Estimation of the Deformation Gradient Tensor by Particle Tracking Near a Free Boundary with Quantified Error

Background

Obtaining accurate displacement measurements for large material deformation and/or rotation presents a distinct challenge to digital image correlation (DIC) due to cumulative and decorrelation errors, particularly near material boundaries.

Objective

We aim to accurately measure the deformation gradient tensor near boundary discontinuities in situations of large deformation and large deformation gradients.

Methods

To achieve this goal, the locations of randomly distributed particles are tracked using an open-source particle-tracking software, Trackpy. A least-squares estimate of the deformation gradient tensor field uses nearest-neighbor material vectors and a first-order Finite Difference (FD) approximation, circumventing common errors in other methods. The error caused by FD approximation and that incurred by measurement are derived and tested with exhaustive numerical simulations. Furthermore, a uniaxial tensile test and mode-I fracture experiment are conducted with particle-embedded hydrogels to validate the method.

Results

Numerical results corroborate a theoretical expression of measurement error. They show that the FD error increases while the measurement error decreases for a growing estimating radius. Moreover, measurement error is linearly correlated to displacement noise. A benchmark uniaxial tensile test validates the accuracy of the proposed estimator, and the near-crack-tip measurements in a tensile fracture experiment demonstrate the estimator's capabilities near a free surface, when a material undergoes large deformation and rotation. The results of the displacement and strain data are benchmarked against kinematic data obtained using an open-source DIC software, Ncorr. Computation time for both methods is compared.

Conclusions

A deformation gradient tensor estimator is developed based on a particle tracking technique and a least squares routine. Theoretical error bounds on the estimator are verified by numerical simulations, and the method's capability is confirmed by physical experiments in evaluating large deformation and rotation near a free boundary. The proposed estimator is expected to open a door towards future material tests and experimental mechanics studies, especially in large deformation and large rotation scenarios.

Estimation of elastic strain by integrated image correlation on electron diffraction patterns

High-angular-resolution electron backscattered diffraction (HR-EBSD) has been developed to study local elastic strains in crystals. An integrated digital image correlation (DIC) procedure for high resolution diffraction patterns, as recently proposed to bypass several problems of the conventional cross-correlation-based algorithm, was implemented. Through two examples of experimental data where the algorithm was used and compared to conventional means, the current paper illustrates the benefits of the integrated DIC method. It is found that both measurement uncertainty and computation time were simultaneously reduced. Moreover, an enhanced robustness was obtained for relatively high misorientations relative to methods based on cross-correlation. Different computing conditions are explored on experimental data. A number of practical usage conditions are proposed to achieve better precision and speed.