Mode I Fracture Load Predictions of Adhesive T-joints

This paper presents fracture data and a finite element analysis for adhesive T-joints, It is shown that fracture loads of T-joints, bonded with two different structural epoxies and subjected to either tensile loading or three-point bending, can be predicted using a fracture mechanics approach. Fracture loads were predicted by calculating the applied energy release rate, G, using finite element methods, and comparing that with a critical value, G_c, determined experimentally using double-cantilever-beam specimens. By recording the failure sequence of the bondline with a video camera attached to a microscope, it was seen that subcritical crack propagation took place prior to final fracture of the bondline. Accounting for the observed subcritical crack propagation in the finite element analysis gave a good agreement between the actual and the calculated fracture loads.     

Accelerated thermal fatigue of lead-free solder joints as a function of reflow cooling rate

Leadless chip resistor (LCR) assemblies were manufactured using both traditional tin-lead (Sn37Pb) and lead-free (Sn3.8Ag0.7Cu) solders. The leadfree test vehicles were assembled using three different cooling rates: 1.6°C/sec, 3.8°C/sec, and 6.8°C/sec. They were then exposed to accelerated thermalcycling (ATC) tests between 0°C and 100°C with a 10–14°C/min ramp rate and a 5-min dwell time. The test results indicated that these lead-free solder joints had better creep-fatigue performance than the tin-lead solder joints. The LCR built with the medium cooling rate showed the longest fatigue life compared with the resistors built with the normal cooling rate of 1.6°C/sec and the higher cooling rate 6.8°C/sec. The number of cycles to failure was significantly correlated to the void defect rate. Failure analyses were done using cross-sectioning methods and scanning electron microscopy (SEM). Finite-element models were built to analyze the inelastic, equivalent strain range in solder joints subjected to thermal-cycling conditions with different degrees of solder wetting. The results indicated that poor wetting increases strains throughout the joint significantly, which is in accordance with the ATC results.     

Thermal stress concentration factors for defects in plated-through-vias

Plated-through-vias (PTVs) are subject to thermal stress during soldering and in service. Plating and manufacturing defects in the PTV walls (barrels) can create stress concentrations that frequently become the sites of crack initiation during thermal fatigue. This is of growing concern as processing temperatures increase due to the use of lead-free solders, and boards become thicker generating increased stress as PTV aspect ratios rise, making it more difficult to achieve uniform plating thickness throughout the barrel. Finite element analysis (FEA) has been used to develop correlations that can be used to calculate the stress concentration factors (SCFs) for five typical defects as a function of various geometric parameters. In terms of their severity, the defects were ranked as: (1) rapid thickness reduction (SCF  13), (2) occasional waviness (SCF  4.6), (3) gradual thickness reduction (SCF  4), (4) wicking (SCF  4) and (5) waviness (SCF  3.1). The SCF due to an internal pad and the influence of an external pad-barrel corner crack were also investigated. The maximum stress at the defect is found by multiplying the SCF by the von Mises stress at the mid-plane of the corresponding idealized PTV. The latter can be found using either an analytical model or correlations as a function of the aspect ratio and board-to-barrel thickness ratio that were developed using FEA.     

An Analytical Elasto-Creep Model of Solder Joints in Leadless Chip Resistors: Part 1—Development and Verification

A novel two-dimensional model is presented for multiaxial thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of solder joints in leadless chip resistor (LCR) assemblies. The model is applicable to both plane stress and plane strain conditions, and incorporates both global and local expansivity mismatches. Interfacial thermal stresses are approximated using elementary strength of materials theory under arbitrary time-dependent thermal loading. Partial differential equations are linearized through a simple finite difference discretization procedure. The model is mathematically straightforward, and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The paper presents comparisons with finite element results and considers the mechanics of solder creep accumulation and stress relaxation as predicted by the model.     

Comparison of Weibull small samples using Monte Carlo simulations

The evaluation of the functional reliability of different designs is a common task and times to failure can be compared using the likelihood ratio test. In the microelectronics industry, as in many others, the high cost of testing places severe restrictions on the sample size. Moreover, the products in these tests are often new and do not have previous reliability histories. These factors make the selection of the Type I and Type II errors in comparison tests very difficult. This paper presents the Monte Carlo simulation results of Type II errors for the likelihood ratio test of comparison as a function of the Type I error and the (small) sample size. Our conclusions are summarized as follows: (1) the common microelectronics industry standard sample size of 32 is often insufficient to reach satisfactory conclusions; (2) small sample tests should only be used for prescreening for significant differences; and (3) when only small samples are available, the Type I and the Type II errors must be selected carefully to prevent misleading conclusions. Copyright © 2006 John Wiley & Sons, Ltd.     

Crack path selection in the fracture of fresh and degraded epoxy adhesive joints

The crack paths and fracture surfaces of aluminum–epoxy adhesive joints were characterized as a function of the mode ratio of loading and the amount of degradation that had been generated using the open-faced aging technique. A finite element (FE) model was used to predict the extent of the plastic zone at different crack growth lengths and mode ratios, and a close relationship was found between the evolution of the plastic zone and the previously reported R-curve behavior of these joints. The micro-topography of the fracture surfaces, measured using an optical profilometer, showed that a ductile–brittle transition occurred in the fracture behavior of the joints as degradation progressed. The crack path in the (brittle) degraded specimens was normal to the first principal stress, but could not be predicted in the undegraded joints because of its highly three-dimensional nature. Based on the distribution of the maximum von Mises stress in the adhesive layer ahead of the crack tip, a crack growth mechanism was proposed that is consistent with these experimental observations and explains the highly three-dimensional nature of fracture in these highly constrained joints.     

Blistering as a Form of Degradation in Adhesive Joints

Water-filled blisters were observed to form during accelerated aging experiments with aluminum adherends and two structural epoxy adhesives. Both closed adhesive joints and open-face specimens were affected. The blisters grew with time, originated both in the adhesive and at the epoxy-aluminum interface, and were found only at 100% relative humidity at both 65°C and 85°C; blisters were never observed at 85% relative humidity or lower. The same water-soluble ionic species were found in the blister liquid, the two adhesives and water that had been in contact with adhesive samples for an extended period. It is proposed that the blisters grew under the influence of osmosis, originating in water clusters at microscopic voids. Contamination of the aluminum adherends by residual etching solution, although not a necessary precondition for blistering, could facilitate this process by lowering the partial pressure at which water condenses and by creating higher osmotic pressures.     

Jet properties and mixing chamber flow in a high-pressure abrasive slurry jet: part I—measurement of jet and chamber conditions

Techniques to enhance the performance of a high-pressure abrasive slurry jet micro-machining process (HASJM) were investigated by altering the conditions within the jet. The slurry flow rate was controlled using six inlet tubes (cross-sectional areas of 0.2, 0.46, 1.27, 1.77, 3.08, and 4.51 mm²), and was found to have a large effect on the conditions within the mixing chamber. The tubes permitted the use of high-concentration slurry solutions, which resulted in increased machining rates and the ability to machine glass targets without cracking by using a minimum particle concentration of 17 wt%. Slurry tubes producing large slurry flow rates caused the mixing chamber to flood, resulting in a much lower jet velocity. The size of the smallest slurry tube size that caused the mixing chamber to flood was dependent on the pump operating pressure, and varying from 1.27 mm² at 134 MPa, to 1.5 mm² at 233 MPa. Mixing chamber flooding significantly reduced the erosion rate of the jet and increased the machining time, as discussed in the second part of this two-part paper. Mixing chamber pressures were found to be low enough to cause boiling, which increased the jet diameter and the width of features that could be machined without a mask.     

Indentation-induced buckling of organic coatings part II: measurements with impacting particles

The impact-induced buckling and delamination of a thin coating was analysed for the purpose of predicting the amount of coating removed when a single particle was launched, at a given velocity, against a coated substrate. A novel post-buckling analysis is presented in which the coating is modelled as a clamped disk prevented from buckling at an arbitrarily set inner radius, due to the presence of the indenting particle. A method for calculating the arrest strain energy release rate and mode mix of interfacial delamination cracks, based on the coupling of the presented buckling analysis with an existing strain energy release rate analysis is then presented. A method to estimate the critical interfacial shear stress at crack initiation is also outlined. An accompanying paper compares experimental results with the results of this analysis, and shows how the results can be used in the context of blast cleaning.     

Analytical Peel Load Prediction as a Function of Adhesive Stress Concentration

Peel data for two epoxy adhesives and a recent model of the adhesive stresses in the peel geometry are used to investigate the effectiveness of two constitutive models and several adhesive failure criteria. The failure criteria are based on either the critical strain energy-release rate or the critical von Mises strain at the peel root, both taken as functions of the “loading zone length” (LZL), defined as a measure of the degree of stress concentration at the root of the peeling adherend. The peel model uses LZL as an independent parameter that captures the effects of the peel angle, adherend thickness, and the mechanical properties of the adhesive and adherend. Both the energy- and strain-based failure criteria can be used to predict the steady-state peel load with an average absolute error of less than 10% over the range of conditions that were examined.