Fatigue crack growth behaviour of tungsten carbide-cobalt hardmetals

Fatigue crack propagation studies have been carried out on a range of WC-Co hardmetals of varying cobalt content and grain size using a constant-stress intensity factor double torsion test specimen geometry. Results have confirmed the marked influence of mean stress (throughK _max), which is interpreted in terms of static modes of fracture occurring in conjunction with a true fatigue process, the existence of which can be rationalized through the absence of any frequency effect. Dramatic increases in fatigue crack growth rate are found asK _max approaches that value of stress intensity factor ( 0.9K_IC) for which static crack growth under monotonic load (or static fatigue) occurs in these materials. Lower crack growth rates, however, produce fractographic features indistinguishable from those resulting from fast fracture. These observations, and the important effect of increasing mean free path of the cobalt binder in reducing fatigue crack growth rate, can reasonably be explained through a consideration of the mechanism of fatigue crack advance through ligament rupture of the cobalt binder at the tip of a propagating crack.     

Effects of mode mix upon fracture behavior of a solder joint

Results of fracture experiments of brass/solder/brass sandwich CTS (Compact Tension-Shear) specimens are presented together with observations of the crack propagation behavior and the fractographs. The fracture behaviors of the interface crack are analyzed by the finite element method with a modified boundary layer formulation. Several fracture mechanisms and the corresponding criteria are examined. And the crack growth behavior and fracture toughness are predicted. As the results various crack growth procedures such as the crack jump to another interface on the opposite side, the nucleation of a new crack far from the initial crack front, and the asymmetric relation of fracture toughness versus mode mix J _c– can be successfully explained. The fractographs, the crack growth behaviors, and stress-strain distribution along the interface are inter-related.     

Microstructure and room-temperature mechanical properties of Si3N4 with various α/β phase ratios

After polycrystalline silicon nitride samples with various / phase ratios were fabricated by uniaxial hot-pressing under vacuum, their microstructures, -to- transformations, and grain-growth mechanisms were then characterized by electron microscopy. Room-temperature fracture toughness (KIC) increased with increasing -phase content, and a value of 7.0 ± 0.5 MPa m1/2 was obtained for a sample that contained 60 vol% phase. The increase in KIC is the result of an increase in elongated-grain fractions with increasing content, which promotes energy absorption by crack deflection, as well as by grain debonding, pullout, and bridging mechanisms.     

The stacked lamellar texture on the fracture surfaces of fibre composites

A fracture surface texture, which has been variously termed as lacerations, hackles or serrations, is often observed on the matrix surface of fibre composites, most often in resin-rich regions. This texture, referred to here as a stacked lamellar texture to emphasize its plate-like nature, was studied in an E-glass/epoxy composite. Scanning electron fractographs of these materials suggest that the stacked lamellar texture arises from crack fingers due to a meniscus instability mechanism interacting with a reorienting stress field.     

Interfacial and mechanical properties of environment-friendly “green” composites made from pineapple fibers and poly(hydroxybutyrate-co-valerate) resin

Physical and tensile properties of pineapple fibers were characterized. Tensile properties of pineapple fibers, like most natural fibers, showed a large variation. The average interfacial shear strength between the pineapple fiber and poly(hydroxybutyrate-co-valerate) (PHBV) was 8.23 MPa as measured by the microbond technique. Scanning electron microscopy (SEM) photomicrographs of the microbond specimens revealed an adhesive failure of the interface. Fully degradable and environment-friendly green composites were prepared by combining pineapple fibers and PHBV with 20 and 30% weight content of fibers placed in a 0°/90°/0° fiber arrangement. Tensile and flexural properties of these green composites were compared with different types of wood specimens. Even though tensile and flexural strength and moduli of these green composites were lower than those of some wood specimens tested in grain direction, they were significantly higher than those of wood specimens tested in perpendicular to grain direction. Compared to PHBV virgin resin, both tensile and flexural strength and moduli of these green composites were significantly higher. SEM photomicrographs of the fracture surface of the green composites, in tensile mode, showed partial fiber pull-out indicating weak bonding between the fiber and the matrix.     

Fatigue striation in a wide range of crack propagation rates up to 70 μm/cycle in a ductile structural steel

The relationship between striation spacing and fatigue crack propagation rate up to 70 m/cycle was investigated for a ductile structural steel, qualified as JIS SM58Q. A modified compact-type specimen 400 mm wide and a centre-cracked specimen 200 mm wide were tested at a stress ratio, R, of 0 and 0.8. The fracture surface of the specimen was examined in detail under a scanning electron microscope. The crack propagation rate was expressed by a power function of the range of stress intensity factor from 0.1 to 70 m/cycle for R=0 and to 0.5 m/cycle for R=0.8. The striation spacing coincided with the fatigue crack propagation rate over the range 0.1 to 70 m/cycle. The profile of striation was found to be a ridge and valley type, and the ridges on one fracture surface coincided with those on the matching surface. It is suggested that the striation is formed by a plastic blunting mechanism.     

Mechanical properties of injection moulded styrene maleic anhydride (SMA) Part II Influence of short glass fibres and weldlines

The dependence of the various mechanical and fracture properties on the volume fraction ofshort glass fibres in the styrene maleic anhydride (SMA) polymer was investigated. Special attention has been given to describing the dependence of various mechanical properties on the volume fraction of the glass fibres, f by way of the rule of mixtures. It was found that, strength, elastic modulus and fracture toughness, all follow a simple rule-of-mixtures of the form Qc=Qff+Qm(1–f), where Qc is the measured quantity for the composite, Qm and Qf are the corresponding values for the matrix and the fibre, respectively, and is the overall efficiency of the fibres, taking into account the orientation and the length of the fibres in the composite. It was also found that, while the presence of the weldline had no significant effect upon elastic modulus, its presence significantly reduced tensile strength and the fracture toughness of SMA and its composites. © 1998 Kluwer Academic Publishers     

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.     

A micromechanics theory for the transformation toughening of two-phase ceramics

Summary Based on the principle of thermodynamic equilibrium, the condition of stress-induced phase transformation in a two-phase ceramic is established. The development makes use of the change of potential energy that was calculated with a mean-field approach. In this process the elastic heterogeneity of the constituent phases, and the shape and volume concentration of the randomly oriented metastable ellipsoidal inclusions, are fully accounted for. Both the transformation heightH of the process zone with a steadily growing crack and the fracture toughness increment K of the transforming system are derived. The derived theory is then used to address the effect of inclusion shape and elastic inhomogeneity on the transformation toughening of two-phase ceramics. By considering the metastable ellipsoidal inclusions as phase 1 and the stable matrix as phase 0, it is found that, when ₁/₀>1, flat-like discs always provide a larger transformation-height while spherical ones provide the smallest, and vice versa. As the ratio of ₁/₀ increases, the size of the process zone also increases. For the toughness increment, the results indicate that thin-disc inclusions are again the most effective toughening medium. It is further found that Poisson's ratio of the constituent phases also has a significant effect; the combination ofv ₁0.5 for the inclusions andv ₁0 for the matrix has the best enhancement for fracture toughness. But whenv ₁, the toughness increment K all approaches to an asymptotic value regardless of the values of Poisson's ratios. Some explicit solutions of toughness change for several distinctive shapes of inclusions are also derived for the first time.     

Effect of martensitic transformation in Ti–15 at %V β-phase particles on lamellar boundary decohesion in γ-TiAl Part II Finite element analysis of crack-bridging phenomenon

The commercial finite element package ABAQUS has been used to analyse the crack bridging process by Ti-15 at%V -phase particles dispersed in -TiAl matrix in the presence of particle–matrix decohesion. Both the particle–matrix decohesion potential and the -phase materials constitutive relations are found to have a major effect on the ductility, fracture toughness and failure mode of the – two-phase material. The interface potential is found to primarily affect the distribution of the normal interface strength ahead of the advancing interfacial crack and the mode (gradual versus sudden) of decohesion. The -phase materials constitutive relations are found to influence the location of nucleation of the interfacial cracks and, in turn, the mode of decohesion. A metastable -phase that can plastically deform at low stress levels by undergoing a stress-assisted martensitic transformation, but experience a high rate of strain hardening is found to give rise to the largest levels of ductility and fracture toughness is the – two-phase material. © 1998 Kluwer Academic Publishers     

Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens

Specimen size and geometry effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain an important technological impediment in industrial applications of fracture mechanics and in the on-going development of consensus fracture testing standards. This investigation employs 3-D nonllinear finite element analyses to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE(B) specimens, with and without side grooves. Crack front conditions are characterized in terms of J-Q trajectories and the constraint model for cleavage fracture toughness proposed previously by Dodds and Anderson. An extension of the toughness scaling model suggested here combines a revised in-plane constraint correction with an explicit thickness correction derived from extreme value statistics. The 3-D analyses provide effective thicknesses for use in the statistical correction which reflect the interaction of material flow properties and specimen aspect ratios, a/W and W/B, on the varying levels of stress triaxiality over the crack front. The 3-D computational results imply that a significantly less strict size/deformation limit, relative to the limit indicated by previous plane-strain computations, is needed to maintain small-scale yielding conditions at fracture by a stress-controlled, cleavage mechanism in deep notch SE(B) and C(T) speciments. Moreover, the analyses indicate that side grooves (20 percent) should have essentially no net effect on measured toughness values of such specimens. Additional new results made available from the 3-D analyses also include revised -plastic factors for use in experimental studies to convert measured work quantities to thickness average and maximum (local) J-values over the crack front. To estimate CTOD values, new m-factors are included for use in the expression 131-1.     

Strength variations of reaction-sintered SiC heterogeneously containing fine-grained β-SiC

Strength variations of reaction-sintered SiC were examined to determine the effect of the volume fraction of fine-grained -SiC domain. The fracture strength significantly decreased with an increase in the volume fraction of the -SiC domain, and eventually fell to the strength of the -SiC domain alone. Furthermore, a substantial difference in the crack deflection was found between the indentation microfracture formed in a structure containing fine-grained -SiC and that in the typical structure of reaction-sintered SiC. This showed that the fracture toughness decreased on account of the -SiC layer.     

Experimental and numerical studies in model composites Part II: Numerical results

A numerical approach using the boundary element method for strength and toughness of a composite with long aligned fibers is reported. The three-dimensional problem is reduced to a two-dimensional one by substituting the rows of fibers with layers of appropriate width and elastic constants. The configuration examined in this work is a compact tension specimen similar to that used in the experimental studies (Part I, [1]). The experimental results on strength and apparent fracture toughness are compared with the numerical results. For the particular geometry and fiber spacing, the numerical simulations are in good agreement with the experimental findings, i.e. the composite's strength _A , scales with the fiber spacing , in the form of _A . Using the numerical formalism a number of different geometries was examined. The simulations suggested that if the external specimen characteristics remain the same and the fiber spacing in the direction of crack advance is changed, then the strength of the composite specimen can be expressed _A . If the fiber spacing varies in both directions simultaneously, for a certain range of , it can be considered that the composite's strength _A , is proportional to _A .     

Ultrasonic study of the temperature and pressure dependences of the elastic properties of β-silicon nitride ceramic

Ultrasonic wave velocity measurements have been used to determine the elastic stiffness moduli and related elastic properties of high-purity, dense -Si₃N₄ ceramic samples as functions of temperature in the range 150–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. Due to its covalently bonded, rigid structural framework -Si₃N₄ is an elastically stiff material; the elastic stiffness moduli of the ceramic at 295 K are: C _L = 396 GPa, = 119 GPa, B ^S = 238 GPa, E = 306 GPa, Poisson's ratio = 0.285. The longitudinal elastic stiffness C _L increases with decreasing temperature and shows a knee at about 235 K; the decrease in slope below the knee indicates mode softening. The shear elastic stiffness shows mode softening which results in a plateau centred at about 235 K and an anomalous decrease with further reduction in temperature. The hydrostatic-pressure derivatives of elastic stiffnesses at 295 K are (C _L/P) _P=0 = 4.5 ± 0.1, (B ^S/P) _P=0 = 4.3 ± 0.1 and (/P) _P=0 = 0.17 ± 0.02 (pressure < 0.12 GPa). An interesting feature of the nonlinear acoustic behaviour of this ceramic is that, in the pressure range above 0.12 GPa, the values obtained for (/P) _P=0 and the shear mode Grüneisen parameter (_S) are small and negative, indicating acoustic-mode softening under these higher pressures. Both the anomalous temperature and pressure dependences of the shear elastic stiffness indicate incipient lattice shear instability. The shear _S(=0.005) is much smaller than the longitudinal _L(=1.18) accounting for the thermal Grüneisen parameter ^th(=1.09): since the acoustic Debye temperature _D(=923 ± 5 K) is so high, the shear modes play an important role in acoustic phonon population at room temperature. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic -Si₃N₄.     

Interlaminar Fracture Toughness of CF/PEI and GF/PEI Composites at Elevated Temperatures

An experimental study has been conducted to assess temperature effects on mode-I and mode-II interlaminar fracture toughness of carbon fibre/polyetherimide (CF/PEI) and glass fibre/polyetherimide (GF/PEI) thermoplastic composites. Mode-I double cantilever beam (DCB) and mode-II end notched flexure (ENF) tests were carried out in a temperature range from 25 to 130°C. For both composite systems, the initiation toughness, G _IC,ini and G _IIC,ini, of mode-I and mode-II interlaminar fracture decreased with an increase in temperature, while the propagation toughness, G _IC,prop and G _IIC,prop, displayed a reverse trend. Three main mechanisms were identified to contribute to the interlaminar fracture toughness, namely matrix deformation, fibre/matrix interfacial failure and fibre bridging during the delamination process. At delamination initiation, the weakened fibre/matrix interface at elevated temperatures plays an overriding role with the delamination growth initiating at the fibre/matrix interface, rather than from a blunt crack tip introduced by the insert film, leading to low values of G _IC,ini and G _IIC,ini. On the other hand, during delamination propagation, enhanced matrix deformation at elevated temperatures and fibre bridging promoted by weakened fibre/matrix interface result in greater G _IC,prop values. Meanwhile enhanced matrix toughness and ductility at elevated temperatures also increase the stability of mode-II crack growth.     

The essential work of plane stress ductile fracture of a strain-aged steel

The paper reports the results of an experimental investigation on the essential work of fracture of a strain-aged low carbon (0.1% C) temper-rolled 16-gauge sheet steel which has been subjected to pre-strain levels of 2 to 12% and ageing temperatures of 80 and 100C. Deep edge-notched tension specimens were used to determine the specific essential work by extrapolating the straight-line relationship between the specific work of fracture (W _f) and ligament length (I) to zero ligament length. The strain-aged steels at 80 and 100 give approximately the same specific essential fracture work of 0.18 to 0.20 J mm^–2 which is independent of the amount of prestrain. Advancing crack opening displacements (C.O.D.) have also been analysed, which give 0.60 to 0.63 mm for the strain-aged steels. For comparison, the prestrained but unaged steels have a higher essential work of fracture of 0.275 J mm^–2 and a larger C.O.D. of 0.73 mm. It is concluded, therefore, that the causes of strain-ageing embrittlement are primarily due to the reduction of both the essential work of fracture and the advancing C.O.D. at the crack tip end region.     

Strength distributions and size effects for 2D and 3D composites with Weibull fibers in an elastic matrix

Monte Carlo simulation and theoretical modeling are used to study the statistical failure modes in unidirectional composites consisting of elastic fibers in an elastic matrix. Both linear and hexagonal fiber arrays are considered, forming 2D and 3D composites, respectively. Failure is idealized using the chain-of-bundles model in terms of -bundles of length , which is the length-scale of fiber load transfer. Within each -bundle, fiber load redistribution is determined by local load-sharing models that approximate the in-plane fiber load redistribution from planar break clusters, as predicted from 2D and 3D shear-lag models. As a result the -bundle failure models are 1D and 2D, respectively. Fiber elements have random strengths following either a Weibull or a power-law distribution with shape and scale parameters and , respectively. Under Weibull fiber strength, failure simulations for 2D -bundles, reveal two regimes: When fiber strength variability is low (roughly >2) the dominant failure mode is by growing clusters of fiber breaks, one of which becomes catastrophic. When this variability is high (roughly 0<<2) cluster formation is suppressed by a dispersed failure mode due to the blocking effects of a few strong fibers. For 1D -bundles or for 2D -bundles under power-law fiber strength, the transitional value of drops to 1 or lower, and overall, it may slowly decrease with increasing bundle size. For the two regimes, closed-form approximations to the distribution of -bundle strength are developed under the local load-sharing model and an equal load-sharing model of Daniels, respectively. The results compare favorably with simulations on -bundles with up to 1500 fibers.     

The fracture toughness of a nickel-aluminium bronze

Critical stress intensity factors for two slightly different compositions of nickel-aluminium bronze were estimated usingJ-integral testing methods. The material was in cast form and tested as 10 mm thick three-point bend bars. Toughness values were 125 MN m^–3/2 and crack tip opening displacements were 0.3 mm. The crack tip opening displacements were too small to be accurately and reproducibly measured. Specimens tested with 0.2 mm wide spark-machined slits gave equivalent toughness values to specimens pre-fatigue cracked, within experimental error.     

Lifetime distributions for unidirectional fibrous composites under creep-rupture loading

Monte-Carlo simulations and theoretical modeling are used to study the statistical failure modes and associated lifetime distribution of unidirectional 2D and 3D fiber-matrix composites under constant load. Within the composite the fibers weaken over time and break randomly, and the matrix undergoes linear viscoelastic creep in shear. The statistics of fiber failure are governed by the breakdown model of Coleman (1958a), which embodies a Weibull hazard functional of fiber load history imparting power-law sensitivity to fiber load with exponent , and Weibull lifetime characteristics with shape parameter . The matrix has a power-law creep compliance in shear with exponent . Fiber load redistribution at breaks is calculated using a shear-lag mechanics model, which is much more realistic than idealized rules based on equal, global or local load-sharing. The present study is concerned only with the `avalanche' failure regime discussed by Curtin and Scher (1997) which occurs for sufficiently large , and whereby the composite lifetime distribution follows weakest-link scaling. The present Monte-Carlo failure simulations reveal two distinct failure modes within the avalanche regime: For larger , where fiber failure is very sensitive to load level, the weakest link volume fails in a `brittle' manner by the gradual growth of a cluster of mostly contiguous fiber breaks, which then abruptly transitions into a catastrophic crack. For smaller , where this load sensitivity is much less, the weakest link volume shows `tough' behavior, i.e., distributed damage in terms of random fiber failures until the failure of a critical volume and its catastrophic extension. The transition from brittle to tough failure mode for each within the avalanche regime is gradual and depends on the matrix creep exponent and Weibull exponent . Also, as increases above zero the sensitivity of median composite lifetime to load level increasingly deviates from power-law scaling known to occur in the elastic matrix case, =0. By probabilistic modeling of the dominant failure modes in each regime we obtain distribution forms and various scalings for damage growth, and for carefully chosen sets of parameter values we analytically extend simulation results on small composites (limited by current computer power) to more realistic sizes. Our analytical strength distributions are applicable for >2 in 2D, and 4 in 3D. The 2D bound coincides with the avalanche-percolation threshold derived by Curtin and Scher (1997) using entirely different arguments.     

Fracture toughness analysis of circumferentially-cracked round bars

The accuracy and the domain of applicability of approximate formulae used to evaluate the fracture toughness of circumferentially-Cracked Round Bars (CRBs) are established using finite element calculations. In the elastic plastic fracture mechanic (EPFM) domain, new formulae are developed which increase largely the accuracy and the domain of applicability. The loss of constraint is evaluated through the Q-factor allowing to determine the domain of validity of one-parameter fracture toughness characterisation. At the same time, an appropriate crack length to bar radius ratio is proposed. A micromechanical model of cleavage fracture in the transition region is proposed where both the specimen size and loss of constraint correction are taken into account. This model allows to measure plane strain fracture toughness using small CRB.