The evaluation of strain at an internal point: investigating the accuracy and precision of different patterns of three-dimensional strain transducers

A comprehensive experimental analysis of several different configurations of three-dimensional strain gauge transducers, employed to calculate the strain at an internal point within a system, under the influence of the same strain field has been undertaken. A definitive conclusion as to which transducer pattern would yield the most accurate and precise results is not available in the literature. The overarching aim of the research was to experimentally corroborate a determination to this uncertainty associated with transducer design. To this end, four transducer designs, two orthogonal and two tetrahedral type patterns, were manufactured. The transducers with orthogonal patterns were constructed using three stacked rosettes, each with three gauges, and their orientation differentiated the patterns. The tetrahedral transducers, with included angles of 60 and 90, were constructed with nine single element gauges. A comprehensive programme of preliminary testing established governing principles for testing the three-dimensional models. Four transducers were embedded within the same prismatic epoxy model and tested under various loading conditions. It was found that the orthogonal patterns produced more precise and accurate results for the strain tensor terms. Both orthogonal patterns had over 90% of their tensor terms within their 99% confidence intervals. The tetrahedral patterns had much poorer results with 53% to 69% of their terms within their 99% confidence intervals. The derived principal strain values were also of interest as the axes of the transducers were not aligned with the principal directions. Again, the two orthogonal transducers produced the more accurate results with over 82% of their terms lying within their 99% confidence intervals. However, the tetrahedral patterns had values between 57% and 79% within range. The research also had a particular focus on biomedical engineering problems, with focus on analysis of femoral implants. A concern that arose during testing of the prismatic model was the imposition of boundary constraints and their implications on experimental femoral implant models under load. The restriction of movement of the femoral head induces a concomitant side load on the system; this must be taken into consideration during analysis. A second tapered epoxy model, with a metal insert, was manufactured containing a transducer, of an orthogonal pattern, to examine the effect that strain gradients may have on the calculation of the final strain tensor in embedded strain gauge work. It was shown that, if strain gradients are present during testing, they do not adversely affect the calculation of the tensor terms when adopting the following recommendations: the gauges are kept small; are positioned in close proximity to one another; and are used within large scale models. In summary, it can be concluded that orthogonal three-dimensional strain gauge transducers proved to be the most accurate and precise designs to use for the determination of strain at an internal point within a system; considerable care should be taken when applying boundary constraints to experimental set-ups so as not to induce unwanted attendant effects; adverse affects of strain gradients that may be acting across the transducer should not affect the final tensor when large scale model are used with small strain gauges kept close together.