Channel Cracks Research Articles

Numerical estimation of fracture toughness from indentation-induced circumferential cracking in thin films on ductile substrates

In this paper, a method to estimate fracture toughness, Γf, from the first indenter-induced circumferential crack in a thin film is suggested. The method is based on the stresses in the film and finite element simulations are used to estimate these stresses. The film is taken to be linear elastic while plasticity is included in the substrate. Delamination is not taken into account in the method and the film is perfectly bonded to the substrate. The stress in the film is used to estimate the location where the circumferential crack will initiate from a defect in the film surface. The location is found to be at a distance away from the indenter which correlate with experiments. Also, the stress is used to calculate the stress intensity factor and the energy release rate for a plane strain crack. The energy release rate for the plane strain crack is then used to calculate the energy release for a crack channeling around the indenter forming the circumferential crack. By the energy release rate for the channeling crack fracture toughness is estimated independent of the initial defects in the film provided such defects exist. If the initial defects are smaller than a required minimum value, fracture toughness is overestimated by this method and this overestimation is calculated. Besides fracture toughness, the energy release rate for the channeling crack is used to estimate the depth of the plane strain crack which is found to be smaller than the film thickness.The method is used to estimate the fracture toughness, Γf, for an alumina (Al2O3) film using the critical indentation depth. In order to verify the result the estimated crack radius is compared to the actual radius of the circumferential crack in the alumina. The differences between the two radius is found to be within a few percent.

Interfacial Cyclic Fatigue of Atomic-Layer-Deposited Alumina Coatings on Silicon Thin Films

A microresonator-based interfacial fatigue testing technique was used to investigate the subcritical delamination of atomic-layer-deposited alumina coatings along the sidewalls of deep-reactive-ion-etched monocrystalline silicon thin films. This technique ensures loading conditions relevant to microelectromechanical system devices, including kHz testing frequency and fully reversed cyclic stresses. Four different coating thicknesses (4.2, 12.6, 25, and 50 nm) were investigated in two environments (30 °C, 50% relative humidity (RH) and 80 °C, 90% RH). Fatigue damage, in the form of channel cracks and delamination of the alumina coating, was found to accumulate slowly over more than 1 × 10(8) cycles. The average delamination rates increase with increasing energy release rate amplitude for delamination, modeled with a power law relationship. In the harsher environment, the rates are roughly 1 order of magnitude higher. Additionally, a few tests under static load were conducted for which no delamination (or crack growth) occurred, demonstrating that the governing interfacial fatigue mechanism is cycle-dependent.

Transverse fracture of canine teeth

The critical conditions to effect transverse fracture in canine teeth of carnivores in lateral loading are analyzed. The teeth are modeled as tapered coaxial beams with uniformly thin enamel coats. A stress analysis is first carried out using beam theory, and stress intensity factors for inward propagating cracks at the location of maximum tensile stress along the lingual face are then determined. The fracture begins as arrested channel cracks within the enamel, followed by stable penetration around the tooth and into the dentin to the point of failure. Two- and three-dimensional finite element models are used to evaluate the full fracture evolution. The analysis yields an explicit scaling relation for the critical fracture load in terms of characteristic tooth dimensions, notably tooth height and base radius. The role of enamel, ignored in previous ‘strength of materials’ analyses, is shown to be important in determining the precursor crack equilibrium prior to full fracture. Implications concerning allometry are briefly discussed.

In-situ Tensile Straining of Metal Films on Polymer Substrates under an AFM

ABSTRACTMetal films on polymer substrates are commonly used in flexible electronic devices and as gas barrier coatings. One way to evaluate the fracture and adhesion properties of such film systems is the fragmentation test. In the fragmentation test a film-substrate system is strained in tension under an optical microscope or inside a scanning electron microscope to observe the cracking and delamination events in situ. The technique works very well for brittle metal and ceramic films. However, when ductile films are strained they deform plastically before cracks and buckles appear. Therefore, a tensile straining device was developed to fit under an AFM for in situ observation of ductile metal films on polymer substrates. With the new in situ device the first occurrence of plastic deformation in the form of localized thinning of the film and channel cracks are visible. These features can only be detected through a height difference in the AFM images and not with optical or scanning electron micrographs. A comparison to brittle Cr films on polymer substrates was performed.

The influence of residual thermal stresses on the mechanical properties of multilayer α-Al2O3/TiCxN1 − x coatings on WC/Co cutting tools

Orientation maps of the microstructures of four α-Al2O3 and TiCxN1−x multilayer coatings on WC–Co cemented carbide tool bit inserts were used to create realistic models for finite element calculations of residual thermal stresses. The calculations show that channel cracks in the coatings relieve thermal stresses and that the amount of stress relieved increases with film thickness. The hardness and fracture toughness of the coatings, measured by nano-indentation, are inversely correlated to the calculated mean thermal stress, where the hardest sample has the smallest calculated mean thermal stress. The calculations also indicate that cracks spaced more closely than about 50μm are not effective in further reducing residual stresses.

On delamination growth from channel cracks in thin-film coatings

Interfacial fracture (delamination) originating from channel or tunnel cracks is a common failure mode in layered structures. While this subject has been addressed extensively, little is known on the actual process of fracture. It is this aspect which is of concern here. The evolution of delamination damage is followed in situ using an all-transparent system designed to reduce material variability and thermal stresses. The specimen is composed of two glass plates glued onto a polycarbonate slab by a RT epoxy resin. With a proper control of the glass surface, stable delamination growth from a single channel crack occurs. This growth evolves smoothly from the tip of the channel crack, although the delamination area is generally irregular and non-symmetric. The fracture resistance varies greatly between nominally identical samples, attesting to a great sensitivity to such irregularity as well as to bonding surface conditions. The effect of system variables on delamination growth is evaluated using a 2D FEA. The analysis predicts general trends observed in the tests, and it indicates means for an optimal design against premature failure. Finally, the merit of evaluating fracture toughness of ultra-thin films using the channel cracking approach is discussed.

Three-dimensional numerical analysis of stress intensity factors at the intersection of a crack and pore channels with star-like cross-section

The three-dimensional numerical analysis of stress intensity factors (SIF) at the intersection of a main crack (MC) and pore channels has been performed. Each channel consists of three channel cracks (CC) united by their mouths on the channel axis. It has been shown that the rupture of the MC face by the differently oriented CC gives rise to the local SIF at the MC front that is differs more than twice from the mean SIF. The maximum local SIF for the CC the plane of which is parallel to the MC front is four times higher than the SIF for the CC the plane of which is perpendicular to the MC front. The total shearing and tearing mode SIF at the CC front has three local maxima. One maximum is located at the intersection of the CC front with a plane, to which the MC face belongs. Additional peaks are located at some distance from both sides of this plane.

Debonding and fracture of ceramic islands on polymer substrates

We perform in-situ uniaxial tensile tests on polyimide substrates with patterned ceramic islands. The islands fail by either channel cracking or debonding from the substrate, depending on island size and thickness. To understand why different failure modes occur, we have analyzed the fracture and debonding of stiff islands on deformable substrates. Using finite element simulations, we find that the maximum tensile strain in the islands increases with island size, but decreases with island thickness. The maximum energy release rate for island/substrate debonding, in contrast, increases with both island size and thickness. Assuming that the islands do not fracture if the maximum tensile strain in the islands is lower than a critical value and that no debonding occurs if the maximum energy release rate is smaller than the interfacial toughness, the critical substrate strains for island fracture and debonding can be calculated. If the islands are thick and small, the critical debonding strain is small, and the islands fail by debonding. If the islands are large and thin, the critical fracture strain is small, and the islands fail by channel cracking. When the two critical strains are similar, debonding and cracking are expected to co-exist. Experimental observations confirm these findings.

Quantitative Study on the Correlation Between Solid Oxide Fuel Cell Ni-YSZ Composite Anode Performance and Sintering Temperature Based on Three-dimensional Reconstruction

The effects of sintering temperatures on the performances and durabilities of conventional nickel-yttria-stabilized zirconia composite solid oxide fuel cell anodes were investigated. The anode microstructures after reduction and 100 hours operation were quantitatively analyzed by three-dimensional reconstruction based on focused ion beam-scanning electron microscopy technique. Percolation of nickel, yttria-stabilized zirconia and pore phases and three phase boundary densities were quantitatively calculated. The anode sintered at 1450°C has been found to show the minimum ohmic resistance and polarization resistance. The differences of ohmic resistances between the anodes can be quantitatively explained by the difference of active three phase boundary density. Besides, the anode sintered at 1450°C could operate without large-scale channel cracks which may cause damage and relatively fast degradation. The lowest degradation rate of anode sintered at 1450°C is attributed to the strengthened YSZ network for maintaining Ni phase percolation compared to the other two sintering temperatures.

Inverse effect of thickness on the ductility in nanocrystalline Cu films

Abstract The ductility of nanocrystalline Cu films with different thickness ranging from 40 nm to 600 nm was tested by uniaxial tension. The ductility of the films was determined by the changes of the statistical crack density and the electrical resistance with tensile strain. It was found that the ductility decreases with increasing the film thickness, exhibiting an inverse size effect compared to the previous results. The 40-nm-thick Cu films sustain strains up to 20% without cracks, while the 600-nm-thick Cu films fracture at only 5% with channel cracks. The effective interfacial bond strength between the films and the substrate is suggested to be responsible for the ductility of Cu films.

Mechanical properties and scratch resistance of filtered-arc-deposited titanium oxide thin films on glass

The mechanical properties and the scratch resistance of titanium oxide (TiO 2) thin films on a glass substrate have been investigated. Three films, with crystalline (rutile and anatase) and amorphous structures, were deposited by the filtered cathodic vacuum arc deposition technique on glass, and characterized by means of nanoindentation and scratch tests. The different damage modes (arc-like, longitudinal and channel cracks in the crystalline films; Hertzian cracks in the amorphous film) were assessed by means of optical and focused ion beam microscopy. In all cases, the deposition of the TiO 2 film improved the contact-mechanical properties of uncoated glass. Crystalline films were found to possess a better combination of mechanical properties (i.e. elastic modulus up to 221 GPa, hardness up to 21 GPa, and fracture strength up to 3.6 GPa) than the amorphous film. However, under cyclic sliding contact above the critical fracture load, the amorphous film was found to withstand a higher number of cycles. The results are expected to provide useful insight for the design of optical coatings with improved contact-damage resistance.

Effects of green density difference on camber development during the cofiring of a bi-layer glass-based dielectric laminate

Effects of green density difference on camber and stress development during the cofiring of a bi-layer glass-based dielectric laminate have been investigated. A larger shrinkage rate is observed for the tape with a lower green density, toward which camber develops during cofiring. The sintering mismatch stress, which is calculated from the camber development during cofiring, is much less than those of sintering potentials. Similar data are also obtained for the stress calculated using the linear shrinkage rate difference from the dilatometric measurements. The above results account for the absence of defects, such as de-densification, de-bonding and channel cracks in the cofired multilayer laminates.

Periodic cracking of films supported on compliant substrates

When a tensile strain is applied to a film supported on a compliant substrate, a pattern of parallel cracks can channel through both the film and substrate. A linear-elastic fracture-mechanics model for the phenomenon is presented to extend earlier analyses in which cracking was limited to the film. It is shown how failure of the substrate reduces the critical strain required to initiate fracture of the film. This effect is more pronounced for relatively tough films. However, there is a critical ratio of the film to substrate toughness above which stable cracks do not form in response to an applied load. Instead, catastrophic failure of the substrate occurs simultaneously with the propagation of a single channel crack. This critical toughness ratio increases with the modulus mismatch between the film and the substrate, so that periodic crack patterns are more likely to be observed with relatively stiff films. With relatively low values of modulus mismatch, even a film that is more brittle than the substrate can cause catastrophic failure of the substrate. Below the critical toughness ratio, there is a regime in which stable crack arrays can be formed in the film and substrate. The depth of these arrays increases, while the spacing decreases, as the strain is increased. Eventually, the crack array can become deep enough to cause substrate failure.

Stress Intensity Factors at the Intersection of a Crack and Pore Channels with Various Cross-Sections

Changes of stress intensity factors (SIF) of a flat main crack with rectilinear front which cuts the system of regular parallel pore channels normally to their direction are determined. Channels had cross-sections in the form of a circle, an equilateral triangle, a triangle with the concave sides of constant curvature and a starlike crack. It is shown that SIF on the main and channel cracks may have comparable values.

Concomitant Channel Cracking and Interfacial Delamination in Polymer/Oxide Nano Hybrid Permeation Barriers in Flexible Electronics

ABSTRACTPolymer/oxide nano hybrid multilayer permeation barriers are emerging as a promising solution to the stringent barrier requirement of flexible electronics. Yet the mechanical failure of the multilayer permeation barriers could be fatal to their barrier performance. We study two co-evolving failure mechanisms of the multilayer permeation barriers under tension, namely, the cracking of the inorganic oxide layer and the delamination along the oxide-organic interface, using computational modeling. An effective driving force for the oxide layer cracking is determined, which decreases as the oxide-organic interfacial adhesion increases.

Channel cracking in inelastic film/substrate systems

Studies on channel cracking are generally limited to elastic films on elastic or inelastic substrates. There are important applications were the cracking process involves extensive plasticity in both the film and substrate, however. In this work steady-state channel cracking in inelastic thin-film bilayers undergoing large-scale yielding from thermal or mechanical loading is studied with the aid of a plane-strain FEA. The plasticity of the film and substrate, represented by a Ramberg–Osgood constitutive law, each increases the energy release rate (ERR) relative to the linearly-elastic case. This effect is more pronounced under mechanical loading where the entire bilayer undergoes large-scale yielding. To help assess the analytic approach some fragmentation tests are performed using a well-bonding epoxy/aluminum system. The analysis reproduced well the observed dependence of crack initiation strain on film thickness. Ultra-thin films may be well represented by an elastic-perfectly plastic response. For such films on a flexible support the ERR remains fixed as the applied strain exceeds the yield strain of the film. Accordingly, a critical coating thickness exists below which no channel cracking is possible. The explicit relations and graphical data presented may be used for optimal design of such structures against premature failure as well as for determining fracture energy of ductile thin films.

Bubble-induced cavitation effect upon solid surfaces

The dynamic damage during cavitation erosion is of a spall nature and results from the interference of rarefaction waves. Spherical shock waves, which arise due to the collapse of cavitation bubbles, generate shock waves in the target. The rarefaction waves appear when the velocity of the contact boundary decreases below the sound velocity in the target material and the shock waves emerge at the free surface. The coordinate of the rarefaction wave formation site determines the zone of potential damage. The interference of rarefaction waves creates the spall channel crack, near which the coaxial cylindrical cracks are formed-as a rule, in the dynamic fatigue regime-in the course of subsequent loading.

Ductility of thin copper films on rough polymer substrates

Electronic components in modern flexible electronics are connected by interconnects, which typically have the form of metal films resting on polymer substrates. This paper firstly studies experimentally the ductility of Cu films deposited on polyimide substrate with roughened surface (due to sandblasting) and finds that, upon tensile loading along the direction of film surface, the density of surface cracks in the film decreases with increasing surface roughness. The method of finite elements is subsequently employed to study the distribution of tensile stresses in the film and their influence on film cracking (initiation and propagation). It is demonstrated that a rough (curved) interface can reduce the tensile stresses along the film surface so as to restrain channel cracking of the film. Finally, the cohesive zone model is used to study the initiation and spreading of damage in the film and interfacial debonding of the curved interface. Both the interfacial damage and interface crack length are reduced as a result of interface roughening.

On strain-localized damage in nanoscale Cu–Ta multilayers on a flexible substrate

Through the careful examination of the tensile-deformed Cu–Ta multilayers with individual layer thickness of 10 nm, we found that alignment of grain boundaries occurred in the localized deformation zone close to channel cracks on the top Cu layer. Quantitative measurement of the variation amplitude of grain boundary path and theoretical analysis indicated that nanometer-scale movement of grains appeared to accommodate the localized plastic deformation in the Cu–Ta multilayer. The possible mechanisms for the nanometer-scale movement of the grains in the nanoscale metallic multilayer were evaluated.

Case studies of earthquake-induced effects on concrete channels

Case studies are presented for two concrete lined channels shaken by strong ground motions during the 1994 Northridge earthquake, the high speed channel (HSC) and bypass channel (BC), on the Los Angeles Department of Water and Power’s Van Norman Complex. Performances of these two channels as they pass through different subsurface materials identify several important seismic aspects and the critical role of geotechnical earthquake engineering in assessing channel behaviors. Preliminary evaluations using detailed mapping of channel cracks, permanent ground movements, subsurface profiles, and nearby strong ground motion recordings from the 1994 earthquake show that the channel liners may have been damaged from both transient motions and permanent ground movements. Damage from permanent ground deformations is obvious by observation; therefore simplified analyses are presented only for transient movements. Site specific transient response analyses are performed to provide an initial assessment of the differing effects from transient and permanent ground movements on HSC and BC liner damage. These case studies are helpful for introducing the potential for lifeline damage from transient movements within zones of permanent ground movement, a concept not well understood in the earthquake engineering community.