Mechanics and micromechanisms of fatigue crack growth in brittle solids

This paper is concerned with the mechanics and micromechanisms of stable mode I crack growth in brittle solids subjected to compression-compression fatigue and tension-tension fatigue loads. Constitutive models, results of finite element analyses, and experimental observations are described for monolithic ceramics and ceramic-matrix composites, plain concrete, and a transformation-toughened ceramic in an attempt to deduce a general theory on the origin of mode I fracture in notched plates under uniaxial cyclic compression at room temperature. An analysis of the residual stress field which develops at elevated temperatures in response to power law creep and far-field compressive cyclic loads is also presented. The principal driving force for mode I fracture in cyclic compression is the generation of a near-tip zone of residual tension, when the deformation at the notch-tip leaves permanent strains upon unloading from the far-field compressive stress. The results indicated that materials with very different microscopic deformation mechanisms, i.e., microcracking, dislocation plasticity, martensitic transformation, interfacial debonding/slip, or creep, exhibit a macroscopically similar, stable fracture under far-field cyclic compression because the zone of residual tension is embedded in material which is elastically strained in compression. It is shown that cyclic compression loading offers a unique method for fatigue precracking notched specimens of brittle solids prior to tensile fracture testing, whereby an unambiguous interpretation of the critical stress intensity factors for crack initiation and growth can be achieved. Fatigue crack growth characteristics of a transformation-toughened ceramic and a creeping ceramic composite under tension-tension fatigue loads are also discussed.     

Grain size effects on cyclic fatigue and crack-growth resistance behaviour of partially stabilized zirconia

Cyclic fatigue crack growth and crack-resistance behaviour was studied in partially stabilized zirconia (PSZ) with three different cubic-phase grain sizes following sub-eutectoid heat treatments. Raman spectroscopy was used to determine the extent of phase transformation around the cracks for both cyclic and monotonic loading conditions. All tests were on long, through thickness cracks using compact-tension specimens. Predictions of crack-tip shielding were made following determination of toughening parameters using crackresistance data. It was found that the dominant factors affecting cyclic fatigue-crack growth were the level of crack-tip shielding, as a result of phase transformation, and the intrinsic toughness of the material. Grain size did not appear to significantly affect fatigue crack-growth behaviour.     

Flexural strength,fracture toughness and fatigue crack growth behaviour of chromium alloyed γ-base TiAl

Mechanical properties of -base titanium aluminides strongly depend on microstructural parameters. Flexural strength, fracture toughness and fatigue crack growth properties were estimated for the cast and heat-treated (HT-TiAlCr) and cast, heat treated and isothermal forged (ITF-TiAlCr) chromium alloyed -base titanium aluminides at room temperature. HT-TiAlCr possessed superior fracture properties compared to ITF-TiAlCr. Toughening due to microcracks, and crack bridging by uncracked ligaments were observed in the test materials. Presence of lamellar grains in HT-TiAlCr increased the crack growth resistance and contributed positively to fracture properties. The coarse grain size promoted large crack deflection and fracture surface mismatch and caused high levels of crack closure in HT-TiAlCr. Combined crack-tip blunting and bridging by ductile -phase was significant in the case of ITF-TiAlCr. Fracture mechanisms of test materials were investigated and correlated to the fracture properties.     

Torsional fracture of fatigue pre-cracked ceramic rods

This paper describes the results of an experimental investigation of the room temperature fracture toughness of polycrystalline aluminium oxide (average grain size 3 m) in pure torsion (Mode III). Circumferentially notched cylindrical rods were stressed in uniaxial cyclic compression to introduce à fatigue pre-crack, following a technique proposed earlier; subsequently, the rods were fractured in quasi-static torsion. The critical stress intensity factor for fracture initiation in Mode III is about 2.3 times higher than that measured for Mode I. The mechanisms of quasi-static torsional fracture are contrasted with those observed in the tensile failure of ceramics. The Mode III failure mechanisms in ceramics are also compared with the relatively more familiar cases of torsional fracture in metallic materials. The effects of crack face rubbing and interference between fracture surface asperities on torsional fracture behaviour are highlighted.On leave from Institute of Applied and Technical Physics, Technical University of Vienna, Karlsplatz 13, A-1040, Vienna, Austria.     

Mechanisms of fatigue-crack propagation in ductile and brittle solids

The mechanisms of fatigue-crack propagation are examined with particular emphasis on the similarities and differences between cyclic crack growth in ductile materials, such as metals, and corresponding behavior in brittle materials, such as intermetallics and ceramics. This is achieved by considering the process of fatigue-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 nature of these mechanisms in ductile and brittle materials and their specific dependence upon the alternating and maximum driving forces (e.g., ΔK andK _max) provide a useful distinction of the process of fatigue-crack propagation in different classes of materials; moreover, it provides a rationalization for the effect of such factors as load ratio and crack size. Finally, the differing susceptibility of ductile and brittle materials to cyclic degradation has broad implications for their potential structural application; this is briefly discussed with reference to lifetime prediction. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cyclic fatigue crack growth behaviour in β-(Si–Al–O–N) at ambient and elevated temperatures

Four-point bending fatigue tests on a hot-pressed sintered Sm–-(Si–Al–O–N) ceramic were conducted at room temperature, 900 °C and 1000 °C in air under different load ratios and cyclic frequencies. The growth of indentation cracks was measured during the fatigue tests. The results indicate that the cyclic fatigue crack growth threshold is lower and crack growth rates are higher, for given values of K_max, at 1000 °C than those at room temperature. The cyclic fatigue crack growth behaviour at 900 °C is similar to that at room temperature. It was found that the crack growth retardation due to cyclic fatigue loading is much more pronounced at higher frequencies. An increase in cyclic frequency from 1 to 10 Hz cause a reduction of up to two orders of magnitude in crack propagation rates. High-temperature cyclic fatigue crack growth rates increased and threshold stress intensity factor ranges decreased with increasing load ratio. Possible mechanisms for cyclic crack growth are discussed.     

Mechanical properties of monolithic AIN and SiCw/AIN composites

Flexural, tensile, and high cycle fatigue test data are presented for pressureless sintered aluminium nitride (AIN) and hot-pressed aluminium nitride reinforced with silicon carbide whiskers (SiC_w/AIN). Tests were conducted at ambient temperature. The SiC_w/AIN composites consisting of 30wt% SiC_w produced significant increases in flexural strength, tensile strength, and tensile fatigue strength compared to monolithic AIN. Increases were nearly double in all cases. Corresponding strain-to-failures measured in tensile tests increased from 0.04% in monolithic AIN to 0.10% in the SiC_w reinforced composite. Fracture surfaces showed evidence of whisker-toughening mechanisms due to additions of SiC_w whiskers. High-cycle fatigue results indicated that both materials have the ability to sustain higher stress levels in the cyclic tests compared to the tensile experiments. The improved performance under cyclic testing is explained in terms of strain-rate effects. The times at or near peak stress are considerably less under high-cycle fatigue testing (20 Hz) compared to tensile tests (strain rate = 0.5%min^–1).     

The failure of amalgam dental restorations due to cyclic fatigue crack growth

In this study a restored mandibular molar with different Class II amalgam preparations was examined to analyze the potential for restoration failure attributed to cyclic fatigue crack growth. A finite element analysis was used to determine the stress distribution along the cavo-surface margin which results from occlusal loading of each restoration. The cyclic crack growth rate of sub-surface flaws located along the dentinal cavo-surface margin were determined utilizing the Paris law. Based on similarities in material properties and lack of fatigue property data for dental biomaterials, the cyclic fatigue crack growth parameters for engineering ceramics were used to approximate the crack growth behavior. It was found that flaws located within the dentine along the buccal and lingual margins can significantly reduce the fatigue life of restored teeth. Sub-surface cracks as short as 25 m were found capable of promoting tooth fracture well within 25 years from the time of restoration. Furthermore, cracks longer than 100 m reduced the fatigue life to less than 5 years. Consequently, sub-surface cracks introduced during cavity preparation with conventional dental burrs may serve as a principal source for premature restoration failure. ©©1999©Kluwer Academic Publishers     

Ductile–brittle fatigue and fracture behaviour of aluminium/PMMA bimaterial 3PB specimens

Fracture toughness and fatigue crack growth tests and numerical simulations on 3PB specimens were carried out to study the behaviour of a crack lying perpendicular to the interface in a ductile/brittle bimaterial. Polymethylmethacrylate acrylic (PMMA) and aluminium alloy 2024 T531 were joined together using epoxy resin. A precrack was introduced into the ductile material and tests were carried out to obtain fracture toughness and fatigue properties. The body force method and elastic–plastic finite-element analyses were used to simulate the experimental stress intensity K_I and cracking behaviour under monotonic and cyclic loads. It was found that the bimaterial fatigue crack growth rate is higher than that for monolithic aluminium 2024 but lower than the rate for a monolithic PMMA. This agreed with the trend for the fracture toughness values and was consistent with the numerical method results. The initial Mode I stable ductile cracking in the aluminium appears to ‘jump’ the interface and continues under mixed fracture Mode (I and II) in the PMMA material up to the final failure. A consistency between the simulation methods has indicated that the bimaterial fatigue crack growth is dominantly elastic with a small plastic zone near the crack tip.     

Low-cycle fatigue strength under step loading of a Si3N4 + SiC nanocomposite at 1350°C

The low-cycle fatigue behaviour of a hot pressed silicon nitride/silicon carbide nanocomposite and a reference monolithic Si₃N₄ have been investigated in 4-point bending at 1350°C in air using stepwise loading. The nanocomposite was prepared using 20% of SiCN amorphous powder as an additive, together with 5% yttria, to crystalline -silicon nitride powder. Two types of specimen have been tested, with and without a sharp notch (notch tip radius 10 m) at applied loads from 50 N with steps of 25 N and from 50 N with steps of 50 N, respectively. Five cycles have been performed at all applied load levels with an amplitude of 50 N for both types of specimen. The deflection of the specimens has been recorded up to specimen failure. The failure load of the unnotched nanocomposite was significantly higher than that of the monolithic material whereas for the notched specimens only a small difference has been found between the failure loads of the monolithic and the composite. Notched specimens of both materials exhibited a similar size of the slow crack growth area at catastrophic fracture, whereas for unnotched specimens the size of the slow crack growth area was significantly larger for the monolithic ceramic. The nanocomposite exhibits higher fatigue strength due to its higher resistance against stress corrosion damage and stress corrosion crack growth.     

Static mode fatigue crack propagation and generalized stress intensity correlation for fatigue–brittle polymers

Stable fatigue crack propagation is predominantly described by the Paris power law correlation of the crack growth rate with the amplitude cyclic stress intensity. The Paris relationship works well for most ductile materials but does not capture the response for fatigue–brittle materials lacking a cyclic damage mechanism, including ceramics and many polymers. Instead, crack growth rate of fatigue–brittle materials correlates to the peak cyclic stress intensity factor, \(\hbox {K}_{\mathrm{max}}\). This work shows that \(\hbox {K}_{\mathrm{max}}\) correlation of fatigue crack growth is derived directly from static mode crack tip behavior with constant correlation coefficients, and that \(\Delta \hbox {K}\) correlations are not generally applicable for static mode crack propagation in fatigue–brittle polymers. This derivation predicts load ratio, frequency, and waveform effects, which are included in a general static mode fatigue crack propagation law. Fatigue crack propagation data of a known fatigue–brittle polymer are presented to demonstrate static mode crack propagation behavior correlation with \(\hbox {K}_{\mathrm{max}}\) with constant parameters.     

Fatigue limits in noncyclic loading of ceramics with crack-resistance curves

Fatigue properties in the noncyclic loading of ceramics with R-curves are studied. Particular attention is directed to the potential role of R-curves in the enhancement of fatigue limits. A numerical algorithm for solving the appropriate differential equations of rate-dependent failure is developed. Our formalism specifically incorporates a crack-size dependent toughness function, based on grain-localized interfacial bridging, and a hyperbolic-sine velocity function, representative of a fundamental activation process. In a case study, dynamic fatigue (constant stressing rate) and static fatigue (constant applied stress) data for a coarse-grained alumina with a pronounced R-curve are analysed. With foreknowledge of the toughness parameters, the intrinsic crack-tip velocity function is deconvoluted. This intrinsic function is distinguished from the usual apparent, or shielded, (and demonstrably nonunique) function determined directly from the external load. It is confirmed that the R-curve, by virtue of its stabilizing influence on the crack growth, significantly enhances the fatigue limit, and confers the quality of flaw tolerance on fatigue lifetimes.Guest Scientist: on leave from the Department of Materials Science and Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, USA.     

Crack growth in transforming ceramics under cyclic tensile loads

The mechanisms of stable growth of short fatigue cracks (crack length up to 1 mm) at room temperature in magnesia-partially stabilized zirconia subjected to cyclic tensile loads were investigated. Single edge-notched specimens were fractured in the four-point bend configuration under cyclic and quasi-static tensile loads. At a load ratio of 0.1, the threshold stress intensity factor range, K, for fracture initiation in cyclic tension is as low as 3.4 M Pam^1/2, and catastrophic failure occurs at K=6.6 M Pam^1/2. For crack length less than 1 mm and for plane strain conditions, growth rates are highly discontinuous, and periodic crack arrest is observed after growth over distances of the order of tens of micrometres. Crack advance could only be resumed with an increase in the far-field stress intensity range. The mechanisms of short crack advance in cyclic tension are similar to those observed under quasi-static loads, and the tensile fatigue effect appears to be a manifestation of static failure modes. A model is presented to provide an overall framework for the tensile fatigue crack growth characteristics of partially stabilized zirconia. Experimental results are also described to demonstrate the possibility of stable room temperature crack growth under cyclic tension in fine-grained tetragonal zirconia polycrystals, partially stabilized with Y₂O₃. The growth of cracks in transformation-toughened ceramics is found to be strongly influenced by the crack size and shape, stress state and specimen geometry.     

A new approach to detect and size closed cracks by ultrasonics

The effect of a crack on time-of-flight of shear waves (4.5 MHz) polarized in perpendicular (t ) and parallel (t ) directions to the crack surface, propagating parallel to the direction of crack growth is investigated. The first and second back-wall echoes are used instead of the weak crack-tip echo for the measurement of time-of-flight. The measurement is made for fatigue cracks grown by different loading histories in ferritic steel (pressure vessel steel A533B-1) under the condition of no loading. The normalized time-of-flight (t –t )/t at the crack position is found to change proportionally as the ratio of crack depth to specimen width increases. The change is mainly due to the effect of plastic deformation occurring around the crack ont . It is shown that the depth of tightly closed fatigue crack in austenitic stainless steel (AISI 304) also can be evaluated under the condition of no loading by using this relationship.     

FATIGUE CRACK GROWTH LAWS FOR BRITTLE AND DUCTILE MATERIALS INCLUDING THE EFFECTS OF STATIC MODES AND ELASTIC-PLASTIC DEFORMATION

A fatigue crack growth damage accumulation model is used to derive laws for the fatigue crack growth rates of brittle and ductile materials. The damage accumulated during cyclic loading is assumed to be proportional to the cyclic change in the plastic displacement in the crack tip yielded zone. The static mode contribution to the fatigue damage is assumed to be proportional to some power of the crack tip displacement. The laws are applicable in either the small or large scale yielding regimes provided that the stress ratio remains positive. Static modes are assumed to be controlled by the fracture toughness value in brittle materials, and by the gradient of the crack growth resistance curve in ductile materials. In the analysis of ductile materials it is assumed that the crack growth resistance of the material is not significantly altered by fatigue crack growth.
The growth rate equations are expressed in terms of the near field value of the J -integral, i.e. the value which would be calculated from assuming the material deformed in a non-linear elastic manner during the increasing load part of the fatigue cycle. Examples are given of the predictions of the growth law for ductile materials. It is predicted that after the initiation of stable tearing the crack growth rate, when expressed in terms of the cyclic change in the stress intensity factor, depends on both the structural geometry and the degree of crack tip plastic deformation. In both brittle and ductile materials the fatigue crack growth rate is predicted to accelerate as the failure criteria relevant to static crack instability are approached.     

Acoustic Emission Study of Fatigue Cracks in Materials Used for AVLB

The Armored Vehicle Launch Bridge (AVLB) is subjected to cyclic loading during launching as well as during tank crossings. The cyclic loading causes cracks to initiate in critical bridge components, and then to propagate. Unless these cracks are detected and repaired before they rapidly grow to reach their critical stage of propagation, the failure of bridge components can occur. Three AVLB components, the splice doubler angle, the splice plate, and the bottom chord, are susceptible to fatigue damage. In the present study, laboratory fatigue tests on the materials used for the components, aluminum 2014-T6, aluminum 7050-T765, and ASTM A36 steel, were conducted using the acoustic emission (AE) fatigue crack monitoring technique. A total of fourteen compact-tension specimens were prepared in this study: six aluminum 2014-T6, four aluminum 7050-T76511, and four ASTM A36 steel specimens. The characteristics of AE signals associated with the stress intensity factor, K, were obtained to understand AE behavior corresponding to the fatigue crack growth in the materials. Several AE parameters, such as AE counts, energy, and hits, have been shown to be useful tools for detecting cracks, providing early warnings, and preventing failure of the AVLB structures. A major jump in AEcount rate as well as AE hit rate occurred when K_max reached a value of about 30~MPam (27 ksiin.) for aluminum 2014-T6 specimens and about 50 MPam (46 ksiin.) for aluminum 7050-T76511 specimens. Also, AE source location techniques were able to successfully locate the path ofcrack propagation.     

Crack propagation in ceramics under cyclic loads

Stable crack growth is observed in notched plates of polycrystalline alumina subject to fully compressive far-field cyclic loads at room temperature in a moist air environment andin vacuo. The fatigue cracks propagate at a progressively decreasing velocity along the plane of the notch and in a direction macroscopically normal to the compression axis. The principal failure events leading to this effect are analysed in terms of notch-tip damage under the far-field compressive stress, microcracking, frictional sliding and opening of microcracks, and crack closure. An important contribution to such Mode I crack growth arises from the residualtensile stresses induced locally at the notch-tip when the deformation within the notch-tip process zone leaves permanent strains upon unloading from the maximum nominal compressive stress. It is shown that the phenomenon of crack growth under cyclic compressive stresses exhibits a macroscopically similar behaviour in a wide range of materials spanning the very ductile metals to extremely brittle solids, although the micromechanics of this effect are very different among the various classes of materials. The mechanisms of fatigue in ceramics are compared and contrasted with the more familiar examples of crack propagation under far-field cyclic compression in metallic systems and the implications for fracture in ceramic-metal composites and transformation toughened ceramic composites are highlighted. Strategies for some important applications of this phenomenon are recommended for the study of fracture mechanisms and for the measurement of fracture toughness in brittle solids.     

Regularities in the Main-Crack Propagation and Dislocation Structure Evolution in the Fracture Zone of VT22 Alloy at Various Frequencies of Cyclic Loading

We have studied the relationship between the dislocation structure in the fracture zone and fractographic features of the main-crack propagation in a Ti–5%Al–5%V alloy tested for cyclic crack growth resistance in symmetrical tension–compression at frequencies of 140, 600, 3000, and 10000 Hz. It is demonstrated that the prevailing Types of dislocation structure are cellular over the near-threshold K range and of band-Type structure for the remaining values of the stress intensity factor range. For these Types of structure of the alloy studied at all loading frequencies, the characteristic micromechanism of fracture is the formation of fatigue striations. In the region of low K values, the above-mentioned Types of substructure, and thus fatigue striations, are most commonly formed along certain crystallographic planes and directions. As the K values grow, the crack sensitivity to crystallographic orientation decreases. The effect of the loading frequency on the regularities and mechanisms of fatigue crack growth is governed by two main factors: the processes of plastic deformation at the crack tip during the pre-fracture period and the interaction between the crack front and the initial and formed structural and substructural elements. The appearance of the brittle-fracture elements with increasing loading frequency is due to a rather high sensitivity of the -phase to the loading rate.     

Crack propagation and fatigue in zirconia-based composites

This paper reviews existing published studies on crack propagation behavior of zirconia-based composites. The first part of the paper is concerned with slow crack growth (SCG) under static loading. SCG in zirconia ceramics is shown to be a consequence of stress corrosion by water molecules at the crack tip. The influence of transformation toughening on SCG is discussed in terms of a stress intensity factor acting to reduce the net driving force for propagation. This proposition is in agreement with results obtained on 3Y-TZP and Mg-PSZ ceramics. A master curve is proposed which could be applied roughly to all zirconia ceramics. The influence of zirconia addition to alumina ceramics (ZTA ceramics) is also discussed. The second part of the paper deals with SCG under cyclic loading. A mechanical degradation of all zirconia-based composites is observed by a decrease of crack shielding. This degradation of zirconia-based composites under cyclic loading leads to increased velocities as compared to the static fatigue case. A master curve is also obtained, as in the case of static fatigue. Cyclic fatigue results are interpreted in terms of stress corrosion at the crack tip assisted by a decrease of the reinforcement.     

Fatigue microcrack growth in a nickel-base superalloy

The growth of very small fatigue microcracks was studied in a powder metallurgy nickel-base superalloy. A novel specimen containing a small crack was used, with crack growth rates being measured optically at high magnification. Interaction between the crack and the material microstructure was observed in a cyclic loading stage within a scanning electron microscope.It was found that microcracks grew initially at rates more rapid than those corresponding to conventional fracture mechanics (large crack) specimens. The rate undergoes a transient decrease with increasing crack length, dropping below the corresponding plot for large cracks, before beginning to increase in accordance with large crack results, ultimately merging with the latter. These results are discussed in terms of microstructure and crack growth mode, and the findings considered in light of the few studies of cyclic microcrack growth which have previously been correlated with fracture mechanics.