A novel specimen shape for measurement of linear strain fields by means of digital image correlation

Abstract

Strains on the surface of engineering structures or biological tissues are non-homogeneous. These strain fields can be captured by means of Digital Image Correlation (DIC). However, DIC strain field measurements are prone to noise and filtering of these fields influences measured strain gradients. This study aims to design a novel tensile test specimen showing two linear gradients, to measure full-field linear strain measurements on the surface of test specimens, and to investigate the accuracy of DIC strain measurements globally (full-field) and locally (strain gauges' positions), with and without filtering of the DIC strain fields. Three materials were employed for this study: aluminium, polymer, and bovine bone. Normalized strain gradients were introduced that are load independent and evaluated at two local positions showing 3.6 and 6.9% strain change per mm. Such levels are typically found in human bones. At these two positions, two strain gauges were applied to check the experimental strain magnitudes. A third strain gauge was applied to measure the strain in a neutral position showing no gradient. The accuracy of the DIC field measurement was evaluated at two deformation stages (at [Formula: see text] 500 and 1750 μstrain) using the root mean square error (RMSE). The RMSE over the two linear strain fields was less than 500 μstrain for both deformation stages and all materials. Gaussian low-pass filter (LPF) reduced the DIC noise between 25% and 64% on average. As well, filtering improved the accuracy of the local normalized strain gradients measurements with relative difference less than 20% and 12% for the high- and low-gradient, respectively. In summary, a novel specimen shape and methodological approach are presented which are useful for evaluating and improving the accuracy of the DIC measurement where non-homogeneous strain fields are expected such as on bone tissue due to their hierarchical structure.

Figure 1

(a) Specimen’s geometry derived from Eq. (12), w(x) shows how the curvature of the specimen changes; in red and blue the high- and low-gradient ROIs are shown, respectively. L1 is the high-gradient ROI and where SG1 is placed. L2 is a neutral ROI connecting the high-gradient ROI with the low-gradient ROI, L2 shows constant strain and where SG2 is placed. L3 is the low-gradient ROI and where SG3 is placed. (b) The theoretical strain distribution along the specimen’s length. The high- and low-strain gradients are shown in red (steeper curve) and blue, respectively. Constant strain (in green) connects both gradient regions.

Figure 2

FE model including boundary conditions and mesh. The displacement was applied on the top of the specimen, while the bottom was constrained to mimic the experimental conditions. No material parameters (Elastic modulus) were assigned to the specimens because only strains were calculated and the FE simulation is displacement control. A poisson’s ratio of 0.3 was assigned for all specimens.

Figure 3

Preparation steps of the bovine bone specimens. (a) Bone specimens were sliced using an Exakt cutter, (b) SG1, SG2 and SG3 were applied on the specimen’s back, (c) mechanical test setup, (c1) the bone specimen was fixed to external clamps, and (c2) speckle patterns were applied on the specimen’s front.

Figure 4

RMSE computational method. (a, b) FE and DIC full-field data analysis respectively, (a1, b1) the full-field surface strain from FE and DIC, (a2, b2) cropping of the linear regions excluding the boundary nodes, (a3, b3) a 53 mm × 5 mm mesh grid for aligning the measurement points into a regular grid, (a4, b4) the high- and low-gradient ROIs from the middle line along the specimen’s length were extracted, (a5, b5) SGs ROIs were cropped at SG1 and SG3.

Figure 5

Stress–strain curve of all tested specimens. Aluminium in red, bovine bone in green and polymer in blue. The error evaluation was done at two deformation stages, approximately at 500 μstrain and 1750 μstrain. Five specimens were tested from each material.

Figure 6

Full-Field linear strains at the two deformation stages, for (a) aluminium, (b) polymer, and (c) bovine bone. The strain is plotted along the specimen’s ROI (53 mm), the strain was obtained from the high- and low-gradient ROIs, as in Fig. 5a4 and b4. The FE, analytical, DIC and DIC filtered strain are plotted in blue, magenta, light-green and dark green, respectively. DIC-LPF refers to the DIC strain fields after Gaussian LPF was applied.

Figure 7

RMSE for the linear strain gradients ROIs at the two deformation stages for the three tested materials.

Figure 8

Two-dimensional visualization of the DIC full-field strain measurements of one polymer and one bovine bone specimens. At both deformation stages; the reference strain from the FE model for this specific specimen, the DIC strains (original and filtered) are shown.

Figure 9

The normalized strain gradients at SG1 (6.9% per mm) and SG3 (3.6% per mm) is plotted for two deformation stages for aluminium, polymer, and bovine bone. The normalized strain gradient was calculated according to Eq. (2).