Geometric Compatibility Factor Research Articles

Analysis of strain localization and slip transfer based on composite Schmid factor in TA19 titanium alloy

The correlation between slip behavior and strain localization was investigated through in-situ tensile experiment. The relationship between slip transfer and crystallographic orientation was analyzed using the composite Schmid factor (CSF), where CSF=mout+minm' (min and mout represent the Schmid factor (SF) of incoming and outgoing slip systems, respectively, m' is the geometric compatibility factor). The results show that for adjacent equiaxed α (αeq) grains without slip transfer, it will induce significant strain localization around αeq/αeq grain boundary due to the accumulation of massive dislocations on grain boundary. The initiation of secondary slip in αeq grain would exacerbate strain localization within the grain, as it promotes the dislocation pile-ups and entanglement. The slip behavior is largely related to the crystallographic orientation of the two adjacent αeq grains. Based on statistical analyses, for slip transfer, the slip system with the largest CSF is more likely to act as an easily initiated outgoing slip system. It can be attributed to that the CSF could reflect the synergistic effect of applied stress and the local shear stress induced by incoming slip system on the slip transfer behavior. However, with the increase of strain, some outgoing slip systems without the largest CSF can also be initiated, which may be associated with the complicated local stress state induced by the initiation of slip systems in multiple adjacent αeq grains before the initiation of outgoing slip system.

Analysis of the crack initiation and short crack propagation of laser cladding IN718 enduring fretting fatigue at 650 ℃

In order to reveal the behaviors of crack initiation and short fatigue crack propagation in laser cladding IN718 under high temperature conditions, very high cycle fretting fatigue (VHCFF) experiments were conducted at 650 ℃ with a transverse clamping force of P=400N and different axial stress loading conditions to obtain S_N data. The surface wear morphology and fracture morphology characteristics were analyzed by scanning electron microscope (SEM) and white light interferometer. Additionally, the microstructure characteristics of grains in the short fatigue crack region were examined through electron back scatter diffraction (EBSD). Parameters such as equivalent grain size, grain elastic modulus, Schmid factor, geometric compatibility factor, twist angle, and tilt angle were considered in the analysis of the characteristics of fatigue crack initiation and propagation. The results indicate that fretting fatigue cracks tend to initiate on grains with higher Schmid factors, larger equivalent grain size, and lower grain elastic modulus on the fretting contact surface. Moreover, the short fatigue cracks tend to propagate along the grains with the microstructural features of the high Schmid factor, the geometric compatibility factor of m′>0.4, the twist angle of α<50°, and the tilt angle of β<50°.

Revealing the mechanism of ductility discrepancy between two 2205 duplex stainless steels containing layered and island austenite through in-situ experiment

A notable discrepancy in tensile ductility was observed between two 2205 duplex stainless steels (DSS) containing layered and island-like austenite microstructures. The deformation behavior of both DSS 2205 was compared through in-situ Electron Backscatter Diffraction (EBSD) and Scanning Electron Microscope (SEM) techniques. The results indicated that the microscopic deformation mechanism for both DSS 2205 was governed by dislocation slip. The observed tensile ductility disparity was attributed to differences in dislocation slip behavior. In DSS 2205 with island austenite, slip transfer and blocking across grain boundaries occurred simultaneously, which was determined by the geometrical compatibility factor (m') calculations of adjacent ferrite and austenite grains. This intensified plastic inhomogeneities and promoted non-Schmid dislocation slip behavior. While in layered austenite of DSS 2205, the activation of slip system strictly adhered to the principle of maximizing the Schmid factor. Multiple slip systems in the ferrite on {110} and {112} planes were activated, inducing cross-slip, which enhanced ductility. The better ductility of DSS 2205 featuring layered austenite compared to the counterpart was further explained by quantitative analysis of geometrically necessary dislocations (GND) distribution in both phases and kernel average misorientation (KAM) values during deformation.

Investigation of active slip modes via in-grain misorientation axis and strain compatibility of TA2 alloy during in-situ tensile deformation

Slip is an important mechanism to coordinate the deformation in metal materials. Grain boundary can hinder slip transfer, thus lead to strain concentration. This work focus on the law of slip coordination deformation, texture evolution and strain compatibility under different strains. Based on the electron backscattered diffraction (EBSD) technique, the in-situ tensile tests of TA2 alloy were carried out at strain of 2 %, 4 % and 6 %, the activate law of slip under different strains was analyzed by the in-grain misorientation axes (IGMA) method and was verified by Schmid factor (SF). The relationship between grain orientation and strain compatibility at grain boundaries was discussed by calculating the geometric compatibility factor (m′). The results show that the multi-system slip coordination deformation at initial deformation, and the prismatic slip dominates the deformation as the increase of strain. The texture is preferentially distributed in the transverse direction (TD) as the deformation proceeds. The strain concentration is mainly related to the lack of effective plastic deformation mechanism to complete strain transfer at grain boundaries.

Effect of pre-strain on critical conditions for hydrogen-induced delayed cracking and crack nucleation characteristic of DP1180 steel

Hydrogen-induced delayed cracking represents a significant threat to the dependable performance of advanced high-strength steel. This study employed constant load tensile tests to uncover critical conditions for hydrogen-induced delayed cracking of DP1180 steel plate, establishing a precise relationship between pre-strain, threshold stress, and critical hydrogen concentration. Furthermore, this research explored dislocation slip transfer at grain boundaries, utilizing geometric compatibility factor (m') and residual Burgers vector (br), and analyzed slip characteristics at martensite/martensite, ferrite/ferrite, and martensite/ferrite interfaces. These findings provide valuable references for the safety assessment of DP1180 in hydrogen-exposed environments.

Microstructural insights into fatigue short crack propagation resistance and rate fluctuation in a Ni-based superalloy manufactured by laser powder bed fusion

The microstructural sensitivity of fatigue short crack path and its propagation rate in a Ni-based superalloy GH4169 manufactured by laser powder bed fusion (LPBF) was investigated at room temperature. In-situ digital image correlation (DIC) observation and post-mortem microstructural analysis around the crack path were performed. The results show that the intragranular cracks developed in the shear cracking mode are closely aligned along the activated slip bands in the γ-matrix grains with the crystallographic characteristics of parallel to the γ-{111} slip planes. Multiple slip was also activated, causing the crack retardation or deflection. Low-angle grain boundaries and subgrain boundaries were shown to cause deflections of intragranular cracking, while high-angle grain boundaries significantly arrested the short crack propagation. Moreover, the resistance of grain boundaries to short cracking was assessed using combined metrics including the crystallographic and microstructural parameters of twist angle, the Schmid factor and the geometrical compatibility factor. These site-specific microstructural analyses around the crack path provide insights into the microstructural origins of resistance to the short crack propagation as well as an interpretation of the observed significant fluctuations in the crack propagation rate.

Investigation into effect of grain sizes on deformation behavior of AZ31 alloys in different loading conditions

The AZ31 magnesium alloy with different grain sizes was prepared by adjusting the heat treatment process, and then the tension and compression tests were carried out to explore the effect of grain sizes and loading conditions on the microstructures and properties of the magnesium alloy. The Hall-Petch slope presented dramatic anisotropy under tension (181 Mpa· μm1∕2) and compression (115 Mpa· μm1∕2), the geometric compatibility factor (m′) and the difference in activation stress between the initiated deformation modes of two neighboring grains (σd) were calculated to analyze the anisotropy quantitatively. In compression, it was found that the elongation increased with further grain coarsening, which was attributed to the fact that more twins were initiated in the coarse grains and the preferred initiation of twinning to inhibit competitive crack initiation.

In-situ study of damage mechanisms in Mg–6Li dual-phase alloy

Interfaces play a crucial role in influencing the mechanical properties of Mg alloys. For Mg–Li dual-phase alloy, the type of interfaces is complex, which includes both grain boundary and phase boundary, and the influence of such interfaces on the damage nucleation is yet to be explored. In this paper, in-situ scanning electron microscopy (SEM) based measurements were carried out to investigate the meso‑scale damage nucleation mechanisms of the Mg–6Li dual-phase alloy. Results show that 94.8% of cracks are nucleated at the α-Mg grain boundary in the post-uniform elongation stage, while 5.2% are at phase boundary and almost no crack at the β-Li grain boundary. The initiation of α-Mg grain boundary cracks is attributed to strain incompatibility, which induces micro-strain localization, and then causes grain boundary sliding (GBS) and crack nucleation. Deformation compatibility analysis reveals that the geometric compatibility factor (Mk) can be used to predict the nucleation of α-Mg grain boundary crack. When Mk is lower than 0.075, α-Mg grain boundary cracks tend to form. Few cracks are generated at the phase boundary is due to the mild strain partitioning between α-Mg phase and β-Li phase and may also be partly attributed to multiple slip systems in body-centered cubic (BCC)-structured β-Li phase, which can accommodate well with the deformation of adjacent α-Mg phase.

Quasi-in situ observation of extension twinning of AZ31 magnesium alloy under co-directional dynamic compression

In this paper, twinning nucleation and microstructure evolution of AZ31 magnesium alloy were investigated during the quasi-in situ dynamic compression. The microstructure characterization of the sample before and after deformation was performed via electron backscatter diffraction and transmission electron microscopy. The strain accommodation was estimated by selecting twinning variants and using the geometric compatibility factor (m'). The nucleation behavior of 55.4% extension twinning obeyed Schmid's law under high strain rate compression. The non-Schmidt twinning variants with the highest geometric compatibility factor (m') in the active twinning system of adjacent grains were activated in paired twins that affected the twining nucleation and variant selections.

Revealing the effect of misorientation on the deformation behavior of a Mg-Y alloy from the perspective of local strain

The addition of rare earth (RE) elements in magnesium alloys may significantly enhance the ductility of magnesium alloys, which is generally attributed to the decrease of stacking fault energy, the reduced critical resolved shear stress (CRSS) differences among different deformation modes and the weakening of basal texture. Rare earth elements also change the misorientation between adjacent grains of magnesium alloy, whose effects on the deformation behavior and thus the ductility of magnesium alloy were not emphasized before. In this work, ex-situ high-resolution digital image correlation (HR-DIC) coupled with electron backscatter diffraction (EBSD) was used to reveal the effect of the misorientation on the deformation behavior of a Mg-Y binary alloy from the perspective of local strain. It is shown that the heterogeneity of local strain is largely dependent on the misorientation between adjacent grains. For the intergranular deformation, three scenarios are observed, namely strain transfer, strain concentration and suppressed deformation, which mainly occurs at low misorientation, moderate misorientation and high misorientation, respectively. In addition, much more non-basal slip is found to be activated near the grain boundaries with moderate misorientation angles due to the high geometric compatibility factor (m’B-Pr/Py), which is favorable for the intergranular deformation compatibility, thus reducing the strain concentration near grain boundaries and achieving high ductility. For the intragranular deformation, a wide range of misorientation between adjacent grains in the Mg-Y alloy causes multiple basal slip systems to be activated within a grain, which also facilitates work hardening, thus contributing to improving ductility. Therefore, tailoring the misorientation between adjacent grains may be an effective way to improve the ductility of magnesium alloys.

Creep deformation and damage characteristics of nickel-based superalloy GH4169

To further understand the creep behavior of nickel-based superalloys, creep deformation and damage characteristics of nickel-based superalloy GH4169 were investigated systematically by using SEM, EBSD and TEM characterizations in this study. Creep tests were conducted at 650 °C under 820 MPa.The results indicated that the fractions of low-, high-angle, and twin grain boundaries changed significantly after creep. Due to the grain rotation mechanism, the overall microstructure changed from random to preferred crystallographic orientation. <110>//loading direction (LD) oriented grains were rotated to <100>//LD and <111>//LD fibers, resulting in the decrease of <110> fiber, and the increase of <100> and <111> fibers. Cases of <110> oriented grains rotating into <100> and <111> orientations were also provided. Deformation twin and stacking faults were determined as the main deformation mechanisms. The failure of the specimen was induced by intergranular brittle fracture. The grain boundaries with special characteristics, namely high Schmid factor m and low Schmid factor mismatch Δm of neighbouring grains, and low geometric compatibility factor m’, exhibited high susceptibility to cracking.

Quantitative investigation on the {10–12} twinning-detwinning behavior and twinning transfer of an extruded Mg-2.8Y sheet during compression-tension loading via quasi-in-situ EBSD observation

Abundant {10–12} twins appeared in an extruded Mg-2.8Y (wt. %) sheet with rare-earth (RE) texture under compression along the transverse direction (TD). Twinning-detwinning behavior during compression-tension loading was quantitatively investigated via quasi-in-situ EBSD observation. The evolution of deformation mechanisms was quantitatively studied by calculation of the plastic strain fraction of twinning, detwinning, and dislocation slip. Twinning and detwinning were the dominant deformation modes in compression and reverse tension, respectively, owing to their relatively higher Schmid factors (SF) and lowest activation stresses (τ). Twin variants with SF ranking 1st and 2nd were activated preferentially while detwinning with low SF ranking showed high activation. The impact of texture and load path on variant selection was systematically discussed. Moreover, short twin chains only passing through two or three grains caused by twinning transfer were observed. Grain boundary misorientation angle (GBMA) and geometric compatibility factor (m’) were introduced to analyze the crystallographic characteristics of twinning transfer. GBMA ≤34.5° or m’ ≥ 0.80 is a necessary condition for most twinning transfer events. RE texture as well as the nearly uniform distribution of GBMA gave rise to short twin chains and restricted the formation of long twin bands. The relationship between GBMA and m’ was also discussed.

Strain transfer behavior and crystallographic mechanism of crack initiation during cyclic deformation in zirconium

Fully-reversed cyclic deformation of a pure Zr (a thickness of 17 mm) was conducted at two different strain amplitudes (0.4% and 0.8%) to investigate the deformation and crack initiation behaviors based on slip trace analysis. It was found that prismatic 〈a〉 slip with a higher Schmid Factor (m > 0.4) was the dominant deformation mode. The grains containing persistent slip bands (PSBs) tended to go towards [1¯21¯0] pole and the Schmid Factor had a critical value of 0.4 above which prismatic and pyramidal slip were dominant. Fatigue cracks were mainly initiated at PSBs and grain boundaries (GBs). It showed that 61.1% of the cracks were PSB cracks under a strain amplitude of 0.4%, while it decreased to 53.5% at a strain amplitude of 0.8%. PSB cracks were mainly parallel to prismatic 〈a〉 slip with higher Schmid Factor while some cracks tended to be initiated at GBs with higher misorientation angles. The interaction of PSBs with GBs would result in strain transferring to the neighboring grain. Strain transfer was more likely to occur at the condition of the higher geometrical compatibility factor m′, and lower residual Burgers vector Δb, which could reduce strain localization.

Deformation mechanisms of as-extruded Mg–3Bi–1Ca (wt.%) alloy during room-temperature tension

In this work, the deformation mechanisms of the as-extruded Mg–3Bi–1Ca (BX31, wt.%) alloy with strength-ductility synergy during room-temperature tension were studied in detail by in-situ electron backscattered diffraction (EBSD), slip trace analysis, visco-plastic self-consistent (VPSC) modeling and transmission electron microscopy (TEM). The quantitative results of in-situ EBSD and slip trace analysis showed that basal <a> slips offered most of the deformation at the early stage, and with increasing strains the proportions of non-basal slips and {10-12} extension twinning gradually increased. At the medium and later stages, each deformation mode approached to be stable and the macroscopic strain became uniform. The critical resolved shear stresses (CRSSs) of different dislocation slip systems were estimated to establish the VPSC modeling. The VPSC-simulated results were highly consistent with the experimental ones. On the other hand, the microcosmic deformation incompatibility gave rise to the hetero-deformation induced (HDI) stress, caused by the distinct schmid factor (SF) and the low geometrical compatibility factor (m’) between adjacent grains. Geometrically necessary dislocations (GNDs, especially for the pyramidal <c+a> edge dislocations) near grain boundaries would be generated to accommodate the deformation incompatibility. In addition, the basal <a> screw dislocations in {10-12} extension twin interiors were also observed, which provided the extra strain hardening capacity.

Relationship between Σ3 Boundaries, Dislocation Slip, and Plasticity in Pure Nickel.

This study investigated the relationship between the Σ3 boundaries, dislocation slip, and plasticity in pure nickel wires after grain boundary (GB) modification. Both quasi in situ tensile tests and simulations were employed. During plastic deformation, twins surrounded by Σ3 boundaries may exhibit a good deformation coordination. With an increase in strain, the slip systems corresponding to the maximum Schmid factor and the actual activated slip systems remain unchanged. Even sub-grains can maintain the dominant slip system of their origin matrix grains. Slip systems with slip planes (111) and (1-1-1) are the most active. Moreover, random boundaries have strong hindering effects on dislocations, and the nearby stress accumulates continuously with an increase in strain. In contrast, Σ3 boundaries demonstrate weak blocking effects and can release the nearby stress due to their unique interfacial structures, which is favorable for improving plasticity. They are more penetrable for dislocations or may react with the piled dislocations. In addition, some Σ3 boundaries can improve their geometrical compatibility factor with an increase in the strain, which enhances the deformation coordination of the grains. The research results provide a better understanding of the plasticizing mechanism for face-centered cubic (fcc) materials after grain boundary modification.

Transfer or blockage: Unraveling the interaction between deformation twinning and grain boundary in tantalum under shock loading with molecular dynamics

The interaction between {112}<111> deformation twinning and grain boundary in coaxial polycrystalline tantalum under shock compression was studied with molecular dynamics simulation under different grain pair misorientation angles (MA) and geometric compatibility factor (m’). Generally, in the coaxial polycrystal, the value of MA determines the occurrence of twin transfer (TT) or twin blockage (TB), i.e., twin transfer occurs at MA ≤ 29° with twin blockage otherwise. Under TT, the value of m’ affects the selection of twin variants., i.e., the twin system with a larger m’ is easier to active. The morphology of twin pairs is ruler-shaped and lenticular under TT and TB, respectively, with different thickening mechanisms, including grain boundary dislocation emission.

Enhancing mechanical properties of friction stir welded AZ31 alloys by post-weld compression

In this work, the friction stir welded AZ31 joint was processed by a two-step post-weld deformation (i.e. compression at room temperature and an elevated temperature, respectively). The microstructure, texture and mechanical properties were systematically investigated. Profuse extension twins were observed after the first-step cold compression along normal direction, which largely affected the dynamic recrystallisation process during the second-step hot compression. Finally, the grain orientations and their convergence on the weld side were effectively altered, thereby contributing substantially to the enhancement of joint performance. Compared to the original joint, the yield strength, ultimate tensile strength and elongation were improved 64.7%, 20.8% and 52.5%, respectively. The underline strengthening mechanism was discussed by a comprehensive analysis of Schmid factor and geometric compatibility factor.

Heterogeneous fiberous structured Mg-Zn-Zr alloy with superior strength-ductility synergy

• The heterogeneous fiberous structured ZK60 Mg alloy was obtained by conventional extrusion method with high yield strength of ∼ 345 MPa, ultimate tensile strength of ∼ 370 MPa and high tensile strain of ∼ 20.5%, superior than most ZK60 Mg alloys reported so far. • The excellent mechanical properties were mainly attributed to the heterogeneous fiberous structure that was characterized by alternating coarse- and fine-grain layers, nanoscale precipitates and profuse < c + a > dislocations. The novel heterogeneous fiberous structured ZK60 Mg alloy have achieved superior strength-ductility synergy. • A novel design of alternating coarse- and fine-grain layered structure was considered to be a general strategy for promoting the strength-ductility synergy of hexagonal close-packed (hcp) metals. Here we reported a heterogeneous fiberous structured Mg-5.6Zn-0.6Zr (wt%) alloy obtained by conventional extrusion method, which exhibited high yield strength of ∼ 345 MPa, ultimate tensile strength of ∼ 370 MPa, and high tensile strain of ∼ 20.5%, superior to most of the Mg-Zn based alloys reported so far. The extraordinarily high mechanical properties were mainly attributed to the heterogeneous fiberous structure consisting of alternating coarse- and fine-grain layers. Grains in the different layers grew into the neighboring layers, ensuring a good layer bonding. A high Schmid factor and geometric compatibility factor for pyramidal slip led to full slip transfer between the neighboring coarse grains and fine grains, which could help to release the stress concentration and avoid early fracture. The profuse activated <c + a> glide dislocations could render the unprecedented high tensile strain. The constraint by the hard fine-grain domains made the soft coarse-grain domains strong like the hard fine-grain domains, as well as the nanoscale precipitates pinning dislocations, contributed to the high strength. The heterogeneous microstructure design was shown to have synergistic improvement in strength-ductility balance, which could be an inspiring strategy to improve mechanical properties of hexagonal close-packed (hcp) metals.

Geometric compatibility measure m′ for twin transmission: A predictor or descriptor?

In this work, the geometric compatibility factor m’ is critically analyzed to assess whether it can be used to interpret/predict twin transmission (TT) across grain boundaries (GBs). This geometric measure is widely used to relate the likelihood of TT to the misalignment of both the shear and plane-normal directions within a twin set (i.e., incoming and outgoing twin). Using a large set of electron back scattering diffraction (EBSD) data, a detailed statistical analysis of twin-GB interactions is performed for { 10 1 ̅ 2 } tensile twins in hexagonal close-packed (HCP) metals Mg, Zr, and Ti at different strain levels. In addition, a full-field crystal plasticity model is employed to quantify the role of local stresses and the applicability of m’ as a criterion for the TT process. This combined study addresses the following three main questions: (i) What is the fidelity of m’ in describing experimentally observed TTs? (ii) Can m’ be used as a metric to predict/anticipate TT? (iii) Does m’ naturally capture local stress effects? As a descriptor, m’ cannot rationalize ~25% of TT events observed in Mg or more than 50% of TT events in Zr and Ti. As a predictor, the m’-measure does not predict TT events in over ~50% of twin-GB interactions analyzed. Further, the applicability of m’ to describe and predict TT events decreases with an increase in elastic anisotropy, plastic anisotropy, and macroscopic strain levels. Finally, the twinning simulations reveal that m’ does not capture the key effects of local stresses on variant selection upon twin transmission. The local stress induced by the twinning shear transformation plays a dominant role in driving the TT process compared to the geometric alignment of the constituting twins, i.e., m’ .

A Feasible Surface Patterning Method for SEM-DIC: Achieving High-Resolution In Situ Mapping of Local Strain and Microstructure to Reveal the Effect of Slip Transfer on Shear Strain Near Grain Boundaries.

This paper exploited an alternative approach to prepare high-quality speckle patterns by uniformly dispersing nano-silica particles onto sample surfaces, helping digital image correlation (DIC) acquire the maximum spatial resolution of local strain up to 92 nm. A case study was carried out by combining this speckle pattern fabrication method with SEM-DIC and electron backscattering diffraction (EBSD). Thus, in situ mapping of local strain with ultra-high spatial resolution and microstructure in commercially pure titanium during plastic deformation could be achieved, which favored revealing the effect of slip transfer on shear strain near grain boundaries. Moreover, the slip systems could be easily identified via the combination of the SEM-DIC and EBSD techniques even though no obvious deformation trace was captured in secondary electron images. Additionally, the complex geometric compatibility factor $( {m}^{\prime}_c)$ relating to geometric compatibility factors (mʹ) and Schmid factors was proposed to predict the shear strain (εxy) at grain boundaries.