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.     

Microcracks tunneling in brittle matrix composites driven by thermal expansion mismatch

During processing, brittle composites are susceptible to cracks caused by residual stress. Matrix cracks parallel to fibers are considered in this paper. Each crack initiates from a porosity, confined by the neighboring fibers, tunneling in the matrix. The analysis uses the concept of steady-state tunneling, which eliminates several analytical artifacts in a previous calculation. The cracking coefficient is computed for the full range of elastic mismatch and several fiber arrangements, and is presented in a form that can be used in selecting viable constituents. Calculations also demonstrate that fiber-matrix interface plays a major role in cracking. A sliding interface relaxes tunnel edges, and thereby the energy release rate at the tunnel front.     

Matrix cracking of cross-ply ceramic composites

A micromechanics study is presented of the matrix cracking behavior of laminated, fiber-reinforced ceramic cross-ply composites when subject to tensile stressing parallel to fibers in the 0° plies. Cracks extending across the 90° plies are assumed to exist, having developed at relatively low tensile stresses by the tunnel cracking mechanism. The problem addressed in this study is the subsequent extension of these initial cracks into and across the 0° plies. Of special interest is the relation between the stress level at which matrix cracks are able to extend all the way through the 0° plies and the well known matrix cracking stress for steady-state crack extension through a uni-directional fiber-reinforced composite. Depending on the initial crack distribution in the 90° plies, this stress level can be as large as the uni-directional matrix cracking stress or it can be as low as about one half that value. The cracking process involves a competition between crack bridging by the fibers in the 0° plies and interaction among multiple cracks. Crack bridging is modeled by a line-spring formulation where the nonlinear springs characterize the sliding resistance between fibers and matrix. Crack interaction is modeled by two representative doubly periodic crack patterns, one with collinear arrays and the other with staggered arrays. Material heterogeneity and anisotropy are addressed, and it is shown that a homogeneous, isotropic average approximation can be employed. In addition to conditions for matrix cracking, the study provides results which enable the tensile stress-strain behavior of the cross-ply to be predicted, and it provides estimates of the maximum stress concentration in the bridging fibers. Residual stress effects are included.     

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.     

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.     

Tensile fracture of brittle matrix composites: Influence of fiber strength

A stress intensity approach is used to analyze tensile failure of brittle matrix composites that contain unidirectionally aligned fibers held in place by friction. In general, failure may initiate either by growth of a crack in the matrix, or by fracture of fibers that bridge the matrix crack. Subsequently, these failure processes may continue either unstably or stably with increasing applied stress. Solutions to the fracture mechanics analysis are obtained numerically in normalized form, with one microstructural variable, the normalized fiber strength. The analysis defines transitions between failure mechanisms and provides strength/crack-size relations for each mechanism. Explicit relations are derived for the matrix cracking stress (noncatastrophic failure mode), the condition for transition to a catastrophic failure mode, and the fracture toughness in a region of catastrophic failure, in terms of microstructural properties of the composite.     

Cracking mechanisms in thermally cycled Ti-6AI-4V reinforced with SiC fibers

A titanium alloy (Ti-6A1-4V) reinforced with continuous SiC fibers (SCS-6) was thermally cycled between 200 ‡C and 700 ‡C in air and argon. The composite mechanical properties deteriorate with an increasing number of cycles in air because of matrix cracks emanating from the specimen surface. These cracks also give oxygen access to fibers, further resulting in fiber degradation. The following matrix cracking mechanisms are examined: (1) thermal fatigue by internal stresses resulting from the mismatch of thermal expansion between fibers and matrix, (2) matrix oxygen embrittlement, and (3) ratcheting from oxide accumulating within cracks. Matrix stresses are determined using an analytical model, considering stress relaxation by matrix creep and the temperature dependence of materials properties. Matrix fatigue from these cycli-cally varying stresses (mechanism (1)) cannot solely account for the observed crack depth; oxygen embrittlement of the crack tip (mechanism (2)) is concluded to be another necessary damage mechanism. Furthermore, an approximate solution for the stress intensity resulting from crack wedging by oxide formation (mechanism (3)) is given, which may be an operating mech-anism as well for long cracks. S.H. THOMIN, formerly Graduate Student, Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA     

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.     

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.     

Enhancing the Environmentally Assisted Cracking Resistance of Aircraft Quality Al Alloy of Type AA7075 Stiffened with Polymer Matrix Composite Using Cerium Chloride Inhibitor

This study explores a methodology to raise environmentally assisted cracking resistance of alclad Al–Zn–Mg–Cu (AA7075) alloy, used in aircraft structures, stiffened with polymer matrix composite asymmetric patch in order to suppress growth of fatigue cracks. Fracture mechanics studies of adhesively bonded center-pre-cracked Al alloy specimens having stiffeners were carried out in 3.5 wt% sodium chloride environment to understand the effect of cerium chloride inhibitor on the threshold stress intensity for stress corrosion cracking as well as the second-stage (steady-state) crack growth rate. It was observed that in the peak- and the two-step-aged tempers, the crack growth rate of the alloy reduced by two and a half, and four times, respectively, while the threshold stress intensity increased by 14–15% due to the addition of 1000 ppm of this inhibitor. The study offers a method to enhance significantly life of aging aircrafts stiffened with polymer matrix composite.     

Scalings in the statistical failure of brittle matrix composites with discontinuous fibers—I. Analysis and Monte Carlo simulations

This paper addresses the statistical aspects of the failure of unidirectional composites having brittle matrices reinforced with discontinuous brittle fibers. The failure process involves quasi-periodic matrix cracking, frictional sliding of the fibers in fiber break zones and fiber bridging of matrix cracks in a global load-sharing framework. We consider a composite section of “characteristic” length and develop its distribution for strength in terms of certain characteristic stress and length scales. Continuous sections of the fibers follow the usual Weibull distribution for strength. We also introduce random discontinuities along the fiber, originating say from processing damage whose spacins follow a Poisson process where the rate α is the mean number of discontinuities per characteristic length of the fiber. We derive two approximations for the mean and standard deviation of such characteristics composites. A realistic Monte Carlo simulation model is developed to test these analytical results and to study the fiber pull-out properties. The composites turn out to be quite insensitive to initial damage. The mean pull-out length is found to increase with increasing α and becomes independent of the Weibull modulus for large values of α.     

Fatigue in selectively fiber-reinforced titanium matrix composites

Many applications of the Ti alloy matrix composites (TMCs) reinforced with SiC fibers are expected to use the selective reinforcement concept in order to optimize the processing and increase the cost-effectiveness. In this work, unnotched fatigue behavior of a Ti-6Al-4V matrix selectively reinforced with SCS-6 SiC fibers has been examined. Experiments have been conducted on two different model panels. Results show that the fatigue life of the selectively reinforced composites is far inferior to that of the all-TMC panel. The fatigue life decreases with the decreasing effective fiber volume fraction. Suppression of multiple matrix cracking in the selectively reinforced panels was identified as the reason for their lack of fatigue resistance. Fatigue endurance limit as a function of the clad thickness was calculated using the modified Smith-Watson-Topper (SWT) parameter and the effective fiber volume fraction approach. The regime over which multiple matrix cracking occurs is identified using the bridging fiber fracture criterion. A fatigue failure map for the selectively reinforced TMCs is constructed on the basis of the observed damage mechanisms. Possible applications of such maps are discussed.     

Mode I fatigue cracking in a fiber reinforced metal matrix composite

The mode I fatigue crack growth behavior of a fiber reinforced metal matrix composite with weak interfaces is examined. In the longitudinal orientation, matrix cracks initially grow with minimal fiber failure. The tractions exerted by the intact fibers shield the crack tip from the applied stress and reduce the rate of crack growth relative to that in the unreinforced matrix alloy. In some instances, further growth is accompanied by fiber failure and a concomitant loss in crack tip shielding. The measurements are compared with model predictions, incorporating the intrinsic fatigue properties of the matrix and the shielding contributions derived from the intact fibers. The magnitude of the interface sliding stress inferred from the comparisons between experiment and theory is found to be in broad agreement with values measured using alternate techniques. The results also indicate that the interface sliding stress degrades with cyclic sliding, an effect yet to be incorporated in the model. In contrast, the transverse fatigue properties are found to be inferior to those of the monolithic matrix alloy, a consequence of the poor fatigue resistance of the fiber/matrix interface.     

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.     

Mechanical property and fracture behavior of squeeze-cast Mg matrix composites

The present study aims to investigate the microstructure and fracture properties of AZ91 Mg matrix composites fabricated by the squeeze-casting technique, with variations in the reinforcement material and applied pressure. Microstructural and fractographic observations, along with in situ fracture tests, were conducted on three different Mg matrix composites to identify the microfracture process. Two of them are reinforced with two different short fibers and the other is a whisker-reinforced composite. From the in situ fracture observation of Kaowool-reinforced composites, the effect of the applied pressure on mechanical properties is explained using a competing mechanism: the detrimental effects of fiber breakage act to impair the beneficial effects of the grain refinement and improved densification as the applied pressure increases. On the other hand, for the composites reinforced with Saffil short fibers, microcracks were initiated mainly at the fiber/matrix interfaces at considerably higher stress intensity factor levels, while the degradation of fibers was not observed even in the case of the highest applied pressure. This finding indicates that the higher applied pressure yields better mechanical properties, attributable to the Saffil short fibers having relatively high resistance to cracking. Although an improved microstructure was obtained by accommodating the appropriate applied pressure in the short fiber-reinforced composites, their mechanical properties were far below those of conventional A1 matrix composites. In this regard, the Alborex aluminum borate whisker is suggested as a replacement for the short fibers used in the present investigation, to achieve better mechanical properties and fracture toughness.     

The role of fiber bridging in the delamination resistance of fiber-reinforced composites

Delamination cracks in composites may interact with misaligned or inclined fibers. Such interactions often lead to fiber bridging, which causes the nominal delamination resistance to increase as the crack extends. Substantial specimen geometry effects are also involved. An experimental investigation of the role of fiber bridging has been conducted for three different composites. The results are compared with fiber bridging models based on a softening traction law, leading to schemes for predicting trends in delamination resistance with specimen geometry and crack length. Implications for utilizing this effect to suppress the growth of delaminations are presented.     

Time-dependent,environmentally assisted crack growth in nicalon-fiber-reinforced SiC composites at elevated temperatures

Subcritical crack growth measurements were conducted on ceramic matrix composites of β-SiC matrix reinforced with NICALON fibers (SiC/SiC_f); fiber-matrix interphases were of carbon andboron nitride. Velocities of effective elastic cracks were determined as a function of effective applied stress intensity in pure Ar and in Ar plus 2000, 5000, and 20,000 ppm O₂ atmospheres at 1100 °C. Over a wide range of applied stress intensities, theV-K _eff diagrams revealed a stage II pattern in which the crack velocity depends only weakly on the applied stress intensity, followed by a stage III, or power-law, pattern at higher stress intensity. Oxygen increased the crack velocity in stage II and shifted the stage II to III transition to the left. A two-dimensional (2-D) micromechanics approach, developed to model the time dependence of observed crack-bridging events, rationalized the measured effective crack velocities, their time dependence, the stage II to III transition, and the effect of oxygen in terms of the load relaxation of crack-bridging fibers. Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by Battelle under Contract DE-AC06-76RLO 1830 This article is based on a presentation made at the “High Temperature Fracture Mechanisms in Advanced Materials” symposium as a part of the 1994 Fall meeting of TMS, October 2-6, 1994, in Rosemont, Illinois, under the auspices of the ASM/SMD Flow and Fracture Committee.     

Effect of orientation on crystallographic cracking in notched nickel-base superalloy single crystal subjected to far-field cyclic compression

The effects of crystallographic orientation on the fatigue crack initiation and growth under far-field cyclic compression are discussed in single crystals of nickel-base superalloy MAR-M200. Results indicate that cracking occurs primarily due to planar slip on the {111}-type planes. Crystallographic cracking can occur on two or more slip planes simultaneously, but through-thickness cracks are not observed. In addition, it has been shown that the threshold stress intensity for crack initiation shows a strong dependence on orientation. The threshold stress intensity for crack growth in cyclic compression is 5 to 10 times the threshold for crack growth in cyclic tension.     

Crack size effects on the chemical driving force for aqueous corrosion fatigue

Small crack size accelerates corrosion fatigue propagation through high strength 4130 steel in aqueous 3 pct NaCl. The size effect is attributed to crack geometry dependent mass transport and electrochemical reaction processes which govern embrittlement. For vacuum or moist air, growth rates are defined by stress intensity range independent of crack size (0.1 to 40 mm) and applied maximum stress (0.10 to 0.95 Φ_ys). In contrast small (0.1 to 2 mm) surface elliptical and edge cracks in saltwater grow up to 500 times faster than long (15 to 40 mm) cracks at constant δK. Small cracks grow along prior austenite grain boundaries, while long cracks propagate by a brittle transgranular mode associated with tempered martensite. The small crack acceleration is maximum at low δK levels and decreases with increasing crack length at constant stress, or with increasing stress at constant small crack size. Reductions in corrosion fatigue growth rate correlate with increased brittle transgranular cracking. Crack mouth opening, proportional to the crack solution volume to surface area ratio, determines the environmental enhancement of growth rate and the proportions of inter- and transgranular cracking. Small cracks grow at rapid rates because of enhanced hydrogen production, traceable to increased hydrolytic acidification and reduced oxygen inhibition within the occluded cell.