Steady-State Mechanics of Delamination Cracking in Laminated Ceramic-Matrix Composites

A fracture mechanics delamination cracking model has been developed for brittle-matrix composite laminates. The near-tip mechanics is discussed in the context of material orthotropy and composite material inhomogeneities. A fracture mechanics framework based on the near-tip energy release rate and the associated phase angle Ψ has been adopted. In the case of steady-state delamination cracking in a prenotched cross-ply symmetric laminated beam, analytical expressions for the steady-state energy release rate, _ss, have been obtained for the combined applied loading of an axial force and a bending moment. Parameter studies assessing the effects on _ss of load coupling, crack location, and lamination morphology which includes the total number of layers, layer thickness, and material properties are presented. Thus, composite homogenization criteria with respect to the total number of layers placed along the beam height can be obtained for a wide range of material selection. The associated phase angle Ψ at the delamination crack tip is discussed in the context of existing solutions. The analysis has been developed based on a theory for structural laminates. The delamination model can be used in conjunction with experimental data obtained from model geometries to extract the mixed-mode transverse composite fracture toughness. Thus, conditions for stable delamination crack growth can be established and design criteria based on toughness for composite laminates and composite fasteners can be obtained.     

Modeling non-Newtonian slurry convection in a vertical fracture

A model of non-Newtonian slurry convection in a fracture was developed. Based on the simulation [Eskin, D., Miller, M., 2008. A model of non-Newtonian slurry flow in a fracture. Powder Technol. 182, 313-322] and experimental [Tehrani, M.A., 1996. An experimental study of particle migration in pipe flow of viscoelastic fluids. J. Rheology 40, 1057-1077] results on particle migration across a fracture, an accepted modeling system is a three-layer flow consisting of the central core of high particle concentration surrounded by pure fluid layers. The obtained solution describes convection in a small fracture domain where both the mean shear rate and the local particle concentration are known. Numerical study of the developed model shows that the solids settling rate caused by convection is much higher (regularly, by a factor of 10-30) than the particle settling rate, calculated based on an assumption that the particle concentration is uniformly distributed across a fracture. The convection model can be incorporated in one of the known numerical codes for computation of slurry dynamics in a whole fracture. An engineering modification of the convection model allows computing particle slug transport in a fracture.     

Toughening of Layered Ceramic Composites with Residual Surface Compression

Effects of macroscopic residual stresses on fracture toughness of multilayered ceramic laminates were studied analytically and experimentally. Stress intensities for edge cracks in three-layer, single-edge-notch-bend (SENB) specimens with stepwise varying residual stresses in the absence of the crack and superimposed bending were calculated as a function of the crack length by the method of weight function. The selected weight function and the method of calculation were validated by calculating stress intensities for edge cracks in SENB specimens without the residual stresses and obtaining agreement with the stress-intensity equation recommended in ASTM Standard E-399. The stress-intensity calculations for the three-layer laminates with the macroscopic residual stresses were used to define an apparent fracture toughness. The theoretical predictions of the apparent fracture toughness were verified by experiments on three-layer SENB specimens of polycrystalline alumina with 15 vol% of unstabilized zirconia dispersed in the outer layers and 15 vol% of fully stabilized zirconia dispersed in the inner layer. A residual compression of ∼400 MPa developed in the outer layers by the constrained transformation of the unstabilized zirconia from the tetragonal to the monoclinic phase enhanced the apparent fracture toughness to values of 30 MPa^.m^1/2 in a system where the intrinsic fracture toughness was only 5 to 7 MPa^.m^1/2.     

Model Analysis of Multicrack Mechanisms in Ceramic/Superplastic Laminates

Previous experimental results showed that a ceramic/superplastic laminate exhibited multiple cracking in ceramic layers during a three-point bending test. In this work, a model analysis has been developed based on bending theory. It reveals that there are two basic processes that occur after a ceramic layer fractures: one is a relaxation process of the residual stress in the ceramic layer, due to the confinement by the superplastic layers; the other is a shear process of superplastic flow, which originates from the difference in strain rate between the fractured and unbroken ceramic layers. The total stress in an as-fractured ceramic layer is the sum of the residual stress and a shear-accumulated stress, depending on time. When the total stress at a critical distance from the fractured surface exceeds the fracture strength of a ceramic layer, new cracking occurs. There is a critical roller speed below which no multiple cracking occurs, depending on specimen dimensions and material properties. The number of multicracks in one ceramic layer decreases with the progress of the fracture in the laminate, due to the decrease in shear-accumulated stress. The theoretical predications are in good agreement with the experimental results. Moreover, the variations in fracture energy of the laminate due to the multiple cracking are discussed in detail.     

Mullite (3Al2O3·2SiO2)–Aluminum Phosphate (AlPO4), Oxide, Fibrous Monolithic Composites

Mullite–AlPO₄ fibrous monolithic composites were fabricated by a co-extrusion technique using ethylene vinyl acetate (EVA) as a binder. Processing routes such as mixing formulation, extrusion sequence, binder removal cycle, pressing, and sintering procedures are described. An effort to make tougher composites was conducted by modifying the microstructures of the composites. Different kinds of monolithic composites were fabricated by changing the number of filaments, and the composition and thickness of interphase layers, and their microstructural and mechanical properties were characterized. To make the interphase more porous and to facilitate debonding and fiber pullout in the composite, graphite was added as a fugitive "space filler" into the interphase material and then removed. A fibrous monolithic composite with a sintered interphase thickness of 5–10 μm and an interphase composition of 50 vol% graphite and 50 vol% AlPO₄ had a three-point bend strength and a work of fracture of 129 ± 2 MPa and 0.86 ± 0.05 kJ/m², respectively. This corresponded to 42% of the strength but 162% of the work of fracture when compared with the values for a single-phase mullite. Two-layer, mixed 50% two-layer:50% three-layer, and three-layer fibrous monoliths were fabricated and their microstructural and mechanical properties were studied. The difference in the sintering behaviors of the two-layer and three-layer composites is described.     

Stress Corrosion Cracking in a Unidirectional Ceramic-Matrix Composite

A study of matrix cracking in a unidirectional ceramic-matrix composite under static loading conditions has been conducted. The evolution of crack density with time has been measured using both flexure and uniaxial tension tests. Subcritical cracking has been observed at stresses below that required to develop matrix cracks in short-duration, monotonic loading tests. Furthermore, a relatively high final crack density has been observed following extended periods (∼10⁶ s) under static load. A fracture mechanics analysis applicable to subcritical crack growth has been developed and used successfully to model the evolution of matrix cracking with time and applied stress. The model incorporates the properties of the matrix, fibers, and interfaces, as well as the residual stress and the initial flaw distribution in the matrix.     

Statistical modeling for the accumulation of transverse matrix cracking in cross‐ply laminates

A statistical model has been proposed to predict the evolution of matrix cracking in the transverse lamina of cross‐ply laminates subjected to longitudinal tensile loading. The analytical model is based on a fracture mechanics approach which considers that the critical fracture toughness G_c of the 90° layers is not a constant but follows a Weibull distribution. Monte‐Carlo simulation technique is applied to predict the initiation and propagation of transverse cracking in terms of applied stress versus crack density. The effects of the thickness of the 90° layers on progressive damage and failure are also discussed in this study. Good agreements are reached between simulation and experimental results. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers     

Effects of residual stresses on the fracture properties of non-oxide laminated composites

A layered ceramic composite in the AlN–SiC–MoSi₂ system was prepared with the outer layers under residual compressive stress. The mechanical properties of the constituent layers and of the laminated composite were measured. Due to the residual compressive stress, the fracture strength of the laminated composite was higher than the strength of the outer layer material. The fracture toughness of the laminar composite was evaluated by SEVNB. The resulting values were compared with a fracture mechanics model and a good agreement was found between the experimental measurements and the calculated apparent fracture toughness profile.     

Peridynamic-based investigation of the cracking behavior of multilayer thermal barrier coatings

Numerical simulations of the cracking behavior of the top layers of multilayer thermal barrier coatings (TBCs) can effectively reveal the failure mechanisms of the TBCs. Current finite element method (FEM)-based simulation means have been applied to solve certain simple cracking problems in TBCs; however, they cannot effectively describe complex cracking problems in TBCs such as coalescence, intersection, and interference among multiple cracks. Peridynamic (PD), a newly developed mechanical theory, has been widely studied to provide analysis for cracking problems in TBCs. In this paper, a numerical model of TBCs is built by the bond-based PD (BB-PD) theory. Complex cracking behaviors, such as spontaneous crack propagation at both interfacial and internal regions, coalescence, and interference among multiple cracks, are simulated under isothermal cooling and gradient cooling conditions. In addition, the effects of interfacial roughness and calcium–magnesium–alumina–silicate (CMAS) inclusions on the cracking behavior are discussed. The results show that the PD model accurately captures complex cracking behaviors observed via scanning electron microscopy (SEM). Given the ability of the model for analyzing discontinuities in TBCs, it can help to further clarify the fracture mechanisms of TBCs.     

The pull-out and failure of a fiber bundle in a carbon fiber reinforced carbon matrix composite

The interfacial failure is examined for a unidirectionally reinforced carbon fiber/carbon matrix composite. A novel tensile test is conducted which realizes the processes of interfacial debonding and subsequent pull-out of a fiber bundle from the surrounding composite medium. The critical stress at the onset of delamination cracking is related to the fracture energy (the critical energy release rate for mode II cracking). A force-balance equation of a fiber bundle, which is quasi-statically pulled-out of the composite socket, is formulated in terms of the inter- and intra-laminar shear strengths of the composite. This equation is successfully used to estimate the delamination crack length along the debonded fiber bundle, as a function of the stress applied to the bundle.     

Temperature dependent first matrix cracking stress model for the unidirectional fiber reinforced ceramic composites

Based on a kind of equivalence between heat energy and fracture energy, assuming that there is a constant maximum storage of energy that includes both heat energy and fracture energy, a new temperature dependent fracture surface energy model is developed. Using the new model and the classical ACK theory, a temperature dependent first matrix cracking stress model is obtained for the fiber reinforced ceramic composites. According to the model, the temperature dependent first matrix cracking stress of materials can be easily predicted using some basic material parameters such as matrix fracture surface energy and Young’s modulus. The model is verified by comparison with experimental data of SiC fiber reinforced reaction-bonded Si₃N₄ composites at different temperatures. Good agreement is obtained between predicted and experimental data of first matrix cracking stress. The dependency of first matrix cracking stress on fracture surface energy and interfacial shear strength is systematically analyzed.     

Elastic Response and Effect of Transverse Cracking in Woven Fabric Brittle Matrix Composites

This paper examines the linear elastic tensile and fracture behavior of biaxial plain weave SiC/SiC ceramic woven fabric composites. Iso-phase mode and random-phase mode have been adopted to simulate multilayer stacking and to predict the initial linear elastic constants. It has been found that both modes predict very close results. Porosities in the composite affect the stiffness significantly, while fiber undulation shows only minimal effect. The nonlinear stress-strain relation of the composite is due to transverse cracks, which initiate mainly from interyarn pores. In the second part of this paper, two methods, classical fracture mechanics and energy balance approach, have been used to examine the crack initiation and growth. A finite element method and a modified shear-lag method have been developed to evaluate the stress distribution in the yarn with transverse cracks. The composite stiffness reduction due to transverse cracking has been obtained by both the finite element and shear-lag methods. Strain energy release rates of the growth of transverse cracks have been studied by the crack-closure procedure, using finite element methods. Effects of the yarn size and crack position on the strain energy release rate have been quantified. It is concluded that thinner yarns lead to higher critical strains for transverse cracking.     

Indentation Fracture Response and Damage Resistance of Al2O3-ZrO2 Composites Strengthened by Transformation-Induced Residual Stresses

Indentation fracture behavior of three-layer Al₂O₃-ZrO₂ composites with substantial compressive residual stresses was compared with the behaviors of monolithic Al₂O₃ and Al₂O₃-ZrO₂ ceramics without intentionally introduced residual stresses. The indentation cracks were smaller in the three-layer specimens relative to the monolithic specimens in agreement with the predictions of indentation fracture mechanics theory. Indentation and strength testing were used to show that a residual compressive stress of approximately 500 MPa exists in the outer layers of the three-layer composites. The three-layer specimens showed excellent damage resistance in that the strength differential between the three-layer and monolithic indented specimens was maintained at indentation loads up to 1000 N, the maximum indentation load used in the experiments.     

Modeling microvoiding kinetics of rare-earth disilicates in flowing atmospheres containing water vapor

Rare-earth disilicate (REDS, RE₂Si₂O7) layers that may be used as environmental barrier coatings (EBCs) on ceramic matrix composite (CMC) components in high-temperature stages of turbine engines are subject to microvoiding to form porous rare-earth monosilicate (REMS, RE₂SiO₅) layers in flowing atmospheres containing water vapor. A simple microvoiding kinetic model that incorporates both mass transfer of the reaction product Si(OH)₄(g) through the external gas phase boundary layer and pore diffusion of Si(OH)₄(g) through the microvoided layer has been developed. Model predictions are in good agreement with measured growth rates of microvoided layers under low-flowrate steam furnace test and high-flowrate burner rig conditions. Since pore diffusion is generally the rate-limiting step for EBC microvoiding in turbine engines, furnace testing under conditions of kinetic control by gas phase mass transfer is not generally capable of predicting REDS microvoiding rates under engine conditions. The kinetic model can be extended to incorporate changes in pore size and distribution, cracking of the microvoided layer, and introduction and cracking of an additional REMS topcoat to the system. The model can be used to generate a reasonable prediction of the time required to fully microvoid a REDS EBC layer on a CMC component in the hot gas path of an aircraft engine or stationary gas turbine.     

A Layered Alumina Composite Tested at High Temperature in Air

An oxidation-resistant interphase for layered alumina composites was prepared by aerosol spray deposition of submicrometer alumina powder. A model composite specimen was made by placing the interphase between thin layers of monolithic alumina. The composite sandwich was hot-pressed to control the interphase fracture resistance for successful crack deflection. Specimens were tested under four-point bending in air at two crosshead speeds at ambient temperature, 1000°C, and 1200°C. The fracture behavior was temperature dependent, with a higher work of fracture at higher temperatures. Interphase delamination and composite toughening behavior were very pronounced at all temperatures. At the highest temperature, the transition to multiple widely distributed cracks and increased crack deflection may be related to inelastic deformation in the alumina.     

Model for tensile fracture of concrete at high rates of loading

Mechanisms of tensile fracture of concrete are described. A model is developed for an idealized material. The amount of simultaneous cracking and the path of each crack depend on the rate of stressing. The fracture energy and the tensile strength have been determined as functions of the rate of loading. The results of earlier experiments on concrete under impact tensile loading can be explained by this model.     

High-Strength Alumina/Alumina:Calcium-Hexaluminate Layer Composites

The strength degradation of alumina/alumina:calcium-hexaluminate/alumina trilayers, after damage from Hertzian contacts, is evaluated. Relative to the monolithic alumina and alumina:calcium-hexaluminate constituent layer materials, the trilayers show markedly improved strength retention in the damaged state at high contact loads. The outer, fine-grained alumina layers are classically brittle, characterized by cone cracking, whereas the inner alumina:calcium hexaluminate layer is essentially quasi-plastic, with a well-defined "yield" zone that consists of distributed microdamage. The improved strength behavior of the trilayer composite is rationalized in terms of a synergistic interaction between the contact-induced deformation modes in the two layers, with each mode partially ne-gating the effectiveness of the other as a source of failure. This result offers the prospect of hybrid structures with hard outer layers, to provide wear resistance, and soft, tough underlayers, to inhibit brittle fracture.     

Development of functionally graded ZrB2–B4C composites for lightweight ultrahigh-temperature aerospace applications

In the present work, a lightweight three-layer ZrB₂–B₄C functionally graded composite material has been developed by spark plasma sintering route. The functionally graded material (FGM) is free from interlayer defects and displays a smooth transition between the individual layers. The composition of each layer was designed to reduce the overall density without sacrificing the functionality of the material. The density of the FGM is almost 40% lower than monolithic ZrB₂ and 24% lower than ZrB₂–30B₄C rendering it potentially very attractive for high-temperature aerospace applications. A detailed structural characterization of the FGM was carried out to evaluate the elemental distribution in the graded composite, as well as determine the spatial distribution of the crystalline phases. Vickers hardness was measured within each layer and in the interlayer regions to further evaluate the gradient structure and interlayer transitions. Longitudinal elastic constants of the FGM along the thickness and across the layers measured using ultrasound phase spectroscopy showed that despite the gradient structure, the FGM can be treated as a quasi-isotropic solid.     

Mode I and mode II delamination of a chopped strand mat E-glass reinforced vinyl ester composite

The objective of the present work is to investigate mode I and mode II delamination behaviour of chopped strand mat (CSM) E-glass reinforced vinyl ester (VE) composite. Double cantilever beam and end notched flexure tests were carried out to evaluate the mode I and mode II delamination, respectively. The fracture toughnesses were calculated using the experimental calibration method. Results showed that the average mode I and mode II fracture toughnesses were 185 and 2386?N?m^?1, respectively. Furthermore, the mode II–mode I ratio for this material was 12.9. This value was the highest when compared with other composite materials from the literature. Finally, through scanning electron micrographs, the dominant failure mechanisms were found to be matrix cracking, fibre debonding and fibre breakage. In addition, shear cusps were observed in mode II specimen, which signified the shearing between the layers.     

Tensile and fiber dispersion performance of ECC (engineered cementitious composites) produced with ground granulated blast furnace slag

An engineered cementitious composite (ECC) produced with ground granulated blast furnace slag was developed for the purpose of achieving moderately high composite strength while maintaining high ductility, represented by strain-hardening behavior in uniaxial tension. In the material development, single fiber pullout tests and matrix fracture tests were performed, followed by micromechanical analyses to properly select the range of mixture proportion. Subsequent direct tensile tests were employed to assess the strain-hardening behavior of the composite, which exhibited high ductility and strength with the addition of slag. High ductility is most likely due to enhanced workability and fiber dispersion performance which is attributed to the oxidized grain surface of slag, as verified by fiber dispersion tests. These results suggest that, within the limited slag dosage employed in the present study, the contribution of slag to fiber dispersion outweighs the side-effect of decreased potential for saturated multiple cracking, including a slight increase in matrix fracture toughness and fiber/matrix bond strength.