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This article provides an introduction to architected cellular materials, their design, fabrication, and application domain. It discusses design decisions involving the selection, sizing, and spatial distribution of the unit cell, property-scaling relationships, and the integration of cells within an external boundary. It describes how manufacturing constraints influence achievable feature resolution, dimensional accuracy, properties, and defects. It also discusses the mechanical behavior of architected cellular materials and the role of additive manufacturing in their fabrication.

Architected materials such as lattices are capable of demonstrating extraordinary mechanical performance. Lattices are often used for their stretch-dominated behavior, which gives them a high degree of stiffness at low-volume fractions. At the other end of the stiffness spectrum, bending-dominated lattices tend to be more compliant and are of interest for their energy absorption performance. Here, we report a class of ultra-compliant interwoven lattices that demonstrate up to an order of magnitude improvement in compliance over their traditional counterparts at similar volume fractions. This is achieved by selectively decoupling nodes and interweaving struts in bending-dominated lattices, inspired by observations of this structural principle in the lattice-like arrangement of the Venus flower basket sea sponge. By decoupling nodes in this manner, we demonstrate a simple and near-universal design strategy for modulating stiffness in lattice structures and achieve among the most compliant lattices reported in the literature.

Biodiversity provides a massive library of ideas for bio-inspired design, but the sheer number of species to consider can be daunting. Current approaches for sifting through biodiversity to identify relevant biological models include searching for champion adapters that are particularly adept at solving a specific design challenge. While the champion adapter approach has benefits, it tends to focus on a narrow set of popular models while neglecting the majority of species. An alternative approach to bio-inspired design is the comparative method, which leverages biodiversity by drawing inspiration across a broad range of species. This approach uses methods in phylogenetics to map traits across evolutionary trees and compare trait variation to infer structure–function relationships. Although comparative methods have not been widely used in bio-inspired design, they have led to breakthroughs in studies on gecko-inspired adhesives and multifunctionality of butterfly wing scales. Here we outline how comparative methods can be used to complement existing approaches to bio-inspired design, and we provide an example focused on bio-inspired lattices, including honeycomb, and glass sponges. We demonstrate how comparative methods can lead to breakthroughs in bio-inspired applications as well as answer major questions in biology, which can strengthen collaborations with biologists and produce deeper insights into biological function.

Scanning Electron Microscopy (SEM) is traditionally leveraged to image fracture surfaces and generate information for analysis. Conventionally, experts identify patterns of interest in SEM images and link them to fracture phenomena based on knowledge and experience. Such practice has substantial limitations. It relies on expert opinions for decision-making, which poses barriers for practitioners without relevant background; manual inspection must be done for individual SEM images, thus time-consuming and inapt for industrial automation. There is a genuine demand for a fast, automatic method for fractographic pattern recognition. Targeting the problem, this study proposes a two-stage data-driven approach based on clustering. In offline analysis (Stage 1), a clustering algorithm identifies the generic fractographic patterns on part. Each pattern corresponds to a cluster. Expert evaluation of the part’s crack status is leveraged to map individual patterns (clusters) to a crack type. In in-situ monitoring (Stage 2), SEM images of new parts are matched to the clusters from stage 1, which reveals the generic patterns on the part and indicates the potential crack status. The proposed approach enables automatic fractographic analysis without experts. It is demonstrated to be effective on real SEM images of additively manufactured Inconel-718 specimens subjected to high cycle fatigue.

This review article summarizes the current state-of-the-art for biomimicry in additive manufacturing. Biomimicry is the practice of learning from and emulating nature - which can be increasingly realized in engineering applications due to progress in additive manufacturing (AM). AM has grown tremendously in recent years, with improvements in technology and resulting material properties sometimes exceeding those of equivalent parts produced by traditional production processes. This has led to the industrial use of AM parts even in highly critical applications, most notably in aerospace, automotive and medical applications. The ability to create parts with complex geometries is one of the most important advantages of this technology, allowing the production of complex functional objects from various materials including plastics and metals that cannot be easily produced by any other means. Utilizing the full complexity allowed by AM is the key to unlocking the huge potential of this technology for real world applications – and biomimicry might be pivotal in this regard. Biomimicry may take different forms in AM, including customization of parts for individuals (e.g. medical prosthesis, implants or custom sports equipment), or optimization for specific properties such as stiffness and light-weighting (e.g. lightweight parts in aerospace or automotive applications). The optimization process often uses an iterative simulation-driven process analogous to biological evolution – with an improvement in every iteration. Other forms of biomimicry in AM include the incorporation of real biological inputs into designs (i.e. emulating nature for its unique properties); the use of cellular or lattice structures – for various applications and customized to the application; incorporating multi-functionality into designs; the consolidation of numerous parts into one and the reduction of waste, amongst others. Numerous biomimetic design approaches may be used – broadly categorized into customized/freeform, simulation-driven and lattice designs. All these approaches may be used in combination with one another, and in all cases with or without direct input from nature. The aim of this review is to unravel the different forms of biomimetic engineering that are now possible – focusing mainly on functional mechanical engineering for end-use parts, i.e. not for prototyping. The current limits of each design approach are discussed and the most exciting future opportunities for biomimetic AM applications are highlighted.

Architected cellular materials encompass a wide range of design and performance possibilities. While there has been significant interest in periodic cellular materials, recent emphasis has included consideration of aperiodicity, most commonly in studies of stochastic and graded cellular materials. This study proposes a classification scheme for aperiodic cellular materials, by first dividing the design domain into three main types: gradation, perturbation, and hybridization. For each of these types, two design decisions are identified: (i) the feature that is to be modified and (ii) the method of its modification. Considerations such as combining different types of aperiodic design methods, and modulating the degree of aperiodicity are also discussed, along with a review of the literature that places each aperiodic design within the classification developed here, as well as summarizing the performance benefits attributed to aperiodic cellular materials over their periodic counterparts.

Advances in additive manufacturing, computational design tools, and digitization techniques are converging in an exciting new era of engineering design, as humanity has never experienced before. Within this convergent domain, Bio-Inspired Design (BID) is a particularly promising area of research since the potential space for establishing structure-function correlation is vast, and the majority of it is untapped. In this chapter, bio-inspired design is first introduced, specifically in the context of the Laser Powder Bed Fusion (L-PBF) process. Practical approaches for implementing BID for L-PBF are discussed, followed by a discussion of key general design concepts that can be abstracted for BID. Examples of how BID and L-PBF have been combined are then presented, followed by a consideration of some of the most important design constraints posed by the L-PBF process that the bio-inspired designer needs to be aware of. The chapter concludes with a forward looking discussion of opportunities in this domain.

The characterization of additively manufactured cellular materials, such as honeycombs and lattices, is crucial to enabling their implementation in functional parts. One of the characterization methods commonly employed is mechanical testing under compression. This work focuses specifically on the dependence of these tests to the applied strain rate during the test over low strain rate regimes (considered here as 10−6 to 10−1 s−1). The paper is limited to the study of strain the rate dependence of hexagonal honeycomb structures manufactured with four different additive manufacturing processes: one polymer (fused deposition modeling, or material extrusion with ABS), one composite (nylon and continuous carbon fiber extrusion) and two metallic (laser powder bed fusion of Inconel 718 and electron beam melting of Ti6Al4V). The strain rate sensitivities of the effective elastic moduli, and the peak loads for all four processes were compared. Results show significant sensitivity to strain rate in the polymer and composite process for both these metrics, and mild sensitivity for the metallic honeycombs for the peak load. This study has implications for the characterization and modeling of all mechanical cellular materials and makes the case for evaluation and if appropriate, inclusion, of strain rate effects in all cellular material modeling.

The design of cellular materials has recently undergone a paradigm shift, enabled by developments in Additive Manufacturing and design software. No longer do cellular materials have to be limited to traditional shapes such as honeycomb panels or stochastic foams. With this increase in design freedom comes a significant increase in optionality, which can be overwhelming to the designer. This paper aims to provide a framework for thinking about the four key questions in cellular material design: how to select a unit cell, how to vary cell size spatially, what the optimal parameters are, and finally, how best to integrate a cellular material within the structure at large. These questions are posed with the intent of stimulating further research that can address them individually, as well as integrate them in a systematic methodology for cellular material design. Different state-of-the-art solution approaches are also presented in order to provoke further investigation by the reader.

Recent developments in design and manufacturing have greatly expanded the design space for functional part production by enabling control of structural details at small scales to inform behavior at the whole-structure level. This can be achieved with cellular materials, such as honeycombs, foams and lattices. Designing structures with cellular materials involves answering an important question: What is the optimum unit cell for the application of interest? There is currently no classification framework that describes the spectrum of cellular materials, and no methodology to guide the designer in selecting among the infinite list of possibilities. In this paper, we first review traditional engineering methods currently in use for selecting cellular materials in design. We then develop a classification scheme for the different types of cellular materials, dividing them into three levels of design decisions: tessellation, element type and connectivity. We demonstrate how a biomimetic approach helps a designer make decisions at all three levels. The scope of this paper is limited to the structural domain, but the methodology developed here can be extended to the design of components in thermal, fluid, optical and other areas. A deeper purpose of this paper is to demonstrate how traditional methods in design can be combined with a biomimetic approach.

The honeybee&rsquo, s comb has inspired the design of engineering honeycomb core that primarily abstract the hexagonal cell shape and exploit its mass minimizing properties to construct lightweight panels. This work explored three additional design features that are part of natural honeybee comb but have not been as well studied as design features of interest in honeycomb design: the radius at the corner of each cell, the coping at the top of the cell walls, and the interface between cell arrays. These features were first characterized in natural honeycomb using optical and X-ray techniques and then incorporated into honeycomb core design and fabricated using an additive manufacturing process. The honeycomb cores were then tested in out-of-plane compression and bending, and since all three design features added mass to the overall structure, all metrics of interest were examined per unit mass to assess performance gains despite these additions. The study concluded that the presence of an interface increases specific flexural modulus in bending, with no significant benefit in out-of-plane compression, coping radius positively impacts specific flexural strength, however, the corner radius has no significant effect in bending and actually is slightly detrimental for out-of-plane compression testing.

Lattice structures have tailorable mechanical properties which allows them to exhibit superior mechanical properties (per unit weight) beyond what is achievable through natural materials. In this paper, quasi-static and dynamic behavior of additively manufactured stainless steel lattice cylinders is studied. Cylindrical samples with internal lattice structure are fabricated by a laser powder bed fusion system. Equivalent hollow cylindrical samples with the same length, outer diameter, and mass (larger wall thickness) are also fabricated. Split Hopkinson bar is used to study the behavior of the specimens under high strain rate loading. It is observed that lattice cylinders reduce the transmitted wave amplitude up to about 21% compared to their equivalent hollow cylinders. However, the lower transmitted wave energy in lattice cylinders comes at the expense of a greater reduction in their stiffness, when compared to their equivalent hollow cylinder. In addition, it is observed that increasing the loading rate by five orders of magnitude leads to up to about 36% increase in the peak force that the lattice cylinder can carry, which is attributed to strain rate hardening effect in the bulk stainless steel material. Finite element simulations of the specimens under dynamic loads are performed to study the effect of strain rate hardening, thermal softening, and the failure mode on dynamic behavior of the specimens. Numerical results are compared with experimental data and good qualitative agreement is observed., Comment: 20th Biennial Conference of the APS Topical Group on Shock Compression of Condensed Matter

In much of the existing research, SnAgCu solder alloys are characterized at low strain rates, typically in the 10-6 to 1 s-1 range. In this paper, we report experimental results and constitutive models for two popular SnAgCu solder alloys at intermediate and high strain rates, ranging from 10-2 to 103 s-1 at room temperature. These experiments were performed using two different experimental setups: a MTS 810 uniaxial compression tester, and a split-Hopkinson pressure bar. In conjunction with our previous work at lower strain rates (10-6 to 10-3 s-1), these results yield the plastic flow response of these solders over nine decades of strain rate, and demonstrate a remarkably consistent relationship between the yield stress and the strain rate over the entire nine decades. We also develop the Anand viscoplastic constitutive model, and demonstrate that fit parameters for the low-strain rate regime can be extrapolated to accurately predict the experimental response at high strain rates. Thus, the model presented here proffers the capability of modeling solder deformation under a wide range of loading conditions using most commercially available finite element (FE) programs. To illustrate the validity of the model parameters, we develop idealized FE models together with cohesive zone failure descriptions at the interface between the solder and the intermetallic compound. We demonstrate that when used in conjunction with appropriate failure models, the constitutive model developed here accurately captures the empirically observed shift in failure modes from bulk failure to interfacial failure under tensile loading at higher strain rates.

An approach to modeling failure that is inspired by two experimentally observed facts is presented. These observations are: (1) cracks grow as the end result of a irreversible, dissipative process, and (2) fracture has an inherent lengthscale, timescale and/or spatial hierarchy influenced by the (possibly dynamically changing) microstructural state. The second of these facts enables one to view the seemingly deterministic cracks observed at higher levels of hierarchy as resulting from uncertain events at lower-levels of hierarchy associated with microstructural variations. A key mathematical result developed in Information Theory together with the maximum entropy principle of Statistical Mechanics is utilized to derive a form of damage that is “maximally non-committal” about microstructural uncertainty in lower levels of fracture hierarchy. The irrecoverable energy that is expended in the creation of new surfaces or in plastic dissipation is associated with the microstructural damage using continuum therm...

In this study, we focus on investigating the nature of the stress and strain behavior in solder joints and their effect on the hybrid damage modeling approach, which is inspired by cohesive zone modeling and Weibull functions [Towashiraporn, et al., 2005, “A Hybrid Model for Computationally Efficient Fatigue Fracture Simulations at Microelectronic Assembly Interfaces,” Int. J. Solids Struct., 42(15), pp. 4468–4483]. We review well understood principles in elastic-plastic fracture mechanics and more recent work in cohesive zone modeling, that address the nature of the singular solutions at the crack tip and provide insight when dealing with the more complex problem of solder joint fracture. Using three-dimensional finite element analysis of a chip scale package, we systematically examine the stress-strain behavior at the edge of the solder joint along the interface. The singular nature of the behavior manifests itself as mesh dependence of the predicted crack front shape and the cycles to failure. We discuss the conditions under which the predicted crack growth rate is of reasonable accuracy by incorporating a characteristic length measure. We validate predictions made by the hybrid damage modeling approach against a companion experimental study in which crack growth was tracked in packages subjected to accelerated thermal cycling.

Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys, the importance of the load history, and the wide variation in package constructions employed by the microelectronics industry. While material behavior can be captured by means of valid constitutive models, the empirical failure models in common use are strongly dependent on package construction due to the fact that they are derived from tests of solder joints with heterogeneous stress and microstructural variation. Despite this limitation, the empirical models have been used to identify reliable choices among package design alternatives. In this technical brief, some of the key limitations that the user of empirical models must be aware of are addressed. Physical arguments are proposed in order to justify the appropriate assumptions that may be made in the life model. Using data from two different sources in the literature, the constants in the empirical models are shown to be dependent on the solder joint geometry. Alternative fits to experimental data that reduce the dependence of the fits on solder joint geometry are proposed.

Extensive failure analysis was performed on identical, isothermally cycled wafer-level chip scale packages with Sn3.8wt%0.7wt%Ag (SAC387) solder joints. Packages were periodically removed during the cycling process to observe crack front progression. The packages were dipped in liquid nitrogen to reduce solder ductility and then pried apart. The crack areas were observed under an optical microscope. The average crack areas on the corner and mid-edge joints of the package were measured using an image processing software. 50 packages were characterized from 240 to 7200 cycles at every 240 cycles. An average of 20 solder joints per cycle was observed to estimate the crack length and area. A finite element model of this package was constructed in ABAQUS. The solder interconnects of the model were given full plastic and creep properties. Using the failure analysis data and the finite element model, the material constant value in a previously developed hierarchal fracture model was calibrated for SAC387. The ability of the model to predict non-intuitive failure initiation sites due to the under bump metallurgy (UBM) geometry is demonstrated. The hierarchal fracture process model was inspired by information theory and continuum thermodynamics. It was earlier proposed to capture the length-scale and temporal hierarchy inherent in quasi-static fracture processes. This single parameter model allows for a non-empirical, geometry independent approach to predicting crack growth by relating equivalent inelastic dissipations and a material constant to the probability of fracture at a material point.

In heterogeneous micro structures that include several grains, secondary phases and interfaces, cracks are known to initiate and grow through different mechanisms. The failure processes however are not well understood. Solder alloys in general, and Pb-free alloys in particular possess complex, heterogeneous microstructures that evolve in fracture in ways that are challenging to model. Often, underlying a fracture observed under a microscope is a hierarchy of fracture-related phenomenon from atomic to macro length-scales. In this paper we develop a failure model inspired by information theory and continuum thermodynamics to capture the multiscale fracture processes in solder joints. We systematically develop measures of dissipation from continuum thermodynamics for materials described by J2 plasticity theory. Crack growth is known to be dissipative and such measures are natural candidates for predicting failure within a mechanics framework. The dissipation estimates, multiple fracture mechanisms and the notions of continuity, monotonicity and composition borrowed from information theory suggest a single model as being capable of predicting both ductile and brittle types of failures.Copyright © 2009 by ASME

The hierarchal fracture process model is a theory derived from continuum thermodynamics and information theory. This single parameter model provides a non-empirical approach able to predict crack growth for solder interconnects regardless of package or solder interconnect geometry. The model relates inelastic dissipations to the probability of failure at a given material point. The hierarchal fracture process model is used to predict crack growth and fatigue lives in a package with atypical solder interconnect geometry: a quad-flat-no-lead (QFN) package. The fracture model uses the material parameter calibrated for Sn3.8wt%0.7wt%Cu solder in a previous study of wafer-level CSP packages. Finite element models of these packages are created in ABAQUS with the solder interconnects given full creep and plastic properties. The results obtained from the hierarchal fracture process model are validated against the experimentally obtained fatigue lives and cross-sectional images of the crack path.Copyright © 2009 by ASME

Significant work has been done on the characterization of SnAgCu solder alloys at low strain rates (10−6 to 10−2 s−1 ), and as a result, the behavior of solder over these strain rate regimes is well understood. On the other hand, there is a lack of accurate and consistent data for solder at high strain rates. In this paper, we will present data obtained using a servo-hydraulic mechanical tester and split-Hopkinson bar for the Sn3.8wt%Ag0.7wt% Cu solder alloy over strain rates spanning 0.001 to 500s−1 . It is shown that the saturation stress correlates well with strain rate over nine decades on a log-log plot. It is also shown that a fit using Anand model based on low strain rate regime (4×10−6 to 2×10−4 s−1 ) data captures the high strain rate results to a reasonable accuracy. It is commonly observed that in low strain rate failure, as in thermo-mechanical fatigue, failure tends to occur through the bulk of the solder. However in high strain rate failures, as those seen in drop tests, fractures occur through the intermetallic layer. We present finite element simulations of ball shear and ball pull tests using the above high strain rate data. It is demonstrated how the shift in failure mode from the bulk solder to intermetallic compound may be explained based on the high strain rate behavior of the SnAgCu solder alloy.Copyright © 2009 by ASME

The problem of solder joint fatigue is essentially one of fatigue crack growth. However, little work has been done that enables fatigue life predictions by means of tracking the crack front and its growth. Most popular fatigue life models are empirical and therefore, limited in their applicability and in the insight they provide. Analytical fracture mechanics approaches such as the Paris law and the J-integral are of questionable validity due to the fact that several assumptions made in these approaches are not appropriate in the context of solder joint fatigue. Failure in solder joints involves large plastic deformation in a viscoplastic material along with crack growth which is not self-similar and is significantly large relative to the size of the joint. Accurate descriptions of crack growth in solder joints can thus be obtained only by means of an approach that includes (a) the complete constitutive behavior of solder and (b) a non-empirical failure model that does not make the limiting assumptions of small cracks or self-similar crack growth. One such promising approach is the hybrid damage modeling approach, which is inspired by cohesive zone modeling and Weibull functions. In this study, we focus on investigating the nature of the stress and strain behavior in solder joints and its effect on the hybrid model. We review well understood principles in elastic-plastic fracture mechanics and more recent work in cohesive zone modeling, that address the nature of the singular solutions at the crack tip and provide insight when dealing with the more complex problem of solder joint fracture. Using three dimensional finite element analysis of a chip scale package (CSP), we systematically examined the stress-strain behavior at the edge of the solder joint along the interface. The singular nature of the behavior manifests itself as mesh dependence of the predicted crack front shape and the cycles to failure. We discuss the conditions under which the predicted crack growth rate is of reasonable accuracy, by incorporation of a characteristic length measure. We validate predictions made by the hybrid damage modeling approach against a companion experimental study in which crack growth was tracked in packages subjected to accelerated thermal cycling. In the first part, we discussed the effects of choice of constitutive model (elasticity, deformation and incremental plasticity and creep) and finite deformation on the nature of the singularity at the crack tip and the resulting mesh sensitivity. We used a conventional crack-in-plate analysis to first study the effects and then investigate similar effects in the more complex problem of a solder joint. In the second part, presented here, a characteristic length is introduced in an attempt to mitigate the mesh dependence, and shown to improve results for the predictions of crack growth in both, the crack-in-plate and the solder joint models.

Predicting reliability of solder joints requires a thorough understanding of solder constitutive behavior. Recent studies on SnAgCu solder alloys have reported that pre-test conditions of aging-time and aging-temperatures can be factors that significantly affect solder constitutive behavior. The results presented here are a part of ongoing efforts to construct constitutive models that can predict aging affects on behavior of SnAgCu solder alloys. In this work, creep test results on aged Sn3.8Ag0.7Cu samples are reported, and aging effects are discussed primarily on secondary creep behavior and on microstructure. Aging effects on primary creep are observed, and will be discussed, and modeled in a future work. Experiments to characterize behavior were carried out using double-lap shear tests on specimens specifically prepared to represent realistic microstructures, and mitigate effects of joint geometry, and stress heterogeneity during test conditions. Aging temperatures of -10deg C, 25deg C, 75deg C and 125deg C, and aging times of 15, 30, 60 and 90 days (at each aging temperature) were selected as different levels of factors in a statistically designed experiment. Previous studies have focused on developing constitutive models without due considerations to aging effects, the results presented herein augment aging-informed constitutive model development efforts that are currently in progress.

Solder joints are subjected to different loading conditions depending on the application environment. Desktop and server applications for example, involve thermomechanical fatigue loads at low-strain rates and the dominant mode of failure is creep fatigue. Mobile electronics applications on the other hand, are subject to dynamic stresses on the solder joint during impact. In our previous work, we developed a constitutive model based on mechanical test data at low strain rates. Experiments were carried out using double-lap shear test specimens of specially prepared solder assemblies over strain rate regimes of 10-6 to 10-3 s-1 [D. Bhate et al.]. In this work, the previous experimental results are augmented with tests performed at higher strain rates (10-3 to 102 s-1) at room temperature. These experiments were performed using two different experimental setups: a MTS 810 uniaxial compression tester and a Split Hopkinson Pressure Bar (SHPB). The experimental results demonstrate a remarkably consistent relationship between the yield stress and the strain rate over eight decades of strain rate! We also fit the data to viscoplastic constitutive models popularly available in commercial finite element programs. Although the constitutive models are built using data at low strain rate regimes, the model is shown to be a reasonable fit to the experimental data over the entire strain rate regime under consideration (10-6 to 102 s-1). The differences in observed behavior under compression and tension are discussed, along with a microstructural study of the samples used in the tests.

Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys and the importance of the load history. Long experience with Sn–Pb solder alloys together with empirical fatigue life models such as the Coffin–Manson rule have helped us identify reliable choices among package design alternatives. However, for the currently popular Pb-free choice of SnAgCu solder joints, designing accelerated thermal cycling tests and estimating the fatigue life are challenged by the significantly different creep behavior relative to Sn–Pb alloys. In this paper, a hybrid fatigue modeling approach inspired by nonlinear fracture mechanics is developed to predict the crack trajectory and fatigue life of a solder interconnection. The model is shown to be similar to well accepted cohesive zone models in its theoretical development and application and is anticipated to be computationally more efficient compared to cohesive zone models in a finite element setting. The approach goes beyond empirical modeling in accurately predicting crack trajectories and is validated against experiments performed on lead-free as well as Sn–Pb solder joint containing microelectronic packages. Material parameters relevant to the model are estimated via a coupled experimental and numerical technique.

The need for predicting fatigue life in solder joints is well appreciated at the present time. Currently, however, there are very few experimentally validated material parameters for popular SnAgCu alloys. Furthermore, the validity of Coffin-Manson life models, being empirical, also needs to be explored for these alloys which creep in a manner significantly different from SnPb solder alloys. In this paper, we present a modeling approach inspired by cohesive zone theory of modern fracture mechanics and Weibull distributions of material failure. The approach relies on the accurate estimation of inelastic strains at the crack tip estimated through finite element analysis, which are then used to make decisions on crack propagation. Like most popular cohesive zone models, the modeling approach presented here requires the estimation of two parameters. Unlike most cohesive zone models however, no special elements are needed in the finite element model and estimation of the parameters is more straightforward. We demonstrate the applicability of the modeling approach via the simulation of fatigue crack growth in Sn3.8Ag0.7Cu solder joints subjected to anisotropic thermal cycling. Anisotropic thermal cycling conditions were created experimentally using a simulated power cycling testing device and fatigue crack fronts were tracked at different life cycles using traditional dye-and-pry methods. The experiments were repeated for varying temperature profiles. Experimental results were coupled with numerical analysis to obtain fracture parameters for Sn3.8Ag0.7Cu. The model and the parameters were then validated by verifying their predictive ability against a variety of temperature profiles. In a separate study, the authors have developed a time hardening creep model for describing the behavior of Sn3.8Ag0.7Cu. The time hardening model accounts for primary and secondary creep and does not restrict itself to the assumption of steady state creep. The need for accurate estimation of inelastic strains in the finite element model is thus met using a valid constitutive model to describe solder creep behavior. The ability of the model to predict three dimensional crack fronts for a variety of fatigue loading environments, with sufficient accuracy, is a key result of this work.

Compared to Sn-Pb solder joints, our understanding of the fatigue of SnAgCu solder joints is far from complete. The challenges to achieving a complete understanding of SnAgCu solder joint fatigue arise partly from their significantly different creep behavior and vulnerability to micro structure evolution (aging). In this paper, we present results from thermal fatigue tests carried out with the help of a simulated power cycling tester. The test specimens were 1.27 mm pitch Ceramic Ball-Grid Array (CBGA) components with two lead-free solder alloy compositions - Sn3.8Ag0.7Cu and Sn3.0Ag0.5Cu. The components were subjected to hot dwells at 100degC for 10, 30 and 60 minutes to study the effect of dwell time on the fatigue life -a total of 48 components were tested. The resulting failure data was fit to a Weibull distribution. The packages were stored at room temperature prior to testing and the effect of the time of storage on the fatigue life was also studied. Finite element analyses were performed to study the effect of hot dwell time on the fatigue life of the CBGA component.

Constitutive models for SnAgCu solder alloys are of great interest at the present. Commonly, constitutive models that have been successfully used in the past for Sn-Pb solders are used to describe the behavior of SnAgCu solder alloys. Two issues in the modeling of lead-free solders demand careful attention: (i) Lead-free solders show significantly different creep strain evolution with time, stress and temperature, and the assumption of evolution to steady state creep nearly instantaneously may not be valid in SnAgCu alloys and (ii) Models derived from bulk sample test data may not be reliable when predicting deformation behavior at the solder interconnection level for lead-free solders due to the differences in the inherent microstructures at these different scales. In addition, the building of valid constitutive models from test data derived from tests on solder joints must deconvolute the effects of joint geometry and its influence on stress heterogeneity. Such issues have often received insufficient attention in prior constitutive modeling efforts. In this study all of the above issues are addressed in developing constitutive models of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu solder alloys, which represent the extremes of Ag composition that have been mooted at the present time. The results of monotonic testing are reported for strain rates ranging from 4.02E-6 to 2.40E-3 s−1 . The creep behavior at stress levels ranging from 7.8 to 52 MPa are also described. Both types of tests were performed at temperatures of 25°C, 75°C and 125°C. The popular Anand model and the classical time-hardening creep model are fit to the data and the experimentally obtained model parameters are reported. The test data are compared against other reported data in the literature and conclusions are drawn on the plausible sources of error in the data reported in the prior literature.Copyright © 2007 by ASME

Microsystems present several challenging reliability-related issues on account of their micron-scale dimensions. Many of these micron sized devices consist of compliant beam- or plate-like microstructures that are in close proximity to a substrate or other structural parts. If such structures come into contact, short-range adhesive forces can pin them together if they cannot be overcome by the elastic restoring forces of the deformed microstructures. This phenomenon of adhesion, often called stiction, depends on the structural response of the micro structure itself, as well as on the nature of the adhesive forces between the contacting surfaces. In this study we develop an approach to model adhesion in microsystems in a computationally feasible finite element environment, and demonstrate its capability via a companion experimental study. The modeling approach adopts the principles of three dimensional linear elastic fracture mechanics (LEFM) and extends it to thin-film plate-like microstructures. Extensive experimental work is done to study the behavior of adhesion in micro structure cantilever beams and square and circular plates. The finite element code is validated against analytically predicted and experimentally observed behavior to corroborate its effectiveness

Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys and the load history. Long experience with Sn-Pb solder alloys together with empirical fatigue life models such as the Coffin-Manson rule have helped us identify reliable choices among package design alternatives. However, for the currently popular Pb-free choice of SnAgCu solder joints, designing accelerated thermal cycling tests and estimating the fatigue life are challenged by the significantly different creep behavior relative to Sn-Pb alloys. This study is divided into two parts: In the first part, a hybrid fatigue modeling approach inspired by nonlinear fracture mechanics is discussed. The hybrid fatigue model has been shown to predict the crack trajectory and fatigue life of a Sn-Pb solder interconnection subjected to both isothermal accelerated thermal and anisothermal power cycling conditions. In the second part, results of experimental characterization via fatigue testing of microelectronic packages with SnAgCu solder interconnections subjected to anisothermal power cycling conditions are described. Packages of different geometries were tested to study the effects of these variations on the estimation of fatigue life. The afore mentioned hybrid model relies on the estimation of two fracture parameters which are to be determined experimentally. In this study, a novel technique involving tracking crack fronts in solder interconnections as a function of number of fatigue cycles is proposed to estimate these fracture parameters that can be then used to model fatigue crack growth using the hybrid modeling technique.

Commonly, constitutive models of solder alloys are derived from mechanical tests performed on either bulk solder specimens or on specially assembled BGA test coupons where the stresses are borne by solder ball interconnects. It has been widely recognized that models derived from bulk sample test data may not be reliable when predicting deformation behavior at the solder interconnect level due to the differences in the inherent microstructures at these different scales. This is particularly critical for lead-free SnAgCu solder alloys owing to their complex microstructures. There are two primary challenges associated with developing models from solder interconnect level test data: the experimental complexity associated with accurately resolving and controlling displacement at the scale of the interconnection, and the non-uniformity of stresses inherent in the solder interconnection geometry. In testing at interconnection level, published studies have used testing techniques that don't control deformation at the interconnect and have made uniformity of stress (and strain) approximations that are mostly invalid. Developing constitutive models from such data can produce erroneous results. In this study, we first demonstrate tests that control deformation at the interconnection level. We then show how heterogeneous stress distribution in solder interconnects can significantly affect the constitutive modeling of solder alloys and describe the conditions under which approximations may be made in the determination of accurate constitutive models. We validate our approach through experimental testing on Sn3.8Wwt%Ag0.7Wt%Cu solder joints and finite element analysis

Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys and the load history. Long experience with Sn-Pb solder alloys together with empirical fatigue life models such as the Coffin-Manson rule have helped us identify reliable choices among package design alternatives. However, for the currently popular Pb-free choice of SnAgCu solder joints, designing accelerated thermal cycling tests and estimating the fatigue life are challenged by the significantly different creep behavior relative to Sn-Pb alloys. In this paper, a hybrid fatigue modeling approach inspired by nonlinear fracture mechanics is developed to predict the crack trajectory and fatigue life of a solder interconnection subjected to both isothermal accelerated thermal and anisothermal power cycling conditions. The model is shown to be similar to well accepted cohesive zone models in its approach and application and is anticipated to be computationally more efficient in a finite element setting. The approach goes beyond empirical modeling in accurately predicting crack trajectories. It is argued that such non-empirical models that capture the physics of material degradation and failure can form the basis for determining meaningful Pb-free solder environmental testing conditions as well as the acceleration factors relative to field use