Numerical Simulation

Abstract

By knowing the shape and fatigue model of the CZM discussed in Chaps. 2 and 3, it is possible to start simulating the fatigue of bonded joints. But before that, we need to be familiar with the different aspects of a numerical CZM-based fatigue life analysis and this is the main goal of this chapter. Due to their popularity, many commercial programs have already included cohesive elements and cohesive laws in their material and element libraries. However, there are some differences between the CZMs used in these FE codes, as discussed in this chapter. According to the procedure discussed above, the first step in this process is to choose the CZM shape, defining the cohesive properties, and assigning these properties to the adhesive layer. At this stage, users need to be familiar with the stress state in cohesive elements, damage propagation path, mesh strategy used with cohesive elements, etc. Two different numerical strategies can be followed to define the cohesive layer. The most common approach is to define a finite cohesive layer thickness with cohesive elements. The second strategy is to use cohesive contact. All these aspects are discussed in this chapter. CZM fatigue models are not usually listed in the material library of FE programs and users therefore need to embed the fatigue analysis into the FE codes using subroutines. Different subroutines are available in Abaqus and can be employed for this purpose. USDFLD, UMAT, and UEL are the most common of these. All these routines are discussed in this chapter. Finally, the chapter is concluded by presenting some examples where bonded steel substrates were analyzed in terms of fatigue using a load envelope fatigue model and by the aim of UMAT and UEL subroutines.