An Analysis of the Factors Influencing the Data Derived from a Plug Type Three‐Dimensional Strain Rosette under Compression and Torsion

Abstract

The embedding of three‐dimensional strain rosettes embedded into epoxy models provides an experimental technique for analysing complex structures; however, this technique has been known to produce data that were difficult to explain in terms of their physical significance. To gain a greater insight into the behaviour of a three‐dimensional strain rosette used in this way, a three‐dimensional strain rosette was embedded into each of two separate prismatic bars of square cross‐section and subjected to fundamental tests of compression and torsion in standard commercial testing machines. In initial tests on a bar containing a three‐dimensional strain rosette (Bar A) the data derived from the individual gauges sometimes departed from the theoretical values by more that 30 μe. After critical evaluation of the procedures used for making and testing Bar A, further tests were carried out on Bar B, which led to a reduction in the difference between theoretical and experimental data to 14 μe, acceptable for most practical purposes. The use of square plugs containing three‐dimensional strain rosettes which are embedded into square cavities in the model, and the measurement of the actual direction cosines of the gauges on the square plug prior to embedment is a distinct advantage over the use of cylindrical plugs. In addition, the use of testing machines with a fixed base as opposed to a floating lower platen is recommended.

A Comparison of Various Patterns of Three‐Dimensional Strain Rosettes

“…Table 3(i) indicates very high values for the sum of the squares for transducer (c) of Figure 1, implying that the sine waves were not very good fits to the data, particularly for gauges 1, 4, 7 and 9. This is thought to be due to the backlash in the frame of the Avery–Dennison testing machine as reported previously [12]. It can also be seen that the orientation of the model in the testing machine radically affects the results.…”

“…Considering initially the variance–covariance matrices in Table 1, these do not take into account gauge misalignment errors, as they have a negligible effect on the numbers in the matrices: patterns (a) and (b) which are based on the findings of Ref. [5] and patterns (c) and (d) which are based on the findings of Refs [6, 12], respectively, have the same [ T ′ T ] −1 matrix, where the orthogonal strains have some minor entanglements with covariance terms but the shearing strain terms are completely orthogonal and are bracketed between the transducers of types (e), (f) and (g) designed in Ref. [10] and the new tetrahedron (h).…”

“…A variation in this design was developed theoretically [4] but never evaluated experimentally. Further new patterns were investigated [4, 6, 12]. Rossetto et al.…”

A comparison of three‐dimensional embedded strain transducers, compression tested within the same strain field while offset at an angle with the principal axes

“…It has been established previously that rotating the bar and fitting sine waves (necessary to eliminate the adverse effects of lack of platen parallelism) [8] and altering the type of transmission element used to transfer load to the bar caused significant departures from the mean values [8]. To determine whether the aforementioned effects, together with carrying out the tests on a different machine and powering all three gauges (refer to Pattern E Figure 1) on a single rosette instead of just one, produced any significant bias, a 2 4 factorial experiment was carried out by repeating the tests twice (see Table 1).…”

“…A prismatic bar used in a previous research study [8] was used in this preliminary testing (a similar bar is shown in Figure 3). The prismatic bar (1) with the embedded transducers (2) (four in total: two in front and two behind) was loaded in compression along the z ‐direction via the transmission element (3), which was directly attached to the load cell (25 kN capacity) (4), and the spherical pad (5) was pressed on the prismatic bar.…”