Stress and force measurement uncertainties in 3D granular materials

Abstract

We have developed and employed a 3D particle stress tensor and contact force inference technique that employs synchrotron X-ray tomography and diffraction with an optimization algorithm. We have used this technique to study stress and force heterogeneity, particle fracture mechanics, contact-level energy dissipation, and the origin of wave phenomena in 3D granular media for the past five years. Here, we review the technique, describe experimental and numerical sources of uncertainty, and use experimental data and discrete element method simulations to study the method’s accuracy. We find that inferred forces in the strong force network of a 3D granular material are accurately determined even in the presence of noisy stress measurements.

Assessing continuum plasticity postulates with grain stress and local strain measurements in triaxially compressed sand

“…Tests were performed at 20, 30, and 35 MPa applied confining pressure, p c , at the Advanced Photon Source (APS) beamtime ID-1. Elevated confining pressures were used to ensure that grain strains were measurable via 3DXRD, which has a strain resolution of 10 −4 for on-diagonal and 5 × 10 −5 for off-diagonal strain tensor components ( 68 , 69 ), and therefore necessitates elevated sample stresses to induce measurable strains within grains. Sample sizes were also limited by the 1.5 × 1.5 mm X-ray beam size and the 144-h continuous experiment time limit at ID-1, during which all equipment and sample setup, detector calibration, and measurements must be performed.…”

“…Using the known elastic constants and orientations of each SiO 2 crystal, Hooke’s law was used to calculate stress tensors for each grain (with 12 MPa on-diagonal and 6 MPa off-diagonal resolution). Errors in individual grain strain and stress tensor measurements are known to be normally distributed with SDs approximately equal to the resolutions noted above ( 68 , 69 ). Measured grain strains and calculated stresses are therefore as likely to be higher as they are to be lower than their true values.…”

“…Lattice constants , , α = β = 90°, γ = 120° were used, which provided a mean grain stress consistent with the applied mean grain stress in each experiment and a grain completeness exceeding 80%, a metric often used to ensure accurate position, orientation, and strain fits for each grain ( 84 , 85 ). Based on prior work with these grains ( 68 , 69 ), we estimate that the fitting process generated grain strain tensors with 10 −4 resolution for on-diagonal and 5 × 10 −5 for off-diagonal tensor components. This corresponds to grain stress resolution of about 12 MPa and 6 MPa for on- and off-diagonal stress tensor components, respectively.…”