TY - JOUR

T1 - Fracture toughness of bonds using interfacial stresses in four-point bending test

AU - Abdelhadi, Ousama M.

AU - Ladani, Leila

AU - Razmi, Jafar

N1 - Funding Information:
This work was supported by the National Research Foundation of Korea (NRF), funded by the Korea government (MSIP) (No. 2018R1D1A1B07048271). This research was also supported by Kyungpook National University Development Project Research Fund, 2019.

PY - 2011/12

Y1 - 2011/12

N2 - Bond strength is an important factor in electronic and photonic packaging. Measuring bond characteristics, strength, and fracture toughness is particularly difficult in microelectronic devices where miniaturized bonds are used (e.g.; wafer bonding and 3 dimensional integrated circuits). Since applying load directly to the bonds is proven difficult, four-point bending test with notched specimen has been typically used to facilitate fracture toughness measurements at small scale. This method is based on experiencing large peeling and shear stresses at the interface of two layers of different materials at the notch. However, there is a lack of analytical solution that can be used to determine the peeling and shear stresses at the interface of four-point bend specimen. This manuscript presents analytical modeling of peeling and shear stresses in tri-layer four-point bend specimens. Strength of materials approach with the assumption of small strains, within elastic region, is adopted in this study for evaluation of stresses and displacements. Furthermore, beam theory is utilized to develop equations that describe the moments and shear forces in the assembly due to the four-point bending loads. Second and fourth order differential equations are derived for shear and peeling stresses respectively at the interfaces of the assembly. Boundary conditions are determined based on load, supports and shear force and moment diagrams of the assembly. The problem solution is obtained by solving the governing differential equations instantaneously using standard methods. Finite-Element-based simulation is used to compare with and verify the analytical solution. This work also presents an alternative approach where the stresses at the notch are used to determine the fracture toughness. An experiment is conducted on a specimen with intermetallic material as bond material. The analytical approach is then verified with the results of four-point bending experiment and is validated using the conventional technique (which is based on energy equilibrium and presented by Eq. (60)).

AB - Bond strength is an important factor in electronic and photonic packaging. Measuring bond characteristics, strength, and fracture toughness is particularly difficult in microelectronic devices where miniaturized bonds are used (e.g.; wafer bonding and 3 dimensional integrated circuits). Since applying load directly to the bonds is proven difficult, four-point bending test with notched specimen has been typically used to facilitate fracture toughness measurements at small scale. This method is based on experiencing large peeling and shear stresses at the interface of two layers of different materials at the notch. However, there is a lack of analytical solution that can be used to determine the peeling and shear stresses at the interface of four-point bend specimen. This manuscript presents analytical modeling of peeling and shear stresses in tri-layer four-point bend specimens. Strength of materials approach with the assumption of small strains, within elastic region, is adopted in this study for evaluation of stresses and displacements. Furthermore, beam theory is utilized to develop equations that describe the moments and shear forces in the assembly due to the four-point bending loads. Second and fourth order differential equations are derived for shear and peeling stresses respectively at the interfaces of the assembly. Boundary conditions are determined based on load, supports and shear force and moment diagrams of the assembly. The problem solution is obtained by solving the governing differential equations instantaneously using standard methods. Finite-Element-based simulation is used to compare with and verify the analytical solution. This work also presents an alternative approach where the stresses at the notch are used to determine the fracture toughness. An experiment is conducted on a specimen with intermetallic material as bond material. The analytical approach is then verified with the results of four-point bending experiment and is validated using the conventional technique (which is based on energy equilibrium and presented by Eq. (60)).

KW - Four-point bending

KW - Fracture toughness

KW - Interfacial shear and peeling stresses

KW - Stress intensity factor

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U2 - 10.1016/j.mechmat.2011.09.006

DO - 10.1016/j.mechmat.2011.09.006

M3 - Article

AN - SCOPUS:80155214041

SN - 0167-6636

VL - 43

SP - 885

EP - 900

JO - Mechanics of Materials

JF - Mechanics of Materials

IS - 12

ER -