Finite-Element Model: Geometry and Loading

The bending properties of different meshing elements have been studied with linear elastic analysis and then the dimensions and boundary condition of the viscoelastic model were defined. The continuum three-dimensional twenty – node-reduced (C3D20R) element was selected for its good agreement with the linear elastic analytic solution for the vertical deflection of a thick plate. This model had 56 elements and all elements were arranged in a single layer. The lin­ear elastic model for blister formation in a thick plate was used as reference for the viscoelastic finite-element simulation in this chapter.

In this particular case, a three-dimensional (3D) half-circular model was considered. As long as the symmetry conditions hold at the edges, the radial symmetry in the pressurized circular plate allows any size of pie slices or seg­ments to be used in the model. A 3D finite-element model was developed using ABAQUS version 6.8 (SIMULIA Scandinavia Abaqus Scandinavia AB SE-72210 Vasteras SWEDEN).

Modeling blister growth in MA has been done by Michalski [11] and blister formation in thermo-viscous material was studied by Rogosch [12]. In this pa­per, a 3D model is established to simulate the time-dependent vertical blister deflection of a thick plate for different types of loading amplitudes.

The geometric finite-element model setup of the 3D plate is shown in Fig. 6(b), where the entire contact area between the plate and supporting sub­strate is constrained in all df (uX = uY = uZ = 0, where uX, uY, and uZ are displace­ment in x, y, and z axis, respectively, and uRX = uRY = uRZ = 0, where uRX, uRY, and uRZ are rotational displacements in x, y, and z axis, respectively). This condi­tion of support represents full adhesion to a rigid substrate beyond the area of the interface. Symmetry plane x-z has a degree of freedom uY = 0. A uniform pressure load of 0.03 MPa is applied over the entire region (blister radius) of the circular half-plate. The pressure load applied in this model is the same as the pressure used in the laboratory test, which is described below. A constant average temperature of 59 °C is used in the finite-element simulation model. This temper­ature is measured during the experiment as mentioned in the next section.