An Approach to Estimate Interface Shear Stress of Ceramic Matrix Composites from Hysteresis Loops

An approach to estimate interface shear stress of ceramic matrix composites during fatigue loading has been developed in this paper. By adopting a shear-lag model which includes the matrix shear deformation in the bonded region and friction in the debonded region, the matrix crack space and interface debonding length are obtained by matrix statistical cracking model and fracture mechanics interface debonding criterion. Based on the damage mechanisms of fiber sliding relative to matrix in the interface debonded region upon unloading and subsequent reloading, the unloading counter slip length and reloading new slip length are determined by the fracture mechanics method. The hysteresis loops of four different cases have been derived. The hysteresis loss energy for the strain energy lost per volume during corresponding cycle is formulated in terms of interface shear stress. By comparing the experimental hysteresis loss energy with computational values, the interface shear stress corresponding to different cycles can then be derived. The theoretical results have been compared with experimental data of three different ceramic composites.     

Modeling Loading/Unloading Hysteresis Behavior of Unidirectional C/SiC Ceramic Matrix Composites

The loading/unloading tensile behavior of unidirectional C/SiC ceramic matrix composites at room temperature has been investigated. The loading/unloading stress–strain curve exhibits obvious hysteresis behavior. An approach to model the hysteresis loops of ceramic matrix composites including the effect of fiber failure during tensile loading has been developed. By adopting a shear-lag model which includes the matrix shear deformation in the bonded region and friction in the debonded region, the matrix cracking space and interface debonded length are obtained by matrix statistical cracking model and fracture mechanics interface debonded criterion. The two-parameter Weibull model is used to describe the fiber strength distribution. The stress carried by the intact and fracture fibers on the matrix crack plane during unloading and subsequent reloading is determined by the Global Load Sharing criterion. Based on the damage mechanisms of fiber sliding relative to matrix during unloading and subsequent reloading, the unloading interface reverse slip length and reloading interface new slip length are obtained by the fracture mechanics approach. The hysteresis loops of unidirectional C/SiC ceramic matrix composites corresponding to different stress have been predicted.     

An elastic-plastic shear lag model for fracture of layered coatings

We present a phenomenological model describing cracking under uniaxial tensile strain of a brittle thin film on a deformable substrate with an elastic-plastic interface layer. The model yields an analytical solution predicting average crack density and average crack opening as a function of applied strain and material parameters. The model has been applied to experimental data for cracks in thin SiO_x films on PET substrates.     

Contact damage in TiN coatings on steel

Damage mechanisms beneath Vickers indentations are examined on 5 μm TiN film deposited on stainless steel substrate as a function of load. Prominent mode of cracking includes surface edge cracks and subsurface inclined cracks. No interfacial delaminations were noted at the TiN/steel interface. The tangential traction, radial stress and shear stress distribution around an axisymmetric indentation field are used to assess the driving force for crack propagation.     

Mechanical and thermal properties of physical vapour deposited alumina films Part II Elastic, plastic, fracture, and adhesive behaviour

Two mechanical characterization techniques were used to deduce the elastic, plastic, fracture, and adhesive properties of non-reactive physical vapour deposited alumina films of varying thickness on Al₂O₃-TiC substrates deposited at two different substrate biases. Depth-sensing indentation at both nano- and macroscopic load scales was used to determine the elastic and plastic properties of the films. Gravity-loaded Vickers indentation was performed to examine the fracture properties of the film and of the interface. Novel fracture mechanics models were developed to describe indentation-induced film fracture by channel cracks and indentation-induced interface delamination. The former model was used to determine the film toughness and the latter model was used to deduce the interfacial fracture resistance of the films and correctly predicted the effect of changing film thickness. Both models described the measured crack lengths with indentation load well and were used to identify the transition from radial and lateral cracking to channel and interfacial cracking.     

Slip-band behavior and crack initiation in polycrystalline copper under multiaxial low-cycle fatigue—a damage mechanics approach

A damage mechanics approach to formation of slip bands and initiation of fatigue cracks was investigated in the present paper. The nucleation and growth behaviors of slip bands and cracks in the low-cycle fatigue region were experimentally observed for pure copper under multiaxial cyclic stresses of combined tension-compression and torsion (the ratios of torsional to axial strain ranges were 0,2 and ∞). The statistical distributions of orientation for slip bands and grain-boundary cracks with respect to the stress biaxiality were examined through observation. Analyses based on geometrical modelings of slip-band formation and grain-boundary cracking were carried out to simulate the experimental results. The approach proposed in the study was found to succeed in evaluating the trends of slip-band and grain-boundary cracks depending on the biaxial stress states.     

An explicit elastic solution for a brittle film with periodic cracks

A two-dimensional explicit elastic solution is derived for a brittle film bonded to a ductile substrate through either a frictional interface or a fully bonded interface, in which periodically distributed discontinuities are formed within the film due to the applied tensile stress in the substrate and consideration of a “weak form stress boundary condition” at the crack surface. This solution is applied to calculate the energy release rate of three-dimensional channeling cracks. Fracture toughness and nominal tensile strength of the film are obtained through the relation between crack spacing and tensile strain in the substrate. Comparisons of this solution with finite element simulations show that the proposed model provides an accurate solution for the film/substrate system with a frictional interface; whereas for a fully bonded interface it produces a good prediction only when the substrate is not overly compliant or when the crack spacing is large compared with the thickness of the film. If the section is idealized as infinitely long, this solution in terms of the energy release rate recovers Beuth’s exact solution for a fully cracked film bonded to a semi-infinite substrate. Interfacial shear stress and the edge effect on the energy release rate of an asymmetric crack are analyzed. Fracture toughness and crack spacing are calculated and are in good agreement with available experiments.     

Matrix cracking and interface debonding in fiber-reinforced cement-matrix composites

The processes of matrix cracking and interface debonding were studied using the high sensitivity Moire interferometry technique. The experiments were conducted with continuous steel fiber reinforced cementitious composites subjected to uniaxial tension. The initiation and propagation of cracking and debonding were observed during the tests with the specimens of different fiber-volume ratios. Based on the experiments, the fiber stress, the interface slip, the interface shear stress, and the matrix strain distribution were calculated. It was shown that interfacial frictional shear stresses were not constant either along the whole interface or at different loading levels. The strain localization was observed in the matrix where it was bonded to the fiber. The average contribution of the matrix was greater for the composites with the higher fiber-volume ratio.     

Analysis of a shear-lag model with nonlinear elastic stress transfer for sequential cracking of polymer coatings

Analyzing a shear-lag model, the evolution of the fragment size distribution in the sequential cracking of polymer coatings under uniaxial loading is investigated. This study elucidates the role of a nonlinear elastic stress transfer mechanism at the interface on the fragmentation kinetics. Using a nonlinear expression for the shear stress at the interface, analytical expressions for the stress and the strain in the coating are derived. In the initial stage of cracking, the strain in a fragment equals the substrate's strain everywhere except in the exclusion zone at the fragments' edges. In the later stages of fragmentation, the stress and the strain in a fragment attain a universal scaling form with pronounced maxima in the centers of the fragments. Assuming a three parameter Weibull distribution for the statistical distribution of the coating's strength, analytical expressions for the fragment size distribution in the initial stage and numerical results for the fragment size distribution in the later stages of the cracking process are derived.     

内嵌弹性区和结合力模型在薄膜/基底界面断裂中的应用

薄膜/基底结构是微电子学和材料科学中广泛应用的典型结构。由于加工工艺中材料力学、热学性能失配等原因导致的薄膜中出现的残余应力,是界面裂纹的萌生和扩展的重要原因。采用三参数(Γ₀, /σ_y,t)的修正的断裂过程区结合力模型,讨论了在塑性氛围下裂尖解理断裂的过程,裂尖应力分布,裂尖形貌和表征裂纹尖端断裂过程区特征参数对断裂过程的影响,并应用到均质金属薄膜/陶瓷基底结构中残余应力导致界面裂纹起裂和扩展的全过程分析中。     

Study of failure of EB-PVD thermal barrier coating upon near-α titanium alloy

The cracking failure of a conventional thermal barrier coating (TBC), consisting of a near-α titanium substrate, a NiCoCrAlY bond coat (BC), and a 8 wt.% yttria-stabilized zirconia ceramic layer deposited by electron beam-physical vapor deposition (EB-PVD) method, was studied by cyclic furnace testing and isothermal exposure. The scanning electron microscope, electron probe microanalysis, and microhardness indentation were used to probe the failure mechanism. It is found that due to the mismatch of the coefficient of thermal expansion, the as-deposited BC is suffered the long-term tensile creeping at room temperature. During the high-temperature exposure, the TBC locally rumples, bringing in-plane tensile stress at the shoulders, and out-of-plane tensile stress at the peak of the rumpled BC, where primal cracks are originated. During the cooling period, the ridges of substrate pulled by the local rumpling of the BC blocks the contracting of the BC, originating new cracks in planar BC, and aggravating the original cracks. Furthermore, the oxidation products pushed into the BC and the 8YSZ enlarges the TBC and cracks the substrate along the weakest diffused grain boundaries. The cracking failure related to the diffusion of the BC to the substrate is also discussed.     

THE PROGRESSION OF BENDING FATIGUE IN INCONEL 625

Abstract— Inconel 625 (N06625) was fatigued in reversed bending and the sequence of surface damage observed. A comparison was made with nickel and Monel K500 studied previously. It was found that, as with nickel, slip markings were present at one cycle even in high life samples. In the Inconel 625, the slip was always planar, multiple slip was common and a plethora of secondary slip was associated with most crack fronts. A noticeable distinction, from nickel and Monel, was the absence of any intergranular cracking. Microhardness measurements revealed that, as with Monel and in contrast to nickel, strain amplitudes high enough to give surface zone hardening led to short lives. from which the inference was made that the inherent fatigue properties of Inconel 625 are inferior to nickel, for advantage cannot be taken of its high strain hardening exponent. Nevertheless, the fatigue limit, as in nickel remains above the yield stress because cracks only initiate when the grains are replete with slip and a rumpled topography has developed.     

Cracking behavior of evaporated amorphous silicon films

The residual stress in amorphous silicon films deposited by evaporation is investigated with different substrate temperatures. The stress measured from all the films studied in this paper is tensile. The level of stress decreases from 580 MPa to 120 MPa with increasing substrate temperature from 60 °C to 350 °C. When the film becomes thicker, strain increases and cracks are formed for stress relaxation. 10 µm thick amorphous Si films are deposited at 350 °C without cracks. This cracking behavior is theoretically studied and confirmed by experiment.     

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.     

Contact damage evolution in a diamond-like carbon (DLC) coating on a stainless steel substrate

A diamond-like carbon thin film was coated onto a stainless steel substrate using plasma assisted chemical vapour deposition (PACVD). Instrumented indentation and scratching were used, supported by focused ion beam (FIB) microscopy, to explore deformation and fracture behaviours of this coating system. The formation and growth of ring and radial cracks in the coating, as well as plastic flow in the ductile substrate, were observed to be the predominant deformation processes for this coating system. Lateral cracking occurred at the interface of the coating/substrate following indentation, but in the middle of the coating following scratching. No evidence of plastic flow within the coating was observed. Coating deformation is, therefore, controlled by its fracture energy. An indentation-energy-based model was applied to evaluate the fracture toughness of the coating.     

Synergistic Effects of Temperature and Oxidation on Matrix Cracking in Fiber-Reinforced Ceramic-Matrix Composites

In this paper, the synergistic effects of temperatrue and oxidation on matrix cracking in fiber-reinforced ceramic-matrix composites (CMCs) has been investigated using energy balance approach. The shear-lag model cooperated with damage models, i.e., the interface oxidation model, interface debonding model, fiber strength degradation model and fiber failure model, has been adopted to analyze microstress field in the composite. The relationships between matrix cracking stress, interface debonding and slipping, fiber fracture, oxidation temperatures and time have been established. The effects of fiber volume fraction, interface properties, fiber strength and oxidation temperatures on the evolution of matrix cracking stress versus oxidation time have been analyzed. The matrix cracking stresses of C/SiC composite with strong and weak interface bonding after unstressed oxidation at an elevated temperature of 700 °C in air condition have been predicted for different oxidation time.     

Mechanical behaviour of TiC film coated on molybdenum by magnetron sputtering

The TiC film, which is coated on molybdenum by magnetron-sputtering, is analysed after the molybdenum substrate is tensile-tested to rupture at 300 to 1070 K. At 300 K some portion of the film exfoliated during the molybdenum substrate deformation. The degree of exfoliation is proportional to the substrate strain up to about 30% elongation, and is proportional to the square root of the film thickness. The maximum shear stress which is generated at the interface between the film and the substrate during the deformation is estimated by the measurement of the distance between cracks. From the estimated maximum shear stress, the adhesive strength of the present TiC film is evaluated to be about 400 MN m^?2.     

正交铺设陶瓷基复合材料单轴拉伸行为

采用细观力学方法对正交铺设陶瓷基复合材料单轴拉伸应力-应变行为进行了研究。采用剪滞模型分析了复合材料出现损伤时的细观应力场。采用断裂力学方法、 临界基体应变能准则、 应变能释放率准则及Curtin统计模型4种单一失效模型确定了90°铺层横向裂纹间距、 0°铺层基体裂纹间距、 纤维/基体界面脱粘长度和纤维失效体积分数。将剪滞模型与4种单一损伤模型结合, 对各损伤阶段应力-应变曲线进行了模拟, 建立了复合材料强韧性预测模型。与室温下正交铺设陶瓷基复合材料单轴拉伸应力-应变曲线进行了对比, 各个损伤阶段的应力-应变、 失效强度及应变与试验数据吻合较好。分析了90°铺层横向断裂能、 0°铺层纤维/基体界面剪应力、 界面脱粘能、 纤维Weibull模量对复合材料损伤及拉伸应力-应变曲线的影响。      

On debonding of thin films

Debonding of a thin film from a large substrate is analyzed by an interface crack model. Based on a solution to interface cracks given by the author, energy release rate and stress intensity factors at the interface crack between the film and the substrate under general film edge loads are determined analytically. The solution is favorably compared with the result from the literature. Thermal stress intensities due to a uniform temperature change are also considered. The solution may be helpful for the analysis and testing of thin film debondings.     

Cracking mechanism in AlN(11―20)/α-Al2O3(1―102) heteroepitaxial films grown by MOCVD

The cracking mechanism in AlN(1120)/-Al₂O₃(1102) heteroepitaxial film grown by MOCVD is discussed. The crystal structure and microstructure of an AlN/Al₂O₃ film and an AlN/GaN/Al₂O₃ film are compared using high-resolution X-ray diffractometry, optical microscopy, scanning electron microscopy, and transmission electron microscopy. In the AlN/Al₂O₃ film, cracks parallel to the [1100]_AlN direction and perpendicular to the interface of the film and the substrate are observed. The cracks do not propagate to the AlN film surface. The tips of the cracks are widest in the AlN film, and the cracks narrow as they penetrate deeply into the substrate. On the other hand, in the AlN/GaN/Al₂O₃ film, no cracks are observed. A concave curvature is observed in the AlN film with cracks on the Al₂O₃ substrate along the [0001]_AlN direction, whereas a convex curvature is observed in the AlN film without cracks. On the basis of these results, the cracks, formed in the AlN film due to the tensile stress along the [0001]_AlN direction during the epitaxial growth, propagate to the AlN film surface and into the Al₂O₃ substrate. On the other hand, in the AlN/GaN/Al₂O₃ film, it seems that the GaN buffer layer suppresses the tensile stress; as a consequence, no cracks occur.