Mechanisms Of Fatigue-crack Propagation In Ductile And .

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International Journal of Fracture 100: 55–83, 1999. 2000 Kluwer Academic Publishers. Printed inthe Netherlands.Mechanisms of fatigue-crack propagation in ductileand brittle solidsR.O. RITCHIEMaterials Sciences Division, Lawrence Berkeley National Laboratory, and Department of Materials Science andMineral Engineering, University of California, Berkeley, CA 94720-1760, U.S.A.Received 21 January 1998; accepted in revised form 22 May 1998Abstract. The mechanisms of fatigue-crack propagation are examined with particular emphasis on the similaritiesand differences between cyclic crack growth in ductile materials, such as metals, and corresponding behavior inbrittle materials, such as intermetallics and ceramics. This is achieved by considering the process of fatiguecrack growth as a mutual competition between intrinsic mechanisms of crack advance ahead of the crack tip(e.g., alternating crack-tip blunting and resharpening), which promote crack growth, and extrinsic mechanismsof crack-tip shielding behind the tip (e.g., crack closure and bridging), which impede it. The widely differingnature of these mechanisms in ductile and brittle materials and their specific dependence upon the alternatingand maximum driving forces (e.g., 1K and Kmax ) provide a useful distinction of the process of fatigue-crackpropagation in different classes of materials; moreover, it provides a rationalization for the effect of such factors asload ratio and crack size. Finally, the differing susceptibility of ductile and brittle materials to cyclic degradationhas broad implications for their potential structural application; this is briefly discussed with reference to lifetimeprediction.Key words: Fatigue-crack propagation, crack-tip shielding, metals, ceramics, intermetallics, intrinsic and extrinsicmechanisms.1. IntroductionCyclic fatigue involves the microstructural damage and failure of materials under cyclically varying loads. Structural materials, however, are rarely designed with compositions andmicrostructures optimized for fatigue resistance. Metallic alloys are generally designed forstrength, intermetallics for ductility, and ceramics for toughness; yet, if any of these materialssee engineering service, their structural integrity is often limited by their mechanical performance under cyclic loads. In fact, it is generally considered that over 80 percent of all servicefailures can be traced to mechanical fatigue, whether in association with cyclic plasticity, sliding or phsyical contact (fretting and rolling contact fatigue), environmental damage (corrosionfatigue), or elevated temperatures (creep fatigue). Accordingly, a large volume of literaturehas been amassed particularly over the past twenty-five years, dealing with the mechanics andmechanisms of mechanical fatigue failure [e.g., Suresh, 1991; Ellyin, 1997]; however, the vastmajority of this research pertains solely to metallic materials.Despite this preponderance of information on metal fatigue, there has been an increasinginterest of late in the use of high-strength, brittle materials, such a ceramics, intermetallicsand their respective composites, for structural applications where cyclic loading is critical[e.g., Harrison and Winstone, 1996; Kochendörfer, 1996]. This has been particularly focusedat elevated temperature applications, e.g., for fuselage and especially engine components(Kochendörfer, 1996), but in the case of ceramics at lower temperatures too, e.g., for biomed-

56R.O. RitchieFigure 1. Schematic variation of fatigue-crack propagation rate (da/dN) with applied stress intensity range (1K),for metals, intermetallics and ceramics.ical implant devices (Ritchie, 1996). Examples of such ‘advanced materials’ are the use ofsilicon nitride ceramics for automobile turbocharger wheels and engine valves and pyrolyticcarbon for prosthetic cardiac devices, and the contemplated use of composite ceramics forgas turbine blades. Similarly, intermetallic alloys, such as the γ -based titanium aluminides,have been considered for applications such as automobile engine valves and blades in gasturbines. Whereas these materials offer vastly improved specific strength at high temperaturescompared to conventional metallic alloys, they suffer in general from a pronounced lack ofdamage tolerance in the form of an extreme sensitivity to pre-existing flaws. Moreover, it hasbecome apparent that similar to metals, such brittle solids can additionally show a markedsusceptibility to premature failure under cyclic fatigue loading [e.g., Dauskardt et al., 1987].The mechanisms associated with fatigue-crack propagation in brittle materials, such asmonolothic and composite ceramics and intermetallics, are quite distinct from those commonly encountered in metal fatigue; moreover, their crack-growth rate (da/dN) behaviordisplays a markedly higher sensitivity to the applied stress intensity (K) than is observedin most metals (Figure 1) (Ritchie and Dauskardt, 1991). However, by considering crackgrowth as a mutual competition between intrinsic microstructural damage mechanisms, whichpromote crack extension ahead of the tip, and extrinsic crack-tip shielding mechanisms, whichact primarily behind the tip to retard crack growth (Ritchie, 1988) a specific commonality ofbehavior between the fatigue of ductile and brittle materials can be found, differing only inthe relative importance of the intrinsic and extrinsic mechanisms.It is therefore the objective of this paper to describe this commonality by comparing andcontrasting the salient mechanisms affecting the propagation of fatigue cracks in ductile and

Mechanisms of fatigue-crack propagation in ductile and brittle solids57Figure 2. Schematic illustration of mutual competition between intrinsic mechanisms of damage/crack advanceand extrinsic mechanisms of crack-tip shielding involved in crack growth.brittle materials. We begin with a brief review of the distinction between the intrinsic andextrinsic mechanisms which can affect the critical and subcritical growth of cracks.2. Intrinsic and extrinsic mechanismsAs noted above, the critical and subcritical extension of a crack can be considered to be a resultof the mutual competition of two classes of mechanisms (Figure 2). Crack growth is promotedahead of the crack tip by intrinsic microstructural damage mechanisms, and impeded byextrinsic mechanisms acting primarily behind the crack tip, which serve to ‘shield’ the cracktip from the far-field driving forces (Ritchie, 1988).In metallic materials, intrinsic damage mechanisms typically involve processes which create microcracks or voids, e.g., by dislocation pile-ups or interface decohesion, in the highlystressed region ahead of the tip, leading to classical failure by cleavage, intergranular crackingor microvoid coalescence; comparable mechanisms under cyclic loads involve the repetitiveblunting and resharpening of the crack tip [e.g., Pelloux, 1969; Neumann, 1969]. Extrinsicshielding mechanims, conversely, result from the creation of inelastic zones surrounding thecrack wake or from physical contact between the crack surfaces via wedging, bridging, sliding or combinations thereof (Figure 3) (Ritchie, 1988). Examples of ‘zone shielding’ aretransformation and microcrack toughening in ceramics and rocks, where the in situ dilatantphase transformations or the microcracking of precipitates/particles ahead of the crack tipcan lead to inelastic zones in the crack wake which impart closing tractions on the cracksurfaces. Examples of ‘contact shielding’ are the bridging tractions imposed across a crack byunbroken fibers, laminated layers or a particulate phase in composite materials, or the wedgingof corrosion debris or fracture surface asperities during crack closure in metal fatigue.It is important to note that the intrinsic mechanisms are an inherent property of the material,and thus are active irrespective of the length of the crack or the geometry of the test specimen;under monotonic loads, for example, they control the driving forces (e.g., the stress intensity)to initiate cracking. Extrinsic mechanisms, conversely, act in the crack wake and are thus

58R.O. RitchieFigure 3. Schematic illustration of the mechanisms of extrinsic toughening, involving crack deflection andcrack-tip shielding by inelastic zone or contact between the crack surfaces (Ritchie, 1988).critically dependent on crack size and (to a lesser extent) geometry; they are responsible forthe development of resistance-curve (R-curve) behavior and thus play a prominent role inthe driving forces required for continued growth of the crack. The implications of this arethat where extrinsic shielding mechanisms are active, rising R-curve toughness behavior and‘small-crack’ effects are to be expected, both phenomena resulting from the crack-growthproperties being dependent upon crack size. Moreover, since extrinsic mechanisms can haveno effect on crack initiation (since there is no crack wake), the microstructural factors affecting(large) crack growth may be quite different from those affecting crack initiation (or small crackgrowth).

Mechanisms of fatigue-crack propagation in ductile and brittle solids59In general, ductile materials are toughened intrinsically, e.g., through mobile dislocationactivity to induce a significant plastic-zone size, although under cyclic loading extrinsic mechanisms play an important role in the form of crack closure. In contrast, brittle materials, suchas ceramics, are invariably toughened extrinsically [e.g., Evans, 1990; Becher, 1991], via suchmechanisms as transformation toughening and crack bridging, the latter through interlockinggrains in many monolithic ceramics or by uncracked ligaments or unbroken reinforcementphases in composites and laminates.From the perspective of finding any commonality in mechanisms of fatigue-crack growthin different materials, it is the specific nature and, more significantly, the relative importance ofthe intrinsic (damage) versus extrinsic (shielding) mechanisms which distinguishes the cyclicfatigue behavior of ductile and brittle solids. This is in turn governs the specific dependenciesof the alternating and maximum stress intensities on crack-growth rates, i.e., how da/dNdepends upon 1K and Kmax (and thus how the resulting lifetime is a function of the alternatingor maximum stresses), and the relationships between the thresholds for fatigue-crack growth(1KTH and Kmax,TH ) and the crack-initiation (Ko ) and steady-state (Kc ) fracture toughnessvalues.We begin with a brief review of the mechanics and mechanisms affecting cyclic crackgrowth in ductile metallic materials.3. Fatigue-crack propagation in ductile metallic materials3.1. G ENERALCONSIDERATIONSSubcritical crack growth can occur at stress intensity K levels generally far less than thefracture toughness Kc in any metallic alloy when cyclic loading is applied (1KTH /Kc 0.1 0.4). In simplified concept, it is the accumulation of damage from the cyclic plasticdeformation in the plastic zone at the crack tip that accounts for the intrinsic mechanismof fatigue crack growth at K levels below Kc . The process of fatigue failure itself consistsof several distinct processes involving initial cyclic damage (cyclic hardening or softening),formation of an initial ‘fatal’ flaw (crack initiation), macroscopic propagation of this flaw(crack growth), and final catastrophic failure or instability.The physical phenomenon of fatigue was first seriously considered in the mid nineteenthcentury when widespread failures of railway axles in Europe prompted Wöhler in Germany toconduct the first systematic investigations into material failure under cyclic stresses circa 1860(Wöhler, 1860). However, the main impetus for research directed at the crack propagationstage of fatigue failure, as opposed to mere lifetime calculations, did not occur until the mid1960s, when the concepts of linear elastic fracture mechanics and so-called ‘defect-tolerantdesign’ were first applied to the problem of subcritical flaw growth (Paris et al., 1961; Johnsonand Paris, 1967). Such approaches recognize that all structures are flawed, and that cracksmay initiate early in service life and propagate subcritically. Lifetime is then assessed on thebasis of the time or number of loading cycles for the largest undetected crack to grow tofailure, as might be defined by an allowable strain, or limit load, or Kc criterion. Implicit insuch analyses is that subcritical crack growth can be characterized in terms of some governingparameter (often thought of as a crack driving force) that describes local conditions at the cracktip yet may be determined in terms of loading parameters, crack size, and geometry. Linearelastic and nonlinear elastic fracture mechanics have, to date, provided the most appropriatemethodology for such analyses to be made.

60R.O. RitchieFigure 4. Schematic illustration of the typical variation in fatigue-crack growth rates da/dN, as a function of theapplied stress-intensity range 1K in metallic materials, showing the regimes of primary growth-rate mechanismsand effects of several major variables on crack-growth behavior (Ritchie, 1977).The general nature of fatigue-crack growth in metallic materials and its description usingfracture mechanics can be briefly summarized by the schematic diagram in Figure 4 showingthe variation in da/dN with the nominal stress-intensity range (1K Kmax Kmin ) (Ritchie,1977). In actuality, the growth rates depend upon numerous factors other than 1K, althoughthis is the primary variable in metal fatigue, viz.:da/dN f [1K, Kmax (or R), v, environment, wave form . . .],(1)where the load ratio R is the ratio of minimum to maximum applied loads ( Kmin /Kmax forpositive R), and v is the frequency. Specifically, results of fatigue-crack growth rate tests formost ductile materials display the following characteristics: (1) a region at low values of 1Kand da/dN (less than 10 9 m/cycle) in which fatigue cracks appears dormant below thefatigue threshold, 1KTH ; (2) an intermediate region ( 10 9 to 10 6 m/cycle) of power-lawbehavior described by the Paris equation (Paris and Erdogan, 1963):da/dN C(1K)m ,(2)where C and m ( 2 to 4) are material scaling constants; and (3) an upper region of accelerating crack growth (above 10 6 m/cycle) as Kmax approaches Kc or gross plasticdeformation of the specimen, e.g., at the limit load. Similar approaches have been suggestedfor crack growth under large-scale yielding [e.g., Dowling and Begley, 1976] where growthrates have been related to a cyclic J -integral (1J ) or range of crack-tip opening displacement(1 CTOD).

Mechanisms of fatigue-crack propagation in ductile and brittle solids61Figure 5. Fatigue-crack propagation in a bulk amorphous metal (metallic glass), Zr41.2 Ti13.8 Cu12.5 Ni10 Be22.5 ,showing (a) fatigue-crack propagation rates scaling with the 1 CTOD 0.011K 2 /σ0 E 0 (where σ0 is the flowstress and E 0 is the appropriate Young’s modulus), and (b) crack growth occurring via ductile striation formation(Gilbert et al. 1997). Arrow in (b) indicates direction of crack growth.3.2. M ECHANISTICASPECTS3.2.1. Intrinsic mechanismsFatigue failure in metals is generally characterized by a transgranular ductile striation mechanism. Such striations represent local crack-growth increments per cycle and have been hypothesized to oocur via a mechanism of opening and blunting of the crack tip on loading,followed by resharpening of the tip on unloading (Laird and Smith, 1962). Several theoreticalmodels for such growth (often termed stage II crack propagation) have been proposed that relyon the fact that, where plastic zones are sufficiently large compared to microstructural dimensions, plastic blunting at the crack tip is accommodated by shear on two slip-systems roughly45 to the crack plane (Pelloux, 1969; Neumann, 1969). Recognizing that such sliding-off islargely irreversible, new crack surface can be created during cyclic crack advance either bysimultaneous or alternating slip on these two systems. This damage process is the primaryintrinsic mechanism promoting crack advance.Simple models for striation formation [e.g., McClintock, 1967] predict that an upper-boundestimate for the increment of crack advance per cycle should be proportional to the cycliccrack tip opening displacement (1 CTOD):da1K 2, 1CTOD βdN2σ0 E 0(3)where σ0 and E 0 are respectively the appropriate flow stress and Young’s modulus, and βis a proportionality constant, of order 0.1-0.5, reflecting the efficiency of crack-tip bluntingand reversibility of slip. This approach provides a first-order description of crack-growth ratebehavior in the mid-range of growth rates (regime B in Figure 4), as shown for example byrecent results on a bulk amorphous Zr-Ti-Cu-Ni-Be metal where crack advance occurs by a

62R.O. Ritchiestriation mechanism (Figure 5) (Gilbert et al., 1997), although it is an insufficient descriptionat high growth rates and in the near-threshold regime.At high growth rates as Kmax Kc (regime C in Figure 4), Equation 2 underestimatesmeasured growth rates due to the occurrence of monotonic fracture mechanisms (static modes)which replace or are additional to striation growth. Such mechanisms include cleavage, intergranular cracking and microvoid coalescence and their presence results in growth-ratebehavior that is markedly sensitive to microstructure and Kmax (or R) (Ritchie and Knott,1973). Conversely, at very low growth rates where 1K 1KTH (regime A in Figure 4),Equation 2 overestimates measured growth rates and behavior becomes markedly sensitive toKmax , microstructure and environment; the Kmax dependence in this regime, however, resultsprimarily from crack closure. At such near-threshold levels, the scale of local plasticity (i.e.,the plastic-zone size, ry ) approaches microstructural size-scales, and measured growth ratesbecome less than an interatomic spacing per cycle, indicating that crack advance is not occurring uniformly over the entire crack front [e.g., Ritchie, 1977]. Crack-growth mechanismsin this regime (typically where ry is smaller than the grain size) generally are faceted [e.g.,Yoder et al., 1979], often being referred to as ‘microstructurally sensitive’ or ‘crystallographic’fatigue, and reflect more of a single shear mode of crack advance with associated mode II plusmode I displacements, particularly in coarse planar-slip materials.3.2.2. Extrinsic mechanismsAlthough the primary mechanism motivating fatigue-crack extension in ductile materials, i.e.,crack-tip blunting and resharpening, is intrinsic and controlled principally by 1K (or moreprecisely the local plastic strain range), extrinsic crack closure mechanisms act in the crackwake to oppose this. Such wedge shielding (Ritchie, 1988) results from local deformation,fracture and chemical processes which induce physical contact between the mating crack surfaces at positive loads during the fatigue cycle. Elber (1970) originally proposed that closurearises from the constraint of surrounding elastic material on the residual stretch in materialelements previously plastically strained at the tip (plasticity-induced closure). Since the crackcannot propagate while it remains closed, the net effect is to reduce the nominal (applied) 1Kvalue to some lower effective (local) value 1Keff actually experienced at the crack tip:1Keff Kmax Kcl , Kmax Kmin ,(Kmin 6 Kcl )(Kcl 6 Kmin ),(4)where Kcl is the stress intensity to close the crack. There are, however, several mechanisms ofclosure which assume greater importance at near-threshold levels, where CTODs are small andapproach the dimensions of the ‘wedge’. These processes rely on wedging mechanisms insidethe crack from corrosion debris, fracture surface asperities, or, in the case of environmentallyassisted fatigue, fluid inside the crack, as reviewed in (Suresh and Ritchie, 1984).Crack closure arising from crack surface corros

crack growth as a mutual competition between intrinsic mechanisms of crack advance ahead of the crack tip (e.g., alternating crack-tip blunting and resharpening), which promote crack growth, and extrinsic mechanisms of crack-tip shielding behind the tip (e.g., crack closure and bridging), which impede it. The widely differing

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