Background:: Subcritical crack growth can occur in a brittle material when the stress intensity factor is smaller than the fracture toughness if an oxidizing agent (such as water) is present at the crack tip. Objective:: We present a novel bi-material beam specimen which can measure environmentally assisted crack growth rates. The specimen is “self-loaded” by residual stress and requires no external loading. Methods:: Two materials with different coefficient of thermal expansion are diffusion bonded at high temperature. After cooling to room temperature a subcritical crack is driven by thermal residual stresses. A finite element model is used to design the specimen geometry in terms of material properties in order to achieve the desired crack tip driving force. Results:: The specimen is designed so that the crack driving force decreases as the crack extends, thus enabling the measurement of the crack velocity versus driving force relationship with a single test. The method is demonstrated by measuring slow crack growth data in soda lime silicate glass and validated by comparison to previously published data. Conclusions:: The self-loaded nature of the specimen makes it ideal for measuring the very low crack velocities needed to predict brittle failure at long lifetimes.
Interfacial toughness quantifies resistance to crack growth along an interface and in this investigation the toughness of an aluminum/epoxy interface was measured as a function of surface roughness and test temperature. The large strain response of the relatively ductile epoxy adhesive used in this study was also characterized. This epoxy adhesive exhibits intrinsic strain-softening after initial compressive yield and then deforms plastically at a roughly constant flow stress until it rapidly hardens at large compressive strains. We find that interface toughness scales as the product of the temperature dependent epoxy yield strength and a length scale that characterizes surface roughness. The proposed scaling is based upon dimensional considerations of a model problem that assumes that the characteristic length scale of both the roughness and the crack-tip yield zone is small relative to the region dominated by the linear elastic asymptotic crack-tip stress field. Furthermore, the model assumes that interfacial failure occurs only after the epoxy begins to harden at large strains. The proposed relationship is validated by our interfacial toughness measurements.
Subcritical crack growth can occur in a glass when the stress intensity factor is less than the fracture toughness if water molecules are present. A novel bi-material beam specimen is proposed to investigate environmentally assisted crack growth (EACG). Two materials with different coefficients of thermal expansion are diffusion bonded at high temperature and cooled to the room temperature which introduces residual stress in the beam. A Finite element (FE) model is developed and initially validated with an analytical model. Steady-state crack (SSC) depth at which mode II stress intensity factor (KII) is zero and the corresponding mode I stress intensity factor (KI) value are obtained for different material pairs and thickness ratios of the top and bottom materials using the FE model. Crack propagation path is also predicted. We finally modify the geometry of the specimen to generate non-constant KI values as the crack propagates.
We have developed a novel specimen for studying crack paths in glass. Under certain conditions, the specimen reaches a state where the crack must select between multiple paths satisfying the KII = 0 condition. This path selection is a simple but challenging benchmark case for both analytical and numerical methods of predicting crack propagation. We document the development of the specimen, using an uncracked and instrumented test case to study the effect of adhesive choice and validate the accuracy of both a simple beam theory model and a finite element model. In addition, we present preliminary fracture test results and provide a comparison to the path predicted by two numerical methods (mesh restructuring and XFEM). The directional stability of the crack path and differences in kink angle predicted by various crack kinking criteria is analyzed with a finite element model.
We have developed a novel specimen for studying crack paths in glass. Under certain conditions, the specimen reaches a state where the crack must select between multiple paths satisfying the Kπ 0 condition. This path selection is a simple but difficult benchmark case for both analytical and numerical methods of predicting crack propagation. We document the development of the specimen, using an uncracked and instrumented test case to study the effect of adhesive choice and validate the accuracy of both a simple beam theory model and a finite element model. In addition, we present preliminary fracture test results and provide a comparison to the path predicted by two numerical methods (mesh restructuring and XFEM).
This note examines the effect of interfacial roughness on the initiation and growth of channel cracks in a brittle film. A conformal film with cusp-like surface flaws that replicate the substrate roughness is investigated. This type of surface flaw is relatively severe in the sense that stress diverges as the cusp-tip is approached (i.e., there is a power-law stress singularity). For the geometry and range of film properties considered, the analysis suggests that smoothing the substrate could substantially increase the film’s resistance to the formation of the through-the-thickness cracks that precede channel cracking. However, smoothing the substrate’s surface has a relatively modest effect on the film stress needed to propagate a channel crack.
The performance and reliability of many mechanical and electrical components depend on the integrity of po lymer - to - solid interfaces . Such interfaces are found in adhesively bonded joints, encapsulated or underfilled electronic modules, protective coatings, and laminates. The work described herein was aimed at improving Sandia's finite element - based capability to predict interfacial crack growth by 1) using a high fidelity nonlinear viscoelastic material model for the adhesive in fracture simulations, and 2) developing and implementing a novel cohesive zone fracture model that generates a mode - mixity dependent toughness as a natural consequence of its formulation (i.e., generates the observed increase in interfacial toughness wi th increasing crack - tip interfacial shear). Furthermore, molecular dynamics simulations were used to study fundamental material/interfa cial physics so as to develop a fuller understanding of the connection between molecular structure and failure . Also reported are test results that quantify how joint strength and interfacial toughness vary with temperature.
The Cohesive zone (CZ) fracture analysis techniques are used to predict the initiation of crack growth from the interface corner of an adhesively bonded butt joint. In this plane strain analysis, a thin linear elastic adhesive layer is sandwiched between rigid adherends. There is no preexisting crack in the problem analyzed, and the focus is on how the shape of the traction–separation (T–U) relationship affects the predicted joint strength. Unlike the case of a preexisting interfacial crack, the calculated results clearly indicate that the predicted joint strength depends on the shape of the T–U relationship. Most of the calculations used a rectangular T–U relationship whose shape (aspect ratio) is defined by two parameters: the interfacial strength σ* and the work of separation/unit area Γ. The principal finding of this study is that for a specified adhesive layer thickness, there is any number of σ*, Γ combinations that generate the same predicted joint strength. For each combination there is a corresponding CZ length. We developed an approximate CZ-like elasticity solution to show how such combinations arise and their connection with the CZ length.
A simple, mode-mixity dependent toughness cohesive zone model (MDGc CZM) is described. This phenomenological cohesive zone model has two elements. Mode I energy dissipation is defined by a traction–separation relationship that depends only on normal separation. Mode II (III) dissipation is generated by shear yielding and slip in the cohesive surface elements that lie in front of the region where mode I separation (softening) occurs. The nature of predictions made by analyses that use the MDGc CZM is illustrated by considering the classic problem of an elastic layer loaded by rigid grips. This geometry, which models a thin adhesive bond with a long interfacial edge crack, is similar to that which has been used to measure the dependence of interfacial toughness on crack-tip mode-mixity. The calculated effective toughness vs. applied mode-mixity relationships all display a strong dependence on applied mode-mixity with the effective toughness increasing rapidly with the magnitude of the mode-mixity. The calculated relationships also show a pronounced asymmetry with respect to the applied mode-mixity. As a result, this dependence is similar to that observed experimentally, and calculated results for a glass/epoxy interface are in good agreement with published data that was generated using a test specimen of the same type as analyzed here.
Large-scale, high-throughput production of nano-structured materials (i.e. nanomanufacturing) is a strategic area in manufacturing, with markets projected to exceed $1T by 2015. Nanomanufacturing is still in its infancy; process/product developments are costly and only touch on potential opportunities enabled by growing nanoscience discoveries. The greatest promise for high-volume manufacturing lies in age-old coating and imprinting operations. For materials with tailored nm-scale structure, imprinting/embossing must be achieved at high speeds (roll-to-roll) and/or over large areas (batch operation) with feature sizes less than 100 nm. Dispersion coatings with nanoparticles can also tailor structure through self- or directed-assembly. Layering films structured with these processes have tremendous potential for efficient manufacturing of microelectronics, photovoltaics and other topical nano-structured devices. This project is designed to perform the requisite R and D to bring Sandia's technology base in computational mechanics to bear on this scale-up problem. Project focus is enforced by addressing a promising imprinting process currently being commercialized.
This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. Under this aegis we developed new theory and a number of novel techniques to describe the fracture process at the atomic scale. These developments ranged from a material-frame connection between molecular dynamics and continuum mechanics to an atomic level J integral. Each of the developments build upon each other and culminated in a cohesive zone model derived from atomic information and verified at the continuum scale. This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. The effort is predicated on the idea that processes and information at the atomic level are missing in engineering scale simulations of fracture, and, moreover, are necessary for these simulations to be predictive. In this project we developed considerable new theory and a number of novel techniques in order to describe the fracture process at the atomic scale. Chapter 2 gives a detailed account of the material-frame connection between molecular dynamics and continuum mechanics we constructed in order to best use atomic information from solid systems. With this framework, in Chapter 3, we were able to make a direct and elegant extension of the classical J down to simulations on the scale of nanometers with a discrete atomic lattice. The technique was applied to cracks and dislocations with equal success and displayed high fidelity with expectations from continuum theory. Then, as a prelude to extension of the atomic J to finite temperatures, we explored the quasi-harmonic models as efficient and accurate surrogates of atomic lattices undergoing thermo-elastic processes (Chapter 4). With this in hand, in Chapter 5 we provide evidence that, by using the appropriate energy potential, the atomic J integral we developed is calculable and accurate at finite/room temperatures. In Chapter 6, we return in part to the fundamental efforts to connect material behavior at the atomic scale to that of the continuum. In this chapter, we devise theory that predicts the onset of instability characteristic of fracture/failure via atomic simulation. In Chapters 7 and 8, we describe the culmination of the project in connecting atomic information to continuum modeling. In these chapters we show that cohesive zone models are: (a) derivable from molecular dynamics in a robust and systematic way, and (b) when used in the more efficient continuum-level finite element technique provide results that are comparable and well-correlated with the behavior at the atomic-scale. Moreover, we show that use of these same cohesive zone elements is feasible at scales very much larger than that of the lattice. Finally, in Chapter 9 we describe our work in developing the efficient non-reflecting boundary conditions necessary to perform transient fracture and shock simulation with molecular dynamics.
Interfacial delamination is often the critical failure mode limiting the performance of polymer/metal interfaces. Consequently methods that measure the toughness of such interfaces are of considerable interest. One approach for measuring the toughness of a polymer/metal interface is to use the stressed-overlayer test. In this test a metal substrate is coated with a sub-micron thick polymer film to create the interface of interest. An overlayer, typically a few tenths of a micron of sputtered tungsten, is then deposited on top of the polymer in such a way as to generate a very high residual compressive stress within the sputtered layer ({approx} 1-2 GPa). This highly stressed overlayer induces delamination and blister formation. The measured buckle heights and widths are then used in conjunction with a fracture mechanics analysis to infer interfacial toughness. Here we use a finite element, cohesive-zone-based, fracture analysis to perform the required interfacial crack growth simulation. This analysis shows that calculated crack growth is sensitive to the polymer layer thickness even when the layer is only 10's of nanometers thick. The inward displacement of the overlayer at the buckle edge, which is enabled by the relatively low polymer compliance, is the primary cause of differences from a rigid substrate idealization.
Film durability is a primary factor governing the use of emerging thin film flexible substrate devices where compressive stresses can lead to delamination and buckling. It is of particular concern in gold film systems found in many submicron and nanoscale applications. We are therefore studying these effects in gold on PMMA systems using compressively stressed tungsten overlayers to force interfacial failure and simulations employing cohesive zone elements to model the fracture process. Delamination and buckling occurred spontaneously following deposition with buckle morphologies that differed significantly from existing model predictions. Moreover, use of thin adhesive interlayers had no discernable effect on performance. In this presentation we will use observations and simulations to show how substrate compliance and yielding affects the susceptibility to buckling of gold films on compliant substrates. We will also compare the fracture energies and buckle morphologies of this study with those of gold films on sapphire substrates to show how changing substrate compliance affects buckle formation.
Deformation and fracture of thin films on compliant substrates are key factors constraining the performance of emerging flexible substrate devices. These systems often contain layers of thin polymer, ceramic and metallic films and stretchable interconnects where differing properties induce high normal and shear stresses. As long as the films remain bonded to the substrates, they may deform far beyond their freestanding form. Once debonded, substrate constraint disappears leading to film failure. Experimentally it is very difficult to measure properties in these systems at sub-micron and nanoscales. Theoretically it is very difficult to determine the contributions from the films, interfaces, and substrates. As a result our understanding of deformation and fracture behavior in compliant substrate systems is limited. This motivated a study of buckle driven delamination of thin hard tungsten films on pure PMMA substrates. The films were sputter deposited to thicknesses of 100 nm, 200 nm, and 400 nm with a residual compressive stress of 1.7 GPa. An aluminum oxide interlayer was added on several samples to alter interfacial composition. Buckles formed spontaneously on the PMMA substrates following film deposition. On films without the aluminum oxide interlayer, an extensive network of small telephone cord buckles formed following deposition, interspersed with regions of larger telephone cord buckles. On films with an aluminum oxide interlayer, telephone cord buckles formed creating a uniform widely spaced pattern. Through-substrate optical observations revealed matching buckle patterns along the film-substrate interface indicating that delamination occurred for large and small buckles with and without an interlayer. The coexistence of large and small buckles on the same substrate led to two distinct behaviors as shown in Figure 2 where normalized buckle heights are plotted against normalized film stress. The behaviors deviate significantly from behavior predicted by rigid elastic solutions. To address this issue we developed a finite element analysis technique that employed a cohesive zone model to simulate interfacial crack growth. Specifying the traction-separation relationship, cohesive strength, and work of separation along with film thickness, film stress, and film and substrate properties, buckle width and height were determined as a function of interfacial toughness. The simulations indicate that an analysis based on rigid substrate solutions significantly underestimate toughness for prescribed buckle widths: a result consistent with an analysis by Yu and Hutchinson that pieced together a solution based on non-linear plate theory with a solution for the linear film on substrate problem. More importantly, the results defined a lower limiting bound to seemingly disparate buckle deflection data. The variance from linear elastic behavior, especially for the small buckles, indicates more than substrate compliance is controlling behavior. Comparison of the experimental results with cohesive zone simulations suggests that the two buckle behaviors are associated with different levels of substrate yielding. In this presentation we will use the results to show how substrate compliance and deformation affect delamination and buckling of films on compliant substrates and provide a means to predict device performance.
A cohesive zone, finite element fracture analysis is based upon a traction-separation relation. Our recent work has used molecular dynamics simulations to derive general traction-separation relationships for interfacial fracture between two brittle materials under mix-mode loading conditions. Here we apply our method to explore the effects of elastic constants of the two materials on the traction-separation relationship. A comparison and discussion of our results will be provided.
Development of flexible thin film systems for biomedical, homeland security and environmental sensing applications has increased dramatically in recent years [1,2,3,4]. These systems typically combine traditional semiconductor technology with new flexible substrates, allowing for both the high electron mobility of semiconductors and the flexibility of polymers. The devices have the ability to be easily integrated into components and show promise for advanced design concepts, ranging from innovative microelectronics to MEMS and NEMS devices. These devices often contain layers of thin polymer, ceramic and metallic films where differing properties can lead to large residual stresses [5]. As long as the films remain substrate-bonded, they may deform far beyond their freestanding counterpart. Once debonded, substrate constraint disappears leading to film failure where compressive stresses can lead to wrinkling, delamination, and buckling [6,7,8] while tensile stresses can lead to film fracture and decohesion [9,10,11]. In all cases, performance depends on film adhesion. Experimentally it is difficult to measure adhesion. It is often studied using tape [12], pull off [13,14,15], and peel tests [16,17]. More recent techniques for measuring adhesion include scratch testing [18,19,20,21], four point bending [22,23,24], indentation [25,26,27], spontaneous blisters [28,29] and stressed overlayers [7,26,30,31,32,33]. Nevertheless, sample design and test techniques must be tailored for each system. There is a large body of elastic thin film fracture and elastic contact mechanics solutions for elastic films on rigid substrates in the published literature [5,7,34,35,36]. More recent work has extended these solutions to films on compliant substrates and show that increasing compliance markedly changes fracture energies compared with rigid elastic solution results [37,38]. However, the introduction of inelastic substrate response significantly complicates the problem [10,39,40]. As a result, our understanding of the critical relationship between adhesion, properties, and fracture for hard films on compliant substrates is limited. To address this issue, we integrated nanomechanical testing and mechanics-based modeling in a program to define the critical relationship between deformation and fracture of nanoscale films on compliant substrates. The approach involved designing model film systems and employing nano-scale experimental characterization techniques to isolate effects of compliance, viscoelasticity, and plasticity on deformation and fracture of thin hard films on substrates that spanned more than two orders of compliance magnitude exhibit different interface structures, have different adhesion strengths, and function differently under stress. The results of this work are described in six chapters. Chapter 1 provides the motivation for this work. Chapter 2 presents experimental results covering film system design, sample preparation, indentation response, and fracture including discussion on the effects of substrate compliance on fracture energies and buckle formation from existing models. Chapter 3 describes the use of analytical and finite element simulations to define the role of substrate compliance and film geometry on the indentation response of thin hard films on compliant substrates. Chapter 4 describes the development and application of cohesive zone model based finite element simulations to determine how substrate compliance affects debond growth. Chapter 5 describes the use of molecular dynamics simulations to define the effects of substrate compliance on interfacial fracture of thin hard tungsten films on silicon substrates. Chapter 6 describes the Workshops sponsored through this program to advance understanding of material and system behavior.
Fatigue cracking in metals has been and is an area of great importance to the science and technology of structural materials for quite some time. The earliest stages of fatigue crack nucleation and growth are dominated by the microstructure and yet few models are able to predict the fatigue behavior during these stages because of a lack of microstructural physics in the models. This program has developed several new simulation tools to increase the microstructural physics available for fatigue prediction. In addition, this program has extended and developed microscale experimental methods to allow the validation of new microstructural models for deformation in metals. We have applied these developments to fatigue experiments in metals where the microstructure has been intentionally varied.
The performance and the reliability of many devices are controlled by interfaces between thin films. In this study we investigated the use of patterned, nanoscale interfacial roughness as a way to increase the apparent interfacial toughness of brittle, thin-film material systems. The experimental portion of the study measured the interfacial toughness of a number of interfaces with nanoscale roughness. This included a silicon interface with a rectangular-toothed pattern of 60-nm wide by 90-nm deep channels fabricated using nanoimprint lithography techniques. Detailed finite element simulations were used to investigate the nature of interfacial crack growth when the interface is patterned. These simulations examined how geometric and material parameter choices affect the apparent toughness. Atomistic simulations were also performed with the aim of identifying possible modifications to the interfacial separation models currently used in nanoscale, finite element fracture analyses. The fundamental nature of atomistic traction separation for mixed mode loadings was investigated.
Recently published results for a rigid spherical indenter contacting a thin, linear elastic coating on a rigid planar substrate have been extended to include the case of two contacting spheres, where each sphere is rigid and coated with a thin, linear elastic material. This is done by using an appropriately chosen effective radius and coating modulus. Finally, the earlier work has also been extended to provide analytical results that span the transition between the previously derived Derjaguin–Müller–Toporov (DMT)-like (work of adhesion/coating-modulus ratio is small) and Johnson–Kendall–Roberts (JKR)-like (work of adhesion/coating-modulus ratio is large) limits.
An unavoidable by-product of a metallic structure's use is the appearance of crack, corrosion, erosion and other flaws. Economic barriers to the replacement of these structures have created an aging civil and military infrastructure and placed even greater demands on efficient and safe repair and inspection methods. As a result of Homeland Security issues and these aging infrastructure concerns, increased attention has been focused on the rapid repair and preemptive reinforcement of structures such as buildings and bridges. This Laboratory Directed Research and Development (LDRD) program established the viability of using bonded composite patches to repair metallic structures. High modulus fiber-reinforced polymer (FRP) material may be used in lieu of mechanically fastened metallic patches or welds to reinforce or repair damaged structures. Their use produces a wide array of engineering and economic advantages. Current techniques for strengthening steel structures have several drawbacks including requiring heavy equipment for installation, poor fatigue performance, and the need for ongoing maintenance due to continued corrosion attack or crack growth. The use of bonded composite doublers has the potential to correct the difficulties associated with current repair techniques and the ability to be applied where there are currently no rehabilitation options. Applications include such diverse structures as: buildings, bridges, railroad cars, trucks and other heavy machinery, steel power and communication towers, pipelines, factories, mining equipment, ships, tanks and other military vehicles. This LDRD also proved the concept of a living infrastructure by developing custom sensors and self-healing chemistry and linking this technology with the application of advanced composite materials. Structural Health Monitoring (SHM) systems and mountable, miniature sensors were designed to continuously or periodically assess structural integrity. Such systems are able to detect incipient damage before catastrophic failure occurs. The ease of monitoring an entire network of distributed sensors means that structural health assessments can occur more often, allowing operators to be even more vigilant with respect to flaw onset. In addition, the realization of smart structures, through the use of in-situ sensors, allows condition-based maintenance to be substituted for conventional time-based maintenance practices. The sensitivity and reliability of a series of sensor systems was quantified in laboratory and real-world environments. Finally, self healing methods for composite materials were evolved--using resin modules that are released in response to the onset of delaminations--so that these components can provide a living infrastructure with minimal need for human intervention. This program consisted of four related research elements: (1) design, installation, and performance assessment of composite repairs, (2) in-situ sensors for real-time health monitoring, (3) self healing of in-service damage in a repair, and (4) numerical modeling. Deployment of FRP materials and bonded joints requires proper design, suitable surface preparation methods, and adequate surveillance to ensure structural integrity. By encompassing all 'cradle-to-grave' tasks --including design, analysis, installation, durability, flaw containment, and inspection--this program is designed to firmly establish the capabilities of composite doubler repairs and introduce technology to incorporate self-monitoring and self-healing (living structures) methodologies. A proof-of-concept repair was completed on a steel highway bridge in order to demonstrate the potential of composite doubler technology for critical infrastructure use.
A classical mechanistic model was developed to capture the existence of pre-sliding tangential deflection (PSTD) in contacting polysilicon and coated polysilicon surfaces. For the purposes of modeling asperity friction, experiments have shown, and been supported through detailed finite element analyses, that frictional forces developed through tangential sliding scale linearly through a material parameter known as the junction strength. A junction strength model coupled with a discrete quasi-static contact mechanics analysis, using contacting surface descriptions sampled by AFM from actual polysilicon surfaces, predicts inelastic tangential displacements that are qualitatively consistent with observed PSTD response. The simulations imply that the existence of PSTD depends not only on the spatial characteristics of contacting surfaces, but also on the local loading characteristics.
The primary goals of the present study are to: (1) determine how and why MEMS-scale friction differs from friction on the macro-scale, and (2) to begin to develop a capability to perform finite element simulations of MEMS materials and components that accurately predicts response in the presence of adhesion and friction. Regarding the first goal, a newly developed nanotractor actuator was used to measure friction between molecular monolayer-coated, polysilicon surfaces. Amontons law does indeed apply over a wide range of forces. However, at low loads, which are of relevance to MEMS, there is an important adhesive contribution to the normal load that cannot be neglected. More importantly, we found that at short sliding distances, the concept of a coefficient of friction is not relevant; rather, one must invoke the notion of 'pre-sliding tangential deflections' (PSTD). Results of a simple 2-D model suggests that PSTD is a cascade of small-scale slips with a roughly constant number of contacts equilibrating the applied normal load. Regarding the second goal, an Adhesion Model and a Junction Model have been implemented in PRESTO, Sandia's transient dynamics, finite element code to enable asperity-level simulations. The Junction Model includes a tangential shear traction that opposes the relative tangential motion of contacting surfaces. An atomic force microscope (AFM)-based method was used to measure nano-scale, single asperity friction forces as a function of normal force. This data is used to determine Junction Model parameters. An illustrative simulation demonstrates the use of the Junction Model in conjunction with a mesh generated directly from an atomic force microscope (AFM) image to directly predict frictional response of a sliding asperity. Also with regards to the second goal, grid-level, homogenized models were studied. One would like to perform a finite element analysis of a MEMS component assuming nominally flat surfaces and to include the effect of roughness in such an analysis by using a homogenized contact and friction models. AFM measurements were made to determine statistical information on polysilicon surfaces with different roughnesses, and this data was used as input to a homogenized, multi-asperity contact model (the classical Greenwood and Williamson model). Extensions of the Greenwood and Williamson model are also discussed: one incorporates the effect of adhesion while the other modifies the theory so that it applies to the case of relatively few contacting asperities.
The effect of the density and in-plane distribution of interfacial interactions on crack initiation in an epoxy-silicon joint was studied in nominally pure shear loading. Well-defined combinations of strong (specific) and weak (nonspecific) interactions were created using self-assembling monolayers. The in-plane distribution of strong and weak interactions was varied by employing two deposition methods: depositing mixtures of molecules with different terminal groups resulting in a nominally random distribution, and depositing methyl-terminated molecules in domains defined lithographically with the remaining area interacting through strong acid-base interactions. The two distributions lead to very different fracture behavior. For the case of the methyl-terminated domains (50 μm on a side) fabricated lithographically, the joint shear strength varies almost linearly with the area fraction of strongly interacting sites. From this we infer that cracks nucleate on or near the interface over nearly the entire range of bonded area fraction and do so at nearly the same value of local stress (load/bonded area). We postulate that the imposed heterogeneity in interfacial interactions results in heterogeneous stress and strain fields within the epoxy in close proximity to the interface. Simply, the bonded areas carry load while the methyl terminated domains carry negligible load. Stress is amplified adjacent to the well-bonded regions (and reduced adjacent to the poorly bonded regions), and this leads to crack initiation by plastic deformation and chain scission within the epoxy near the interface. For the case of mixed monolayers, the dependence is entirely different. At low areal density of strongly interacting sites, the joint shear strength is below the detection limit of our transducer for a significant range of mixed monolayer composition. With increasing density of strongly interacting sites, a sharp increase in joint shear strength occurs at a methyl terminated area fraction of roughly 0.90. We postulate that this coincides with the onset of yielding in the epoxy. For methyl-terminated area fractions less than 0.85, the joint shear strength becomes independent of the interfacial interactions. This indicates that fracture no longer initiates on the interface but away from the interface by a competing mechanism, likely plastic deformation and chain scission within the bulk epoxy. The data demonstrate that the in-plane distribution of interaction sites alone can affect the location of crack nucleation and the far-field stress required.
This one-year feasibility study was aimed at developing finite element modeling capabilities for simulating nano-scale tests. This work focused on methods to model: (1) the adhesion of a particle to a substrate, and (2) the delamination of a thin film from a substrate. Adhesion was modeled as a normal attractive force that depends on the distance between opposing material surfaces while delamination simulations used a cohesive zone model. Both of these surface interaction models had been implemented in a beta version of the three-dimensional, transient dynamics, PRESTO finite element code, and the present study verified that implementation. Numerous illustrative calculations have been performed using these models, and when possible comparisons were made with existing solutions. These capabilities are now available in PRESTO version 1.07.
A test method, the Tensile Brazil Nut Sandwich (TBNS) specimen, was developed to measure mixed-mode interfacial toughness of bonded materials. Interfacial toughness measured by this technique is compared to the interfacial toughness of thin film adhesive coatings using a nanoindentation technique. The interfacial toughness of solvent-cast and melt-spun adhesive thin films is compared and found to be similar. Finally, the Johnson-Kendall-Roberts (JKR) technique is used to evaluate the cleanliness of aluminum substrates.
The Microsystems Subgrid Physics project is intended to address gaps between developing high-performance modeling and simulation capabilities and microdomain specific physics. The initial effort has focused on incorporating electrostatic excitations, adhesive surface interactions, and scale dependent material and thermal properties into existing modeling capabilities. Developments related to each of these efforts are summarized, and sample applications are presented. While detailed models of the relevant physics are still being developed, a general modeling framework is emerging that can be extended to incorporate evolving material and surface interaction modules.
Polymer stresses around sharp corners and in constrained geometries of encapsulated components can generate cracks leading to system failures. Often, analysts use maximum stresses as a qualitative indicator for evaluating the strength of encapsulated component designs. Although this approach has been useful for making relative comparisons screening prospective design changes, it has not been tied quantitatively to failure. Accurate failure models are needed for analyses to predict whether encapsulated components meet life cycle requirements. With Sandia's recently developed nonlinear viscoelastic polymer models, it has been possible to examine more accurately the local stress-strain distributions in zones of likely failure initiation looking for physically based failure mechanisms and continuum metrics that correlate with the cohesive failure event. This study has identified significant differences between rubbery and glassy failure mechanisms that suggest reasonable alternatives for cohesive failure criteria and metrics. Rubbery failure seems best characterized by the mechanisms of finite extensibility and appears to correlate with maximum strain predictions. Glassy failure, however, seems driven by cavitation and correlates with the maximum hydrostatic tension. Using these metrics, two three-point bending geometries were tested and analyzed under variable loading rates, different temperatures and comparable mesh resolution (i.e., accuracy) to make quantitative failure predictions. The resulting predictions and observations agreed well suggesting the need for additional research. In a separate, additional study, the asymptotically singular stress state found at the tip of a rigid, square inclusion embedded within a thin, linear elastic disk was determined for uniform cooling. The singular stress field is characterized by a single stress intensity factor K{sub a} and the applicable K{sub a} calibration relationship has been determined for both fully bonded and unbended inclusions. A lack of interfacial bonding has a profound effect on inclusion-tip stress fields. A large radial compressive stress is generated in front of the inclusion-tip when the inclusion is well bonded, whereas a large tensile hoop stress is generated when the inclusion is unbended, and frictionless sliding is allowed. Consequently, an epoxy disk containing an unbended inclusion appears more likely to crack when cooled than a disk containing a fully bonded inclusion. A limited number of tests have been carried out to determine if encapsulant cracking can be induced by cooling a specimen fabricated by molding a square, steel insert within a thin, epoxy disk. Test results are in qualitative agreement with analysis. Cracks developed only in disks with mold-released inserts, and the tendency for cracking increased with inclusion size.
There has been considerable progress in recent years towards developing a stress intensity factor-based method for predicting crack initiation at a sharp, bimaterial comer. There is now a comprehensive understanding of the nature of multi-material, two-dimensional, linear-elastic, wedge-tip stress fields. In general, the asymptotic stress state at the apex of dissimilar bonded elastic wedges (i.e. at an interface comer) can have one or more power-law singularities of differing strength and with exponents that can be real or complex. There are, however; many configurations of practical importance, (e.g. adhesively bonded butt joints, hi-material beams, etc.) where interface-comer stresses are described by one, real-valued power-law singularity. In such cases, one can reasonably hypothesize that failure occurs at a critical value of the stress intensity factor: when K{sub a}=K{sub ac}.This approach is completely analogous to LEFM except that the critical stress intensity factor is associated with a discontinuity other than a crack. To apply the K{sub ac} criterion, one must be able to accurately calculate K{sub a} for arbitrary geometries. There are several well-established methods for calculating K{sub a}. These include matching asymptotic and detailed finite element results, evaluation of a path-independent contour integral, and general finite element methods for calculating K. for complex geometries. A rapidly expanding catalog of K{sub a} calibrations is now available for a number of geometries of practical interest. These calibrations provide convenient formulas that can be used in a failure analysis without recourse to a detailed numerical analysis. The K{sub ac} criterion has been applied with some notable successes. For example, the variation in strength of adhesively bonded butt joints with bond thickness and the dependence of this relationship on adhered stiffness is readily explained. No other one-parameter fracture criterion is able to make this sort of prediction. Nevertheless, the interface-corner fracture toughness approach is just in its initial states of development, and its strengths and limitations must be more clearly defined. There are still numerous issues yet to be resolved, including the development of methods for treating time-dependent response, three-dimensional comers, large-scale yielding, and the development of a criterion that can be applied when the comer stress state is not characterized by a single K{sub a}.
The relationships between fundamental interfacial interactions, energy dissipation mechanisms, and fracture stress or fracture toughness in a glassy thermoset/inorganic solid joint are not well understood. This subject is addressed with a model system involving an epoxy adhesive on a polished silicon wafer containing its native oxide. The proportions of physical and chemical interactions at the interface, and the in-plane distribution, are varied using self-assembling monolayers of octadecyltrichlorosilane (ODTS). The epoxy interacts strongly with the bare silicon oxide surface, but forms only a very weak interface with the methylated tails of the ODTS monolayer. The fracture stress is examined as a function of ODTS coverage in the napkin-ring (pure shear) loading geometry. The relationship between fracture stress and ODTS coverage is catastrophic, with a large change in fracture stress occurring over a narrow range of ODTS coverage. This transition in fracture stress does not correspond to a wetting transition of the epoxy. Rather, the transition in fracture stress corresponds to the onset of deformation in the epoxy, or the transition from brittle to ductile fracture. The authors postulate that the transition in fracture stress occurs when the local stress that the interface can support becomes comparable to the yield stress of the epoxy. The fracture results are independent of whether the ODTS deposition occurs by island growth (T{sub dep} = 10 C) or by homogeneous growth (T{sub dep} = 24 C).
This report summarizes materials issues associated with advanced micromachines development at Sandia. The intent of this report is to provide a perspective on the scope of the issues and suggest future technical directions, with a focus on computational materials science. Materials issues in surface micromachining (SMM), Lithographic-Galvanoformung-Abformung (LIGA: lithography, electrodeposition, and molding), and meso-machining technologies were identified. Each individual issue was assessed in four categories: degree of basic understanding; amount of existing experimental data capability of existing models; and, based on the perspective of component developers, the importance of the issue to be resolved. Three broad requirements for micromachines emerged from this process. They are: (1) tribological behavior, including stiction, friction, wear, and the use of surface treatments to control these, (2) mechanical behavior at microscale, including elasticity, plasticity, and the effect of microstructural features on mechanical strength, and (3) degradation of tribological and mechanical properties in normal (including aging), abnormal and hostile environments. Resolving all the identified critical issues requires a significant cooperative and complementary effort between computational and experimental programs. The breadth of this work is greater than any single program is likely to support. This report should serve as a guide to plan micromachines development at Sandia.
While surface cleaning is the most common process step in DOE manufacturing operations, the link between a successful adhesive bond and the surface clean performed before adhesion is not well understood. An innovative approach that combines computer modeling expertise, fracture mechanics understanding, and cleaning experience to address how to achieve a good adhesive bond is discussed here to develop a capability that would result in reduced cleaning development time and testing, improved bonds, improved manufacturability, and even an understanding that leads to improved aging. A simulation modeling technique, polymer reference interaction site model applied near wall (Wall PRISM), provided the capability to include contaminants on the surface. Calculations determined an approximately 8% reduction in the work of adhesion for 1% by weight of ethanol contamination on the structure of a silicone adhesive near a surface. The demonstration of repeatable coatings and quantitative analysis of the surface for deposition of controlled amounts of contamination (hexadecane and mineral oil) was based on three deposition methods. The effect of the cleaning process used on interfacial toughness was determined. The measured interfacial toughness of samples with a Brulin cleaned sandblasted aluminum surface was found to be {approximately} 15% greater than that with a TCE cleaned aluminum surface. The sensitivity of measured fracture toughness to various test conditions determined that both interfacial toughness and interface corner toughness depended strongly on surface roughness. The work of adhesion value for silicone/silicone interface was determined by a contact mechanics technique known as the JKR method. Correlation with fracture data has allowed a better understanding between interfacial fracture parameters and surface energy.
The relationship between the nature and spatial distribution of fundamental interfacial interactions and fracture stress/fracture toughness of a glassy adhesive-inorganic solid joint is not understood. This relationship is important from the standpoint of designing interfacial chemistry sufficient to provide the level of mechanical strength required for a particular application. In addition, it is also important for understanding the effects of surface contamination. Different types of contamination, or different levels of contamination, likely impact joint strength in different ways. Furthermore, the relationship is also important from the standpoint of aging. If interfacial chemical bonds scission over time due to the presence of a contaminant such as water, or exposure to UV, etc, the relationship between joint strength/fracture toughness and interface strength is important for predicting reliability with time. A fundamental understanding of the relationship between joint strength and fundamental interfacial interactions will give insight into these issues.
This report focuses on the relationship between the fundamental interactions acting across an interface and macroscopic engineering observable such as fracture toughness or fracture stress. The work encompasses experiment, theory, and simulation. The model experimental system is epoxy on polished silicon. The interfacial interactions between the substrate and the adhesive are varied continuously using self-assembling monolayer. Fracture is studied in two specimen geometries: a napkin-ring torsion geometry and a double cantilevered beam specimen. Analysis and modeling involves molecular dynamics simulations and continuum mechanics calculations. Further insight is gained from analysis of measurements in the literature of direct force measurements for various fundamental interactions. In the napkin-ring test, the data indicate a nonlinear relationship between interface strength and fracture stress. In particular, there is an abrupt transition in fracture stress which corresponds to an adhesive-to-cohesive transition. Such nonlinearity is not present in the MD simulations on the tens-of-nanometer scale, which suggests that the nonlinearity comes from bulk material deformation occurring on much larger length scales. We postulate that the transition occurs when the interface strength becomes comparable to the yield stress of the material. This postulate is supported by variation observed in the fracture stress curve with test temperature. Detailed modeling of the stress within the sample has not yet been attempted. In the DCB test, the relationship between interface strength and fracture toughness is also nonlinear, but the fracture mechanisms are quite different. The fracture does not transition from adhesive to cohesive, but remains adhesive over the entire range of interface strength. This specimen is modeled quantitatively by combining (i) continuum calculations relating fracture toughness to the stress at 90 {angstrom} from the crack tip, and (ii) a relationship from molecular simulations between fracture stress on a {approx} 90 {angstrom} scale and the fraction of surface sites which chemically bond. The resulting relationship between G{sub c} and fraction of bonding sites is then compared to the experimental data. This first order model captures the nonlinearity in the experimentally-determined relationship. A much more extensive comparison is needed (calculations extending to higher G{sub c} values, experimental data extending to lower G{sub c} values) to guide further model development.