Grain Boundaries Research Articles

Effects of plasma electrolytic polishing on the surface and mechanical properties of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si specimen fabricated by laser powder bed fusion

The high roughness of titanium alloy specimen fabricated by laser powder bed fusion (LPBF) may limit the application of LPBF technology. Plasma electrolytic polishing (PEP) can effectively reduce the surface roughness of metal samples. In this study, an orthogonal test was designed to investigate the effects of polishing time, voltage and electrolyte temperature on the reduction of roughness and wall thickness of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si specimens fabricated by LPBF. The surface roughness of the specimen decreased from Ra = 49.1 μm to Ra = 9.1 μm and the thickness decreased from 1.72 mm to 1.38 mm after the PEP. Due to the recoil pressure induced by rupture of vapor-gaseous envelope (VGE) and the annealing effect caused by electron impact, the width of α/α' grains on the surface of TC11 specimen decreased from 0.51 μm to 0.46 μm; the mean value of geometrically necessary dislocations (GND) increased by 9.8 %; the proportion of high angle grain boundaries (HAGBs) increased from 75.2 % to 80.8 %; the proportion of twin grain boundary length increased from 2.9 % to 11.9 %, and the activated twin variant type increased from 2 to 4. The number of pores in the samples reduced from 85 to 2 after PEP, which resulted in the improvement of tensile and fatigue properties. The ultimate strength and elongation of the tensile specimens increased by 6.2 % and 53.5 % respectively. The infinite fatigue life maximum stress of the high cycle fatigue specimen increased by 62.5 %. Another reason for the improvement of mechanical properties may be the self-healing of microcracks and the electroplasticity in the specimens.

Quantitative model for grain boundary effects on strength-electrical conductivity relation

Fine-long shaped grains have been proved to be an efficient design approach to overcome the traditional trade-off relation between strength and electrical conductivity (EC) of metal wires. However, quantitative models linking grain shape parameters to both strength and EC remain scarce, limiting the precise optimization of material properties. In this study, grain boundaries (GBs) were classified into parallel or perpendicular ones to establish the quantitative models. Accordingly, a novel model for calculating the EC of fine-long shaped grains was proposed by first parallel-connecting the parallel GBs with the matrix, then series-connecting them with the vertical GBs. The EC calculated using this new model shows a small error band of only 0.5 %, indicating an excellent accuracy of EC calculation. Besides, a quantitative model for calculating the strength based on grain width was also developed. Consequently, the general effects of grain shape parameters including grain width, grain length, grain volume and grain aspect ratio on the strength and EC were quantitatively revealed. This work does not only advance the principle for achieving high strength and high EC through fine-long shaped grains from a qualitative concept to a quantitative framework but also offers valuable insights for the quantitative analysis of GB effects on strength and EC in other materials.

Dielectric response, non-Ohmic behaviors and humidity-sensing characteristics: Tin doping in sodium yttrium copper titanate ceramics

The impact of tin (Sn4+) doping on sodium yttrium copper titanate (Na0.5Y0.5Cu3Ti4O12) ceramics, prepared using a conventional mixed-oxide route, was thoroughly investigated in terms of microstructure, dielectric properties, electrical response, non-linear behaviors, and humidity-sensing characteristics. All sintered ceramics showed a dense micro-structure and a pure Na0.5Y0.5Cu3Ti4O12 phase without any secondary phases. The doped Na0.5Y0.5Cu3Ti4−xSnxO12 ceramics, with x = 0.05, demonstrated excellent dielectric properties, including a low dielectric loss tangent (∼0.032) and a giant dielectric permittivity (∼1.8 × 104) across a wide temperature range. Sn4+ doping improved the non-linear behaviors at 25 °C in Na0.5Y0.5Cu3Ti4O12, with a reduced dielectric loss tangent corresponding to an enhanced grain boundary (GB) response. The colossal dielectric response is attributed to the internal barrier layer capacitor model, which relates to the Schottky barrier height (ΦB) at the GBs. Notably, the ΦB values for the Na0.5Y0.5Cu3Ti4O12 ceramic increased with Sn4+ ion doping. Additionally, an in-depth study of the humidity-sensing properties of the Sn4+-doped Na0.5Y0.5Cu3Ti4O12 material revealed that the capacitance at 1 kHz increased with increasing relative humidity levels, from 30 % to 90 %, suggesting potential applications in humidity-sensing technologies.

Janus-like Structure and Resonance Level Actualized Ultralow Lattice Thermal Conductivity and Enhanced ZTave in Mg3(Sb, Bi)2-Based Zintls.

Grain boundary (GB) engineering includes grain size and GB segregation. Grain size has been proven to affect the electrical properties of Mg3(Sb, Bi)2 at low temperatures. However, the formation mechanism of GB segregation and what kind of GB segregation is beneficial to the performance are still unclear. Here, the Ga/Bi cosegregation at GBs and Mg segregation within grains optimize the transport of electrons and phonons simultaneously. Ga/Bi cosegregation promotes the formation of Janus-like structures due to the diverse ordering tendencies of liquid Mg3Sb2 and Mg3Bi2 and the absence of a solid solution of Ga/Bi. The Janus-like structure significantly reduces the room-temperature lattice thermal conductivity by introducing diverse microdefects. Meanwhile, a coherent interface between the nano Mg segregation region and the matrix is formed, which reduces the thermal conductivity without affecting the carrier transport. Furthermore, the band structure calculations show that Ga doping introduces the resonance level, increasing the Seebeck coefficient. Finally, the lattice thermal conductivity reaches ∼0.4 W m-1 K-1, and a high average ZT of 1.21 between 323 and ∼773 K is achieved for Mg3.2Y0.02Ga0.03Sb1.5Bi0.5. This work provides guidance for improving the thermoelectric performance via designing cosegregation.

Selective laser melting of 2507 duplex stainless steel: Effect of energy density on microstructure and corrosion resistance

Duplex stainless steel (DSS) is widely used in the marine, petroleum, chemical, automotive, and other fields owing to its excellent mechanical properties and corrosion resistance. However, the research on duplex stainless steel prepared by additive manufacturing is still limited. In this paper, high-density 2507 DSS was successfully prepared by selective laser melting (SLM) additive manufacturing. The effects of energy density on the formability, phase composition, microstructure and corrosion properties of SLM 2507 DSS were investigated. The results showed that with the decrease of the energy density, the density of the specimen increases first and then decreases, and the density achieves 99.18% with the energy density of 190.5 J/mm3. The types of phases are not affected by the energy density, i.e., all 2507 DSS samples prepared by SLM showed a ferrite phase. The YOZ (parallel to the building direction) plane of the SLM 2507 DSS samples showed predominantly columnar grains attributed to the high temperature gradient and epitaxial growth characteristics. With the increase of energy density, the average grain size decreases slightly from 16.97 μm to 15.78 μm, the KAM value decreases slightly from 1.15 to 1.05, and the low angle grain boundaries (LAGBs) increase significantly from 68.4% to 74.8%. The SLM 2507 DSS sample exhibited excellent corrosion resistance. The self-corrosion potential of the sample is 136 mV and the self-corrosion current density is 2.066 × 10−8 A/cm2 at the maximum density. This investigation provides a new approach for the preparation of super duplex stainless steel, which can provide a theoretical basis and guidance for industrialized application.

Enhancing strength and irradiation tolerance of Mg alloy via co-addition of Mn and Ca elements

The Mg alloys with combination of high strength and excellent irradiation resistance are currently required for research reactors. In this work, the novel Mg-3Mn-0.5Ca alloy with a high strength of over 300 MPa has been fabricated via co-addition of Mn and Ca elements. Moreover, the Xe ion implantation (300 °C/4.5 × 1015 ions/cm2) is conducted for pure Mg, Mg-3Mn and Mg-3Mn-0.5Ca alloys. Microstructure characterization shows that the number density of dislocation loops is comparable between Mg-3Mn and pure Mg, while the phase boundary of nano-Mn particles could act as the sink to absorb more Xe atoms, resulting in the abundant formation of Xe bubbles in the matrix of irradiated Mg-3Mn alloy. With further minor addition of Ca element, the formation of Xe bubbles and dislocation loops in Mg-3Mn-0.5Ca alloy has been obviously suppressed, and the abundant grain boundaries (GBs) due to grain refinement then act as the sink region for Xe precipitation. The limited number density of Xe bubbles leads to the extremely low swelling ratio in Mg-3Mn-0.5Ca alloy, ∼0.08 %. The result above suggests that the Mn and Ca co-addition could enhance the mechanical properties and irradiation tolerance of Mg alloys, simultaneously. The present low-alloying strategy would provide a new design reference for novel nuclear materials.

Predicting image processing-normalized DL-EPRT performance from Rudimentary Cihal method-based counterpart

Conventional DL-EPRT was extrapolated into accounting for inherent inconsistencies amongst grain boundary (GB) dimensions whilst correlating two distinct methods of ir/ia normalization, namely the approximate Cihal method (CM) and the relatively involved image processing (IP). Inasmuch as facilitating the forecast of IP- from CM-based normalizations, the full spectrum of plausible predictive models was subjected to cross validations that revealed those emanating from GB length-based endeavors to be quadratic with R2 and mean error (E) of 0.9215 and 0.5769, respectively. Meanwhile, GB area normalizations succumbed to a linear polynomial yielding R2 and E values of 0.8795 and 0.3664, respectively.

The evolution behavior and mechanism of γ' particles during hot deformation in a new P/M nickel-based superalloy

Double-cone (DC) hot compression experiments were carried out for the hot extruded (HEXed) new powder metallurgy (P/M) nickel-based superalloy A1, and the evolution behavior, mechanism of γ' particles in the process of hot deformation of A1 alloy were investigated. The consequences indicate that a rise in strain and strain rate promotes the dissolution of secondary γ' phases (γ's) as well as the dissolution and precipitation of primary γ' phases (γ'p), and the deformation temperature mainly promotes the dissolution of γ' particles. The distribution of γ' particles in the deformed and dynamic recrystallized (DRXed) grains is different, and the grain boundary (GB) migration that occurs during DRX leads to the dissolution and reprecipitation of γ' particles at the interface front. Dislocation accumulation leads to the deformation of γ' particles, which are elongated along the vertical strain direction. Some of the γ'p split due to the stress concentration brought about by dislocation accumulation and the γ's are sheared by dislocations. The evolution of γ' particles is a diffusion-controlled process, and the GBs and dislocations can be used as an additional diffusion channel for solute elements.

{10-12} twinning transfer behavior in compressed high-purity hafnium

The interaction between twins and grain boundaries (GBs) significantly influences material deformation and fracture behavior. In the present study, high-purity hafnium (Hf) was subjected to compression at both room temperature and under liquid nitrogen cooling conditions. Twinning transfer (TT) behavior of {10–12} <−1011> extension twin was thoroughly and statistically investigated. Results show that compression temperature affects the misorientation angle (MA) for TT. Under room temperature compression, twins can transfer across GBs with MAs below 30° and partially transfer across GBs with MAs between 30° and 50°. When compressed under liquid nitrogen cooling, twins can traverse the GBs with MAs below 40° and partially traverse the GBs with MAs above 40° and with a maximum MA of 77°. The MA, Schmidt factor (SF) value, and geometrical compatibility parameter m’ of twinning systems in neighboring grains influence the TT. Favorable conditions for TT include low MAs, high SF and m’ values. Stress concentration caused by incoming twins can be alleviated through TT with high m’ at GBs with low MAs. For GBs with high MAs, stress concentration can also be alleviated through TT or twinning-slipping transfer with high m’. Extension and growth of outgoing twins contribute to further stress concentration relief.

Revealing the Effect of Dynamic Structural Evolution on Triple Junction Deformation Mechanism: Molecular Dynamics Simulations and an Energetic Model

Abstract Triple junction (TJ) migration is a plastic deformation mechanism in polycrystalline metals mediated by the interplay between neighboring grain boundaries (GBs). Compared with GB migration, the dynamic change of TJ structure during migration and its impact on subsequent TJ behavior is often overlooked. In this study, we explore the effect of dynamic TJ structure evolution on TJ deformation mechanism in a face-centered cubic metal Au model using molecular dynamics simulations. Our analysis reveals that the dislocation accumulation at TJ due to inconsistent disconnection nucleation from neighboring GBs can influence the stick-slip behavior of TJ migration. With the dynamic change of TJ structure, the velocity of TJ migration is gradually reduced, leading to a transition from TJ migration to dislocation emission from TJ. We have developed an energetic model to evaluate the critical stresses required for TJ migration and dislocation emission, providing an explanation of the competition between TJ migration and dislocation emission. Our findings deepen the understanding of TJ-governed plastic deformation mechanisms in polycrystalline materials.

Learning grain boundary segregation behavior through fingerprinting complex atomic environments

Although continuum-scale segregation is a well-documented behavior in multi-species materials, detailed site-specific behavior remains largely unexplored. This is partially due to the complexity of analyzing materials at the requisite time and length scales for describing segregation with full atomic accuracy. Here, we better evaluate the segregation behavior of disordered grain boundary (GB) atomic environments through leveraging a set of Strain Functional Descriptors (SFDs) to generate an atomic descriptor (i.e., fingerprint). Using this atomic fingerprint, we resolve key relationships between atomic structure and segregation energy. Machine learning (ML) techniques are utilized in concert with this SFD fingerprint to elucidate complex relationships relating segregation potential to changes in specific features of the local Gaussian density captured by the SFDs. Finally, we identify relationships that indicate both individual and joint structure-property correlations. Linking atomic segregation energy to key structural features demonstrates the value of higher-order descriptors for uncovering complex structure-property relationships at an atomic scale.

Enhanced comprehensive mechanical properties of laser additive manufactured TC17 by design of new heat treatment based on continuous cooling transition

Heat treatment is critical for enhancing the mechanical properties of high strength titanium alloys, especially for exploiting the potential of laser additive manufactured titanium alloys. In this work, the influence of the cooling rate of continuous cooling transition on microstructure evolution and mechanical behavior was investigated in TC17 titanium alloy fabricated by laser directed energy deposition (LDED) technology. It was found that the number density and orientation characteristics of grain boundary α phases (αGB) are jointly influenced by the cooling rate and the structure of β/β grain boundaries (GBs). The average number density (λavg) of αGB has a consistent trend with the degree of variant selection (DVS) for precipitated α clusters subsequently, which is attributed to the autocatalytic effect of the pre-existing α on the post-precipitated α phases. The largest λavg of αGB and the highest DVS of α clusters could be simultaneously obtained at a suitable cooling rate (4 °C/min). In that case, plenty of α/β phase interfaces and dominant variant type ensure high strength, meanwhile, the combinations of activated multi-slip systems and varied crack propagation paths extend work-hardening to maintain greater plastic deformation. This paper provides a novel thought for designing customized heat treatments of LDEDed high strength titanium alloys, and more importantly, promotes the engineering applications of large and complex components prepared by additive manufacturing technology.

Negative effect of lanthanum tungstate on the mechanical properties of W-La2O3 alloys

With the rapid development of the photovoltaic industry, tungsten alloys have been selected to replace the high‑carbon steel to fabricate the busbars for diamond wire saws due to their superior mechanical properties, and the La2O3 doped tungsten alloy has been widely used. However, the yield of eligible W alloy wires is not very high due to serious wire breakage problems during the production process, especially in the solid-liquid mixing route. To discover the possible reason, the commonly produced lanthanum tungstate (La30W17O96) in the solid-liquid mixing route has been systematically studied in the work, and its possible influence on the mechanical properties is also explored. It is found that the La30W17O96 leads to the formation of brittle second phases at grain boundaries (GBs), which weakens the intergranular bonding, resulting in a significant decrease in the compressive strength of tungsten alloys, manifested as intergranular fracture. Transmission electron microscopy (TEM) analysis reveals that these second phases are consisted of polycrystalline La6W2O15, La2W3O12 and amorphous states, and the La30W17O96 can decompose into a more stable structure during sintering. This work highlights the destructive effect of La30W17O96 on the intrinsic properties of tungsten alloys and provides a new perspective for solving the problem of tungsten wire breakage.

Unraveling impacts of polycrystalline microstructures on ionic conductivity of ceramic electrolytes by computational homogenization and machine learning

The ionic conductivity at the grain boundaries (GBs) in oxide ceramics is typically several orders of magnitude lower than that within the grain interior. This detrimental GB effect is the main bottleneck for designing high-performance ceramic electrolytes intended for use in solid-state lithium-ion batteries, fuel cells, and electrolyzer cells. The macroscopic ionic conductivity in oxide ceramics is essentially governed by the underlying polycrystalline microstructures where GBs and grain morphology go hand in hand. This provides the possibility to enhance the ion conductivity by microstructure engineering. To this end, a thorough understanding of microstructure–property correlation is highly desirable. In this work, we investigate numerous polycrystalline microstructure samples with varying grain and grain boundary features. Their macroscopic ionic conductivities are numerically evaluated by the finite element homogenization method, whereby the GB resistance is explicitly regarded. The influence of different microstructural features on the effective ionic conductivity is systematically studied. The microstructure–property relationships are revealed. Additionally, a graph neural network-based machine learning model is constructed and trained. It can accurately predict the effective ionic conductivity for a given polycrystalline microstructure. This work provides crucial quantitative guidelines for optimizing the ionic conducting performance of oxide ceramics by tailoring microstructures.

Intergranular fracture, grain-boundary structure, and dislocation-density interactions in FCC bicrystals

A dislocation-density based crystalline plasticity (DCP) and nonlinear finite element (FE) analysis were used to predict, and fundamentally understand how and why fracture nucleation and propagation are related to the interrelated microstructural mechanisms of dislocation-density pileups, GB structure, orientation, and total and partial dislocation density interactions within and adjacent for a random low angle grain boundary (LAGB) and a random high angle GB (HAGB). The GB orientations and structures were obtained from micropillar experiments, such that LAGBs and the HAGBs can be accurately represented and used for the modeling predictions. The normal stress, density of pileups, and dislocation-density accumulation along and within the GB were higher for the low angle GB bicrystal. These interrelated phenomena delineate how fracture for high angle GBs nucleate and propagate at lower nominal strains than the lower angle GB bicrystal case. These predictions underscore how fundamental mechanisms can be identified and used to understand how failure nucleates and propagates for different GB structures and orientations.

A polycrystal plasticity-cellular automaton integrated modeling method for continuous dynamic recrystallization and its application to AA2196 alloy

Continuous dynamic recrystallization usually dominates the microstructural evolution in hot working of aluminum alloys, in which the high-angle grain boundaries of new grains mainly originate from the gradual increase in subgrain misorientation angles. In this work, an integrated computational method is proposed to simulate continuous dynamic recrystallization process of aluminum alloys by coupling three-dimensional cellular automaton and visco-plastic self-consistent models. The stress response, dislocation accumulation and recovery, and evolution of crystal orientations are computed in the context of polycrystal plasticity; the formation and rotation of subgrains, followed by stored energy and curvature-driven boundary migration, are captured and visualized by cellular automaton. The non-octahedral slip mode {110}<110> is additionally introduced to capture the 〈001〉 texture during hot compression. A universal cell topology deformation method is adopted to achieve an effective track of grain morphology evolution during plastic deformation. The proposed simulation framework is validated through simulating the isothermal uniaxial compression process of AA2196 alloy under different temperatures and strain rates. The orientation dependence of CDRX during compression is numerically reproduced by correlating the subgrain formation and rotation process with the activation state of slip systems. The simulated macroscopic flow stress, 3D microstructure and inherent microstructural characteristics such as subgrain size, subgrain boundaries and textures are in good agreement with the experimental results. The proposed method provides an effective and efficient tool for multi-scale simulation of hot forming process of aluminum alloys.

The texture evolution near the shear band and corresponding impact on the microvoid nucleation and crack propagation of Ti6242s alloys under high strain rates

This study investigates the texture evolution near the adiabatic shear bands (ASBs) and its impact of on the adiabatic shear failure mechanism, focusing on microvoid nucleation and crack propagation in Ti6242s alloy with an equiaxed α microstructure under high strain rates, using a split Hopkinson pressure bar (SHPB) for the experiments. To achieve this, the initial microstructure was used to enable the texture with the c-axis perpendicular to the loading direction. After compression, the initial texture transformed into two main texture components through different mechanisms. One texture component, aligned parallel to the loading direction, is strongly associated with the {10 1‾ 2} tensile twins, which were widely distributed near the ASBs with their c-axis are 85° to the parent grains in the initial microstructure. The other texture component, with its c-axis perpendicular to the ASB, is formed by the basal slip activation during adiabatic shear deformation. Besides, it should be noted that twinning resulted in the formation of hard grains (with the c-axis of α-grains parallel to the loading direction), increasing the number of hard-soft grain boundaries. A key finding of this paper is the presence of numerous microvoids near the ASB mainly initiated at soft-hard grain boundaries (approximately 65 %), attributed to stress concentration at the boundaries of soft-hard grains, making these boundaries potential nucleation sites for microvoids. Additionally, basal slip bands in the equiaxed α grains provide rapid channels, accelerating the crack propagation rate. This study provides new insights into refining the adiabatic shear failure mechanism under dynamic loading.

Gapped and Rotated Grain Boundary Revealed in Ultra-Small Au Nanoparticles for Enhancing Electrochemical CO2 Reduction.

Although gapped grain boundaries have often been observed in bulk and nanosized materials, and their crucial roles in some physical and chemical processes have been confirmed, their acquisition at ultrasmall nanoscale presents a significant challenge. To date, they had not been reported in metal nanoparticles smaller than 2 nm owing to the difficulty in characterization and the high instability of grain boundary (GB) atoms. Herein, we have successfully developed a synthesis method for producing a novel chiral nanocluster Au78(TBBT)40 (TBBT=4-tert-butylphenylthiolate) with a 26-atom gapped and rotated GB. This nanocluster was precisely characterized using single-crystal X-ray crystallography and mass spectrometry. Additionally, an offset atomic defect linked to the peripheral Au(TBBT)2 staple was found in the structure. Comparing it to similarly face-centered cubic-structured Au36(TBBT)24, Au44(TBBT)28, Au52(TBBT)32, Au92(TBBT)44, and ~5 nm nanocrystals, the bridging Au78(TBBT)40 nanocluster exhibited higher catalytic activity in the electroreduction of CO2 to CO. This enhanced activity was explained through density functional theory calculations and X-ray photoelectron spectroscopy analysis, which highlight the impact of GBs and point defects on the surface properties of metal nanoclusters in balancing intermediate adsorption and product desorption.

Thermal deformation behavior of a Ni-Cr-Fe superalloy and its effect on corrosion resistance: A comprehensive analysis of strain rate and temperature effects

Thermal deformation behavior of a Ni-Cr-Fe superalloy billet were investigated by hot compression experiments under temperatures of 900–1200 °C and strain rates of 0.001–1 s−1, and the corrosion properties of the superalloy after thermal deformation were also evaluated by electrochemical tests. Compression experiments determined that lower strain rates and higher temperatures reduce the superalloy's stress levels. The Arrhenius-type model accurately described the thermal deformation behavior of the superalloy. Furthermore, the optimal hot working domain was identified between 1120 and 1170 °C and strain rates of 0.001–0.01 s−1. Microstructure observations showed that the dynamic recrystallization (DRX), characterized by grain boundary bending nucleation and consumption of numerous dislocations is the main mechanism leading to grain refinement during thermal deformation. The results of the electrochemical corrosion tests proved that the corrosion predominantly occurred near the grain boundaries (GBs) of deformed grains, worsening with increased deformation temperatures.

Low cycle fatigue and cycle hardening behavior of heterogeneous Ni2Co1Fe1V0.5Mo0.2 medium entropy alloy

Low-cycle fatigue behavior of high-entropy alloy (HEAs) and medium-entropy alloys (MEAs) have rarely been reported in literature though it is critical for industrial applications. In our previous work, a non-equiatomic Ni2Co1Fe1V0.5Mo0.2 MEA was designed by adding V and Mo elements with bigger atomic size to heighten solution strengthening effect. Due to larger atomic size mismatch and more severe lattice distortion, the Ni2Co1Fe1V0.5Mo0.2 MEA exhibits stronger strain hardening effect than that in CoCrFeMnNi HEA. In present work, the low-cycle fatigue behavior of the non-equiatomic Ni2Co1Fe1V0.5Mo0.2 MEA with heterogeneous grain structures was further investigated. The heterogeneous Ni2Co1Fe1V0.5Mo0.2 MEA exhibits high fatigue resistance at 0.25 % strain amplitude (51285 N), attributed to the pronounced dislocation planar slip and formation of stacking faults. At 0.3 % and 0.5 % strain amplitudes, dislocation interactions (including tangles and microbands) induced by extensive dislocation cross-slip result in obvious cyclic hardening but reduced lifetime. The findings assess the effect of solid solution strengthening on the fatigue behavior of MEAs. The fatigue cracks form either along slip bands in large grains or grain boundaries of small grains.