Dynamic stress responses at the edges of adhesive layers in lap strap joints of half-infinite length subjected to impact loads

Stress analyses of adhesively bonded lap joints having half-infinite lengths were performed using a half-closed-form approach. To simplify the boundary conditions, the lap strap joint configuration was adopted. The stress variation with respect to time at the edge of the adhesive layer in the joint configuration was investigated. The formulation of the joint kinematics using the dynamic Volkersen model yields simultaneous partial differential equations. The Laplace transforms of the equations yield simultaneous ordinary differential equations that can be solved assuming that the adherends of the joint have the same cross-sectional dimensions and are made of the same material. The transfer function between the stress or stress wave as inputs and shear stress histories at the edges of the adhesive layer as outputs is obtained. The response of the dynamic system can be described by a Bessel function when an impulse stress is applied to the joint. The indicial response of the joint can be calculated by the integration of the impulse response over time. The stress variation with time caused by the variable applied stress can also be calculated by convolution integration of the impulse response and the variable stress in the time domain. The transfer function of the dynamic system is more complex when a stress wave is applied. In this case, the impulse response of the system can be described with a series solution.