Temperature Dependent TAPO Model for Failure Analysis of Adhesively Bonded Joints due to Temperature Induced Service Loading

The Toughened Adhesive Polymer (TAPO) material model is available in LS-DYNA with Keyword *MAT_252. The model describes the mechanical behaviour of crash optimised high-strength adhesives under crash conditions and takes elasticity, viscoplasticity and damage due to plastic deformation into account. In this contribution, the TAPO model is extended by temperature dependent viscoelasticity, plasticity and damage considering rate and temperature effects below and beyond the yield strength. Here, the focus of the material model is to predict failure of joints, which are bonded with ductile-modified adhesives and subjected to service loading with low strain rates due to temperature changes. Therefore, a linear thermoviscoelastic model is arranged in series to a thermal strain element and the S T .-V ENANT element for the TAPO model. The linear viscoelastic material behaviour below the yield strength is represented by a generalised M AXWELL solid with different parallel chains of springs and dashpots describing the equilibrium and the overstress. The temperature dependency of the viscosities of the M AXWELL chains is taken into account with the reduced time, which depends on the shift function in the theory of thermorheologically simple materials. Furthermore, the yield strength and the parameters of the nonlinear isotropic hardening stress are empirical functions of temperature. These functions are defined in the range from ambient temperature to nearly glass transition. In addition, the critical and failure strain in the damage evolution of the TAPO model are extended with functions of temperature following J OHNSON and C OOK . By reason of numerical efficiency, the equations of the TAPO model are reduced to the interface theory and implemented into LS-DYNA as a “user defined cohesive model” assuming a thin adhesive layer between the adherends. Thus, the local interface traction is described as a functional of the local separation vector. The parameters of the constitutive equations are identified by fitting the model response to data of shear tests with the thick adherend shear specimen (TASS) and tension tests with the but joint specimen (BJS) conducted within the range from ambient temperature to nearly glass transition. Numerical examples for the model verification and validation are discussed.