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

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.