Cracking of brittle films on elastic substrates

An analysis is presented that relates the crack spacing in a brittle film on an elastic substrate to the stress in the film, its thickness and fracture toughness. This analysis differs from an earlier one presented by one of the authors in that it considers the effect of a sequential, rather than a concerted, propagation of cracks, and predicts a larger crack spacing. The validity of the present analysis was confirmed by experimental results from a model system consisting of epitaxial PrBa₂Cu₃O_7−x films on SrTiO₃ substrates. The experimentally observed relationship between the crack spacing and the film thickness was in excellent agreement with the theory.     

The effect of fiber-matrix debond energy on the matrix cracking strength and the debond shear strength

The matrix cracking model given by Budiansky, Hutchinson and Evans [J. Mech. Phys. Solids34, 167 (1986)] is extended to include the effect of fiber-matrix bonding in a unidirectional fiber-reinforced composite. By use of an energy balance analysis, the work of debonding Γ_d is related to a characteristic critical interface shear stress τ_d and to the frictional interface sliding resistance τ_f by the expression τ_d − τ_f = √4G_mΓ_d/av, where G_m is the matrix shear modulus, a, the fiber radius, and v the function of fiber volume exceeds the background fiber tensile stress far from the crack by a fixed calculable amount. Finally, the combined effect of τ_f and adhesion on the intercrack spacing is predicted for the case where multiple cracks develop in the matrix.     

A rationalisation of fatigue thresholds in pearlitic steels using a theoretical model

From a detailed re-examination of results in the literature, the effects of microstructure sizes, namely interlamellar spacing, pearlitic colony size and the prior austentitic grain size on the thresholds for fatigue crack growth (ΔK_th) and crack closure (K_{cl, th}) have been illustrated. It is shown that while interlamellar spacing explicitly controls yield strength, a similar effect on ΔK_th cannot be expected. On the other hand, the pearlitic colony size is shown to strongly influence ΔK_th and K_{cl, th} through the deflection and retardation of cracks at colony boundaries. Consequently, an increase in ΔK_th and K_{cl, th} with colony size has been found. The development of a theoretical model to illustrate the effects of colony size, shear flow stress in the slip band and macroscopic yield strength on K_{cl, th} and ΔK_th is presented. the model assumes colony boundaries as potential sites for slip band pile-up formation and subsequent crack deflection finally leading to zig-zag crack growth. Using the concepts of roughness induced crack closure, the magnitude of K_{cl, th} is quantified as a function of colony size. In deriving the model, the flow stress in the slip band has been considered to represent the work hardened state in pearlite. Comparison of the theoretically predicted trend with the experimental data demonstrates very good agreement. Further, the intrinsic or closure free component of the fatigue threshold, ΔK_{eff, th} is found to be insensitive to colony size and interlamellar spacing. Using a criterion for intrinsic fatigue threshold which considers the attainment of a critical fracture stress over a characteristic distance corresponding to interlamellar spacing, ΔK_th values at high R values can be estimated with reasonable accuracy. The magnitude of ΔK_th as a function of colony size is then obtained by summing up the average value of experimentally obtained ΔK_{eff, th} values and the predicted K_{cl, th} values as a function of colony size. Again, very good agreement of the theoretically predicted ΔK_th values with those experimentally obtained has been demonstrated.     

Ductile-brittle fracture transition due to increasing crack length in a medium carbon steel

A phenomenon of ductile-brittle fracture transition with increasing normalized crack length in CS1030 steel has been observed in notch bend specimens. It is found that for stationary cracks in three-and four-point bend specimens the transition occurs at about a/W = 0.2. For propagating cracks in four-point bend specimens, this transition occurs at larger a/W ratios in some specimens but there is no transition in three-point bending. The Ritchie-Knott-Rice (RKR) critical stress model for cleavage fracture, in combination with finite element analyses of crack tip stress fields, successfully explains the ductile-brittle transition with relative crack length. The model also successfully predicts critical values of the CTOD for cleavage fracture.     

Influence of microstructure on fatigue behavior and surface fatigue crack growth of fully pearlitic steels

This work examined the influence of microstructure on the surface fatigue crack propagation behavior of pearlitic steels. In addition to endurance limit or S(stress amplitude)-N(life) tests, measurements of crack initiation and growth rates of surface cracks were conducted on hourglass specimens at 10 Hz and with aR ratio of 0.1. The microstructures of the two steels used in this work were characterized as to prior austenite grain size and pearlite spacing. The endurance tests showed that the fatigue strength was inversely proportional to yield strength. In crack growth, cracks favorably oriented to the load axis were nucleated (stage I) with a crack length of about one grain diameter. Those cracks grew at low ΔK values, with a relatively high propagation rate which decreased as the crack became longer. After passing a minimum, the crack growth rate increased again as cracks entered stage II. Many of the cracks stopped growing in the transition stage between stages I and II. Microstructure influenced crack propagation rate; the rate was faster for microstructures with coarse lamellar spacing than for microstructures with fine lamellar spacing, although changing the prior austenite grain size from 30 to 130 jμm had no significant influence on crack growth rate. The best combination of resistance to crack initiation and growth of short cracks was exhibited by microstructures with both a fine prior austenite grain size and a fine lamellar spacing. Formerly with Carnegie Mellon University     

Scaling laws for fatigue crack

A set of scaling laws has been developed for describing intermittent as well as continuous fatigue crack growth of large cracks in steels in the power-law regime. The proposed scaling laws are developed on the basis that fatigue crack growth occurs as the result of low-cycle fatigue (LCF) failure of a crack-tip element whose width and height correspond to the dislocation cell size and barrier spacing, respectively. The results show that the effects of microstructure on fatigue crack growth can be described entirely in terms of a dimensionless microstructural parameter, ξ, which is defined in terms of yield stress, fatigue ductility, dislocation cell size, and dislocation barrier spacing. For both discontinuous and continuum crack growth, the crack extension rate,da/dN, scales with ξ and(ΔK/E) ^m, where ΔK is the stress intensity range, m is the crack growth exponent, andE is Young's modulus. Application of the model to high-strength low-alloy (HSLA) and conventional ferritic, ferritic/pearlitic, and martensitic steels reveals that the lack of a strong microstructural influence on fatigue crack growth in the power-law regime is due to increasing yield stress and fatigue ductility with decreasing dislocation barrier spacing, which leads to a narrow range of ξ values and crack growth rates. Variation ofda/dN data with microstructure in HSLA-80 steels is explained in terms of the proposed model. Other implications of the scaling laws are also presented and discussed in conjunction with several fatigue models in the literature.     

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.     

Bridge toughening enhancement in double-notched MoSi2/Nb model composites

Single-ply composites containing both laminate and continuous Nb fiber reinforcement coated with A1₂O₃ debond coatings in an MoSi₂ matrix are used as model systems for investigating bridge toughening concepts for various precrack configurations. When cracks are introduced symmetrically on either side of the ductile phase with zero crack offset spacing (S = 0), a minimum amount of energy is expended in plastic deformation and the local rupture process in the metal, as measured by the area of the force displacement curve in tension. For asymmetric precracks introduced on either side of the ductile reinforcement, as the offset spacing,S, was varied from 1 to 20R (R being the ductile phase half-thickness), the overall extension continuously increased within the bridging ligament. The effective ligament gage length was nearly equal to the crack spacing in the limiting case of a weak interface. However, the ductile Nb phase developed a Nb₅Si₃ reaction layer on its surface which was strongly bonded to the Nb and was found to undergo periodic cracking, leading to numerous shear bands within the ductile phase. This unique and previously unreported mode of metal deformation in shear loading has been analyzed using a simple geometric model. The results indicate that the profusion of shear bands is the primary source of toughening enhancement in the case of asymmetric crack geometry, which was not recognized in prior work of this type. 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.     

The Significance of Crack Initiation Stage in Very High Cycle Fatigue of Steels

Different stages of the Very High Cycle Fatigue (VHCF) crack evolution in tool steels have been explored using a 20 kHz ultrasonic fatigue testing equipment. Extensive experimental data is presented describing VHCF behaviour, strength and crack initiating defects in an AISI H11 tool steel. Striation measurements are used to estimate fatigue crack growth rate, between 10^?8 and 10^?6 m/cycle, and the number of load cycles required for a crack to grow to critical dimensions. The growth of small fatigue cracks within the “fish‐eye” is shown to be distinctively different from the crack propagation behaviour of larger cracks. More importantly, the crack initiation stage is shown to determine the total fatigue life, which emphasizes the inherent difficulty to detect VHCF cracks prior to failure. Several mechanisms for initiation and early crack growth are possible. Some of them are discussed here: crack development by local accumulation of fatigue damage at the inclusion – matrix interface, hydrogen assisted crack growth and crack initiation by decohesion of carbides from the matrix.     

Crack deflection: Implications for the growth of long and short fatigue cracks

The influences of crack deflection on the growth rates ofnominally Mode I fatigue cracks are examined. Previous theoretical analyses of stress intensity solutions for kinked elastic cracks are reviewed. Simple elastic deflection models are developed to estimate the growth rates of nonlinear fatigue cracks subjected to various degrees of deflection, by incorporating changes in the effective driving force and in the apparent propagation rates. Experimental data are presented for intermediate-quenched and step-quenched conditions of Fe/2Si/0.1C ferrite-martensite dual phase steel, where variations in crack morphology alone influence considerably the fatigue crack propagation rates and threshold stress intensity range values. Such results are found to be in good quantitative agreement with the deflection model predictions of propagation rates for nonlinear cracks. Experimental information on crack deflection, induced by variable amplitude loading, is also provided for 2020-T651 aluminum alloy. It is demonstrated with the aid of elastic analyses and experiments that crack deflection models offer a physically-appealing rationale for the apparently slower growth rates of long fatigue cracks subjected to constant and variable amplitude loading and for the apparent deceleration and/or arrest of short cracks. The changes in the propagation rates of deflected fatigue cracks are discussed in terms of thelocal mode of crack advance, microstructure, effective driving force, growth mechanisms, mean stress, slip characteristics, and crack closure.     

A Comparative Study on Dwell Fatigue of Ti-6Al-2Sn-4Zr-xMo (x = 2 to 6) Alloys on a Microstructure-Normalized Basis

The dwell effects of Ti624x (x = 2 to 6) alloys, including dwell fatigue life debit, fracture mode and strain accumulation, were characterized and compared. With increasing Mo content, the dwell fatigue life debit decreases quickly, and dwell fatigue fracture exhibits a transition from subsurface to surface initiation. Accompanying these changes, the accumulated strain decreases, and the pattern of secondary cracks loses morphological features typical of dwell cracks. These variations in the fatigue behavior of Ti624x were attributed on the fundamental level to the dual effects of Mo: It decreases the β transus of titanium and, as a slow diffuser, reduces the rate of phase transformation from β to α. A higher Mo content encourages nucleation of multiple variants of α laths and promotes the transition from aligned colonies to basketweave microstructure during cooling after β forging. As a result both the grain size and microtexture intensity of α grains in the two-phase processed and heat treated microstructure are reduced. Smaller grain size of the alloys with higher Mo content produces smaller slip band spacing and reduces accumulated strain during dwell fatigue, thus reducing propensity for crack initiation. Microtexture was shown to be the direct cause of dwell sensitivity, and their relationship was described with the aid of a two-region redistribution model based on a previous two-element redistribution model proposed by Bache.     

Microscopic characteristics of fatigue crack propagation in aluminum alloy based particulate reinforced metal matrix composites

Microscopic characteristics of fatigue crack propagation in two aluminum alloy (A356 and 6061) based particulate reinforced metal matrix composites (MMCs) were investigated by carrying out three point bending fatigue tests. The impedance offered by the reinforcing particles against fatigue crack propagation has been studied by plotting the nominal and actual crack lengths vs number of cycles. Surface observation shows that fatigue cracks tend to develop along the particle-matrix interface. In the case of Al (A356) MMCs, stronger interaction of fatigue crack with Si particles, as compared to SiC particles, was evident. In both MMC materials, particle debonding was more prominent as compared to particle cracking. The attempted application of Davidson's model to calculate ΔK_th indicated that for cast MMCs the matrix grain including the surrounding reinforcing particles has to be considered as a large “hard particle”, and the grain boundary particles themselves behave like an hard “egg-shell” to strengthen the material.     

Subcritical fatigue crack growth in alumina—II. Crack bridging and cyclic fatigue mechanisms

A crack re-notching procedure based on the “hinged straight crack” approximation is used to determine the distribution and magnitude of the bridging traction, σ(X), existing over the faces of the fatigue cracks grown in the experiments of Part I. From this distribution, the σ(u) relation between the bridging tractions and the crack opening is obtained and a simple method is tentatively proposed to measure the magnitude of the crack bridging stress intensity factor, K_b. The characteristics of the σ(X) and σ (u) relations are discussed in the light of the microscopical observations of crack profiles and in terms of the distribution of the frictional and elastic ligaments existing along the faces of the cracks. Crack growth rates and behaviour under different values of stress ratio R are compared and mechanisms of fatigue crack growth vs static crack growth are proposed.     

The influence of solid-state and liquid-phase bonding on fatigue at Al/Al2O3 interfaces

Fracture and fatigue experiments have been conducted on liquid phase bonded (LPB) and solid-state bonded (SSB) aluminum-alumina interfaces. The LPB interfaces contain voids and dendritic FeAl₃ precipitates, whereas SSB interfaces are relatively defect-free. These precipitates result in local embrittlement, yet both interfaces are strong and tough. Upon cyclic loading, mode 1 cracks in both systems grow alternately along the interface and within the A1. The development of a tortuous crack path elevates the apparent fatigue threshold through crack closure. Under mixed mode loading, fatigue cracks approaching SSB interfaces propagate through the A1 rather than along the interface. Conversely, for LPB interfaces, mixed mode cyclic crack growth along the interface occurs in preference to propagation in the A1. Correlation between the striation spacing and the crack tip opening displacement suggests a growth mechanism based on crack tip blunting.     

Periodic oxide cracking on fe2.25Cr1 Mo produced by high-temperature fatigue tests with a compression hold

Long, straight cracks perpendicular to the stress axis are seen on the oxidized surface of specimens of Fe2.25Cr1Mo cycled with a compressive hold at high temperatures. The cracks in the oxide are periodically spaced. They resemble cracks observed in a brittle film on a ductile substrate after a tension test of the substrate. They also resemble the parallel multiple fractures that occur in a brittle matrix of a composite with ductile fibers undergoing tension. We apply both the model of a brittle film on a ductile substrate and of the brittle matrix composite to explain the observed intercrack spacing. Cracks in the oxide film lead to localized oxidation of the metal in the region around their intersection with the oxide-metal interface. These cracks are seen to penetrate the metal. Stress concentrations from deep grooves that form during compression hold fatigue, together with crack initiation from the oxide, lead to a shortened cycle life.     

Fracture toughness: A rationalization of the role of microstructure in an α-β titanium alloy

The role of microstructure in affecting fracture toughness is examined by considering how microstructure affects the formation of a critical increment of crack extension leading to catastrophic fracture. It is proposed that this critical increment of crack extension occurs by void formation ahead of the main crack and growth back to it. Factors affecting void nucleation and void growth are, therefore, examined in this connection. Published data on the Ti-5.25Al-5.5V-0.9Fe-0.5Cu alloy are used for this purpose. In equiaxed(E) α structure voids nucleate at Eα/agedβ matrix interfaces for both tensile and fracture toughness tests. Although the interparticle spacing, A, is four times more effective than priorβ grain size,D _β, in controlling void growth rate,G _L, in a tensile test,D _β is at least five times more effective in controlling fracture toughness. For Widmanstätten plus grain boundary (W + GB) α structures there are marked similarities betweenG _Lbehavior as a function of GBa thickness, J, and the contribution of J to fracture toughness. These similarities have led to the proposal that the increase in fracture toughness, ΔK_Q, with increasingl is due to blunting of the crack tip, and the plateau in ΔK_Q which follows, with increasingl, is due to a balance between blunting and sharpening processes. Blunting occurs by crack penetration into GBα. The sharpening occurs by void formation and growth along GBα/agedβ interfaces back to the main crack.     

Effect of phase morphology on fatigue crack growth behavior of α-β titanium alloy—A crack closure rationale

Effect of phase morphology on fatigue crack growth (FCG) resistance has been investigated in the case of an α-β titanium alloy. Fatigue crack growth tests with on-line crack closure measurements are performed in the microstructures varying in primary α (elongated/equiaxed/Widmanstätten) and matrix β (transformed/metastable) phase morphologies. The microstructures comprising metastable β matrix are observed to yield higher FCG resistance than those for transformed β matrix, irrespective of primary α phase morphology (equiaxed or elongated). But, the effect of primary α phase morphology is dictated by the type of β phase (transformed or metastable) matrix. It is observed that in the microstructures with metastable β matrix, the equiaxed primary α as second phase possesses higher FCG resistance as compared to that of elongated α morphology. The trend is reversed if the metastable β matrix is replaced by transformed β phase. The fatigue crack path profiles are observed to be highly faceted. The detailed fractographic investigations revealed that tortuosity is introduced as a result of cleavage in α or β or in both the phases, depending upon the microstructure. The crack closure concept has been invoked to rationalize the phase morphology effects on fatigue crack growth behavior. The roughness-induced and plasticity-induced crack closure appear to be the main mechanisms governing crack growth behavior in α-β titanium alloy.     

The effect of microstructure on fracture toughness and fatigue crack growth behavior in γ-titanium aluminide based intermetallics

Ambient-temperature fracture toughness and fatigue crack propagation behavior are investigated in a wide range of (γ+α ₂) TiAl microstructures, including single-phase γ, duplex, coarse lamellar (1 to 2 mm colony size (D) and 2.0 μm lamellar spacing (λ)), fine lamellar (D ∼ 150 μm, λ=1.3 to 2.0 μm), and a powder metallurgy (P/M) lamellar microstructure (D=65 μm, λ=0.2 μm). The influences of colony size, lamellar spacing, and volume fraction of equiaxed γ grains are analyzed in terms of their effects on resistance to the growth of large (>5 mm) cracks. Specifically, coarse lamellar microstructures are found to exhibit the best cyclic and monotonic crack-growth properties, while duplex and single-phase γ microstructures exhibit the worst, trends which are rationalized in terms of the salient micromechanisms affecting growth. These mechanisms primarily involve cracktip shielding processes and include crack closure and uncracked ligament bridging. However, since the potency of these mechanisms is severely restricted for cracks with limited wake, in the presence of small (<300 μm) cracks, the distinction in the fatigue crack growth resistance of the lamellar and duplex microstructures becomes far less significant.     

Correlation of Microstructure with Mechanical Properties of Zr-Based Amorphous Matrix Composite Reinforced with Tungsten Continuous Fibers and Ductile Dendrites

A Zr-based amorphous matrix composite reinforced with tungsten continuous fibers in an amorphous LM2 alloy matrix containing ductile ?? dendrites was fabricated without pores or defects by the liquid pressing process, and its tensile and compressive properties were examined in relation with microstructures and deformation mechanisms. Overall, 68?vol pct of tungsten fibers were distributed in the matrix, in which 35?vol pct of ?? dendrites were present. The LM2 composite had the greatly improved tensile strength and elastic modulus over the LM2 alloy, and it showed a stable crack propagation behavior as cracks stopped propagating at the longitudinal cracks of tungsten fibers or ductile ?? dendrites. According to the compressive test results, fracture did not take place at one time after the yield point, but it proceeded as the applied loads were sustained by fibers, thereby leading to the maximum strength of 2432?MPa and plastic strain of 16.4?pct. The LM2 composite had the higher strength, elastic modulus, and ductility under both tensile and compressive loading conditions than the tungsten-fiber-reinforced composite whose matrix did not contain ?? dendrites. These distinctively excellent properties indicated a synergy effect arising from the mixing of amorphous matrix and tungsten fibers, as well as from the excellent bonding of interfaces between them.