM Conference, Session A13, Paper 55, Orlando, FL, May 18-2, T. Bell, E. Catalano, Z. Zhong, J. Ooi, and J. Rotter, Evaluation of the Edinburgh powder tester, Proceedings of the International Congress on Particle Technology, 27, pages Luca Parrella, Diego Barletta, Renee Boerefijn, and Massimo Poletto, Comparison Between a Uniaxial Compaction Tester and a Shear Tester for the Characterization of Powder Flowability, KONA Powder and Particle Journal, Vol. 26 (28), pages Dietmar Schulze, Powders and Bulk Solids: Behavior, Characterization, Storage and Flow, Springer Berlin Heidelberg, J. Williams, A. Birks, and D. Bhattacharya, The direct measurement of the failure function of a cohesive powder, Powder Technology, Vol. 4 (1971), pages L. Maltby, and G. Enstad, Uniaxial tester for quality control and flow property characterization of powders, Bulk Solids Handling, Vol. 13 (1993), pages Tim Freeman is managing director of Freeman Technology (tim.freeman@freemantech.co.uk). He holds a degree in mechatronics from the University of Sussex in Brighton, England and is a frequent contributor to industry conferences in the area of powder characterization and processing. Freeman Technology Tewkesbury, England +44-() For further reading Find more information on this topic in articles listed under Particle analysis in Powder and Bulk Engineering s article index in this issue or the Article Archive on PBE s website, (All articles listed in the archive are available for free download to registered users.)