Grain size effects in the strain hardening of polycrystals

The degree to which the flow stress of a polycrystal is sensitive to grain size is discussed in terms of the distribution of slip and dislocation structure that develops in the vicinity of grain boundaries as deformation proceeds. The point of view is taken that the two principal classes of grain boundary hardening models, namely, those based on dislocation pile-ups and those based on dislocation density concepts respectively represent special cases of a single rationale developed in this paper. Grain boundary strengthening is intimately related to strain hardening which is affected by slip mode,i.e., the number of slip systems and the ability to cross slip. The effects of substitutional solute elements on grain boundary strengthenings is considered to be a consequence of their influence on slip modes rather than on their interaction with dislocation sources.     

Microstructural effects and crack closure during near

Near threshold fatigue crack growth behavior of a high strength steel under different tempered conditions was investigated. The important aspect of the study is to compare the crack growth behavior in terms of the closure-free component of the threshold stress intensity range, ΔK _th,eff While a systematic variation in the absolute threshold stress intensity range with yield strength was observed, the trend in the intrinsic ΔK _th or ΔK _th,eff exhibited a contrasting behavior. This has been explained as due to the difference in fracture modes during near threshold crack growth at different temper levels. It is shown that in a high strength and high strain hardening microstructure, yielding along crystallographic slip planes is difficult and hence it exhibited a flat transgranular fracture. In a steel with low strain hardening characteristics and relatively low strength, a tendency to crystallographic planar slip is observed consequently resulting in high ΔK _th. Occurrence of a predominantly intergranular fracture is shown to reduce intrinsic ΔK _th drastically and increase crack growth rates. Also shown is that crack closure can occur in high strength steels under certain fracture morphologies. A ‘transgranular planar slip’ during the inception of a ‘microstructure sensitive’ crack growth is essential to promote intergranular and faceted fracture. The occurrence of a maximum in the fraction of intergranular fracture during threshold crack growth corresponds to the ΔK value at which the cyclic plastic zone size becomes equal to the prior austenitic grain size.     

In-situ observation on microfracture behavior ahead of the crack tip in 63Sn37Pb solder alloy

In-situ transmission electron microscopy (TEM) tensile tests on as-cast and aged 63Sn37Pb solder alloys were conducted, and the fracture behavior in nanometer scale ahead of the crack tip was inspected and discussed. Results show that the fracture was completed by connecting the discontinuous cracks or voids. Dislocation behavior was concentrated along the grain boundaries for as-cast samples, and displayed mainly as dislocation climb. The crack was intergranular dominated under the lower strain rate. While remarkable mutual dislocation emission was detected in the aged solder. Transgranular cracks were dominant in the fractured area, and they propagated by linking up with the nanometer scale cracks ahead of the crack tips under the effective promotion of the inverse dislocation emission. At the same time, the partial interphase or intergranular cracks in the thinned area were also found. Under this condition, a new critical stress intensity factor K′_C to define the mutual dislocation emission was proposed.     

Strength and ductility of Ni3Ga with and without boron

Experiments have shown that upon alloying Ni-rich Ni₃Ga with 0.11 at.% boron the contribution of the grain boundaries to both the yield stress and the hardness is reduced by about 40%. Correspondingly, the ductility is increased from about 2% elongation to about 10% elongation, although the fracture mode remains predominantly intergranular. In dry oxygen or under reduced pressure, the ductility of the boron-free alloy, increases to about 3%, as it does when the alloy is strained in air at a high rate (⪞10⁻²s⁻¹). Auger electron spectroscopy revealed an enrichment of boron at grain boundaries in the doped alloy. In situ TEM straining experiments showed that in both alloys slip is transmitted from grain to grain through the nucleation of dislocations at the heads of dislocation pile-ups. Slip dislocations are comprised of pairs of a/3 〈211〉 superlattice partials coupled by a superlattice intrinsic stacking fault. The effects of boron on the mechanical behaviour are explained in terms of the nucleation of dislocations at the heads of pile-ups and the accommodation/transmission of slip at/across grain boundaries.     

On the contribution of concurrent grain growth to strain

Flow behavior and microstructural evolution in an Al-Cu eutectic alloy of equiaxed grains were investigated over ε ≃ 2× 10⁻⁶ to 2 × 10⁻² s⁻¹ andT = 400° to 540 °C. Depending on the test conditions, there appeared either strain hardening or strain softening predominantly in the early part of the σ-ε curves. The microstructural observations showed evidence for grain growth, development of zig-zag boundaries, dislocation interactions, and cavitation. The grain growth adequately accounts for the observed strain hardening at higher temperatures and lower strain rates. However, at lower temperatures the strain hardening can be only partly accounted for by the observed grain growth; under this condition, some dislocation interactions also contribute to the strain hardening. The presence of cavitation causes strain softening predominantly at higher strain rates. Therefore, to develop a proper understanding of the superplastic behavior of the Al-Cu eutectic alloy, it is necessary to take into account the influence of dislocation interactions and cavitation along with that of grain growth.     

In-Situ observation on microfracture behavior ahead of the crack tip in 63Sn37Pb solder alloy

in-situ transmission electron microscopy (TEM) tensile tests on as-cast and aged 63Sn37Pb solder alloys were conducted, and the fracture behavior in nanometer scale ahead of the crack tip was inspected and discussed. Results show that the fracture was completed by connecting the discontinuous cracks or voids. Dislocation behavior was concentrated along the grain boundaries for as-cast samples, and displayed mainly as dislocation climb. The crack was intergranular dominated under the lower strain rate. While remarkable mutual dislocation emission was detected in the aged solder. Transgranular cracks were dominant in the fractured area, and they propagated by linking up with the nanometer scale cracks ahead of the crack tips under the effective promotion of the inverse dislocation emission. At the same time, the partial interphase or intergranular cracks in the thinned area were also found. Under this condition, a new critical stress intensity factor K _c ^′ to define the mutual dislocation emission was proposed.     

In-Situ observation on microfracture behavior ahead of the crack tip in 63Sn37Pb solder alloy

in-situ transmission electron microscopy (TEM) tensile tests on as-cast and aged 63Sn37Pb solder alloys were conducted, and the fracture behavior in nanometer scale ahead of the crack tip was inspected and discussed. Results show that the fracture was completed by connecting the discontinuous cracks or voids. Dislocation behavior was concentrated along the grain boundaries for as-cast samples, and displayed mainly as dislocation climb. The crack was intergranular dominated under the lower strain rate. While remarkable mutual dislocation emission was detected in the aged solder. Transgranular cracks were dominant in the fractured area, and they propagated by linking up with the nanometer scale cracks ahead of the crack tips under the effective promotion of the inverse dislocation emission. At the same time, the partial interphase or intergranular cracks in the thinned area were also found. Under this condition, a new critical stress intensity factorK _c ^′ to define the mutual dislocation emission was proposed.     

The effect of matrix strength on void nucleation and growth in an alpha-beta titanium alloy,CORONA-5

This work was undertaken to examine the effect of increasing matrix strength at constant equiaxed microstructure on void nucleation and growth in the titanium alloy, CORONA-5, Ti-4.5Al-5Mo-1.5Cr. A martensite and a beta matrix were used in the as-quenched and the heat treated conditions. For each matrix, fine and coarse alpha sizes were produced and a third size of alpha was used for the as-quenched condition of the martensite series. The processing procedures produced an aligned alpha structure which was most pronounced in the fine structure. Void nucleation occurred in an aligned fashion and took place predominantly atα /martensite orα/β interfaces. An explanation is offered for the aligned nucleation in terms of nonuniform deformation of the banded structure which appeared most prominently after heat treatment to produce the coarser microstructure. An incubation strain was found for both types of matrices. The incubation strain increased for the interface in the following order: martensite/martensite,α /martensite, andα/ β. The incubation strain for martensite/martensite interfaces was relatively independent of the matrix strength. Void growth as a function of true strain was generally found to occur in two stages, a slow stage I and a more rapid stage II. Stage II growth occurred as a result of coalescence of voids growing toward one another from nearby particles. Stage II growth was more rapid for the martensite matrix than for theβ matrix. For the martensite matrix void growth rates could not be accounted for either on the basis of strength or strain hardening rates. However, the longest void growth rate was found to increase as the function λ ^N /d _α ^L increased. λ^N is the interparticle spacing normal to the tensile axis and _α ^L is the alpha particle size parallel to the tensile axis. For the beta matrix void growth rates increased with increasing yield s trength and decreased with increasing strain hardening. It was not possible to relate fracture strength to an extrapolated longest void at fracture as was done in earlier studies. This is explained in terms of the nonuniformity of fracture paths observed in the alloy.     

Primary recrystallization mechanisms in ceramic materials

Data on the mechanisms of primary recrystallization in covalent type ceramics under temperature-and-pressure treatment are generalized and discussed. There are three types of structural transformations governing nucleation during primary recrystallization. I. Formation of intragrain boundaries. As a result of plastic shears boundaries appear to be kinked due to dislocation pile-ups (materials based on 2H BN, 6H SiC). With deformation by total dislocations the boundaries arise as a result of dynamic recovery due to rebuilding of dislocation pile-ups (AlN, β-Si₃N₄, TiB₂). II. Twinning. This structural transformation promotes the formation of recrystallization nuclei in the following cases: a) with insertion of lattice dislocations into the boundaries of strain-induced twins; b) with formation of annealing twins; c) with development of multiple twinning near grain boundaries (3C BN). III. Structural transformations in migrating boundaries: a) splitting of boundaries and ternary junctions (3C BN); b) local bulging of boundaries (3C BN); c) generation of high-angle and platelet twins (3C BN); d) plastic rotation of material microvolumes near grain boundaries (3C BN, SiC). Materials Science Institute, Ukrainian Academy of Sciences, Kiev. Translated from Poroshkovaya Metallurgiya. Nos. 1-2, pp. 63–77, January–February, 1998.     

Crack growth from internal hydrogen—temperature and microstructural effects in 4340 steel

Internal hydrogen effects on stage II crack growth rates in AISI 4340 steel have been studied as a function of test temperature. A model is developed that is physically based in that classical thermodynamics relates to solubility and trapping and Fick’s second law controls hydrogen transport. Both of these are microstructurally related to how trapping affects both the crack initiation site and diffusion to it. For two tempered conditions of 4340 steel, it is shown that there is a test temperature,T ₀, for stage II crack growth, above which the crack does not grow. The fractography associated with test temperatures approachingT ₀ tends toward 100 pct intergranular for both 1340 MPa and 1620 MPa strength levels. At lower test temperatures, there is as much as 50 pct microvoid coalescence or 30 pct quasi-cleavage. In the lower strength condition, hydrogen traps at oxysulfide particles with a binding energy near 75 kJ/mol. Where these intersect the prior austenite grain boundaries, this promotes fingers of intergranular fracture which later triggers tearing of 100 μm size ligaments by microvoid coalescence. For the higher strength material, it is proposed that hydrogen traps along martensite lath intersections with prior austenite grain boundaries, the binding energy being near 27 kJ/mol. This promotes 1 μm size striations along intergranular facets. In both cases the fractography is consistent with a proposed model of stress field concentration of hydrogen, further concentration along trap sites, fracture nucleation at trap sites, and local, discontinuous fracture instabilities.     

The role of dislocation substructures in fatigue crack propagation in copper and alpha brass

The effect of dislocation substructures on fatigue crack propagation (FCP) behavior in copper and alpha brass was studied. Various dislocation substructures were obtained by prestraining in tension. Dislocation cells were formed by this prestraining in copper and 90/10 brass and when they formed the resistance to FCP at intermediate propagation rates (5×10⁻⁹ to ∼10⁻⁷ m/cycle) increased with increasing prestrain. Planar dislocation arrays were observed in 70/30 brass instead of cells, and the effect of prestraining on the FCP resistance was insignificant. From the FCP data for each material it was observed that, regardless of the difference in the dislocation substructures and grain sizes, the two constantsC andm in the Paris equation,da/dN=C(ΔK) ^m, were interrelated. Possible relations between the cyclic strain hardening exponent andm are discussed. The influence of both prestrain and grain size on threshold behavior was also studied.     

The fatigue of pseudoelastic polycrystalline β-cuznsn

The fatigue of polycrystalline pseudoelastic β-CuZnSn has been studied by cycling specimens to fixed stress. The fatigue life was found to decrease with increasing initial strain and decreasing specimen grain size. In both cases the results gave similar stress -vs - fatigue life curves, indicating that stress is the primary parameter controlling fatigue life. The results fitted a curve of the form △ε.N^B _f = constant, whereβ = 0.32 for the total initial strain, andβ = 0.29 for the initial elastic strain. The fatigue life appeared to be independent of strain rate. Fatigue cracks nucleated in the first cycle at three grain intersections and grew along grain boundaries until adjacent cracks linked up. In the later stages of crack growth, some intergranular cracking occurred when there were no suitably oriented grain boundaries. Both the intergranular and transgranular regions showed somewhat ill-defined fatigue striations.     

Aqueous environmental crack propagation in high-strength beta titanium alloys

The aqueous environment-assisted cracking (EAC) behavior of two peak-aged beta-titanium alloys was characterized with a fracture mechanics method. Beta-21S is susceptible to EAC under rising load in neutral 3.5 pct NaCl at 25 °C and −600 mV_SCE, as indicated by a reduced threshold for subcritical crack growth (K _TH ), an average crack growth rate of up to 10 μms, and intergranular fracture compared to microvoid rupture in air. In contrast, the initiation fracture toughness (K _ICi ) of Ti-15-3 in moist air is lower than that of Beta-21S at similar high σ_YS (1300 MPa) but is not degraded by chloride, and cracking is by transgranular microvoid formation. The intergranular EAC susceptibility of Beta-21S correlates with both α-colonies precipitated at β grain boundaries and intense slip localization; however, the causal factor is not defined. Data suggest that both features, and EAC, are promoted by prolonged solution treatment at high temperature. In a hydrogen environment embrittlement (HEE) scenario, crack-tip H could be transported by planar slip bands to strongly binding trap sites and stress/strain concentrations at α colony or β grain boundaries. The EAC in Beta-21S is eliminated by cathodic polarization (to −1000 mV_SCE), as well as by static loading for times that otherwise produce rising-load EAC. These beneficial effects could relate to reduced H production at the occluded crack tip during cathodic polarization and to increased crack-tip passive film stability or reduced dislocation transport during deformation at slow crack-tip strain rates. High-strength β-titanium alloys are resistant, but not intrinsically immune to chloride EAC, with processing condition possibly governing fracture. Formerly Graduate Research Associate, University of Virginia Formerly Graduate Research Associate, University of Virginia     

Grain-size effects on tensile behavior of nickel and AISI 316L stainless steel

The aim of this work is to provide experimental results to understand the grain-size effects on tensile hardening of fcc polycrystalline materials. The contribution of grain size on hardening rate is discussed in terms of backstress (X) and effective-stress (Σ _ef) evolutions in the different hardening stages. Based on this stress partition, the origin of the classical Hall-Petch relationship is clarified at the different levels of microstructural heterogeneities. If the backstresses and effective stresses verified the Hall-Petch formulation, however, the effective stress is less dependent on grain size than the backstress. The grain-size effect on short-range internal stresses (effective stress) is well explained in terms of a mean path length using classical dislocation modeling. The backstress dependence on grain size seems to be mainly the result of intergranular plastic-strain incompatibilities in relation with the formation of a grain-boundary layer in stage I. In others stages (higher plastic strain), the interactions between intergranular and intragranular long-range internal stresses have been illustrated. The degree of these interactions remains unclear.     

The Effect of Grain Size on Fatigue Growth of Short Cracks

The influence of alloy grain size on growth rates of surface cracks 20 to 500 μm in length was studied in Al 7075-T6 specimens prepared in 12 and 130 μn grain sizes. Grain boundaries temporarily interrupt the propagation of cracks shorter than several grain diameters in length. Linear elastic fracture mechanics is inadequate to describe resulting average growth rates which must instead be characterized as a function of cyclic stress amplitude, σ_a, and alloy grain size as well as stress intensity range, σK. These observations are rationalized using two models, one that relates crack closure stress to alloy grain size, and a second that relates the development of microplasticity in a new grain in the crack path to grain size. In addition, growth rates were found to be faster in fully reversed loading than in tension-tension loading, especially in the large grained material. Evidence is presented to demonstrate that this is a consequence of the fatigue induced development of a compressive residual surface stress during tension-tension loading. These complex effects, and the role of grain size in determining short crack growth, are discussed.     

Preparation and properties of fine grain β- CuAlNi strain- memory alloys

A method has been developed to produce grain sizes as small as 5 μm in alloys of β-CuAlNi. The alloys were of eutectoid composition and a procedure was developed for determining the composition of a eutectoid alloy having any required value for transition temperature (M _s ). The thermo-mechanical treatment involved two sequential stages of warm rolling followed by recrystallization. The alloys produced were single phase β-type with no second phase being present. Characteristic two-stage stress-strain curves were obtained for most of the specimens. It was generally found that the tensile strength and strain to failure increased with decreasing grain size according to a Hall-Petch type relationship down to a grain size of 5 μm. A fracture strength of 1200 MPa and a fracture strain of 10 pct were obtained in the best alloy. It was found that the major recovery mode, whether pseudoelastic or strain-memory, did not have any significant effect on the total recovery obtained. Recovery properties were not affected significantly by decreasing grain size, and 86 pct recovery could still be obtained at a grain size of around 10 μm. Grain refinement improved the fatigue life considerably, possibly due to the high ultimate fracture stress and ductile fracture mode. A fatigue life of 275,000 cycles could be obtained for an applied stress of 330 MPa and a steady state strain of 0.7 pct. At fine-grain sizes most of the fractures were due to transgranular-type brittle fracture and micro void-type ductile fracture, depending on the alloy composition. It was suggested that the difference between the alloys was due to differences in oxygen segregation at the grain boundaries.     

Microstructure and fracture toughness of the aged ,β-Ti Alloy Ti-10V-2Fe-M

Fracture mechanics and tensile tests have been performed on the metastable β-Ti alloy Ti-IOV-2Fe-3AI. A variety of microstructures was established by several combinations of forging and heat treatment resulting in different types, morphologies, and volume fractions of the a-phase which precipitates from the matrix-β phase. Both fracture toughness and ductility are strongly reduced by increasing hardening by the secondary a-phase. An elongated primary a-phase (α _p ) shows higher toughness compared to a globular α _p -phase. A thick, continuous subgrain boundary a-film lowers the toughness significantly. For microstructures without primary a a grain boundary α-film does not affect the toughness, while the ductility is drastically reduced. Very attractive combinations of fracture toughness and ductility were found for a microstructure without primary a and without grain boundary α. The results are discussed based on the fractographic observations, and a model is proposed which includes the effect of microstructure and slip distribution on the crack nucleation, the crack growth path, and the crack deviation.     

Microstructure,tensile deformation,and fracture in aged ti 10V-2Fe-3Al

In the /3-Ti alloy Ti-10V-2Fe-3Al a variety ofα-andω-aged microstructures with different yield stresses was established by combinations of forging and heat treatment. Tensile tests have shown that plastic deformation and fracture are strongly influenced by the morphology, size, and volume fraction of the different types of a-phase (primary a, secondaryα, grain boundaryα), as well as by the-phase. A detailed microscopical study revealed several deformation and fracture modes. It appears that at several sites stress and strain concentrations and subsequent void nucleation can occur and that the quantitative combinations of the differentα-types determine which sites are active. The dominant deformation mode for the (α +gb) solution treated andα-aged conditions was a strain localization in theα-aged matrix leading to voids at the interface between aged matrix and primary a-phase. In case of theβ-solution treated andα-aged microstructures the grain boundaryα leads to a strain localization in the softα-film and to void nucleation at grain boundary triple points at low macroscopic strains. Based on the above mechanisms it is discussed in detail how varying size, volume fraction, and morphology of theα-phase affect the ductility. The embrittling effect ofω-particles can be largely reduced by a grain refinement.     

Relationship between anelastic and nonlinear viscoplastic behavior of 316 stainless steel at low homologous temperature

At low homologous temperature the plastic strain rate seems to be controlled largely by dislocation glide friction. However, since a sizeable fraction of the applied stress σ is dissipated in overcoming the strong barriers due to dislocation tangles generated by strain hardening, only a portion of the applied stress is actually expended against the frictional resistance. A recent model for this process, proposed by Hart, includes the role of dislocation pile-ups at the strong barriers. The pile-ups provide a mechanism for producing the internal back stress that reflects the barrier penetration stress. They also appear in the deformation as a stored anelastic strain component. The resultant behavior at low temperature and high stress is similar to that proposed by Gupta and Li. The same model also predicts an anelastic behavior at low stress. Measurements at both high and low stress levels on 316 Stainless Steel have now shown that the predictions of the model are quantitatively consistent at both stress levels.