Dislocation pileups and elastic cracks at a bimaterial interface

Double-ended dislocation pileups and the three modes of cracks at a bimaterial interface have been studied. The elastic field of the cracks are represented by that of a continuous distribution of infinitesimal dislocations. Analytical solutions are obtained for antiplane shear cracks. It is found that the stress intensity at the tip of a double-ended screw dislocation pileup is smaller than that of a single-ended pileup by the factor of (1—a) wherea = (2/π) sin^-1√(l-k)/2 andk = (G₂-G₁)/(G₂ + G₁). G2 and G₁ are the shear moduli of the two constituent phases. Numerical techniques are used to discuss double-ended edge dislocation pileups and tensile and in-plane shear cracks. The crack opening displacements for various bimaterial systems have been determined.     

TEM Study of Microcrack Nucleation and Propagation for 310 Stainless Steel

TEM in situ tensile tests of 310 stainless steel show that a dislocation free zone (DFZ) forms if the displacement keeps constant after dislocations are emitted from a crack tip. The elastic DFZ is gradually thinned and the stress in the DFZ will reach the cohesive strength, resulting in nucleation of nanocracks in it and their bluntness into voids. If continuously tensioning, the inhomogeneously thinning ahead of the crack tip, initiat-ing and connecting of microcracks or microvoids will be observed rather than a DFZ, nanocracks' initiation and bluntness into voids. The inverse pile-up ahead of a loaded crack tip can move back to the crack tip when unloading.     

In situtem observations of nucleation and bluntness of nanocracks in thin crystals of 310 stainless steel

Nucleation and bluntness of nanocracks were studied through in situ tensile tests for thin crystals of 310 stainless steel by transmission electron microscopy (TEM). A dislocation free zone (DFZ) could form after the dislocation emission had just ceased. The DFZ is an elastic zone so that the local stress near the crack tip in the DFZ is possibly up to the cohesive strength, because of which a nanocrack could initiate in the DFZ or at the crack tip. The nanocrack in the DFZ or at the crack tip would blunt into a void or a notch through the increment and movement of dislocations in the plastic zone even when keeping constant displacement. If constant displacement was kept for a long time, nanovoids could initiate in the DFZ through diffusion and enrichment of supersaturation vacancies. The connection of the nanovoids would result in the initiation of nanocracks.     

Modeling of grain-boundary effects and intergranular and transgranular failure in polycrystalline intermetallics

A three-dimensional multiple-slip dislocation-density-based crystalline formation and specialized finite-element formulation were used to investigate dislocation-density transmission and blockage in nickel-aluminide polycrystalline aggregates, which were subjected to dynamic loading conditions, with a macroscopic crack and different distributions of random low-angle and coincident site lattice (CSL) grain boundaries (GBs). An interfacial GB scheme was developed to determine whether dislocation-density pileups or transmissions occur as immobile and mobile dislocation densities evolve along different slip systems. The three-dimensional dislocation-density-based crystalline formulation is based on inter-related mechanisms that can occur due to the generation, trapping, interaction, and annihilation of mobile and immobile dislocation densities that are generally associated with large strain-high-strain-rate plasticity in L1₂-ordered intermetallics. A crack-tip shielding factor was also formulated to delineate between transgranular and intergranular crack growth. The current results indicate that aggregates with a high frequency of Σ33a GBs would be susceptible to blunted transgranular crack growth due to high dislocation-density transmission rates and shear-stress accumulations, and that an aggregate with a high frequency of Σ17b GBs would be susceptible to sharp intergranular growth due to a large number of dislocation-density pileups and an accumulation of large normal stresses ahead of the crack tip.     

Crack-tip dislocation emission arrangements for equilibrium—II. Comparisons to analytical and computer simulation models

Theoretical analyses of thin film effects on an apparent dislocation free zone (DFZ), grain boundary effects on the number of dislocations required for equilibrium and a tip-emission condition to avoid the Rice paradox are compared to the in situ TEM study of Part I. It is first shown that the apparent DFZ is a thin film artifact and, second, that a grain boundary blocked slip band may require half as many dislocations for equilibrium compared to no blockage. It is further shown that the “DFZ” becomes diminishingly small for even relatively low applied stress intensities. Based on a disappearing “DFZ”, an asymptotical solution of Li's grain size analysis leads to the number of dislocations in equilibrium for a given applied stress intensity, friction stress and grain size. With an ad hoc failure criterion, this gives a first order prediction of fracture toughness for a large number of ferritic and ferrite-pearlites steels. Finally, based on local stress distributions obtained from a solution containing tip-emission conditions, it is suggested that a local stress intensity presents a more easily defined brittle fracture criterion. This is applied to observations of dislocation arrangements at large applied stress intensity in Part III.     

Crack propagation near cylindrical voids

Stress intensity factorsK _I andK _II are presented for a planar, sharp-ended crack subjected to nearby line forces and line force doublets. The resulting near crack tip stress field is used to predict the influence of such singularities upon the crack propagation direction. The concept of the criticality of the angle of crack departure from symmetric propagation is introduced and used to compare computer predictions with experiments performed on double cantilever beam (DCB) specimens of 7075 aluminum alloy. The form of the near crack tip elastic equations and the criticality are verified. The critical angle parameter is found to be a material and experimental constant, independent of the strength of the centers of stress.     

Dislocation structures ahead of advancing cracks

Previous transmission electron microscope (TEM) observations of the dislocation structure in the vicinity of a crack suggested that the region immediately ahead of a crack is devoid of dislocations. In the present paper, the results ofin situ TEM deformation experiments in numerous systems are described. The dislocation configurations are generally complex, with dislocations extending from the crack tip(i.e., no dislocation-free zone (DFZ)) and forming complex arrangements in the plastic region in front of the crack tip. Crack advance was accompanied by the emission of dislocations from both the crack tip and nearby sources. These observations are summarized, and the theory of dislocation configurations in front of a crack is reconsidered. This paper is based on a presentation made in the symposium “Interface Science and Engineering” presented during the 1988 World Materials Congress and the TMS Fall Meeting, Chicago, IL, September 26–29, 1988, under the auspices of the ASM-MSD Surfaces and Interfaces Committee and the TMS Electronic Device Materials Committee.     

Quantitative fractography and dislocation interpretations of the cyclic cleavage crack growth process

Fractographic features of cyclic cleavage crack growth in Fe and Fe-binary alloys as a function of applied stress intensity and test temperature are documented. Cyclic striations, cleavage rivers and twist angle misorientations are measured and discussed in terms of geometrical and local stress considerations. It is shown that the river height displacement must account for both twist angle misorientation between adjacent grains and the crack-tip opening displacement of an advancing fatigue crack. With regards to the rate of an advancing cleavage crack, a dislocation dynamics model is derived which qualitatively gives the correct ordering of power-law slopes (da/dN vs ΔK) and growth rate magnitudes as a function of test temperature.     

Gaseous hydrogen embrittlement in FeSi- and Ni-single crystals

Hydrogen embrittlement in FeSi- and Ni-single crystals was examined at low hydrogen pressures (10 mPa ⩽ pH₂ ⩽ 100 kPa). A special technique was used to measure the crack tip opening angle α of a stable growing crack as a function of temperature, hydrogen pressure and rate. The relationship between α and the crack tip opening rate depends on temperature. Three temperature regions can be distinguished, at low temperatures (below 293 K) transport processes control embrittlement, at intermediate temperatures (293 K ⩽ T ⩽ 390 K) hydrogen embrittlement is controlled by the equilibrium concentration of hydrogen in the fracture process zone and at even higher temperatures brittle crack nucleation becomes difficult. The detailed microscopic processes which occur during hydrogen embrittlement are examined using in situ SEM crack propagation studies and SEM fractography. These results as well as examinations of the influence of oxygen-hydrogen mixtures on the fracture process show that the fracture process occurs at a distance of less than 100 nm from the crack tip. Models of hydrogen embrittlement which relate embrittlement either to the decrease of the surface energy or to the increase of hydrogen concentration in the fracture process zone or to the hydrogen coverage at the crack tip are discussed and compared with the experimental results. To explain the results it is assumed that hydrogen embrittlement can be related to the fractional coverage of a special site at the tip of a stressed crack. With this assumption the measurements of the pH₂ and T dependence of α yield that this site can be characterized by an apparent binding energy equal to the isoteric heat of adsorption of hydrogen on Fe-(100)-surfaces but with a coverage between that of an unstressed surface and between that of a deep trap in the bulk.     

Prediction of crack paths in WCCo alloys

A crack propagating through the WCCo microstructure has to choose between paths along the binder/carbide interface and paths across binder regions. The latter paths are selected when the crack enters a binder region at a large angle from the nearest carbide interface, while the interface paths are preferred by cracks entering at a small angle. A critical angle can be defined for the switch from one type of crack path to the other. Empirical data for the area fractions of the two crack paths in widely different WCCo alloys can be accounted for by a single critical angle, φ_c = 25°. Finite element analysis of the stress field in a region of binder enclosed between carbide grains shows that the preferred site for the growth of stress-induced microvoids will move from the carbide grain flanks to the interior of the binder region when the entry angle of the crack exceeds 24°. Thus the observation of a critical angle deciding the crack path is verified by the stress field analysis and given a physical explanation in terms of the most likely site for microvoid formation.     

Nanometer-scale crack initiation and propagation behavior of Fe3Al-based intermetallic alloy

The initiation and propagation of nanometer-scale cracks have been investigated in detail byin situ transmission electron microscope (TEM) observations for the intermetallic compound Fe₃Al under mode I loading. No dislocation was detected and no dislocation emission was found when cracks propagated directly from the thin edge of a double-jet hole where the thickness of the foil was below a critical thinness. Thinning took place in the thicker region of the foils because a great number of dislocations were emitted from the crack tip, and then an electron semitransparent region was formed in front of the crack tip. Following this process, a dislocation-free zone (DFZ) was formed. The maximum normal stress occurs in the zone. Nanometer-scale cracks initiated discontinuously ahead of the main crack tip in the highly stressed zone. The size of the smallest nanocrack observed was about 3 nm, and the tip radius of the nanocracks was less than 1 nm when the applied loading was low. The radius of the main crack tip was about 2.5 nm. The distances between discontinuous nanocracks and the main crack tip were about 5 to 60 nm, depending on the applied tensile loading. A relationship was found between the tensile loading and the nanocrack distance from the crack tip. The distance increases with the tensile loading, which is consistent with an “elastic-plastic” theoretical model.     

A dislocation shielding prediction of the toughness transition during cleavage of semibrittle crystals

An interconnected set of observations assesses current equilibrium models of the ductile-brittle-transition temperature (DBTT). This involvesin situ transmission electron microscopy (TEM) studies of crack-tip dislocations in single and polycrystals and bulk fracture toughness tests at various temperatures. Beyond K_I values of 8 MPa · m^1/2 in both iron-base single and polycrystals, large numbers of redundant dislocations are created, as postulated recently by Weertman. [38] Still, the necessary shielding dislocations, as required by equilibrium, can be detected at values as high as 20 and 40 MPa · m^1/2 byex situ TEM and electron channeling, respectively. In addition, the close approach of dislocations to the crack tip in some of the studies, as opposed to others, suggests that large dislocation free zones (DFZ) are a thin-film artifact. However, a failure criterion based partly on the Rice-Thomson model’21 is both consistent with the absence of a large DFZ and observed fracture toughness variations with test temperature. It is emphasized that this toughness transition is entirely in the semibrittle regime where cleavage is the failure mode. Nevertheless,K _lc values increase from 3 to 60 MPa·m^1/2 with an increase in test temperature. This article is based on a presentation made in the symposium “Quasi-Brittle Fracture” presented during the TMS fall meeting, Cincinnati, OH, October 21–24, 1991, under the auspices of the TMS Mechanical Metallurgy Committee and the ASM/MSD Flow and Fracture Committee.     

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.     

Experimental determination of silica/copper interfacial toughness

Experiments designed to measure the fracture toughness of ceramic-metal interfaces over a wide range of phase angles are described, and a simple approach to data analysis accounting for plasticity effects in specifying interfacial toughness is outlined. A modified version of a fixture proposed by Richard and Benitz [Int. J. Fract.22, R55 (1983)] is used to apply mixed-mode loadings to silica/copper sandwich specimens. The experimentally observed crack trajectories depend on the phase angle of loading. In general, the tendency for initial propagation of the crack to occur in the ceramic increases as the magnitude of the phase angle increases. The introduction of a modest amount of mixed-mode loading resulted in a substantial increase in fracture toughness, from approximately 2.2 J/m² at 3° to 6.4 J/m² at 16° and 8.7 J/m² at −10°. The data clearly indicate that plasticity effects become increasingly important as the magnitude of the phase angle increases.     

Crack propagation near cylindrical voids

Stress intensity factorsK _I andK _II are presented for a planar, sharp-ended crack subjected to nearby line forces and line force doublets. The resulting near crack tip stress field is used to predict the influence of such singularities upon the crack propagation direction. The concept of the criticality of the angle of crack departure from symmetric propagation is introduced and used to compare computer predictions with experiments performed on double cantilever beam (DCB) specimens of 7075 aluminum alloy. The form of the near crack tip elastic equations and the criticality are verified. The critical angle parameter is found to be a material and experimental constant, independent of the strength of the centers of stress.     

Crack growth for the double slip plane crack model-I. The R-curve

The double slip plane (DSP) crack model of Weertman, Lin and Thomson has been used to obtain crack growth equations for the mode II or III crack under a monotonically increasing stress (the R-curve) in this paper. [In a companion paper the growth under cyclic stress (the Paris fatigue crack growth equation) is determined.] The success of the analysis depends upon the fact that the DSP crack closely approximates a Bilby-Cottrell-Swinden (BCS) crack when the slip zone is large compared with the slip plane to crack plane spacing. Consequently the dislocation distribution on the slip planes approximates the BCS crack one ahead of the crack tip. Behind the crack tip a result fortuitous for the analysis is found that the gradient of the dislocation density on a slip plane is proportional to the shear stress on the slip plane. The results obtained are: if the friction stress on a slip plane is constant the crack never propagates catastrophically. Instead crack extension occurs which is proportional to K² where rK is the stress intensity factor. Were the surface energy of a solid to be suddenly reduced, as it might be by the sudden introduction of an active environment, the distance the tip of a stressed stationary crack jumps is proportional to K. The distance jumped, for a large drop in surface energy, is smaller than the crack advance that occurs if the active environment were always present and the crack is monotonically loaded to the same value of K. If work hardening of the friction stress takes place stable crack growth takes place up to a critical K_c value. The R-curve equation is given by an integral which is simple in form but requires a numerical integration or series expansion. The critical K_c value is proportional to the critical K_cb stress intensity factor of a Griffith crack raised to the power (m + 1 )/2m where m is the power exponent of the simulated plastic stress-strain curve. We believe that this paper demonstrates the double slip plane crack model is the first crack model since the Griffith crack model and its variants that can give an explicit fracture equation starting from first principles.     

Fatigue crack growth behavior of 4340 steels

Fatigue crack growth behavior of 4340 steels was investigated in four gaseous environments; laboratory air, wet hydrogen, dry hydrogen and dry helium. Specimen orientation does not affect crack propagation rate results. The effects of R-ratio (load ratio) and environment on crack growth rate properties are interrelated. Increasing R -ratio increases the rates of near-threshold crack propagation. Nevertheless, the effect of R-ratio on crack growth rates in air is much more significant than that in the two dry environments. Interestingly, the R-ratio effect in wet hydrogen is comparable to that in dry environments. At an R-ratio of 0.1, the rates of crack propagation in air are slower than those in dry environments while crack growth rates are essentially identical in wet hydrogen and dry environments. Increasing R -ratio was found to decrease the environmental effect. Furthermore, increasing yield strength from 700 to 1040 MPa does not affect crack propagation behavior. While surface roughness-induced crack closure is thought to be minimal in affecting gaseous-environment near-threshold crack growth behavior of 4340 steels, oxide-induced crack closure governs crack propagation kinetics. It is suggested that in moisture-containing environments, thick oxide deposits measured on fracture surfaces may not result in high crack closure levels. Nevertheless, oxide-induced crack closure rationalized the effects of R-ratio and environment on near-threshold crack growth rate properties. Furthermore, hydrogen embrittlement is believed not to play an important role in influencing wet-hydrogen environment near-threshold crack propagation behavior. At higher ΔK levels (⩾ 12 MPa √m), an “intrinsic” dry hydrogen effect seems to be present, and crack closure, however, cannot account for the environmental effect.     

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.