Impact responses of the fracture parameters of interfacial crack tip such as energy release rate (G, J integral), T stress, stress intensity factor (K), and crack opening displacement (COD) are studied by experimental, analytical and numerical methods.
A new method to extract dynamic T stress term of moving interfacial crack is proposed. Anisotropic bimaterial which has subsonic crack propagation is considered, and interaction energy method is applied. The relation between J based interaction energy $(J^I)$ and T stress is obtained explicitly for the isotropic bimaterial and homogeneous material. The stress fields by the constant T stress and the stress fields by the point force moving with the crack are obtained by using the series expansion method and Stroh formalism. Interaction energy is obtained by Yeh formulation. The relation between JI and T stress and the relation between T stresses in each material of bimaterial do not depend on the velocity of crack but depend only on the properties of each material. These results are the same as those of stationary crack solution.
Three points bending impact test is performed with specially designed bimaterial specimen composed of aluminum and PMMA (Poly-Methyl Methacrylate). Conductive grid line technique is adapted to measure crack initiation and propagation. The crack initiates on a critical time, propagates along the interface, kink to PMMA part, and then propagates toward impact position. The onset of crack propagation and the length of interfacial propagation strongly depend on the initial crack length and position.
Finite element analysis is performed for the experimented specimen under the stationary crack condition. Fracture parameters for the interfacial crack tip are calculated by a programmed post processor which uses both a domain integral method and an interaction energy method. The interaction energy method shows good performance in the decomposition of stress intensity factors and the extraction of elastodynamic T stress with path independency. The phase angle of stress intensity factor varies with time. The relation between energy release rate and phase angle at the onset of crack propagation shows unsymmetrical U shaped curve. COD shows the same result as stress intensity factor. The magnitude of the T stress is not enough to affect the size and shape of plastic deformation area. However, specimens that have negative T stress shows stable crack growth along the interface, and it is verified that the sign of T stress can be used as the condition of stable crack propagation.
Elastodynamic finite element code is developed to investigate fracture parameters for the propagating crack. Four node linear elastodynamic element is used and Newmark formulae is applied to integrate displacement and velocity. Node release method is adapted to simulate crack propagation along the interface. Energy release rate is calculated in the area moving with crack. T stress term is calculated by the interaction energy with a stress field formed by the moving point force. Five examples are solved to show the validity and time history of G and T. The first example is half infinite strip. Energy release rate calculated from numerical analysis agrees well with analytic solution. T stress of steady state condition shows a little different value compared to the stationary result. The second example is homogeneous center cracked tension specimen. Energy release rate decreases with crack velocity for homogeneous material and approaches zero as crack velocity increases to Rayleigh wave velocity. The third example is bimaterial center cracked tension specimen. The magnitude of T stress of fixed lower material is decreased with increasing material mismatch. The forth example is PMMA-steel bimaterial. Numerical result of energy release rate is agree well with experimental result. T stress shows continuous change before and after the crack initiation. The fifth example is aluminum-PMMA specimen. T stress of this specimen shows discontinuous jump when crack initiates.
In summary, the new method to extract T stress term of moving crack by interaction energy method is proposed. Auxiliary stress fields around moving crack by external point force are developed. Bimaterial impact test is performed and impact load, crack initiation and propagation are measured. Numerical analysis is performed for the stationary crack and fracture parameters such as energy release rate, T stress, stress intensity factor and crack opening displacement are obtained efficiently with path independently. The finite element code to simulate crack propagation is developed. Energy release rate and T stress term of moving crack can be obtained by interaction energy method and auxiliary fields which are developed in this study.
