Numerical and experimental study of an interference fitted joint using a large deformation Chaboche type combined isotropic–kinematic hardening law and mortar contact method

Abstract

In this paper the framework of a combined Chaboche type kinematic and isotropic hardening model is explained for large deformation with Henky strain description to evaluate strain ratcheting of interference fitted double shear lap joints near the hole based on the works of Montáns et al. [doi:10.1016/j.mechrescom.2012.03.001] and Henann and Anand [doi:10.1016/j.ijplas.2008.11.008]. The described elasto-plasticity formulation is in the context of hyper-elasticity and based on the dual multiplicative decomposition of the deformation gradient into elastic and plastic parts. The decomposition of plastic part into energetic and dissipative part is considered and a new rheological model is suggested for extension of one term Armestrong–Frederick (A–F) model to multi-component A–F (Caboche) model in finite regime. A brief and simple numerical integration scheme is suggested for integrating the presented kinematic hardening. The suggested integration algorithm reduces the complexity of large deformation and for convenience, allows embedding small strain subroutines. To solve the system of nonlinear equations of the constitutive model, the successive substitution method is suggested for simplifying the solution and reducing the computational cost appreciably. In order to avoid non-smooth interaction between the pin and the hole, and also unrealistic plastic deformation, a well-established and an accurate frictional mortar contact formulation is used and combined with the material nonlinearity. The whole numerical formulations are coded in 3D finite element code in FORTRAN programming language and the code is optimized so that it can be efficient for ratcheting simulation over cycles. The approach shows stability and robustness in convergence due to consistent linearization of all contact and internal forces even in the presence of contact, geometry and high material nonlinearity. To evaluate the efficiency and accuracy of the presented formulations, the ratcheting data from simulation is compared with the experimental ratcheting data from strain gauges attached to the studied double shear lap joints.