Determination of Internal Deformation Field in Asphalt Cores Using X-Ray Computer Tomography

Abstract

Although existing nondestructive evaluation methods and transducers provide useful quantitative information on composite materials, they measure only macroscopic deformations and, often, only after the strain has exceeded a certain predetermined threshold. It is well established, however, that maintenance intervention is more effective if applied early in the deformation process. A new method for computing the microscopic internal displacement fields associated with permanent deformations of three-dimensional asphalt-aggregate cores with complex internal structure and satisfying the small gradient approximation of continuum mechanics is presented. The displacement fields are computed from a sequence of three-dimensional X-ray computed tomography images, obtained using a new imaging protocol developed specifically for mass-fraction and mix-density estimates of composite cores. By assuming that the image intensity of the tomographic images represents a certain conserved property that is incompressible, a constrained nonlinear regression model for motion estimation is developed. Successive linear approximation is then employed and each linear subsidiary problem is solved using variational calculus. The resulting Euler-Lagrange equations are approximated and solved using finite differencing methods and a conjugate gradient algorithm in a multiresolution framework. The method is validated using pairs of synthetic images of plane shear flow. The three-dimensional displacement field in the interior of a cylindrical asphalt/aggregate core loaded to a state of permanent deformation is calculated using this method.