Effects of grain boundary- and triple junction-character on intergranular fatigue crack nucleation in polycrystalline aluminum

The effects of grain boundary- and triple junction-character on intergranular fatigue crack nucleation were studied in coarse-grained polycrystalline aluminum specimens whose grain boundary microstructures were analyzed by SEM-EBSD/OIM technique. Fatigue crack nucleation occurred mainly along grain boundaries and depended strongly on both the grain boundary character and grain boundary configuration with respect to the persistent slip bands. However, it was little dependent on the geometrical arrangements between the grain boundary plane and the stress axis. Particularly, random boundaries become preferential sites for fatigue crack nucleation. The fatigue cracks were also observed at CSL boundaries when the grain-boundary trace on the specimen surface was parallel to persistent slip bands. On the other hand, no intergranular fatigue cracks were observed at low-angle boundaries. The fatigue cracks were observed at triple junctions as well as grain boundaries. Their nucleation considerably occurred at triple junctions where random boundaries were interconnected. The grain boundary engineering for improvement in fatigue property was discussed on the basis of the results of the structure-dependent intergranular and triple junction fatigue crack nucleation.     

Initiation of corrosion fatigue cracks at defined grain boundaries in bicrystals

The fatigue tests in air show that persistent slip bands (PSB's) and cracks nucleate very early at special grain boundaries. At stress amplitudes for which no persistent slip band nucleation was observed in single crystals and which were oriented for single slip, cracks still nucleate at grain boundaries. The endurance limit for special bicrystals lay 50% below the endurance limit of polycrystals. In air, the cracks nucleate at the boundary but propagate within the PSB. From the stress amplitudes at which PSB's nucleate in single crystals and in bicrystals, which have one grain with the same orientation as the single crystals, the additional shear stress due to elastic anisotropy was measured to be 55 MPa. These tests yield an understanding of the behavior of short cracks, which nucleate at special boundaries but cannot propagate further, if they hit an unfavorably oriented boundary for which higher local stresses for propagation were needed.With the same bicrystals, corrosion fatigue tests were carried out in ammonium carbonate solutions. In the solution, crack nucleation was found to depend on frequency and amplitude. Contrary to the behavior in air, the cracks nucleate at and propagate along the grain boundary. Specimens which last for 10⁵ cycles in air only survive 6·10³ cycles at the lowest frequencies tested. In addition, if the stress amplitude is reduced by 27%, it was observed that, for a given frequency, the fatigue life is reduced by more than 90% relative to the fatigue life in air at the same stress level. The susceptibility of special boundaries against corrosion fatigue combined with the observed dependencies on stress amplitude and frequency could be understood on the basis of the slip step dissolution model for SCC.     

Wedge crack nucleation in Type 316 stainless steel

Type 316 austenitic steel has been heat-treated to produce a range of grain sizes and then creep-tested at 625° C at various stresses so as to examine the nucleation and the factors which effect the nucleation of grain-boundary triple point or wedge cracks. An internal marker technique was used to evaluate the extent of the grain-boundary sliding in relation to the total creep strain. Triple point crack nucleation occurred over the entire range of grain sizes and stresses examined when the product of the stress and grain-boundary displacement reached a critical value; the effective surface energy for grain boundary fracture, estimated using an expression derived by Stroh, was in approximate agreement with the surface free energy value indicating that only limited relaxation occurred by plastic deformation. The first cracks were observed to form along grain boundary facets perpendicular to the applied stress direction and with the sliding grain boundaries at high angles (60 to 80°) to the crack growth direction. Subsequent cracking occurred under conditions which deviated slightly from this initial condition, and the increase in crack density with strain was expressed in terms of geometrical factors which take account of the orientation effects.     

Mechanisms of crack nucleation in ice

This paper reviews the literature on the mechanisms by which cracks are nucleated in polycrystalline ice. In the absence of preexisting cracks, crack nucleation is the first step in mechanical failure. A variety of mechanisms have been discussed, mostly involving the propagation of microcracks or precursors from initial sizes below the level of convenient detection to easily observable cracks. True crack nucleation without preexisting precursors requires that stresses be locally concentrated to levels matching the theoretical cleavage or cohesive strength. Candidate mechanisms for this concentration of stress include: dislocation glide (leading to pile-ups of dislocations on particular slip planes); grain-boundary-sliding (leading to stress concentrations at the triple junctions at the edge of grain-boundary facets); thermal expansion of extraneous inclusions (such as produced by progressive freezing of brine pockets upon cooling); and elastic anisotropy of the ice crystals. Both dislocation glide and boundary sliding are kinetic processes in which the stress redistribution occurs at a finite, temperature-dependent rate. These processes also contribute temperature-dependent internal friction and anelasticity and their operation can therefore be independently measured. Elastic anisotropy leads to stress concentrations in an athermal manner and therefore becomes more important at very low temperatures and high loading rates. It has been shown, however, that in the absence of stresses due to brine pockets, the inherent elastic anisotropy of ice is not sufficient to nucleate cracks in purely two-dimensional models, such as perfectly columnar grains in plane strain. Calculated nucleation energies are far beyond available thermal activation energies and some additional stress concentrating effects are required. Irregularities in the third dimension (e.g. jogs in column boundaries) have not been completely investigated. Although inclusions (e.g. brine pockets or particulate inclusions) may sometimes be important, we should not neglect the kinetic processes mentioned above. Various experiments on fresh-water ice have provided evidence that crack nucleation is usually associated with grain boundaries in a manner consistent with grain-boundary sliding and the associated stress concentration fields.     

INITIATION AND GROWTH OF SMALL CRACKS IN DIRECTIONALLY SOLIDIFIED MAR-M247 UNDER CREEP-FATIGUE PART II: EFFECT OF ANGLE NETWEEN STRESS AXIS AND SOLIDIFICATION DIRECTION

This paper deals with the effect of anisotropy on fracture processes of a directionally solidified superalloy, Mar-M247, under a push–pull creep-fatigue condition at high-temperature. Three kinds of specimen were cut from a cast plate such that their axes possess angles of 0°, 45° and 90° with respect to the 〈001〉 orientation that is aligned parallel to the solidification direction (also to the grain boundaries and primary dendrite axis); these specimens being denoted the 0° specimen, the 45° specimen, and the 90° specimen, respectively. The tests were conducted at 1273  K (1000 °C) in air under equal magnitudes of the range of a Δ J -related parameter, Δ W _c , which represents the driving force for crack growth in creep-fatigue. Although the grain boundaries are macroscopically parallel to the solidification direction, they are wavy or serrated microscopically. Small cracks nucleate along parts of the grain boundaries perpendicular to the stress axis in all specimens. The 90° specimen has the shortest crack initiation life and the 0° specimen has the longest. In the 90° and 45° specimens, intergranular cracks continue to nucleate and a main crack is formed along the grain boundary due to the frequent coalescence of small cracks. In the 0° specimen, cracks grow into the grain, and transgranular cracks coalesce along the primary dendrite or grain boundary. The 0° specimen exhibits the slowest crack growth rate and the 90° specimen the fastest. These differences in the initiation and growth behaviour of small cracks cause the longest failure life in the 0° specimen and the shortest in the 90° specimen.     

The influence of temperature cycling on the creep properties of Nickel 201 and Inconel 600 in combustion gas

The effect of temperature cycling on the creep behaviour of Nickel 201 and Inconel 600 in combustion gas has been studied. Specimens were tested both at constant temperature, 900° C, and at 900° C interrupted by temperarature drops down to 510° C. The creep straining has been analysed with respect to a weighted time parameter which includes the creep contribution during the lower temperatures of each cycle. With respect to this compensated time parameter, the temperature variations were generally observed to result in a strong acceleration in creep. The effect seemed to increase with increasing frequency of temperature drops, increasing grain size and decreasing stress. Thus, at low stress levels, large-grained specimens of both alloys experienced an acceleration even inabsolute creep rate upon cycling. The grain size dependency indicates that the destructive effect of the cycles is caused by crack formation. Surface cracking associated with grain boundary oxidation seemed to be the dominant cracking mode. It is suggested that, during creep in oxidizing environments, repeated periods of cooling might strongly accelerate the growth of surface creep cracks due to the difference in thermal expansion between metals and oxides. This difference causes high tensile stresses to arise in the metal in front of the grain boundary oxides, and the stresses are assumed to be high enough to nucleate microcracks along the boundary.     

Microstructural effects on crack closure and propagation thresholds of small fatigue cracks

The crack closure behaviour of microstructurally small fatigue cracks was numerically simulated by combining the crack-tip slip band model with the plasticity-induced crack closure model. A Stage II crack started to propagate from an initiated Stage I crack. When the plastic zone was constrained by the grain boundary or the adjacent grain with higher yield stresses, the crack opening stress increased with crack extension, and the effective component of the stress range decreased. The crack-tip opening displacement range (Δ CTOD ), first decreased with crack extension due to the development of the residual stretch, then increased until the tip of the plastic zone reached the neighbouring grain boundary. When the plastic zone was blocked by the grain boundary, Δ CTOD began to decrease. The arrest condition of cracks was given by the threshold value of Δ CTOD . At the fatigue limit, the arrest of small cracks takes place just after the Stage II crack crosses the grain boundary when the grain boundary does not act as a barrier. Only when the grain boundary has a blocking strength and the yield stress of adjacent grains is not so high, the arrest of Stage II cracks takes place before the crack reaches the grain boundary. The fatigue limit decreases with the mean stress. The predicted relation between the fatigue limit and the mean stress is close to the modified Goodman relation.     

Cyclic stress effects on the grain boundary cracking in Al-Mg solid solution

The difference in the grain boundary deformation between statically and cyclically crept specimens of Al-Mg solid solution has been investigated at the temperature of 580 K and for the peak stress level of 15 to 20 M Pa. In statically crept specimens, the grain boundaries deform irregularly and no crack is formed either at the triple point or along the serrated boundaries. However, in cyclically crept specimens, where the stress frequency, stress amplitude and the ratio of on-load to off-load time are 3 cycles per minute, 90% of maximum peak stress and less than 1, respectively, the grain boundaries remain smooth and wedge-type cracks are formed at the triple points, which results in intercrystalline fracture. On the basis of the experimental observations it is believed that cyclic stressing enhances grain boundary sliding through an accelerated recovery with the help of mechanically generated excess vacancies during cycling. However, due to the constraints of the grain alignment, boundary sliding becomes very difficult and creates an intercrystalline fracture at a triple point. On the other hand, under static stress, since the grain boundary is serrated to decrease the stress concentration at a triple point, a crack hardly forms at the triple point.     

NUCLEATION AND SHORT CRACK GROWTH IN FATIGUED POLYCRYSTALLINE COPPER

Surface evolution in polycrystalline copper specimens with a shallow notch has been studied in interrupted constant strain amplitude cyclic loading. The inhomogeneous strain distribution close to stress amplitude saturation leads to the formation of extrusions and intrusions along persistent slip bands within the grain and also in suitably oriented grain boundaries. Numerous primary cracks within a grain or at a grain boundary are nucleated. Some cracks can grow further either by linking with existing cracks or by nucleation of new elementary cracks ahead of the crack tip. Crack growth rates of individual cracks fluctuate considerably but for each strain amplitude, which results in a saturated plastic strain amplitude, a crack growth rate of an equivalent crack can be established. This crack growth rate was found to depend strongly on the plastic strain amplitude in agreement with the Manson-Coffin law.     

Elastic anisotropy and micro-damage processes in polycrystalline ice Part I: Theoretical formulation

A microstructural damage model is developed for polycrystalline ice deforming at the high end of the quasi-static domain of loading. The formation (nucleation) of microcracks is attributed to the extension of grain boundary precursors under the influence of the applied stresses and microstructural stresses resulting from the elastic anisotropy mechanism. In a compressive stress field, a growing population of stable cracks leads to progressive damage in the material. Nucleation, and hence damage accumulation, is influenced by three random variables-the precursor orientation, the basal plane orientation of the grains adjoining the precursor of interest, and the grain size. Model predictions consist of the following steps: (a) computation of microstructural stresses using a first-order approximation of the Eshelby procedure, (b) analysis of nucleation using a mixed-mode fracture criterion, and (c) computation of the elastic compliance using the self-consistent method. When coupled to a creep model, the relative contribution of microcracking and creep to the total deformation can be delineated.     

Void evolution in nanocrystalline metal film under uniform tensile stress

A theoretical model to describe the nucleation and growth of voids at triple junctions of nanocrystalline metal film under uniform tensile loading is suggested. The void growth rate controlled by grain boundary diffusion under the combined influence of void surface energy, grain boundary interface energy and elastic energy stored in the solid is evaluated. Stress relaxation during uniform tension deformation is finally discussed; the effective stress relaxation distance is also calculated. The stress relaxation not only suppresses the nucleation of voids and cracks, but also influences the void growth rate.     

SiCw/MB15复合材料断裂行为研究

扫描电镜下采用动态拉伸法,原位观察SiCw/MB15复合材料复合材料在动态受载条件下裂纹形成、扩展至断裂的全过程,并对断口进行了分析。结果表明,裂纹主要在折断的晶须处萌生,在主裂纹前端应力集中区内长大、连结,在与主应力垂直方向上形成宏观裂纹。     

Simulating small crack growth behaviour using crystal plasticity theory and finite element analysis

Predictions of small crack growth under cyclic loading in aluminium alloy 7075 are performed using finite element analysis (FEA), and results are compared with published experimental data. A double‐slip crystal plasticity model is implemented within the analyses to enable the anisotropic nature of individual grains to be approximated. Small edge‐cracks in a single grain with a starting length of 6 μm are incrementally grown following a node‐release scheme. Crack‐tip opening displacements (CTOD) and crack opening stresses are calculated during the simulated crack growth, and da/dN against ΔK diagrams are computed. Interactions between the crack tip and a grain boundary are also considered. The computations are shown to accurately capture the magnitude and the variability normally observed in small crack fatigue data.     

A study of the influence of grain boundaries on short crack growth during varying load using a dislocation technique

The propagation of short cracks in the neighbourhood of grain boundaries have been investigated using a technique were the crack is modelled by distributed dislocation dipoles and the plastic deformation is represented by discrete dislocations. Discrete dislocations are emitted from the crack tip as the crack grows. Dislocations can also nucleate at the grain boundaries. The influence on crack growth characteristics of the distance between the initial crack tip and the grain boundary has been studied. It was found that crack growth rate is strongly correlated to the dislocation pile-ups at the grain boundaries.     

Statistics and probabilistic modeling of simulated intergranular cracks

Using Monte Carlo simulation, the statistical properties of intergranular crack trajectories in polycrystalline materials are estimated. The polycrystalline microstructures are two dimensional and are modeled by a Poisson–Voronoi tessellation for the grain geometry and a uniform orientation distribution function for the crystallographic orientation. A heuristic is introduced for determining the path of crack propagation when the crack tip arrives at a grain boundary triple junction. This heuristic applies a combination of two criteria for determining the direction of crack propagation, the maximum circumferential stress criterion, and a criterion in which the crack is assumed to propagate in the direction with the least material resistance. The resistance of grain boundaries is assumed to be related to the crystallographic misorientation at the grain boundary. The trajectories of microcracks can be treated as a random process, and simulation results indicate that the crack process exhibits linear variance growth, the rate of which is related to the importance attached to the circumferential stress and the material resistance in determining the direction of propagation. The rate of variance growth is shown to vary with the average grain diameter, so that microcracks in polycrystals with small grain size will exhibit less spatial uncertainty. The statistics and distributions of the increments of the crack process are also given. Through a small change made to the normalization applied to non-dimensionalize the statistics, the results are extended to polycrystals that have spatially varying grain size. Finally, a probabilistic model is proposed that is able to produce synthetic crack trajectories that replicate the important statistical properties of the simulated cracks. Such a model may prove useful in studies of the transition from micro to macrocracking.     

Microstructural modelling of creep crack growth from a blunted crack

The effect of crack tip blunting on the initial stages of creep crack growth is investigated by means of a planar microstructural model in which grains are represented discretely. The actual linking-up process of discrete microcracks with the macroscopic crack is simulated, with full account of the underlying physical mechanisms such as the nucleation, growth and coalescence of grain boundary cavities accompanied by grain boundary sliding. Results are presented for -controlled mode I crack growth under small-scale damage conditions. Particular attention is focused on creep constrained vs. unconstrained growth. Also the effect of grain boundary shear stresses on linking-up is investigated through shear-modified nucleation and growth models. The computations show a general trend that while an initially sharp crack tends to propagate away from the original crack plane, crack tip blunting reduces the crack growth direction. Under unconstrained conditions this can be partly rationalized by the strain rate and facet stress distribution corresponding to steady-state creep. This revised version was published online in August 2006 with corrections to the Cover Date.     

Microstructural influences on the growth of small cracks in Ti-6Al-4 V

ABSTRACT The effects of microstructure on the growth of small cracks in Ti-6Al-4 V under fatigue loading are presented. The small crack growth is compared with large crack growth. Two large crack tests were performed at a stress ratio of 0.4 and a frequency of 15 Hz. For small crack growth tests, double edge notch specimens were loaded under constant amplitude at four maximum stresses with a stress ratio of 0.4 and a frequency of 15 Hz. A plastic replication technique was used to monitor the small fatigue crack growth rate. The microstructure consists of bands of α and β phases. The present study indicates that the crack growth direction and shape are dependent upon the grain size and grain orientations, and that the crack growth rate seems to be affected by the spacing of α-rich and β-rich bands. Small cracks are propagated at stress intensity factors well below the large crack threshold stress intensity factor.     

Experimentelle Charakterisierung und zweidimensionale Simulation der mikrostrukturbestimmten Ermüdungsrissausbreitung in einer β‐Titanlegierung

In this project the initiation and propagation of short fatigue cracks in the metastable β‐titanium alloy TIMETAL®LCB is investigated. By means of an interferometric strain/displacement gauge system (ISDG) to measure the crack opening displacement (COD) and the electron back scattered diffraction technique (EBSD) to determine the orientation of individual grains the microstructural influence on short crack initiation and growth can be characterized. Finite element calculations show a high influence of the elastic anisotropy on the initiation sites of cracks. Crack propagation takes place transgranulary along slip planes as well as intergranulary along grain boundaries. The crack growth rate depends strongly on the active mechanism at the crack tip which in turn is influenced by crack length, the applied stress and the orientation of the grains involved. The value of the steady state crack closure stress changes from a positive value at low applied stresses (roughness induced) to a negative one at higher applied stresses (due to plastic deformations at the crack tip). The crack growth simulation is realised by a two‐dimensional boundary element technique, which contains the ideas of Navarro und de los Rios. The model includes the sequence of the applied stress amplitude as well as the experimental measured roughness induced crack closure.     

Polycrystalline microstructure, cubic elasticity, and nucleation of high-cycle fatigue cracks

It is well-known that high-cycle fatigue cracks usually nucleate in surface well-oriented grains with a high Schmid factor. A numerical evaluation of the effect of crystalline elasticity anisotropy (which is often neglected) on the stress state in well-oriented grains is presented. Each of these grains is located at the free surface of an aggregate. The other crystallographic orientations are random. Numerous finite element computations are carried out for evaluating the effect of the neighboring grain orientations. Resolved shear stress and normal stress averages are given, as well as scatter parameters and histograms. Several metals, orientations, and loading conditions are considered. For common (anisotropic) metals/alloys such as copper and austenitic steels, the local average resolved shear stress is about 18% smaller than the macroscopic value which induces a Schmid factor value with respect to the macroscopic tensile stress of 0.41 instead of the classical 0.5 value. Relative scatters in resolved shear stress and corresponding normal stress are high (respectively ± 22% and ± 38%). These high scatter values computed for small applied loads can explain many observations taken from the literature showing a large scatter in the plastic slip line feature, dislocation microstructure, microstructurally short crack nucleation, and propagation rate among well-oriented surface grains. Finally, the effects of some geometrical parameters are evaluated (2D/3D effects, subsurface grains....).