Time dependent crack growth in ceramic matrix composites with creeping fibers

Crack growth in ceramic matrix composites with creeping fibers has been investigated using a time dependent bridging law to describe the effect of fibers bridging a matrix crack. The fibers were assumed to creep linearly and the matrix was assumed to be elastic. Time dependent crack growth was predicted assuming that matrix crack growth occurs when the stress intensity factor at the matrix crack tip reaches a constant critical value. Crack growth rates are presented as a function of crack length and time. Domains of stable and unstable crack growth are outlined. The solutions illustrate that stable crack growth consists of a relatively brief period of decerelation followed by acceleration to large crack lengths, with crack velocity approaching constancy only at loads very near the matrix cracking stress and for very long cracks. Finally, the time needed to grow a long matrix crack is compared with a rough estimate for the time needed to rupture fibers. A transition is expected from life dominated by matrix crack growth at low stress to life dominated by fiber creep rupture after crack growth at higher stresses.     

Transverse cracking in fiber-reinforced brittle matrix,cross-ply laminates

The topic addressed in this paper is transverse cracking in the matrix of the 90° layers of a cross-ply laminate loaded in tension. Several aspects of the problem are considered, including conditions for the onset of matrix cracking, the evolution of crack spacing, the compliance of the cracked laminate, and the overall strain contributed by residual stress when matrix cracking occurs. The heart of the analysis is the plane strain problem for a doubly periodic array of cracks in the 90° layers. A fairly complete solution to this problem is presented based on finite element calculations. In addition, a useful, accurate closed form representation is also included. This solution permits the estimation of compliance change and strain due to release of residual stress. It can also be used to predict the energy release rate of cracks tunneling through the matrix. In turn, this energy release rate can be used to predict both the onset of matrix cracking and the evolution of crack spacing in the 90° layers as a function of applied stress. All these results are used to construct overall stress-strain behavior of a laminate undergoing matrix cracking in the presence of initial residual stress.     

Matrix cracking in crossply ceramic matrix composites under quasi-static and cyclic loading

Experimental data are presented for the development of 90° ply and 0° ply cracking in two crossply silicon carbide fibre/calcium aluminosilicate matrix laminates under quasi-static loading. under mechanical fatigue loading it is found that there is an increase in ply crack densities and a corresponding laminate stiffness reduction with cycling. Possible mechanisms to account for these observations are proposed. A model is presented which describes the stress/strain behaviour as a function of crack densities based on assumptions of frictional load transfer between fibre and matrix in the longitudinal plies and elastic bonding between the longitudinal and transverse plies.     

Materials characterization of silicon carbide reinforced titanium (Ti/SCS-6) metal matrix composites: Part I. Tensile and fatigue behavior

Flexural fatigue behavior was investigated on titanium (Ti-15V-3Cr) metal matrix composites reinforced with cross-ply, continuous silicon carbide (SiC) fibers. The titanium composites had an eightply (0, 90, +45, -45 deg) symmetric layup. Fatigue life was found to be sensitive to fiber layup sequence. Increasing the test temperature from 24 °C to 427 °C decreased fatigue life. Interface debonding and matrix and fiber fracture were characteristic of tensile behavior regardless of test temperature. In the tensile fracture process, interface debonding between SiC and the graphite coating and between the graphite coating and the carbon core could occur. A greater amount of coating degradation at 427 °C than at 24 °C reduced the Ti/SiC interface bonding integrity, which resulted in lower tensile properties at 427 °C. During tensile testing, a crack could initiate from the debonded Ti/SiC interface and extend to the debonded interface of the neighboring fiber. The crack tended to propagate through the matrix and the interface. Dimpled fracture was the prime mode of matrix fracture. During fatigue testing, four stages of flexural deflection behavior were observed. The deflection at stage I increased slightly with fatigue cycling, while that at stage II increased significantly with cycling. Interestingly, the deflection at stage III increased negligibly with fatigue cycling. Stage IV was associated with final failure, and the deflection increased abruptly. Interface debonding, matrix cracking, and fiber bridging were identified as the prime modes of fatigue mechanisms. To a lesser extent, fiber fracture was observed during fatigue. However, fiber fracture was believed to occur near the final stage of fatigue failure. In fatigued specimens, facet-type fracture appearance was characteristic of matrix fracture morphology. Theoretical modeling of the fatigue behavior of Ti/SCS-6 composites is presented in Part II of this series of articles. This article is based on a presentation made in the symposium entitled “Creep and Fatigue in Metal Matrix Composites” at the 1994 TMS/ASM Spring meeting, held February 28–March 3, 1994, in San Francisco, California, under the auspices of the Joint TMS-SMD/ASM-MSD Composite Materials Committee.     

Fatigue crack growth in fiber-reinforced metal-matrix composites

Fatigue crack growth in fiber-reinforced metal-matrix composites is modeled based on a crack tip shielding analysis. The fiber/matrix interface is assumed to be weak, allowing interfacial debonding and sliding to occur readily during matrix cracking. The presence of intact fibers in the wake of the matrix crack shields the crack tip from the applied stresses and reduces the stress intensity factors and the matrix crack growth rate. Two regimes of fatigue cracking have been simulated. The first is the case where the applied load is low, so that all the fibers between the original notch tip and the current crack tip remain intact. The crack growth rate decreases markedly with crack extension, and approaches a “steady-state”. The second regime occurs if the fibers fail when the stress on them reaches a unique fiber strength. The fiber breakage reduces the shielding contribution, resulting in a significant acceleration in the crack growth rate. It is suggested that a criterion based on the onset of fiber failure may be used for a conservative lifetime prediction. The results of the calculations have been summarized in calibrated functions which represent the crack tip stress intensity factor and the applied load for fiber failure.     

The mechanics of matrix cracking in brittle-matrix fiber composites

Matrix fracture in brittle-matrix fiber composites is analyzed for composites that exhibit multiple matrix cracking prior to fiber failure and have purely frictional bonding between the fibers and matrix. The stress for matrix cracking is evaluated using a stress intensity approach, in which the influence of the fibers that bridge the matrix crack is represented by closure tractions at the crack surfaces. Long and short cracks are distinguished. Long cracks approach a steady-state configuration, for which the stress intensity analysis and a previous energy balance analysis are shown to predict identical dependence of matrix cracking stress on material properties. A numerical solution and an approximate analytical solution are obtained for smaller cracks and used to estimate the range of crack sizes over which the steady-state solution applies.     

Micromechanics and fatigue crack growth in an alumina-fiber-reinforced magnesium alloy composite

A study has been made of fatigue crack growth through the magnesium alloy ZE41A and a composite of this alloy reinforced with alumina fibers. Crack growth rates were measured and failure mechanisms characterized for specimens with fibers parallel to the loading axis and for two off-axis orientations. Crack opening displacements and matrix and fiber strains in the vicinity of the crack tip were measured using the stereomaging technique. Crack growth rates through the composite were retarded by the fibers. For the composite with fibers at 22.5 deg to the loading axis, fibers were found to fracture in the composite at the same stress as measured for the fibers alone. Fiber fracture was the dominant growth-controlling mechanism for fibers oriented on and 22.5 deg to the loading axis, and little fiber pullout was observed. However, for crack growth through material with fibers oriented at 45 deg to the loading axis, crack growth was found to exist principally through the interface. Driving forces for cracks in interfaces were determined to be smaller than the applied δK. It was found that approximate fatigue crack growth rates through the composites could be predicted from those through the matrix by adjusting the tensile modulus. The upper and lower bounds of fatigue crack growth rate were also computed for the composite using a micromechanics-based model that incorporated observed failure mechanisms. A. McMINN, formerly with Southwest Research Institute, is with Failure Analysis Associates, Washington, D.C.     

Effect of interfacial debonding and sliding on matrix crack initiation during isothermal fatigue of SCS-6/Ti-15-3 composites

Direct observation of initial damage-evolution processes occurring during cyclic testing of an unnotched SCS-6 fiber-reinforced Ti-15-3 composite has been carried out. The aligned fibers break at an early stage, followed by debonding and subsequent sliding along the interface between the reaction layer (RL) and Ti-15-3 alloy matrix. Matrix cracking initiation from the initial broken fiber and RL was avoided. This fracture behavior during cyclic loading is modeled and analyzed by the finite-element method, with plastic deformation of the matrix being considered. The plastic strain in the matrix at the initial crack and at the deflected crack tips, when the interface crack is deflected into the RL after extensive interface debonding propagation, is characterized. The effects of interfacial debond lengths and test temperatures on the matrix cracking mechanism are discussed, based on a fatigue-damage summation rule under low-cycle fatigue conditions. The numerical results provide a rationale for experimental observations regarding the avoidance and occurrence of the matrix cracking found in fiber-reinforced titanium composites.     

On the tensile properties of a fiber reinforced titanium matrix composite—II. Influence of notches and holes

The effects of holes and notches on the ultimate tensile strength of a unidirectionally reinforced titanium matrix composite have been examined. During tensile loading, a narrow plastic strip forms ahead of the notch or hole prior to fracture, similar to that observed in thin sheets of ductile metals. Examination of the fibers following dissolution of the matrix indicates that essentially all the fibers within such a strip are broken prior to catastrophic fracture of the composite. The trends in notch-strength have been rationalized using a fracture mechanics-based model, treating the plastic strip as a bridged crack. The observations suggest that the bridging traction law appropriate to this class of composite is comprised of two parts. In the first, the majority of fibers are unbroken and the bridging stress corresponds to the unnotched tensile strength of the composite; in the second, the fibers are broken and the bridging stress is governed by the yield stress of the matrix, with some contribution derived from fiber pullout. This behavior has been modeled by a two-level rectilinear bridging law. The parameters characterizing the bridging law have been measured and used to predict the notch strength of the composite. A variation on this scheme in which the fracture resistance is characterized by an intrinsic toughness in combination with a rectilinear bridging traction law has also been considered and found to be consistent with the predictions based on the two-level traction law.     

Accelerated Stress Corrosion Crack Initiation of Alloys 600 and 690 in Hydrogenated Supercritical Water

The objective of this study is to determine whether stress corrosion crack initiation of Alloys 600 and 690 occurs by the same mechanism in subcritical and supercritical water. Tensile bars of Alloys 690 and 600 were strained in constant extension rate tensile experiments in hydrogenated subcritical and supercritical water from 593 K to 723 K (320 °C to 450 °C), and the crack initiation behavior was characterized by high-resolution electron microscopy. Intergranular cracking was observed across the entire temperature range, and the morphology, structure, composition, and temperature dependence of initiated cracks in Alloy 690 were consistent between hydrogenated subcritical and supercritical water. Crack initiation of Alloy 600 followed an Arrhenius relationship and did not exhibit a discontinuity or change in slope after crossing the critical temperature. The measured activation energy was 121 ± 13 kJ/mol. Stress corrosion crack initiation in Alloy 690 was fit with a single activation energy of 92 ± 12 kJ/mol across the entire temperature range. Cracks were observed to propagate along grain boundaries adjacent to chromium-depleted metal, with Cr₂O₃ observed ahead of crack tips. All measures of the SCC behavior indicate that the mechanism for stress corrosion crack initiation of Alloy 600 and Alloy 690 is consistent between hydrogenated subcritical and supercritical water.     

Matrix crack spacing in brittle matrix composites

A model describing the evolution of matrix cracks in undirectional continuous fiber, brittle matrix composites is developed. The approach involves calculation off the steady state strain energy release rate available for crack extension in terms of the constituent properties, the applied stress and the distances to the neighboring cracks. Interactions between cracks are found to occur when the crack spacing falls below twice the slip length. The model provides an analytical solution to the crack spacing for periodic arrays of cracks. Comparisons are conducted with predictions derived from computer simulations of random cracking. The effects of the matrix flaw density are briefly considered.     

The micromechanics of fatigue crack growth at 25 °C in Ti-6Al-4V reinforced with SCS-6 fibers

Micromechanics parameters for fatigue cracks growing perpendicular to fibers were measured for the center-notched specimen geometry. Fiber displacements, measured through small port holes in the matrix made by electropolishing, were used to determine fiber stresses, which ranged from 1.1 to 4 GPa. Crack opening displacements at maximum load and residual crack opening displacements at minimum load were measured. Matrix was removed along the crack flanks after completion of the tests to reveal the extent and nature of the fiber damage. Analyses were made of these parameters, and it was found possible to link the extent of fiber debonding to residual COD and the shear stress for fiber sliding to COD. Measured experimental parameters were used to compute crack growth rates using a well-known fracture mechanics model for fiber bridging tailored to these experiments.     

Effect of Stress Level on the High Temperature Deformation and Fracture Mechanisms of Ti-45Al-2Nb-2Mn-0.8 vol. pct TiB2: An In Situ Experimental Study

The effect of the applied stress on the deformation and crack nucleation and propagation mechanisms of a γ-TiAl intermetallic alloy (Ti-45Al-2Nb-2Mn (at. pct)-0.8 vol. pct TiB₂) was examined by means of in situ tensile (constant strain rate) and tensile-creep (constant load) experiments performed at 973 K (700 °C) using a scanning electron microscope. Colony boundary cracking developed during the secondary stage in creep tests at 300 and 400 MPa and during the tertiary stage of the creep tests performed at higher stresses. Colony boundary cracking was also observed in the constant strain rate tensile test. Interlamellar ledges were only found during the tensile-creep tests at high stresses (σ > 400 MPa) and during the constant strain rate tensile test. Quantitative measurements of the nature of the crack propagation path along secondary cracks and along the primary crack indicated that colony boundaries were preferential sites for crack propagation under all the conditions investigated. The frequency of interlamellar cracking increased with stress, but this fracture mechanism was always of secondary importance. Translamellar cracking was only observed along the primary crack.     

Effects of oxidation on the fatigue crack growth resistance and the interfacial properties of a Ti-MMC laminate composite

Fatigue crack growth rates in a [0/90]_2s Ti-6Al-4V/SCS-6 cross-ply laminate, correlated with push-out tests, have been measured to assess the effects of varying test temperature, environment, load ratio (R), and initial stress intensity factor range (ΔK). The fatigue crack growth resistance is degraded in tests at 450 °C in air, but tests carried out at test temperatures of up to 450 °C under vacuum, both at R=0.1 and R=0.5, have shown crack arrest/catastrophic failure transitions (CA/CF), which are similar to those observed for specimens studied at room temperature and at 300 °C in air. Moreover, for such [0/90] composites, the critical role of intact 0 deg fibers bridging in the crack wake, in promoting fatigue crack growth resistance, has been confirmed. Sudden increases of fatigue crack growth rate can be attributed to individual fiber failure(s), which were detected by acoustic emission techniques. The effect of the experimental conditions (environment, test temperature, and duration) on the mechanical behavior (fatigue crack growth rate, push-out tests, and broken fibers pull-out lengths) of this laminate may be explained by the modification of the interfacial zone (decrease in the carbon layer thickness due to oxidation and formation of TiO₂).     

Fatigue crack growth of SM-1240/TIMETAL-21S metal matrix composites at elevated temperatures

A series of high-temperature fatigue crack growth experiments was conducted on a continuous-fiberreinforced SM1240/TIMETAL-21S composite using three different temperatures, room temperature (24 °C), 500 °C, and 650 °C, and three loading frequencies, 10, 0.1, and 0.02 Hz. In all the tests, the cracking process concentrated along a single mode I crack for which the principal damage mechanism was crack bridging and fiber/matrix debonding. The matrix transgranular fracture mode was not significantly influenced by temperature or loading frequency. The fiber debonding length in the crack bridging region was estimated based on the knowledge of the fiber pullout lengths measured along the fracture surfaces of the test specimens. The average pullout length was correlated with both temperature and loading frequency. Furthermore, the increase in the temperature was found to lead to a decrease in the crack growth rate. The mechanism responsible for this behavior is discussed in relation to the interaction of a number of temperature-dependent factors acting along the bridged fiber/matrix debonded zone. These factors include the frictional stress, the radial stress, and the debonding length of the fiber/matrix interface. In addition, the crack growth speed was found to depend proportionally on the loading frequency. This relationship, particularly at low frequencies, is interpreted in terms of the development of a crack tip closure induced by the relaxation of the compressive residual stresses developed in the matrix phase in regions ahead of the crack tip during the time-dependent loading process.     

Response of Quasi-Brittle Materials Reinforced by Short, Aligned Fibers

Pseudo-strain-hardening behavior of quasi-brittle materials reinforced by discontinuous, aligned fibers subjected to uniaxial tension is studied in this paper. An R-curve was used to describe transverse cracking of fiber-reinforced composites. The equivalent inclusion method and Mori-Tanaka theory were used to derive the strain energy release rate of the composites. The proposed model takes into account the influence of fiber distribution. When properties of fiber and matrix are known, the proposed model is capable of predicting whether or not a composite will fail with a single crack or multiple cracks. If a composite fails due to multiple cracks, the model can further predict its pseudo-strain-hardening behavior after the formation of the first transverse crack. The theoretical calculation reasonably matched the experimental results.     

Crack initiation at long radial hydrides in Zr-2.5nb pressure tube material at elevated temperatures

Crack initiation at hydrides in smooth tensile specimens of Zr-2.5Nb pressure tube material was investigated at elevated temperatures up to 300 °C using an acoustic emission (AE) technique. The test specimens contained long, radial hydride platelets. These hydrides have their plate normals oriented in the applied stress direction. Below~100 °C, widespread hydride cracking was initiated at stresses close to the yield stress. An estimate of the hydride’s fracture strength from this data yielded a value of ~520 MPa at 100 °C. Metallography showed that up to this temperature, cracking occurred along the length of the hydrides. However, at higher temperatures, there was no clear evidence of lengthwise cracking of hydrides, and fewer of the total hydride population fractured during deformation, as indicated by the AE record and the metallography. Moreover, the hydrides showed significant plasticity by being able to flow along with the matrix material and align themselves parallel to the applied stress direction without fracturing. Near the fracture surface of the specimen, transverse cracking of the flow-reoriented hydrides had occurred at various points along the lengths of the hydrides. These fractures appear to be the result of stresses produced by large plastic strains imposed by the surrounding matrix on the less ductile hydrides.     

Cracking Characteristics of RC Beams Strengthened with FRP System

The cracking characteristics of fiber-reinforced polymer (FRP) strengthened reinforced concrete (RC) beams in both the short- and long-term is addressed in this paper. First, an empirical equation based on regression analysis of test results obtained from 36 beams was derived for the evaluation of crack widths in FRP-strengthened RC beams under short-term loading. The equation accounts for the effective concrete area in tension, steel stress, proximity of tensile longitudinal reinforcement, and primary crack height. Next, the long-term crack widths of glass FRP-strengthened RC beams under sustained loads were studied. Beams strengthened with glass FRP laminates showed improved cracking characteristics with smaller crack widths compared to conventional RC beams. Based on the investigation, two empirical equations are presented to compute the long-term crack widths in FRP-strengthened beams.     

On the Influence of Alloy Composition on the Additive Manufacturability of Ni-Based Superalloys

The susceptibility of nickel-based superalloys to processing-induced crack formation during laser powder-bed additive manufacturing is studied. Twelve different alloys—some of existing (heritage) type but also other newly-designed ones—are considered. A strong inter-dependence of alloy composition and processability is demonstrated. Stereological procedures are developed to enable the two dominant defect types found—solidification cracks and solid-state ductility dip cracks—to be distinguished and quantified. Differential scanning calorimetry, creep stress relaxation tests at 1000 °C and measurements of tensile ductility at 800 °C are used to interpret the effects of alloy composition. A model for solid-state cracking is proposed, based on an incapacity to relax the thermal stress arising from constrained differential thermal contraction; its development is supported by experimental measurements using a constrained bar cooling test. A modified solidification cracking criterion is proposed based upon solidification range but including also a contribution from the stress relaxation effect. This work provides fundamental insights into the role of composition on the additive manufacturability of these materials.