Numerical Test of Crack Propagation Path in Asphalt Beam Using Coupled Extended Finite Element with Field Variable Method

Abstract

Based on extended finite element coupled with field variable method, fatigue damage numerical test of three point-bending beam with initial notch has been made to predict crack propagation path, numerical results showed : under the fatigue loading with 200Hz, and amplitude is 20KN, length of crack expanding was the biggest and crack grew as some angles with the initial crack during the first loading, crack propagated parallel to the initial angle during the other loading cycle. These results can fit the experiment very well. Using Fortran, A new user subroutine named USDFILD (User subroutine to redefine field variables at a material point) was also provided on the platform of ABAQUS, which can modal the change of physic material with time. This user subroutine can also import fatigue characterize of material into the model.

Propagation of surface cracks on beam blank in the mould during continuous casting

“…The core idea is to introduce a step function representing the crack surface in a conventional finite element displacement function on the basis of unit decomposition; this function is used to characterise crack tip asymptotic displacement [17]. According to Cao et al [18], the XFEM uses the displacement field function u when discrete to the whole.…”

“…According to Cao et al. [18], the XFEM uses the displacement field function when discrete to the whole. Here is the conventional node shape function; the first term on the right-hand side of the above equation, , is the node displacement vector of a conventional finite element solution; the second term is the product of the degree of freedom of node expansion and the displacement step function of the crack surfaces; and the third term is the product of the improved enrichment functions and the crack tip asymptotic function . The first term on the right-hand side is applicable to all nodes of the model; the second term is only applicable to those nodes whose shape function supports are cut by the crack interior; and the last term is valid only for those nodes whose shape function support are cut by the crack tip.…”