ABSTRACT
This paper is concerned with numerical modeling for nondestructive imaging of defects in solids via standing waves excited by a periodic sinewave signal. The stationary solution, purely sinusoidal in an intact sample, contains higher harmonics when damage is present. These harmonics are generated by contact acoustic nonlinearity and form their own standing waves whose intensity maximum usually indicates the position of damage, in a way similar to resonant vibrometry experiments. The key point of the developed numerical tool that describes those wave phenomena is a model of planar damage (crack, delamination) considered here as an inner contact with rough surfaces and friction. The corresponding boundary conditions are given by the previously developed contact model based on the Method of Memory Diagrams (MMD) capable of automating the account for hysteretic frictional effects. Combination of the MMD for boundary conditions and a finite element formulation for waves in a volume (MMD-FEM model) provides a complete description which represents a numerical code applied here for nonlinear standing waves simulations. We present a number of examples obtained for idealized 2D geometry and reveal conditions in which both position and extent of damage are clearly seen as well as cases where only partial detection is possible.
ABSTRACT
Our study aims at the creation of a numerical toolbox that describes wave propagation in samples containing internal contacts (e.g. cracks, delaminations, debondings, imperfect intergranular joints) of known geometry with postulated contact interaction laws including friction. The code consists of two entities: the contact model and the solid mechanics module. Part I of the paper concerns an in-depth description of a constitutive model for realistic contacts or cracks that takes into account the roughness of the contact faces and the associated effects of friction and hysteresis. In the crack model, three different contact states can be recognized: contact loss, total sliding and partial slip. Normal (clapping) interactions between the crack faces are implemented using a quadratic stress-displacement relation, whereas tangential (friction) interactions were introduced using the Coulomb friction law for the total sliding case, and the Method of Memory Diagrams (MMD) in case of partial slip. In the present part of the paper, we integrate the developed crack model into finite element software in order to simulate elastic wave propagation in a solid material containing internal contacts or cracks. We therefore implemented the comprehensive crack model in MATLAB® and introduced it in the Structural Mechanics Module of COMSOL Multiphysics®. The potential of the approach for ultrasound based inspection of solids with cracks showing acoustic nonlinearity is demonstrated by means of an example of shear wave propagation in an aluminum sample containing a single crack with rough surfaces and friction.
