Assessed Interfacial Strength and Elastic Moduli of the Bonding Material from Shear-Off Test Data

“By asking for the impossible, obtain the best possible."

—Italian saying

Background/Incentive

Lap shear testing is widely performed to evaluate the interfacial shear strength and stiffness of composite materials, assemblies, and structures. Outside the field of electronic materials, such testing is usually carried out on fasteners, such as bolts, machine screws, and rivets. In electronics materials science, shear testing is performed to determine the shear strength of a bonding material (adhesive, solder) and can also be used to compare between different bonding materials and/or their thicknesses and/or for different lots for the same bonding material. Here is a brief summary of the existing shear test methods and standards.

ASTM D1002 addresses shear strength of single-lap-joint adhesively bonded metal specimens by tension loading and could be viewed as the most common standard test involving shear. ASTM D732 is the standard test method for shear strength of plastics by using a punch tool. ASTM D2344 is the standard test method for short-beam strength of polymer composite materials and laminates. ASTM D3163 is a standard test method for determining strength of adhesively bonded plastic lap-shear joints in shear by applying tension loading. ASTM D3164 is another standard test method for strength properties of adhesively bonded plastic lap-shear “sandwich” in shear by tension loading. ASTM D5868 provides a test method for lap shear adhesion for fiber reinforced plastic bonding. ASTM D5379 suggests double notch off-axis test rail shear test, as well as torsion tests to check adhesion. Inter-laminar shear strength (ILSS) procedure is suggested by EN ISO 14130, which replaced, with input from. ASTM D2344 and other standards. The test only provides an “apparent” shear strength using an assumed isotropic material stress distribution. This excludes the effect of other stresses due to the flexural loading and contact points. In addition, as follows from the analysis carried out in this paper, the interfacial shearing stress is distributed highly nonuniformly along the interface when shear-off tests are conducted. This important circumstance is not considered by this standard.

The bonding strength of various attachment materials, both adhesives and solders, has always been of significant importance in electronics system engineering and, hence, of great interest to reliability engineers, including modeling effort; therefore, the published work in this field, mostly experimental, is enormous (see, for example, [1-29]). The main shearing strength-related reliability standards in electronics are ASTM F1269-89 "Test Methods for Destructive Shear Testing of Ball Bonds,” 1991 Annual Book of ASTM Standards, vol. 10.04, 1991, ASTM, Philadelphia and JESD22-B117 "BGA Ball Shear,” July 2000, JEDEC Solid State Technology Association.

During the last decade or so, silver sintering has become increasingly important as an attractive bonding technique in power and, particularly, automotive electronics [30-47]. There is an indication that silver sintered pastes have excellent adhesion strength, good performance in active power cycling and in temperature cycling, high thermal stability, and improved performance over tin-silver-copper (SAC) and other lead-free solders widely used today. The bottleneck of the modeling effort, as far as design-for-reliability (DfR) with silver sintering technology is concerned, is the availability of the trustworthy information about the ultimate strength and mechanical properties of the silver sintering material, especially having in mind that these properties might be dependent on the fabrication conditions and the two adherents between which the bonding layer is sandwiched. Accordingly, in the analysis that follows, a simple and physically meaningful analytical stress model is developed in application to shear-off testing of a bonded assembly with an objective to evaluate the magnitude and the distribution of the interfacial shearing stress in the bonding material from the measured shear-off force. The model can also be used for the evaluation of the shear modulus of the bonding material if the corresponding interfacial displacement is also concurrently measured. The experimental data obtained using the suggested model for interpreting shear-off experimental data will enable one to develop a silver sintering material with the best power cycle performance. The model can also be used, of course, for conventional solders and adhesives, including developing of a suitable standard. The model was also used to explain the physics of specially prepared shear-off testing specimens suggested by J. Kivilahti and T. Reinikainen [48-50] to obtain the most accurate information of the solder material properties.

Basic Equation

Consider a bonded elongated assembly schematically shown in Figure 8.1. Its lower component #2 (“substrate”) is rigidly attached to the tester, and the upper component #1 (“chip”) is subjected to an external shearing force T. Using the concept of the interfacial compliance [19] (see Chapter 2), the longitudinal interfacial displacements of these components can be sought in the form

FIGURE 8.1 Bimaterial bonded assembly subjected to shear-off testing.

where the force

acting in the cross sections of component #1 can be found by subtracting the force

acting in the cross sections of component #2 from the total external force T x(x) is thus far unknown interfacial shearing stress;

are the axial compliances of the assembly components; E and E₂ are Young’s moduli of the materials; v, and v₂ are their Poisson’s ratios; h and h₂ are the component thicknesses;

are the interfacial compliances of the components [19]; and

are the shear moduli of the component materials. The origin of the coordinate x is at the left end of the assembly.

The first terms in expressions (8.1) are the displacements of the components’ cross sections caused by the forces T(x) and T₂(x) and determined based on Hooke’s law assuming that all the points of the given cross section of the given component have the same axial displacements. The second terms in (8.1) are, in effect, corrections to this assumption. They consider that the longitudinal interfacial displacements are somewhat greater than the displacements of the inner points of the cross section. The structure of these terms reflects an assumption that the corrections in question can be found as the product of the interfacial compliance of the component and the interfacial shearing stress acting in the given cross section. This is, actually, the substance of the concept of the interfacial compliance (8.19).

The condition of the compatibility of the displacements (8.1) can be written as

where

is the interfacial compliance of the bonding layer, h₀ is its thickness, and G₀ =--—

2(1 + v₀)

is its shear modulus. Introducing expressions (8.1) into the displacement compatibility condition (8.7), the following equation for the sought interfacial shearing stress function x(x) can be obtained:

Here,

is the total interfacial compliance of the assembly and

is its total axial compliance. It is noteworthy that while the total longitudinal interfacial compliance considers the compliance of the bonding layer, the axial compliance is due to the two bonded components only. This assumption is valid as long as the bonding layer is thin, and its Young’s modulus is significantly lower than the Young’s moduli of the component materials. This is usually the case in bonded electronic assemblies.

Differentiating equation (8.9) with respect to the longitudinal coordinate x and considering that, in accordance with relationship (8.2),

the following basic differential equation for the force T] (jc) can be obtained:

Solution to the Basic Equation

The solution to the differential equation (13) can be sought as

Introducing this solution into equation (8.13), one could conclude that this equation is fulfilled, if the relationships

take place. The first formula determines the parameter of the interfacial shearing stress, and the second formula defines the particular solution to the differential equation (8.13). The constants C, and C₂ of integration can be found from the boundary conditions 7,(0) = 0 and 7,(2/) = —T and are as follows:

Then, solution (8.14) yields

Interfacial Shearing Stress

Formula (8.2) indicates that the interfacial shearing stress can be found from (8.17) by differentiation:

This stress changes from

at the origin to its maximum value

at the end, where the external force is applied. For long enough assemblies with stiff interfaces (ft/ > 2.5), the shearing stress (8.19) becomes next-to-zero, and the stress

(8.20) is

This formula indicates that the maximum interfacial shearing stress is proportional

to the parameter к of the interfacial shearing stress and to the ratio of the axial

compliance of component #1 that experiences the direct action of the applied force to the total axial compliance of the assembly. For very short assemblies with compliant interfaces, when cosh 2ft/ can be put equal to one, formulas (8.19) and (8.20) provide the same result. When the force T is measured, the induced interfacial shearing stress can be evaluated, for a long enough specimen, by using formula

(8.21) . Note that if the assembly is fabricated at an elevated temperature and is subsequently cooled down by the temperature Д/ to a low (room, testing) temperature, it experiences already thermally induced stresses caused by the thermally induced force

where Да is the difference in the CTE of the bonded components. If this force is appreciable, formula (8.21) should be replaced with formula

to consider for the fact that the bonding material is subjected to the combined action of the thermally induced and mechanical loading, and its actual ultimate bonding strength is, in effect, higher than that predicted by formula (8.21).

Shear Modulus of the Bonding Material

The maximum interfacial displacement can be found as

Then, the parameter ft of the interfacial shearing stress is

Using the first formula in (8.15), we have:

Then, using formula (8.10), one can determine the interfacial compliance of the bonding material as

Then, the shear modulus of this material can be found as

By assuming a suitable Poisson’s ratio of the bonding material, its Young’s modulus could be tentatively assessed as