A through interface crack between a transversely isotropic pair of materials (+30°/−60°, −30°/+60°)

This study focuses on a delamination between two layers of a fiber-reinforced composite material oriented in the directions θ/(θ − 90°). Two specific interfaces are examined: the +30°/−60° interface and −30°/+60° interface. The delamination in these cases is treated effectively as a crack between two monoclinic materials. The behavior of the stress and displacement fields near the crack tip is studied. The first term of the asymptotic expansion for the stress and displacement fields are found by means of the Stroh and Lekhnitskii formalisms. A general solution is obtained for an interface crack in the x₂ = 0 plane. The crack is between two monoclinic materials with x₂ = 0 a symmetry plane.In order to calculate the stress intensity factors, a three-dimensional interaction energy or conservative M-integral is extended and implemented in conjunction with the finite element method. For the M-integral, the auxiliary fields used are particular cases of the stress and displacement fields obtained earlier. The displacement extrapolation method is also extended for this case. The crack surface displacements obtained from a finite element analysis are employed. The methods are independent of each other; hence, they may be used for validation of the results determined.Three test cases are analyzed to examine the accuracy of the results obtained by means of the M-integral method. In addition, two problems of a central crack in a symmetric composite under different loadings are solved. Those loadings are tension and in-plane shear. Stress intensity factors and the interface energy release rate are obtained along the crack front for all cases.     

Role of plasticity on interface crack initiation from a free edge and propagation in a nano-component

In order to elucidate the role of plasticity on interface crack initiation from a free edge and crack propagation in a nano-component, delamination experiments were conducted by a proposed nano-cantilever bend method using a specimen consisting of ductile Cu and brittle Si and by a modified four-point bend method. The stress fields along the Cu/Si interface at the critical loads of crack initiation and crack propagation were analyzed by the finite element method. The results reveal that intensified elastic stresses in the vicinity of the interface edge and the crack tip are very different, although the Cu/Si interface is identical in both experiments. The plasticity of Cu was then estimated on the basis of the nano-cantilever deflection measured by in situ transmission electron microscopy. The plasticity affects the stress fields; the normal stress near the interface edge is intensified while that near the crack tip is much reduced. Both the elasto-plastic stresses are close to each other in the region of about 10 nm. This suggests that the local interface fracture, namely, the crack initiation at the interface edge and the crack propagation along the interface, is governed by elasto-plastic normal stress on the order of 10 nm.     

Effect of residual stress on delamination from interface edge between nano-films

The focus in this study is on the effect of residual stress on the delamination crack initiation from the interface edge between thin films, Cu/TiN, where the stress is intensified by the free edge effect. The delamination tests, where the mechanical stress is applied on the interface, show that the specimen with the thinner Cu film has an apparently higher strength at the interface edge. The residual stress in the films is then evaluated by curvature measurement of film/substrate coupon and the influence on the delamination is analyzed. The residual stress increases with the increase of film thickness and remarkably intensifies the stress near the edge. By superimposing the contributions of the applied load and the residual stress, a good agreement is obtained in the normal stress intensity near the interface edge at the delamination independent of the Cu thickness. This signifies that the combination of intensified stresses due to the applied load and the residual stress governs the crack initiation at the interface edge, and the toughness at the interface edge is evaluated by the stress intensity factor on the basis of the fracture mechanics concept.     

Effect of interface layer consisting of nanosprings on stress field near interface edge

The purpose of this study is to investigate the effect of an interface layer consisting of discretely arrayed nano-sized elements on stress intensified fields. A material where an interface layer consisting of Ta₂O₅ helical nanoelements (nanosprings) is inserted between dissimilar components is prepared and two types of crack initiation experiments, which possess radically different stress conditions, are carried out. The finite element analyses indicate that the stress fields in the components with and without the interface layer are completely different, and it is experimentally clarified that the fracture mechanics concept cannot be applied to the crack initiation at the dissimilar interface edge with the interface layer. The stress distributions at the crack initiation reveal that the crack initiation is governed by the apparent stress of the nanospring, σ′, at the edge. This signifies that the interface layer eliminates the stress singular field at the interface edge. The criterion of the crack initiation is evaluated as .     

Increase of stress intensity near interface edge of elastic-creep Bi-material under a sustained load

The transition from small-scale creep to large-scale creep ahead of a crack tip or an interface edge with strong elastic stress singularity at the loading instant causes stress relaxation and the decrease of stress intensity in general. However, this study shows that the stress near the interface edge of bi-material with no or weak elastic stress singularity increases after the loading instant and brings about the stress concentration during the transition. In addition, the creep strain distribution of this bi-material after the loading instant is different from that occurred in the transition of an interface edge with strong elastic stress singularity or a crack tip (notch root). The criterion for the increase or decrease of stress intensity near the interface edge proved by the finite element method is proposed in this study. The stress intensity near the interface edge increases when the elastic stress singularity is lower than the creep stress singularity (λ^el < λ^cr) and vice versa.     

Creep crack initiation at a free edge of an interface between submicron thick elements

To clarify the mechanics of time-dependent crack initiation at an interface edge in submicron thick elements due to creep, delamination experiments are conducted using a micro-cantilever bend specimen with a tin/silicon interface edge. After the specimen time-dependently deforms under a constant load, a delamination crack is initiated at the Sn/Si interface edge. In addition, the steady state creep property of Sn is estimated by performing an inverse analysis using a finite element method based on creep deformation experiments conducted for different specimens. Stress analysis using the obtained creep property reveals that stress and strain rate singularities exist at the Sn/Si interface edge under creep deformation. The intensity of the singular field time-dependently increases as the creep region expands, and eventually it becomes a steady state. The stress and strain rate intensities at the steady state correlate well with the crack initiation life, which indicates that the singular stress field near the interface edge governs the creep crack initiation.     

High-cycle fatigue characteristics of quasi-isotropic CFRP laminates over 10 cycles (Initiation and propagation of delamination considering interaction with transverse cracks)

High-cycle fatigue features of over 10⁸ cycles, particularly the initiation and propagation of edge delamination considering the effects of transverse cracks, were investigated using quasi-isotropic carbon-fiber-reinforced plastic (CFRP) laminates with a stacking sequence of [45/0/−45/90]_s in this study. In the relationship between a transverse crack density and initiation and growth of edge delamination, it was found that fatigue damage growth behavior varied depending on applied stress. It was observed that edge delamination initiated and grew at parts where transverse cracks were dense at ordinary applied stress, whereas it was observed that edge delamination grew before or simultaneously with transverse crack propagation at a low applied stress and high-cycle loading. In addition, the critical transverse crack density where delamination begins growing was calculated to evaluate the interaction between transverse crack and edge delamination growth.     

Interfacial fatigue crack propagation in microscopic model composite using bifiber shear specimens

Interfacial fatigue crack growth behavior in GF/epoxy model composites was investigated using bifiber shear (BFS) specimens in a scanning electron microscope. The specimen is composed of two E-glass filaments with diameters of 23 and 40 μm, and bisphenol A type epoxy is impregnated between the filaments. The crack growth behavior under different stress ratios was investigated to clarify the fatigue crack growth mechanism. The change in the crack growth rate, da/dN, was not monotonic with crack length, suggesting a variation in the resistance to fatigue crack growth along a single filament. The resistance to fatigue crack growth of the interface is much smaller than that of composite laminates. The fatigue crack growth mechanism of the glass fiber/epoxy interface under different stress ratios is controlled by the maximum energy release rate, G_max, which is completely different from that of composite laminates.     

Electronic properties of n-ZnO(Al)/p-Si heterojunction prepared by dc magnetron sputtering

The electronic properties of the interface between p-type Si and Al-doped ZnO have been investigated. Films of ZnO(Al) with a thickness of 300 nm were deposited at room temperature by dc magnetron sputtering and subsequently subjected to heat treatment in air in the temperature range 100-400 °C. Current-voltage (I-V), capacitance-voltage (C-V) and deep level transient spectroscopy (DLTS) measurements were used to characterize the electrical properties of the heterostructure. The I-V measurements show a diode-like behavior with a rectification of ~ 3-4 orders of magnitude. However, annealing above 200 °C gives rise to a pronounced recombination/generation current in the depletion region, which correlates with an increase of the carrier concentration close to the interface and indicates defect formation. Indeed, DLTS reveals the presence of two prominent defect states, one at 0.38 eV above the valence band edge (E_v), and the other, formed during the heat treatment above 250 °C, around E_v + 0.43 eV, which is consistent with the I-V and C-V data.     

Initiation of interface crack at free edge between thin films with weak stress singularity

Delamination tests using sandwich type specimens are conducted for eight combinations of materials: thin films formed on silicon substrates which are relatively popular in micro-electronic industry, to develop a method for quantitative evaluation and comparison of crack initiation strength at the free edge. The difficulty stems from the difference of stress singularity, K_ij/r^λ (K_ij: stress intensity, r: distance from free edge and λ: order of stress singularity), where λ is depending on the combination of materials. Thus, the critical K_ij has different dimensions, MPa m^λ, in each interface. Using the experimentally observed delamination load, the stress distribution along the interface is analyzed by boundary element method. Since the orders of stress singularity, λ, in the materials are less than 0.07 (weak singularity), the stress field near the interface edge is almost constant in atomic (nanometer) level. Then, the critical strength for the interface cracking is quantitatively represented by the concentrated stress near the edge. The effects of the several factors such as species of thin films, oxidized interlayers and deposition processes of thin films on the interface strength are evaluated on the basis of this critical stress as well.     

Bulge testing and fracture properties of plasma-enhanced chemical vapor deposited silicon nitride thin films

The mechanical properties and fracture behavior of silicon nitride (SiN_x) thin film fabricated by plasma-enhanced chemical vapor deposition is reported. Plane-strain moduli, prestresses, and fracture strengths of silicon nitride thin films deposited both on a bare Si substrate and on a thermally oxidized Si substrate were extracted using bulge testing combined with a refined load-deflection model of long rectangular membranes. The plane-strain moduli and prestresses of SiN_x thin films have little dependence on the substrates, that is, for the bare Si substrate, they are 133 ± 19 GPa and 178 ± 22 MPa, respectively, while for the thermally oxidized substrate, they are 140 ± 26 GPa and 194 ± 34 MPa, respectively. However, the fracture strength values of SiN_x films grown on the two substrates are quite different, i.e., 1.53 ± 0.33 GPa and 3.08 ± 0.79 GPa for the bare Si substrate and the oxidized Si substrate, respectively. The reference stresses were computed by integrating the local stress of the membrane at the fracture over the edge, surface, and volume of the specimens and fitted with the Weibull distribution function. For SiN_x thin film produced on the bare Si substrate, the volume integration gave a significantly better agreement between data and model, implying that the volume flaws are the dominant fracture origin. For SiN_x thin film grown on the oxidized Si substrate, the fit quality of surface and edge integration was significantly better than the volume integration, and the dominant surface and edge flaws could be caused by buffered HF attacking the SiN_x layer during SiO₂ removal.     

Structure and optical properties of Zr1−xSixN thin films on sapphire

A series of zirconium silicon nitride (Zr_1−xSi_xN) thin films were grown on r-plane sapphire substrates using reactive RF magnetron co-sputtering of Zr and Si targets in a N₂/Ar plasma. X-ray diffraction pole figure analysis, X-ray reflectivity, X-ray photoelectron spectroscopy (XPS), optical microscopy, and optical absorption spectroscopy were used to characterize the film stoichiometries and structures after growth at 200 °C and post-deposition annealing up to 1000 °C in ultra-high vacuum. The atomically clean r-plane sapphire substrates induce high quality (100) heteroepitaxy of ZrN films rather than the (111) orientation observed on steel and silicon substrates, but the addition of Si yields amorphous films at the 200 °C growth temperature. After the annealing treatment, films with Si content x < 0.15 have compressive stress and crystallize into a polycrystalline structure with (100) fiber texture. For x > 0.15, the films are amorphous and remain so even after ultra-high vacuum annealing at 1000 °C. XPS spectra indicate that the bonding changes from covalent to more ionic in character as Si―N bonds form instead of Zr―N bonds. X-ray reflectivity, atomic force microscopy (AFM) and optical microscopy data reveal that after post-deposition annealing the 100 nm thick films have an average roughness < 2 nm, except for Si content near x = 0.15 corresponding to where the film becomes amorphous rather than being polycrystalline. At this stoichiometry, evidence was found for regions of film delamination and hillock formation, which is presumably driven by strain at the interface between the film and sapphire substrate. UV-visible absorption spectra also were found to depend on the film stoichiometry. For the amorphous Si-rich films (x > 0.15), the optical band gap increases with Si content, whereas for Zr-rich films (x < 0.15), there is no band gap and the films are highly conductive.     

Towards an electronic model for CuIn1 − xGaxSe2 solar cells

We model some aspects of highly efficient CuIn_1 − xGa_xSe₂ solar cells with x ≈ 0.3 as well as wide band gap cells with x = 1 and ask for the dominant recombination mechanism which limits the V_oc of these devices. For CuIn_1 − xGa_xSe₂ solar cells with x ≈ 0.3, interface recombination combined with Fermi-level pinning is a possible but unlikely recombination mechanism. We argue that these cells are rather limited by recombination in the quasi-neutral region (QNR) including the back contact. Using the expression for the QNR recombination rate we calculate the derivative of the collection function in the absorber at the space charge region edge which is in reasonable agreement with the experiment. It turns out that the diffusion length must approximate the absorber thickness. Based on this information, we draw a band diagram for a CuIn_1 − xGa_xSe₂ solar cells with x ≈ 0.3 and plot the simulated collection function. For cells with x = 1 (Cu-poor CuGaSe₂), the experimental activation energy of the recombination rate mostly equals the absorber band gap, i.e. E_a ≈ E_g,a = 1.67 eV. As the experimental interface band gap is smaller than E_a, interface recombination must be ruled out. Thus, the carrier lifetime in the Cu-poor CuGaSe₂ absorber should be so small that bulk recombination is more efficient than interface recombination. From this consideration, we postulate an electron lifetime value of 10⁻¹² s for CuGaSe₂.     

3D damage characterisation and the role of voids in the fatigue of wind turbine blade materials

The fatigue mechanisms of Glass Fibre Reinforced Polymer (GFRP) used in wind turbine blades were examined using computed tomography (CT). Prior to mechanical testing, as-manufactured [+45/−45/0]_3,s glass/epoxy specimens were CT scanned to provide 3-dimensional images of their internal microstructure, including voids. Voids were segmented and extracted, and individual characteristics and volumetric distributions were quantified. The coupons were then fatigue tested in uniaxial loading at R = −1% to 40% of the nominal tensile failure stress. Some tests were conducted to failure for correlation with the initial void analysis and to establish failure modes. Other tests were stopped at various life fractions and examined using CT to identify key damage mechanisms. These scans revealed transverse matrix cracking in the surface layer, occurring predominantly at free edges. These free-edge cracks then appeared to facilitate edge delamination at the 45/−45° interface. Propagation from sub-critical, surface ply damage to critical, inner ply damage was identified with either a −45/0° delamination, or a 0° fibre tow failure allowing a crack to propagate into the specimen bulk. Final failure occurred in compression and was characterised by total delamination between all the 45/−45° plies. A quantitative void analysis, taken from the pre-test CT scans, was also performed and compared against the specimens’ fatigue lives. This analysis, to the authors’ knowledge the first of its kind, measured and plotted approximately 10,000 voids within the gauge length of each specimen. The global void measurement parameters and distributions showed no correlation with fatigue life. A local ply-level investigation revealed a significant correlation between the largest void and fatigue life in the region of the laminate associated with the crack propagation from sub-critical to critical damage.     

Crack initiation at free edge of interface between thin films in advanced LSI

Since electronic devices are made of multi-layered sub-micron films, delamination along the interface is one of the major failure mechanisms. This paper aims to develop a method for evaluating the mechanical criterion of interface cracking between thin films on a substrate. The focus is put on crack initiation from the free edge of the interface where the stress concentrates due to the mismatch of elastic deformation. In the evaluation, it is important to exclude plastic deformation and fracture of the thin metal film, because they bring about ambiguity on the measured magnitude of interface strength. In this study, an experimental method is proposed on the basis of fracture mechanics concepts, and the validity is examined by tests on Cu (conductor metal)/TaN (barrier metal) interface in a large-scale integrated circuit. The critical stress intensity at delamination crack initiation is successfully analyzed by the boundary element method.     

Inspection of intermediate stress-induced electronic traps in Si/Al2O3 system

The physical characteristics of device-grade thin silicon film at (1 0 0) grown on α-Al₂O₃ substrate using the chemical vapour deposition (CVD) technique has been studied in this paper. Its thickness, crystalline structure, elemental inter-diffusion in the interface region and the quality were characterized by X-ray diffraction (XRD), Rutherford backscattering spectroscopy (RBS), core level X-ray photoelectron spectroscopy (XPS) and nuclear resonance reaction ²⁷Al(p,γ)²⁸Si, respectively. The results of stoichiometric defect profile and individual silicon suboxide (such as SiO, and Si₂O₃ components with respect to the metallic Si element) formation in the intermediate region were observed. The deep traps located around E_c=0.26eV, in ∼500 nm thick n-type Si films, were attributed to the defects caused by the strain of the silicon lattice. Raman spectroscopy was used to evaluate the compressive stress in the Si film.     

Pre-cracking technique for fracture mechanics experiments along interface between thin film and substrate

Utilizing the difference in interface strength due to fabrication process, a technique for producing a sharp pre-crack between a thin film and a substrate is proposed. A cracked specimen for examining fracture toughness of interface between a sputtered copper (Cu) thin film and silicon (Si) is made by the method. A vacuum-evaporated Cu thin film, which has poor adhesion to Si, is inserted between the sputtered Cu thin film and the Si substrate as a release layer. The release layer debonds from the Si substrate at very low load, and the sharp pre-crack is successfully introduced along the interface. Using the pre-cracked specimen, the interface fracture toughness test is conducted and the critical J-integral, J_C, is evaluated as about 1 J/m² for the sputtered Cu/Si interface.     

Determination of higher order coefficients and zones of dominance using a singular integral equation approach

A method to determine higher order coefficients from the solution of a singular integral equation is presented. The coefficients are defined by , which gives the radial stress at a distance, r, in front of the crack tip. In this asymptotic series the stress intensity factor, k₀, is the first coefficient, and the T-stress, T₀, is the second coefficient. For the example of an edge crack in a half space, converged values of the first 12 mode I coefficients (k_n and T_n, n = 0, … , 5) have been determined, and for an edge crack in a finite width strip, the first six coefficients are presented. Coefficients for an internal crack in a half space are also presented. Results for an edge crack in a finite width strip are used to quantify the size of the k-dominant zone, the kT-dominant zone and the zones associated with three and four terms, taking into account the entire region around the crack tip.     

Influence of cobalt doping on the crystalline structure, optical and mechanical properties of ZnO thin films

Uniform and transparent thin films of Zn_1 − xCo_xO (0 ≤ x ≤ 0.10) were fabricated by sol-gel spin coating technique. Co addition up to x = 0.075, led to refinement in structure and improvement in film quality together with average grain size reduction from 17 nm in undoped ZnO to 15 nm with x = 0.05 and 12 nm with x = 0.10 Co additions. For x ≥ 0.035, CoO (cubic) was detected as the secondary phase. Influence of Co addition on the volume fraction of grain boundaries has been interpreted. Increase in Co content in the range 0 ≤ x ≤ 0.10 led to quenching of near-band edge and blue emissions, decrease in band gap energy (E_g) from 3.36 eV to 3.26 eV, decrease in film thickness and refractive index and an increase in extinction coefficient of Zn_1 − xCo_xO thin films. The change in nature of stress from compressive to tensile with lower to higher doping of Co is corroborative with the angular peak shift of (002) plane of ZnO lattice. An overall increase in microhardness of Zn_1 − xCo_xO thin films up to x = 0.05 is attributed to change in microstructure and evolution of secondary phase and as the secondary phase separates out the overall stress is released leading to lowering of hardness after this concentration. Hall-Petch behavior is also studied and found to obey until x = 0.05, however, considerable deviation after this dopant concentration is attributed to the increase in the volume fraction of grain boundaries, which results from the secondary phase separation from this dopant concentration.     

Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique

The two-dimensional and three-dimensional parametric finite element analysis (FEA) of composite flat laminates with two through-the-width delamination types: 0₄/(±θ)₆//0₄ and 0₄//(±θ)₆//0₄ (θ = 0°, 45°, and “//” denotes the delaminated interface) under compressive load are performed to explore the effects of multiple delaminations on the postbuckling properties. The virtual crack closure technique which is employed to calculate the energy release rate (ERR) for crack propagation is used to deal with the delamination growth. Three typical failure criteria: B-K law, Reeder law and Power law are comparatively studied for predicting the crack propagation. Effects of different mesh sizes and pre-existing crack length on the delamination growth and postbuckling properties of composite laminates are discussed. Interaction between the delamination growth mechanisms for multiple cracks for 0₄//(±θ)₆//0₄ composite laminates is also investigated. Numerical results using FEA are also compared with those by existing models and experiments.