Research on Multiple Griffith Cracks at the Interface of Fine-Grained Piezoelectric Coating/Substrate

The behavior of a fine-grained piezoelectric coating/substrate with multiple Griffith interface cracks under electromechanical loads is investigated. In this work, double coupled singular integral equations are proposed to solve the fracture problems. Both the singular integral equation and single-valued conditions are simplified into an algebraic equation and solved by numerical calculation. Thereby, the intensity factors of electric displacement and stress obtained are used to obtain the expression of the energy release rate. Furthermore, numerical results of the energy release rate with material parameters are demonstrated. Based on the obtained results, it could be concluded that the energy release rate is closely related to the size of the interface cracks and the mechanical-electrical loading. For a bimaterial structure, the fine-grained piezoelectric structure exhibited better material performance compared to the large one.

Loading–Unloading Cycles of Three-Dimensional-Printed Built Bimaterial Structures With Ceramic and Elastomer

This paper studies the loading–unloading behaviors of a three-dimensional (3D)-printing built bimaterial structure consisting of an open-cellular plaster frame filled with silicone. The combination of the plaster (ceramic phase) and silicone (elastomer phase) is hypothesized to possess a nonlinearly elastic property and a better ductility. Four-point bending tests with programmed cycles of preceding deformations were conducted. The results show that there exists a linear–nonlinear transition when the bending deflection is around 2 mm in the first cycle bending. As the cycle proceeds, this linear–nonlinear transition is found at the maximum deflection of the previous cycle; meanwhile, the bending stiffness degrades. It is believed that the occurrence of microcracks inside the plaster frame is the mechanism behind the phenomenon. The silicone provides a strong network suppressing the abrupt crack propagation in a brittle material. The effects of the frame structure and plaster–silicone ratio were also compared. A high plaster content and large cell size tend to have a higher stiffness and obvious linear to nonlinear transition while it also has more significant stiffness degradation.

Cracked bi-Material Plates under Thermomechanical Loading

A bimaterial structure composed of two elastic plates bonded together by an interface with a normal (transverse) crack in the first plate and subjected to monotonically temperature and tension loading is considered. The interface is assumed to exhibit brittle failure at critical shear stress value or progressive damage in a cohesive zone preceding delamination. Using modified Shear lag model, the analytical solution is provided specifying the length of debonding. The critical lengths of a partial debonding along the interface are calculated and the limit value of temperature at full debonding is obtained. The analytical predictions are compared with experimental data and numerical results of Lemaitre and Song. The comparison shows a good agreement and proves the validity of the model used.

Engineering Model for Interfacial Stresses of a Heated Bimaterial Structure with Bond Material Used in Electronic Packages

A model is proposed for the shearing and peeling stresses occurring at the interface of two thin bonded objects as a function of the effect of bond materials at the interface. The existing uniform temperature model proposed by Suhir is upgraded to account for different temperatures of the layers by incorporating a temperature ratio parameter and eventually a correction factor to Suhir's model. Then the model is further upgraded to account for the linear temperature gradients in the layers by incorporating two temperature drop ratios and eventually a second correction factor. This upgraded model can be considered as a generalized one for predicting temperature conditions which may occur in the bonded materials. A simpler method of solution is used to develop this model which does not involve solving integro-differential equations as found in the Suhir's method. The results are presented for the case of die and die attach as commonly found in electronic packaging and are compared to the case where a bond is absent. The results are also compared with those obtained by Finite Element Method (FEM) analysis.

The Peeling Moment–A Key Rule for Delamination Resistance in I.C. Assemblies

The peeling stress near the free edge of a bimaterial beam under uniform temperature change creates a moment which causes both layers to have identical curvatures at the interface. A new formula from beam theory is given for this Peeling Moment. A beam with a negative Peeling Moment resists delamination at the free edge. A physical explanation for the moment is developed; the sign of the Peeling Moment is also the determinant of the location of the equivalent centroid of the bimaterial beam. This provides a valuable new rule for designing resistance to thermomechanical delamination of a bimaterial structure.

Elastic Plastic Analysis of Bimaterial Beams With Strain Hardening

Considerable attention has been paid to the bimaterial thermostat stress analysis problem as regards applications in microelectronic packaging. When a bimaterial beam is subjected to a temperature change, internal stress is developed that generates curvature. The present paper generalizes previous idealizations whereby a linear elastic material response has been assumed. We treat each of the beam materials as elastic-plastic with a bilinear response. A solution is obtained for the stress and deformation in the bimaterial structure following a “strength of materials” approach. While the solution is imperfect in that the stress free boundary conditions at the ends of the strip are not satisfied exactly, it does capture the overall behavior of the bimaterial beam but for the well-known end effect. Several numerical examples are presented using design data for materials commonly encountered in microelectronics applications.