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.     

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.     

Near tip stress intensity factor for an edge-crack in a Pb(ZrxTi1−x)O3 thin film with 90° domain switching under a continuous laser irradiation

The near tip stress intensity factor K_Itip for an edge-crack in a Pb(Zr_xTi_1−x)O₃ thin film was investigated by superposition of the applied stress intensity factor K_Iapp under a continuous laser irradiation and the shielding stress intensity factor ΔK_I for 90° domain switching. Both K_Iapp and ΔK_I were solved by the weight function method, and switching toughening was analyzed based on the small scale domain switching theory. Results show that K_Itip of the edge-crack in the thin film is significantly affected by the initial poling angle, and the edge-crack tip is toughened by the domain switching area with the increase of the initial poling angle. The methodology can predict the fracture toughening of Pb(Zr_xTi_1−x)O₃ thin films quantitatively.     

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.     

Complex variable method of computing Jk for bi-material interface cracks

A method using functions of a complex variable is developed for evaluation of J₁ and a modified J₂ integrals for bi-material interface cracks. This method, used in conjunction with the finite element method, would be useful in the prediction of stress intensity factors for cracks lying between the interface of two dissimilar materials. Since the direct evaluation of J₂ poses difficulties in modeling the singular behavior in the near vicinity around the crack tip for bi-material crack problems, it is modified by evaluating it around a contour path of small radius from the crack tip within the singularity dominated zone. It is shown that the stress intensity factors for a bi-material interface crack can be accurately evaluated using these j_k integrals.     

Dominant stress region for crack initiation at interface edge of microdot on a substrate

In order to examine the mechanics of crack initiation at the free interface edge of a microcomponent on a substrate, delamination tests are carried out for two specimen shapes of Cr microdots on a SiO₂ substrate. The microdots of the first specimen are shaped like the frustum of a round cone. The Cr microdots are successfully delaminated from the SiO₂ substrate in a brittle manner and the critical load is measured by atomic force microscopy (AFM) with a lateral loading apparatus. Stress analysis reveals that a singular stress field exists near the interface edge and the strength for the crack initiation is governed by the intensified normal stress field. The critical stress intensity parameter is evaluated as K_σC ≈ 0.24 MPa m^0.39. Similar delamination tests are conducted for microdots shaped like the frustum of an oval cone. The stress distributions at the crack initiation of this specimen shape show a higher normal stress than the first specimen shape in the region near the interface edge of about x < 40 nm, while it is lower in the region of about x > 50 nm (x: distance from the edge). This suggests a limitation of conventional fracture mechanics: namely, the crack initiation in these specimens is not uniquely governed by the intensity of the singular field. It is found that the delamination crack is initiated when the averaged stress σ_ya in the region of 90-130 nm reaches 190-270 MPa, regardless of the specimen shape. This indicates that the dominant stress region of crack initiation is roughly estimated as 90-130 nm and the criterion is given in terms of the averaged stress in the region.     

Highly a-oriented SrBi2Ta2O9 thin film on (111) Pt/TiO2/SiO2/Si substrate by eclipse pulsed laser deposition

A highly a-oriented SrBi₂Ta₂O₉ thin film with a polycrystalline structure was deposited on a preferentially oriented (111) Pt/TiO₂/SiO₂/Si substrate by eclipse pulsed laser deposition (PLD) method. The SrBi₂Ta₂O₉ thin film exhibited flat and smooth surface with the surface roughness of about 0.5 nm resulting from reducing particulates generated by on-axis PLD. The SrBi₂Ta₂O₉ thin film showed a good ferroelectric property with the high remanent polarization of 12 μC/cm² and the low coercive electric field of 140 kV/cm. For the highly a-oriented SBT thin film, domain switching and reading were performed by Kelvin probe force microscope (KFM). The KFM data indicate a good ferroelectric property of the highly a-oriented SrBi₂Ta₂O₉ thin film with high KFM signals that reflect ferroelectric polarizations.     

Reactive DC sputter-deposited tantalum oxide thin film for all-solid-state switchable mirror

We have developed an all-solid-state switchable mirror of Mg₄Ni/Pd/Ta₂O₅/WO₃/ITO on glass. Each material of Mg₄Ni, Pd, and Ta₂O₅ in the device acts as an optical switching, a proton injector and a solid electrolyte, respectively. The initial state of the device is a reflective state as a mirror and the state changes to a transparent one by applying voltage. In this work, solid electrolyte of Ta₂O₅ thin film was deposited on the WO₃/ITO/glass substrate by reactive DC magnetron sputtering with Ar/O₂ mixture gases. The effect of Ar/O₂ ratio on the electrochemical property of Ta₂O₅ thin film and the optical switching property of the device were investigated. The film deposited at Ar/O₂ of 4.7 had better electrochemical property than that of other films. The transmittance at a wavelength of 670 nm of the device using Ta₂O₅ thin film deposited at Ar/O₂ of 4.7 was reached from the reflective state of 0.1% to the transparent state of 44% less than 15 s by applying voltage of 5 V. The device showed a stable durability of up to 1000 switching cycles.     

Crack-tip fields for matrix cracks between dissimilar elastic and creeping materials

The stress fields near the tip of a matrix crack terminating at and perpendicular to a planar interface under symmetric in-plane loading in plane strain are investigated. The bimaterial interface is formed by a linearly elastic material and an elastic power-law creeping material in which the crack is located. Using generalized expansions at the crack tip in each region and matching the stresses and displacements across the interface in an asymptotic sense, a series asymptotic solution is constructed for the stresses and strain rates near the crack tip. It is found that the stress singularities, to the leading order, are the same in each material; the stress exponent is real. The oscillatory higher-order terms exist in both regions and stress higher-order term with the order of O(r°) appears in the elastic material. The stress exponents and the angular distributions for singular terms and higher order terms are obtained for different creep exponents and material properties in each region. A full agreement between asymptotic solutions and the full-field finite element results for a set of test examples with different times has been obtained.     

Stability and effect of annealing on the optical properties of plasma-deposited Ta2O5 and Nb2O5 films

Tantalum and niobium oxide optical thin films were prepared at room temperature by plasma-enhanced chemical vapor deposition using tantalum and niobium pentaethoxide (M(OC₂H₅)₅) precursors. We studied the evolution of their optical and microstructural properties as a result of annealing over a broad temperature range from room temperature up to 900 °C. The as-deposited films were amorphous; their refractive index, n, and extinction coefficient, k, at 550 nm were n = 2.13 and k < 10^− 4 for Ta₂O₅, and n = 2.24 and k < 10^− 4 for Nb₂O₅. The films contained a small amount of residual carbon (∼ 2-6 at.%) bonded mostly to oxygen. During annealing, the onset of crystallization was observed at approximately T_C1 = 650 °C for Ta₂O₅ and at T_C1 = 450 °C for Nb₂O₅. Upon annealing close to T₁ (300 °C for Nb₂O₅ and 400 °C for Ta₂O₅), n at 550 nm decreased by less than 1%. This was correlated with the decrease of carbon content, as suggested by Fourier transform infrared spectroscopy, elastic recoil detection and static secondary ion mass spectroscopy (SIMS) results. During annealing, we observed phase transition from the δ- (hexagonal) phase to the L- (orthorhombic) phase between 800 °C and 900 °C for Ta₂O₅, and between 600 °C and 700 °C for Nb₂O₅. The structural changes were also marked by silicon diffusion from the substrate into the oxide layer at annealing temperatures above 500 °C for Ta₂O₅ and above 400 °C for Nb₂O₅. As a consequence of oxygen, silicon and metal interdiffusion, the interface between the Si substrate and the metal oxide (Ta₂O₅ or Nb₂O₅) is characterized by its broadening, well documented by spectroscopic ellipsometry and SIMS data.     

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.     

Simultaneous determination of the thermal expansion coefficient and the elastic modulus of Ta2O5 thin film using phase shifting interferometry

Abstract

This paper reports on the application of a phase shifting interferometry technique for the concurrent measurement of the thermal expansion coefficient α_f and the elastic modulus E_f /1 - V_f of Ta₂O₅ thin film. The Ta₂O₅ films were prepared by ion beam sputter deposition. The stresses in the thin films were measured with the phase shifting interferometry technique using two types of circular discs with known thermal expansion coefficients, Young's moduli and Poisson's ratios. The temperature-dependent stress behaviour of Ta₂O₅ films was obtained by heating samples in the range from room temperature to 70°C. The internal stresses of Ta₂O₅ thin films deposited on the BK-7 and Pyrex glass substrates were plotted against the stress measurement temperature, showing a linear dependence. From the slopes of the two lines in the stress versus temperature plot, the thermal expansion coefficient and the elastic modulus of Ta₂O₅ thin film are then calculated.     

Effects of ion energy on internal stress and optical properties of ion-beam sputtering Ta2O5 films

Abstract

The effects of ion-beam energy on the internal stress and optical properties of tantalum pentoxide (Ta₂O₅) thin film have been investigated. Ta₂O₅ thin films were deposited on unheated glass substrates by ion-beam sputter deposition (IBSD) with different ion-beam voltage V _b. The mechanical properties, internal stress and surface roughness, and the optical properties, refractive index and absorption, were studied directly after deposition. The refractive index, extinction coefficient and surface roughness were found to depend on the ion-beam energy. The internal stresses were measured by the phase-shifting interferometry technique. The film stress was also found to be related to V _b, and a high compressive stress of -0.560 GPa was measured at V _b = 750 V. Ta₂O₅/SiO₂ multilayer coatings had smaller average compressive stress than single-layer Ta₂O₅ film.     

Electrical characteristics of Ti-O/Ta2O5 thin film sputtered on Ta/Ti/Al2O3 substrate

The electrical characteristics of Ti-O/Ta₂O₅ films sputtered on Ta/Ti/Al₂O₃ substrate were investigated. Ta (tantalum) was used for the bottom and upper electrodes for the purpose of simplifying the fabrication process and Al₂O₃ substrates were used, which are needed in integral passive devices. Ta/Ti-O/Ta₂O₅/Ta/Ti/Al₂O₃ capacitors were annealed at 700 °C for 60 s in vacuum. The X-ray diffraction pattern (XRD) results showed that as-deposited Ta had a highly preferred orientation, but Ta₂O₅ film had amorphous structure, which was transformed to crystallization structure by rapid thermal heat treatment. We examined the log J-E and C-V characteristics of the dielectric thin films deposited on the Ta bottom electrode. From these results, we concluded that the leakage current could be reduced by introducing a Ti-O buffer layer. The conduction mechanisms of Ta/Ti-O/Ta₂O₅/Ta/Ti/Al₂O₃ capacitors could be interpreted appropriately by hopping conduction in lower field (E<1×10⁵ V/cm) and space-charge-limited current in higher fields (1×10⁵ V/cm<E).     

Magnetically actuated peel test for thin films

Delamination along thin film interfaces is a prevalent failure mechanism in microelectronic, photonic, microelectromechanical systems, and other engineering applications. Current interfacial fracture test techniques specific to thin films are limited by either sophisticated mechanical fixturing, physical contact near the crack tip, or complicated stress fields. Moreover, these techniques are generally not suitable for investigating fatigue crack propagation under cyclical loading. Thus, a fixtureless and noncontact experimental test technique with potential for fatigue loading is proposed and implemented to study interfacial fracture toughness for thin film systems. The proposed test incorporates permanent magnets surface mounted onto micro-fabricated released thin film structures. An applied external magnetic field induces noncontact loading to initiate delamination along the interface between the thin film and underlying substrate. Characterization of the critical peel force and peel angle is accomplished through in situ deflection measurements, from which the fracture toughness can be inferred. The test method was used to obtain interfacial fracture strength of 0.8-1.9 J/m² for 1.5-1.7 μm electroplated copper on natively oxidized silicon substrates.     

A computational model and experimental validation of shielding and amplifying effects at a crack tip near perpendicular strength-mismatched interfaces

The stress field around the crack tip near an elastically matched but strength-mismatched interface body in a bimetallic system is influenced when the crack tip yield or cohesive zone spreads to the interface body. The concept of crack tip stress intensity parameter, K _tip, is therefore employed in fracture analysis of the bimetallic body. A computational model to determine K _tip is reviewed in this paper. The model, based upon i) Westergaard??s complex potentials coupled with Kolosov?CMuskhelishvili??s relations between a crack tip stress field and complex potentials and ii) Dugdale??s representation of the cohesive zone clearly indicates shielding or amplifying effects of strength mismatch across the interface, depending upon the direction of the strength gradient, over the crack tip. The model is successfully validated by conducting series of high cycle fatigue tests over Mode I cracks advancing towards various strength-mismatched interfaces in bimetallic compact tension specimens prepared by electron beam welding of elastically identical weak ASTM 4340 alloy and strong MDN 250 maraging steels.     

Fracture analysis of a surface through-thickness crack in PZT thin film under a continuous laser irradiation

In this paper, the surface crack problem in PZT thin films under a continuous laser irradiation has been investigated by the superposition principle. Using commercial (FEM) software ANSYS 9.0, the piezoelectric fields near the crack tip were solved for surface crack in the finite PZT thin film. The SIFs for crack-tip fields were obtained by using the limited stress extrapolation technique (LSET) and then the energy release rates were calculated by the relation to the intensity factors. When the irradiation time and crack location were changed, the energy release rates G, G_I, and G_e for total, mechanical terms (mode I) and electric contribution were investigated. The results show that the mechanical opening mode I is the main mode for the surface crack under a continuous laser irradiation. However, electric mode IV has inhibiting effect on crack growth. At the beginning of laser irradiation, the surface tiny crack which is close to the centre of film will propagate more easily. During the laser irradiation, the crack which is far from the centre of film will propagate more easily.     

Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique

This paper describes an interface element to calculate the strain energy release rates based on the virtual crack closure technique (VCCT) in conjunction with finite element analysis (FEA). A very stiff spring is placed between the node pair at the crack tip to calculate the nodal forces. Dummy nodes are introduced to extract information for displacement openings behind the crack tip and the virtual crack jump ahead of the crack tip. This interface element leads to a direct calculation of the strain energy release rate (both components G_I and G_II) within a finite element analysis without extra post-processing. Several examples of stationary cracks under impact loading were examined. Dynamic stress intensity factors were converted from the calculated transient strain energy release rate for comparison with the available solutions by the others from numerical and experimental methods. The accuracy of the element is validated by the excellent agreement with these solutions. No convergence difficulty has been encountered for all the cases studied. Neither special singular elements nor the collapsed element technique is used at the crack tip. Therefore, the fracture interface element for VCCT is shown to be simple, efficient and robust in analyzing crack response to the dynamic loading. This element has been implemented into commercial FEA software ABAQUS^® with the user defined element (UEL) and should be very useful in performing fracture analysis at a structural level by engineers using ABAQUS^®.     

Fatigue crack propagation and cyclic deformation at a crack tip

The fatigue crack propagation relation da/dN = f(R)ΔK² can be derived with three assumptions: small scale yielding, material homogeneity and that crack tip stresses and strains are not strongly affected by plate thickness. f(R) is a constant at a given stress ratio, R. The effects of plate thickness and stress ratio on crack tip deformation and fatigue crack growth in 2024-T351 aluminum alloy were studied. High ΔK level in a thin specimen causes crack tip necking. Necking is more pronounced at high stress ratio. Necking causes high maximum strain near a crack tip, ε_max, and fast crack growth rate. In order to avoid the effects of crack tip necking, plates thicker than 2.5 (ΔK/σ_Y(c))² should be used.