| This thesis presents two major works:one is the simplification of the extended finite element method (XFEM), its implementation and application to the qualitative analysis of acoustic emission (AE) phenomenon; the other is the development of the XFEM model to quantitatively analyze AE.Work I:Against crack problem, conventional XFEM introduces the jump function and near-tip asymptotic displacement fields function to represent the crack face and crack tip respectively. This thesis simplifies the XFEM in the following two aspects:one is that only the jump function for discontinuity is added to the interpolation space whereas the base functions for the near-tip asymptotic displacement fields are omitted; the other is that only fully cracked elements (the crack runs through the whole element) are considered whereas partially cracked elements are not considered. In addition, phantom nodes with explicit physical meaning are introduced and the generalized degrees of freedom defined in these phantom nodes are used to replace the degree of freedom associated to the jump functions. The cohesive force on the crack face is considered. One-point stable quadrature scheme with hourglass control is used to accelerate the computation. As a result, the computation effort for the cracked elements, to a large extent, is reduced to the element calculation process of the standard finite element method and the code implementation is simplified accordingly. Such simplified XFEM is employed to qualitatively analyze AE phenomenon and the numerical results of the edge-cracked plate problem is presented.Work II:To further develop an XFEM numerical model which can be used for the quantitative analysis of AE phenomenon, on one hand, this thesis characterizes the AE phenomenon quantitatively by using the ring counts and its rate and derives the relation between ring counts (including its rate) and test voltage based on the AE testing theory. On the other hand, in the framework of the proposed simplified XFEM, by taking into account the external work, strain and surface energy, this thesis establishes the formula to compute the energy of the elastic wave due to AE based on the principle of energy conservation. The quantitative numerical model for AE can be finally obtained by using the relation between the energy and the test voltage given by Harris et al. to link the ring counts and its rate with the AE energy computed by XFEM. The developed model can quantitatively analyze the AE due to dynamic crack propagation and some preliminary results are presented. |
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