Indentation fracture and indentation delamination in ZnO film/Si substrate systems

ZnO films with thicknesses ranging from 0.202 to 1.535?µm were deposited by using the magnetron sputtering technique on Si (100) substrates 525?µm thick. Then, Vickers indentation tests were carried out on the ZnO/Si systems at room temperature, in which the applied load varied from 10?mN to 2.0?N. The experimental results show that only indentation-induced radial cracking occurred in the systems with film thicknesses equal to and thinner than 0.554?µm, from which the residual stress in the films was extracted to be 387?MPa in compression. For the systems with film thicknesses equal to and thicker than 0.832?µm, only indentation-induced delamination occurred when indentation loads were low. Under high indentation loads, radial cracking concurrently occurred with delamination. The radial cracks were invisible at the film surfaces because the crack length was smaller than the delamination size. The critical film thickness for indentation-induced delamination was found to be around 0.7?µm for the ZnO/Si systems. Combining the composite hardness models with the indentation-induced delamination model, we developed a method to determine the interfacial fracture energy between a film and its substrate. The novel method is particularly useful for indentation equipment without any displacement measurement devices. Using the new method, we extracted the interfacial fracture energy to be about 12.2?J?m^?2 and from 9.2 to 11.7?J?m^?2 for the cases without and with buckling respectively of delaminated films. Consequently, the pure mode I interfacial fracture energy was calculated to be 10.4?J?m^?2 for the ZnO/Si systems.     

In situ observation of interfacial debonding process induced by matrix crack propagation in two-dimensional unidirectional model composites

Interfacial debonding behavior is studied for unidirectional fiber reinforced composites from both experimental and analytical viewpoints. A new type of two-dimensional unidirectional model composite is prepared using 10 boron fibers and transparent epoxy resin with two levels of interfacial strength. In situ observation of the internal mesoscopic fracture process is carried out using the single edge notched specimen under static loading. The matrix crack propagation, the interfacial debonding growth and the interaction between them are directly observed in detail. As a result, the interfacial debonding is clearly accelerated in specimens with weakly bonded fibers in comparison with those with strongly bonded fibers. Secondary, three-dimensional finite element analysis is carried out in order to reproduce the interfacial debonding behavior. The experimentally observed relation between the mesoscopic fracture process and the applied load is given as the boundary condition. We successfully evaluate the mode II interfacial debonding toughness and the effect of interfacial frictional shear stress on the apparent mode II energy release rate separately by employing the present model composite in combination with the finite element analysis. The true mode II interfacial debonding toughness for weaker interface is about 0.4 times as high as that for a stronger interface. The effect of the interfacial frictional shear stress on the apparent mode II energy release rate for the weak interface is about 0.07 times as high as that for the strong interface. The interfacial frictional shear stress and the coefficient of friction for weak interface are calculated as 0.25 and 0.4 times as high as those for strong interface, respectively.     

Evaluation on the interfacial fracture toughness of fiber-reinforced titanium matrix composites by push out test

The models for single-fiber push out test are developed to evaluate the fracture toughness G_IIc of the fiber/matrix interface in titanium alloys reinforced by SiC monofilaments. The models are based on fracture mechanics, taking into consideration of the free-end surface and Poisson expansion. Theoretical solutions to G_IIc are obtained, and the effects of several key factors such as the initial crack length, crack length, friction coefficient, and interfacial frictional shear stress are discussed. The predictions by the models are compared with the previous finite element analysis results for the interfacial toughness of the composites including Sigma1240/Ti-6-4, SCS/Ti-6-4, SCS/Timetal 834, and SCS/Timetal 21s. The results show that the models can reliably predict the interfacial toughness of the titanium matrix composites, in which interfacial debonding usually occurs at the bottom of the samples.     

Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part II. Crack propagation: Effect of friction on force-displacement curves

In micromechanical tests for estimating fiber-matrix interfacial properties, such as the pull-out and microbond tests, fiber debonding from a matrix is often accompanied by friction in debonded areas. In the present study, force-displacement curves, which are usually recorded in these tests, were modeled with taking interfacial friction into consideration. The friction stress was assumed, as a first approximation, to be constant across the interface. Two different approaches to interfacial failure were used: the shear-lag approach with a stress-based debonding criterion (the ultimate interfacial shear strength) and the linear elastic fracture mechanics approach using the critical energy release rate as a condition for crack propagation. The force-displacement curves derived from both models are in good agreement with each other and with experimental micromechanical data. It was shown that any pull-out and microbond experiment comprises four stages: (1) linear loading up to the point where debonding starts; (2) stable crack propagation with friction-controlled debonding; (3) catastrophic debonding; and (4) post-debonding friction. Stable crack propagation was shown to be controlled by both friction and release of residual thermal stresses. An algorithm for estimating both fiber-matrix adhesion and interfacial friction from the microbond and pull-out tests data has been proposed.     

Fracture and debonding behavior of coated brittle alumina layer on ductile aluminum substrate wire

The fracture and debonding behavior of the Al₂O₃ layer coated on a ductile aluminum substrate wire was studied experimentally and analytically. When tensile strain was applied, the brittle Al₂O₃ coating layer showed multiple cracking perpendicular to the tensile axis. After the multiple cracking, compressive fracture of the Al₂O₃ layer arose in the circumferential direction when the layer was thinner than around 30 μm, while interfacial debonding between the Al₂O₃ layer and aluminum substrate arose when it was thicker. Such a difference in behavior between thin and thick layers could be accounted for by the difference in the layer thickness-dependence of the tensile radial stress at the interface and the compressive hoop stress of the Al₂O₃ layer calculated by the finite element method; the former stress increases while the latter one decreases with increasing layer thickness.     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

Application of optical 3D measurement on thin film buckling to estimate interfacial toughness

The shape-from-focus (SFF) method has been widely studied as a passive depth recovery and 3D reconstruction method for digital images. An important step in SFF is the calculation of the focus level for different points in an image by using a focus measure. In this work, an image entropy-based focus measure is introduced into the SFF method to measure the 3D buckling morphology of an aluminum film on a polymethylmethacrylate (PMMA) substrate at a micro scale. Spontaneous film wrinkles and telephone-cord wrinkles are investigated after the deposition of a 300 nm thick aluminum film onto the PMMA substrate. Spontaneous buckling is driven by the highly compressive stress generated in the Al film during the deposition process. The interfacial toughness between metal films and substrates is an important parameter for the reliability of the film/substrate system. The height profiles of different sections across the telephone-cord wrinkle can be considered a straight-sided model with uniform width and height or a pinned circular model that has a delamination region characterized by a sequence of connected sectors. Furthermore, the telephone-cord geometry of the thin film can be used to calculate interfacial toughness. The instability of the finite element model is introduced to fit the buckling morphology obtained by SFF. The interfacial toughness is determined to be 0.203 J/m² at a 70.4° phase angle from the straight-sided model and 0.105 J/m² at 76.9° from the pinned circular model.     

Strong interface adhesion in Fe/TiC

As an aid to understanding the superior toughness of Ti-modified steels provided by fine Ti(C,?N) particles, first-principles full-potential linearized augmented plane wave (FLAPW) density functional calculations were performed on the Fe matrix/TiC particle interface. It was found that at equilibrium a strong covalent bonding between Fe–C is formed at the interface, and the magnetic moment of the interface Fe (1.98?μ _B ) is reduced from that of the tetragonally strained structure (2.51?μ_B). We then calculated with a rigid separation model the separation energy curve and the force separation law for the Fe–C debonding process at the interface, which predicts 2.45?J?m_?2 for the work of separation and 30.66 [GPa] for the force maximum. We also found that the strong Fe–C bond provides an interfacial fracture strength equal to that of the pure bcc Fe matrix. A clear picture is given for the microscopic origin of this strong metal/ceramic adhesion based on density of states (DOS) considerations. For a more realistic understanding of the Fe–C bonding, structural optimization calculations were performed at each separation distance. The effect of relaxation was found to be larger at short separation distances than in the large separation region, which leads to a crossover behavior in the separation energy curve from the elastically deformed to the clearly separated regime at a critical distance (～1.75?Å), and to a discontinuity in the force separation law. Despite this large relaxation effect, the work of separation, 2.52?J?m_?2, is not changed much from that of rigid separation.     

Numerical study of transitional brittle-to-ductile debonding of a capsule embedded in a matrix

This work presents a numerical study that addresses the role of the interfacial fracture energy on the debonding process of a capsule embedded in an elastic matrix, which undergoes a uniaxial far-field stress. The motivation of this work is to analyze and to understand the effects of this energy in the framework of the so-called encapsulation-based self-healing cementitious materials, where glass capsules filled with a fluid healing agent are embedded in a cement-based matrix. A two-dimensional plane strain model based on a combination of the classical finite element method and cohesive surface techniques implemented in the commercial code Abaqus^® has been used. It has been found that there exist three types of debonding regimes, ranging from a perfect brittle response up to a ductile-limited response, and whose range of validity is governed by a straightforward dimensionless number able to predict the type of debonding as a function of flexural properties of the capsule and the interface strength.     

Author Index to Volume 8

Pull-out experiments have been carried out with Kevlar fibres embedded in epoxy resin. Friction accompanied debonding, and had to be allowed for in the analysis. The debonding stress was about equal to the matrix strength for 80°C cured epoxies. However, debonding appears to be a brittle fracture process, and the works of fracture corresponding to the apparent interface strengths are very low, ranging from ca. 20-40 Jm^-2 depending on the surface treatment and degree of cure of the resin. Water immersion for 2300 h at room temperature reduced the apparent strengths and works of fracture with some of the surface treated fibres, but not with the untreated fibres. Interface pressures during debonding were 10-15 MPa for the 20°C cured specimens and 20-30 MPa for the 80°C cure. Water soaking markedly reduced the friction coefficients. Post-debonding friction was high, but estimates of the parameters was probably unreliable due to the fibre having a somewhat thick end due to fibrillation when being cut.     

Adhesion and stress of magnesium oxide thin films: Effect of thickness, oxidation temperature and duration

Nanoscale magnesium oxide thin films have been deposited on glass substrate by thermal oxidation (in air) of vacuum evaporated magnesium films. X-ray diffraction (XRD) showed orientation along (2 0 0) and (2 2 0) directions. The mechanical properties of the MgO thin films were found to be the function of thickness (300, 450 and 600 nm), oxidation temperature (573, 623 and 673 K) and oxidation duration (90 and 180 min). As oxidation temperature and oxidation duration increases, adhesion and intrinsic stress were found to increase. Intrinsic stress decreased whereas adhesion increased due to increase in thin film thickness. The value of intrinsic stress was in range 28.902-73.212 (×10⁷ N/m²) and that of adhesion was 12.1-27.4 (×10⁴ N/m²) for the thin film of thickness 300 nm.     

Electronic structure and spin polarization at the NiMnSb/GaAs(110) interface

Within the density functional theory, ab initio calculations of the electronic structure and magnetic properties of the (110) interface between the NiMnSb alloy and GaAs in dependence on configuration of contact atoms are carried out. It is found that two out of six possible atomic configurations of the interface exhibit a high degree of spin polarization, which attains 100% for one of the interfacial structures studied here. It is shown that contacts with a high degree of spin polarization are the most stable with an adhesion energy of about 1.3 J/m².     

Microstructure dependence of yielding and fracture in Cd-Zn alloys

The coefficient of logarithmic work-hardening, the yield stress and the fracture stress of Cd-2 wt. %Zn alloy of different grain diameters and of Cd-17·4 wt. %Zn alloy decrease with increasing working temperature. Two relaxation temperature regions have been found, the low-temperature region of relaxation (below 483 K) and the high-temperature region (above 483 K). The fracture surface energy for Cd-2 wt. % Zn alloy has been calculated and found to be 1·2 J/m² at the two temperature regions of relaxation. X-ray investigations show that the residual internal strains in the deformed samples increase with increasing working temperature and exhibit a peak value at 483 K.     

Mechanism of adhesion between protein-based hydrogels and plasma treated polypropylene backing

We studied the mechanism of adhesion between N₂ plasma treated polypropylene (PP/N₂) backing and a hybrid hydrogel (HG) produced by chemical crosslinking between poly(ethylene glycol) and soy albumin. The work of adhesion, measured by peel testing, was found to be 25 times higher for PP/N₂ compared to untreated PP (≈5.0 J/m² versus ≈0.2 J/m²). In order to understand the adhesion mechanism, we performed a detailed analysis of the surface chemical composition of PP and PP/N₂ using X-ray photoelectron spectroscopy (XPS), chemical derivatization and attenuated total reflectance infra-red (ATR-IR) measurements. The results confirm incorporation of different nitrogen- (amine, amide,…) and oxygen- (hydroxyl, carboxyl,…) containing chemical groups on the PP/N₂ surface. The derivatized functions were primary amine, hydroxyl, carboxyl and carbonyl groups. Chemical derivatization reactions validated the XPS results (except for carbonyl groups), and they clearly underlined the essential role of primary amine groups in the adhesion process. In fact, after derivatization of the amine functions, the work of adhesion was found to be 0.41 ± 0.12 J/m². Participation of amine groups in the formation of covalent bonds at the interface between PP/N₂ and HG was directly confirmed by ATR-IR measurements.     

Effect of interfacial debonding and matrix cracking on mechanical properties of multidirectional composites

In composites, debonding at the fiber–matrix interface and matrix cracking due to loading or residual stresses can effect the mechanical properties. Here three different architectures — 3-directional orthogonal, 3-directional 8-harness satin weave and 4-directional in-plane multidirectional composites — are investigated and their effective properties are determined for different volume fractions using unit cell modeling with appropriate periodic boundary conditions. A cohesive zone model (CZM) has been used to simulate the interfacial debonding, and an octahedral shear stress failure criterion is used for the matrix cracking. The debonding and matrix cracking have significant effect on the mechanical properties of the composite. As strain increases, debonding increases, which produces a significant reduction in all the moduli of the composite. In the presence of residual stresses, debonding and resulting deterioration in properties occurs at much lower strains. Debonding accompanied with matrix cracking leads to further deterioration in the properties. The interfacial strength has a significant effect on debonding initiation and mechanical properties in the absence of residual stresses, whereas, in the presence of residual stresses, there is no effect on mechanical properties. A comparison of predicted results with experimental results shows that, while the tensile moduli E ₁₁, E ₃₃and shear modulus G ₁₂ match well, the predicted shear modulus G ₁₃ is much lower.     

Adhesive fracture of heterogeneous interfaces

We have studied the effect of interface heterogeneity on fracture, at both local and global scales. The single cantilever beam adhesion test was used to investigate interfacial fracture between polycarbonate plates and an elastic/fragile epoxy adhesive. Two surface treatments were applied to a (given) polycarbonate plate giving zones of strong and weak adhesion parallel to the crack direction. Calculated fracture energies differed from those expected from a simple rule-of-mixtures. A perturbation method, proposed by Rice, was used and results compared with crack fronts observed in situ. The technique was applied successfully but the difference in values of stress intensity factor between the zones was found substantially different from the experimental value. In an attempt to explain discrepancies, specimens with discontinuous crack fronts (adhesive and/or plates severed along the strong/weak adhesion frontier) were tested. Good agreement was found with the rule-of-mixtures predictions raising questions about the role of crack front continuity in load transfer.     

Influence of Fibre Taper on the Interfacial Shear Stress in Fibre-Reinforced Composite Materials during Elastic Stress Transfer

The paper is concerned with finite element (FE) analysis of stress transfer from an elastic matrix to an elastic fibre, which need not be a uniform cylinder, in a fibre-reinforced composite material. Axisymmetric models of fibres embedded in co-axial cylindrical matrices were investigated by the FE method. Fibre shapes investigated were cylindrical, ellipsoidal, paraboloidal taper and conical taper. The effects of varying the fibre aspect ratio, q (ranging 200 to 3500) and Young's modulus (relative to that of the matrix), E _f /E _m (ranging 10³ to 10⁶) were investigated. The results show that ellipsoidal and parabolic tapers lead to a similar distribution of interfacial shear stress (τ) to that observed for a uniform cylindrical fibre, except that the magnitude of the stress is higher. For a conical taper (except for q = 200, E _f /E _m = 10⁶), the interfacial stress increases to a maximum between the centre and the end of the fibre and then decreases towards the fibre ends. The effect of fibre taper on the distribution of τvalues is reflected in the axial tensile stress, σ_z , distribution induced in a fibre. For example, for a fibre with a conical taper, the distribution of τ values can lead to an even distribution of σ_z along the length of a fibre.     

Improvement of surface wettability and interfacial adhesion of poly-(p-phenylene terephthalamide) by incorporation of the polyamide benzimidazole segment

In order to investigate the effect of the polyamide benzimidazole group on the surface wettability and interfacial adhesion of fiber/matrix composites, surface features of two kinds of aramid fibers, poly (p-phenylene terephthalamide) fiber (Kevlar-49) and poly-(polyamide benzimidazole-co-p-phenylene terephthalamide) (DAFIII), have been analyzed by X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM) and contact angle analysis (CAA) system, respectively.The results show that with the incorporation of the polyamide benzimidazole segment, more polar functional groups exist on DAFIII surface. The contact angles of water and diiodomethane on DAFIII surface get smaller. The surface free energy of DAFIII increases to 36.5 mJ/m², which is 2.3% higher than that of Kevlar-49. In addition, DAFIII has a larger rough surface compared with that of Kevlar-49 due to different spinning processes. The interfacial shear strength (IFSS) of DAFIII/matrix composite is 25.7% higher than that of Kevlar-49/matrix composite, in agreement with the observed results from surface feature tests. SEM micrographs of failed micro-droplet specimens reveal a strong correlation between the fracture features and the observed test data.     

On the use of energy methods for interpretation of results of single-fiber fragmentation experiments

_We consider fragmentation experiments as a set of experimental results for fiber break density as a function of applied strain. This paper explores the potential for using fracture mechanics or energy methods in interpreting fragmentation experiments. We found that energy does not control fiber fracture; instead, fiber fracture releases much more energy than required to fracture the fiber. The excess released energy can lead to other damage mechanisms such as interfacial debonding. By assuming that all the excess released energy causes interfacial debonding and balancing energy using the energy release rate for debonding, we were able to determine interfacial toughness from fragmentation experiments. A reliable determination of interfacial toughness requires prior knowledge of interphase stress-transfer properties, fiber failure properties, actual damage mechanisms, and the coefficient of friction at the interface.     

Statics and dynamics of adhesion between two soap bubbles

An original set-up is used to study the adhesive properties of two hemispherical soap bubbles put into contact. The contact angle at the line connecting the three films is extracted by image analysis of the bubbles profiles. After the initial contact, the angle rapidly reaches a static value slightly larger than the standard 120^° angle expected from Plateau rule. This deviation is consistent with previous experimental and theoretical studies: it can be quantitatively predicted by taking into account the finite size of the Plateau border (the liquid volume trapped at the vertex) in the free energy minimization. The visco-elastic adhesion properties of the bubbles are further explored by measuring the deviation Δθ_d(t) of the contact angle from the static value as the distance between the two bubbles supports is sinusoidally modulated. It is found to linearly increase with Δr _c/r _c , where r_c is the radius of the central film and Δr _c the amplitude of modulation of this length induced by the displacement of the supports. The in-phase and out-of-phase components of Δθ_d(t) with the imposed modulation frequency are systematically probed, which reveals a transition from a viscous to an elastic response of the system with a crossover pulsation of the order 1rad · s^-1. Independent interfacial rheological measurements, obtained from an oscillating bubble experiment, allow us to develop a model of dynamic adhesion which is confronted to our experimental results. The relevance of such adhesive dynamic properties to the rheology of foams is briefly discussed using a perturbative approach to the Princen 2D model of foams.