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An Al-8Mg-based alloy with high strength and high ductility was developed by adding a grain boundary strengthening element. Zr was predicted to be the most effective element for grain boundary strengthening at 298 K from first-principles calculations. Then, an Al-8Mg-0.2Zr alloy was developed. Grain boundary analysis by high-angle annular dark-field scanning transmission electron microscopy and Auger electron spectroscopy revealed that the added Zr segregated at grain boundaries in the Al-8Mg-0.2Zr alloy. The Al-8Mg-0.2Zr alloy exhibited tensile elongation of 49% with transgranular fracture, whereas the Al-8Mg alloy exhibited tensile elongation of 28% with intergranular fracture after tensile tests at room temperature. We succeeded in developing a high strength and high ductility Al-8Mg-0.2Zr alloy which compensates for the trade-off between strength and ductility in comparison with commercial Al alloys.

High productivity and bath stability of electrodeposition for Al and its alloys from a dimethylsulfone (DMSO2)-aluminum chloride bath are highly desirable characteristics for a wide range of critical applications. However, a long-standing problem for such electrodeposits is S and Cl contamination, which results in limited ductility. In this study, we explored a reduction method for S and Cl in Al electrodeposits from a DMSO2 bath to facilitate plastic elongation of the electrodeposited Al. For 2–5:10 M ratios of aluminum chloride to DMSO2, tailoring the conditions of electrodeposition decreased the S and Cl contents to ∼0.2 at%. The addition of various metal salts revealed that gallium chloride further reduced the S and Cl contents to less than 0.1 at%. This reduction permitted the electrodeposited Al–Ga alloys to exhibit plastic elongation in tensile tests. Based on the results of experiments and first-principles calculations, we discuss the role of Ga in the growth mode of electrodeposits and its effect on grain boundary cohesion. Thus, we elucidate the mechanisms for realizing high strength and ductility in electrodeposited Al alloys.

We electrodeposited bulk nanocrystalline Fe–Ni alloys with a tensile ductility of 12%–24%. We explored the intrinsic ductility of these alloys, taking into consideration the relationship between the ductility and the orientation index and contents of the grain boundary embrittlement element. Applying multiple regression analysis to our findings and those from the literature we found that the ductility of Fe–Ni alloys can be predicted from their orientation index for the (2 0 0) plane and sulfur content. The analysis of our study points to the potential for intrinsic ductility in nanocrystalline Fe–Ni alloys greater than that of the present highest value of 24%.

Al and Al alloys electrodeposited from a dimethylsulfone (DMSO2) bath are typically contaminated with S and Cl. Electrodeposited Al and Al alloys suffer from limited ductility since undesired impurities decrease plastic deformability. Herein, we report an electrodeposition process involving the use of a DMSO2 bath that realizes an Al product with tensile elongation as large as ∼30%. Doping of tin chloride in the DMSO2 bath resulted in a micrometer-scale grain microstructure with sub-µm Sn precipitates distributed along the grain boundaries of the electrodeposited Al. These Sn precipitates on the electrodeposits prevented S and Cl contamination, which is likely the main factor underlying the large tensile elongation in the electrodeposited Al. Furthermore, electrodeposition with varying concentrations of tin chloride pointed to that tin chloride showed enough impurities reducing ability even in trace amounts.

The small amount (0.1 at%) of V addition to Fe–Al alloys promotes AlN precipitation during nitriding and results in substantial surface hardening, in contrast to the normal sluggish precipitation kinetics of AlN during nitriding of Fe–Al binary alloys. The addition of V to Fe–Al alloys can increase the surface hardness to a greater extent than the addition of Ti. First-principles calculations of the interaction energy between an Al atom and an N–s cluster (s = V, Ti, Cr, or Al) show that a V–N cluster has an attractive interaction with an Al atom, and this interaction is stronger than that between a Ti–N cluster and an Al atom, in good agreement with the greater hardening induced by V addition than by Ti addition. These experiments and calculations indicate that solute clusters not only contribute directly to the hardening but also induce alloy nitride precipitation.

Effects of third alloying elements on the transformation strains and phase stabilities of Ti-Nb based alloys at 0 K were investigated using the first-principles calculations. In binary Ti-Nb alloys, the transformation strains and the body-centered cubic high-temperature beta (β) phase stabilities decrease with increasing Nb concentration. In Ti-12.5Nb-6.25X (at.%) alloys, the effects of 46 different alloying elements X on the transformation strains and phase stabilities were also investigated. The addition of Al, Be, Ca, Cu, Ga, Ge, Hf, La, Mg, Sc, Si, Sn, Sr, Y, Zn, and Zr increase the transformation strains, and all alloying elements except for Sc act as the β-phase stabilizing element. Using the calculated values of the effects of alloying elements, x M values were calculated for the different 46 alloying elements, where x M are the X contents of Ti-12.5Nb-X (at.%) ternary alloys where the martensitic transformation start temperatures were equal to 300 K. Then, the transformation strains of Ti-12.5Nb- x M X (at.%) alloys were predicted. The Ti-12.5Nb-17.8Hf (at.%) alloy shows the largest transformation strain value.

The thermal stability of electrodeposited Ni–W alloys has been identified to be due to W segregation. Although a kinetic contribution has been recently proposed, namely, the formation of W-oxides at grain boundaries (GBs) by annealing, the formation mechanism is unclear. In this study, we annealed electrodeposited Ni–W alloys up to 600 °C; then, we examined the mechanical properties and microstructures to deeply understand the thermal stability of Ni–W alloys. Mechanical testing of annealed alloys demonstrated that the proof stress and hardness increased against the increase in annealing temperature in the range of 380–450 °C. At the mesoscale, microstructure observations revealed that the grain size was reduced with increasing temperature from 390 to 450 °C. Finer-grained microstructures were maintained up to the annealing temperature of 520 °C. At the nanoscale, grain boundary structures were directly observed, and the chemistry was also demonstrated. These nanoscale analyses detected S segregation at GBs and triple junctions, whereas oxides and precipitates likely to affect grain growth were not identified. Our results and discussion indicate that transition in the grain size after annealing can be explained by the conventional relationship between the annealing temperature and frequency of abnormal growth grains.

The effect of alloying on the formation enthalpy of TiCu intermetallics was investigated via first-principles calculations to propose a new design method for Ti–Cu-system metallic glasses. The calculation results showed good agreement with the reported experimental results that Ni, Pd, Sn and Zr improve this system’s glass-forming ability. According to the calculation results, a Ti–Zr–Cu–Ga system was designed as a potential new bulk Ti-based metallic glass, and a bulk sample with a 2-mm diameter was fabricated.

Texture change during superplastic deformation was examined and compared in two magnesium alloys with different chemical composition. These alloys were extruded to refine the microstructure. The pre-existing basal texture of both alloys became slightly more random within the bulk probably owing to grain boundary sliding and the accompanying grain rotation. However, the texture changes differed between tensile and compressive deformation along the extrusion (longitudinal) direction. This fact suggests that dislocation slip is important in superplastic deformation. It was concluded that dislocation slip acts primarily as an accommodation mechanism for grain boundary sliding.

Friction stir processing (FSP) is one of the severe plastic deformation (SPD) processes. It has been reported that SPD-processed Al with various purities attained a minimum grain size when Zener-Hollomon parameter is larger than 1016 s-1. The minimum grain size is different by purity level and alloying elements. We investigated the influence of Fe solute atoms on grain refinement of high-purity Al on the condition that Zener-Hollomon parameter was larger than 1016 s-1. FSP was conducted on Al-0.01%Fe, which was fabricated by using 5N Al (99.999% purity). FSP-ed Al-0.01%Fe exhibits the minimum grain size of 1.4 μm, although high-purity aluminums with more than 99.998% exhibits much larger minimum grain sizes of 30-40 μm. Only 101 at.ppm Fe played a critical role in the grain refinement of pure aluminums.

Bulk nanocrystalline Fe-Ni alloys with Ni content of 40-55 at.%, grain size of 12-15 nm, and hardness of 3.9-4.6 were prepared by an electrodeposition. The decrease in the hardness values as grain size decreased was discussed in terms of grain refinement effect, solid solution strengthening, and grain boundary relaxation strengthening. It was found that the change of Ni content could not significant solid solution strengthening, and there were no difference in the state of grain boundary for each sample. Micro X-ray diffraction analysis on the sample after tensile tests showed that the (200) texture was developed but full width at half maximum was not changed. This indicated the potency that the grain boundary activity would be induced by a tensile loading. The softening behavior of electrodeposited Fe–Ni alloys would be related to the transition of the dominant deformation mechanisms.

Parameters for evaluating the glass-forming ability (GFA) in Ti–Cu system metallic glasses were considered by investigating the effect of additional elements (Fe, Co, Ni, Si, Zr, Cr) on structural changes and onset temperatures associated with each exothermic peak on heating. The differential scanning calorimetry curves of Ti–Cu system metallic glasses (added Ni, Cr, Zr) exhibited two exothermic peaks. Moreover, the sample containing Zr maintained its halo peak when the sample was annealed at first exothermic peak. The results indicate that the onset temperature of the second exothermic peak ( T x 2 ) is an important temperature reflecting the resistance of the supercooled liquid to crystallization. The GFA of Ti–Cu system metallic glasses are expressed well by parameters containing T x 2 .

A method for reducing the sulfur content of electrodeposited bulk nanocrystalline Fe–Ni alloys was developed to improve the tensile ductility of the materials and prevent thermal embrittlement caused by the grain boundary segregation of sulfur. Bulk nanocrystalline Fe–Ni alloys were prepared using electrolytes that primarily consisted of iron sulfate and nickel sulfamate combined with manganese chloride (MnCl 2 ). The addition of MnCl 2 in the deposition bath did not produce any significant changes in the Ni content and grain sizes of the electrodeposited alloys. In contrast, the sulfur content in the materials decreased from 840 to 620 at ppm. The bulk nanocrystalline Fe–Ni alloys with low sulfur content exhibited a higher tensile elongation of 16–19% compared to the materials with high sulfur content. Furthermore, after annealing at 200 °C for 3 h, The bulk nanocrystalline Fe–Ni alloys with low sulfur content exhibited a high tensile elongation of 9–10%, whereas the elongation of the materials with high sulfur content was 3%. The results indicate that the plastic elongation of electrodeposited bulk nanocrystalline Fe–Ni alloys can be improved by reducing the amount of sulfur in the materials.

New Ti-based metallic glasses were designed and fabricated in the ternary component alloy system Ti–Zr–Co. The constituent elements of the alloy system were selected based on three empirical rules proposed by Inoue, Turnbull, Senkov and Miracle, and by a new parameter called the effective atomic radius, which is based on the first-principles calculations for 2.78 at.% hcp Ti alloys. The reported scheme based on the concept of binary eutectic clusters was applied to predict the alloy composition that shows a glass transition, Ti44Zr30Co26. We prepared Ti44Zr30 + xCo26 − x, Ti46Zr28 + xCo26 − x, and Ti48Zr26 + xCo26 − x (x = 0, 4, 6, 8) alloy sheets using a single roller method. The new Ti-based ternary metallic glasses exhibited vitrification for many compositions around the predicted composition of Ti44Zr30Co26. The greatest value of the super-cooled region ⊿Tx was 34 K for Ti48Zr32Co20.

A method for enhancement of the mechanical properties of electrodeposited bulk nanocrystalline Fe–Ni alloys was explored. Bulk nanocrystalline Fe–Ni alloys were prepared using electrolytes that primarily consisted of iron sulfate and nickel sulfamate with propionic acid. Varying the concentration of propionic acid in the deposition bath produced no significant change in the C, S, or Ni content or grain sizes of the electrodeposited alloys. In contrast, the hardness of bulk nanocrystalline Fe–Ni alloys increased from 4.0 to 5.0 GPa with the increase of propionic acid concentration from 0 to 3.0 g/L. In addition, the tensile strength also increased from 1.6 to 1.7 GPa while maintaining a good tensile ductility of ~10%. These increases for electrodeposited alloys can be explained by grain boundary relaxation strengthening. After annealing at relatively mild temperatures, the alloys electrodeposited without propionic acid exhibited higher strength than at the as-deposited state, while the strength of the alloys electrodeposited using 3.0 g/L propionic acid remained unchanged. The results of this study indicate that the addition of propionic acid to the deposition bath could remove the excess grain boundary defects of Fe–Ni alloys in as-deposited states, requiring no additional thermal treatments and enhancing the mechanical strength to high levels.

In order to develop a high strength and heat-resistant magnesium alloy, we focused on controlling microstructure of Mg96Zn2Y2 (at %) casting alloy by the addition of a 4th element. Initially, we investigated the effects of zirconium addition and cooling rate for grain refinement on microstructure and mechanical properties. Consequently, Mg95.8Zn2Y2Zr0.2 casting alloy contains fine equiaxed grains (approx. 0.01 mm), and it exhibits tensile and fatigue properties equivalent to or higher than those of commercial aluminum alloys at high temperature above 473 K. At 523 K, this alloy exhibited a tensile strength of 223 MPa nearly twice that of A4032-T6 alloy used in typical automotive pistons. The Mg95.8Zn2Y2Zr0.2 casting alloy also reveals sufficient ductility and good castability, characteristics not common in current heat-resistant magnesium alloys. Next, we focused on controlling microstructure of Mg96Zn2Y2 casting alloy by the addition of Ag. Mg96Zn2Y2 cast alloy is composed of alpha-Mg phase, long-period stacking ordered phase and Mg3Zn3Y2 phase; on the other hand, Mg-Zn-Y-Ag cast alloy had 4th phase by an addition of Ag. A substantial increase in yield strength at room temperature, without grain refining, was the result.

The influence of filler rod composition on the strength of Tungsten Inert Gas (TIG) welded magnesium alloy joint was investigated. Samples were rolled AZ31 (Mg-3Al-1Zn) magnesium alloy as base metal and drawn AZ31, AZ61 and AZ91 magnesium alloys as filler rod. The results show that all fracture points were fusion zone (FZ), and each joint efficiency (=joint strength/ base metal strength) was 70.7%, 80.0% and 73.1% when using AZ31, AZ61 and AZ91 filler rod. When using AZ91 filler rod, 0.2% proof stress was the highest but the elongation was the lowest among the three conditions, and joint efficiency was lower than that when using AZ61 filler rod. It is thought that welded joint was strengthened by solute strengthening, but excess addition of aluminum facilitated crystallization of Mg17Al12 phase. This is the reason why elongation and joint efficiency when using AZ91 filler rod decreased. In conclusion, it is effective to use filler rod which does not excess solid solubility limit.

Recent experimental data have revealed that a small amount of impurity can significantly influence the superplastic behavior in Zn-Al eutectoid superplastic alloy. However, the effect of Si content on the superplastic behavior in Zn-Al alloy has not been reported. In this study, the superplastic behavior at a room temperature of two grades of the Zn-Al eutectoid superplastic alloy was studied under identical conditions of grain size, temperature, and strain rate. These two grades were prepared from high-purity Zn, Al and Al-Si alloy using the same procedure but different Si impurity levels; Zn-Al-10Si and Zn-Al-1000Si contain 10 and 900 wt. ppm of Si, respectively. As a result of annealing treatments, an average grain size of 0.6 μm in both grades. To investigate the effects of Si content on superplastic properties, the tensile tests were performed at a room temperature of 298 K and a constant strain rate of 1×10-3 s-1. Microstructures before and after the tensile tests was observed using a scanning electron microscope. The experimental results show that the elongations decreased with increasing the Si content. In contrast, the flow stress of Zn-Al alloys was not affected by the Si content. On the microstructure observation of the two grades of the Zn-Al alloy before and after the tensile tests, cavities existed at grain boundaries and strain enhanced grain growth was observed.

Effect of typical impurities such as Fe, S, and Cl on mechanical properties of Al electrodeposited from a dimethylsulfone bath (DMSO2bath) were studied. Electrodeposition from a DMSO2bath was conducted to produce the bulk specimens with 0.08–0.24 at.% Fe, 0.47–0.84 at.% S, and 0.59–1.06 at.% Cl, varying the purity of aluminum chloride and current density. Decreasing the current density increased S contents and Cl contents, while the purity of aluminum chloride had no effect on chemical composition of the electrodeposits. The grain sizes were approximately 40–70 nm for Al electrodeposited from a DMSO2bath. The grain sizes decreased with increase in S contents and Cl contents. The electrodeposited bulk nanocrystalline Al exhibited hardness values of 1.56–1.92 GPa. These values were higher than predicted values based on Hall–Petch equation of pure Al. Lattice parameter of samples was less than pure Al. According to Vegard’s law, Fe solute decreases the lattice parameter of Al. These results indicated that the hardness of the electrodeposited bulk nanocrystalline Al was affected by the reduction in the grain size and solid solution strengthening from the Fe contaminant.

Creep tests of ultra-high-purity (99.999%) Al and Al-22.2, 53.6, 101 at.ppm Fe solid solution alloys were conducted at 773 K in the stress range of 2-6 MPa in order to investigate effect of solute Fe on high temperature deformation of Al. Creep resistance was enhanced by addition of Fe in solid solution. The stress exponents of the samples exhibited values of about 5, which indicate that climb-controlled dislocation creep was dominant deformation mechanism. It could be suggested that Fe atoms segregating in dislocations due to the strong interaction between solute Fe atoms and the dislocation enhanced the creep resistance.

Electrodeposition for Al from a dimethylsulfone (DMSO2) bath was consecutively performed, applying two types of current waveforms such as direct current and pulsed current, to investigate the effect of a current type on the preparatory electrodeposition (pre-electrodeposition) process. Electrodeposited Al from a DMSO2 bath has a nanograined structure and high strength. However, the electrodeposits showed no plastic deformability due to the large amount of sulfur and chlorine which were incorporated into the electrodeposits as sulfide and chloride. Therefore, we obtained high purity Al from a DMSO2 bath using pre-electrodeposition process, which could decrease sulfur and chlorine contents without using additives. The sulfur and chlorine contents of electrodeposits, obtained from a DMSO2 bath applying both types current, both decreased to approximately 0.1 at.%. This result indicated that the waveforms made no difference in pre-electrodeposition process.

A relationship between yield stress and grain size was examined in FSP-ed and annealed 5N-Al (99.9996% purity) in order to reveal the relationship on materials with equal chemical composition, because the large positive deviations of yield stress from the Hall–Petch relation obtained by plots with coarse grain size were reported in the fine grain sizes with SPD processed and we focused on amount of impurities during SPD processing about this phenomenon. The purity of FSP-ed samples on this study were 99.9988% Al (Fe +8at.ppm). Annealing this sample at various temperatures, the relationship between yield stress and grain sizes was obtained on materials with equal chemical composition. However, the yield stress of sample as FSP-ed is higher than that following Hall-Petch relation obtained by subsequently annealed samples plots. As a result, the positive deviation is occurred by factors other than the impurities.

New Ti-based ternary metallic glasses were designed and fabricated. A new parameter called effective atomic radius in the Ti solid solution from ab-initio calculation was used to design of the Ti-based metallic glasses. From the effective atomic radius, Ti-Zr-Mn, Ti-Zr-Fe and Ti-Zr-Co systems can be considered as a new Ti-based ternary metallic glass. And the reported scheme based on the concept of binary eutectic clusters is applied to predict alloy composition which shows glass transition.We prepared the Ti42Zr22Mn36, Ti43Zr29Fe28 and Ti44Zr30Co26 alloy sheets by a single-roller method. It showed that sharp diffraction peak corresponding to crystalline phases could be observed in the XRD spectra of Ti42Zr22Mn36 and Ti43Zr29Fe28. While for alloy with Ti44Zr30Co26 no sharp diffraction peak could be found except broad diffraction halos. This result suggests that a critical eutectic temperature in the phase equilibrium for forming glass phase is around 1000°C.

The tensile behavior of electrodeposited bulk nanocrystalline Fe–Ni alloys with a grain size of approximately 15 nm was investigated. Electrodeposited alloys with a nickel content of 43–56 wt% have a single-phase face-centered cubic structure. These alloys exhibited a good combination of tensile strength and ductility in tensile tests at room temperature. In particular, bulk nanocrystalline Fe–44 wt% Ni exhibited the high tensile ductility of 1.7 GPa and significant ductility of 16%, and the tensile specimen after fracture showed clear necking. Fracture surface observation indicated that dimples, the size of which was 10 times the grain size, developed in electrodeposits with high ductility of above 10%. The results of this study point out that grain clusters can have a role in plastic deformation during tensile loading.

Electrodeposited Ni and its alloys typically contain S due to crucial reagents used in the electrodeposition processes. The relative S concentration at the grain boundary (GB) increases when grain sizes are increased by thermal treatments, resulting in a transition from ductile to brittle failure. In this study, we theoretically explored effective solute elements for suppressing thermal embrittlement induced by S segregation to the GBs and experimentally verified the effect of a candidate solute. The GB segregation energies, interaction energy between S and solute, and embrittling potency energy were calculated from first-principles calculations for 57 Ni-based solid solutions. The results of these calculations are discussed based on the McLean and Rice–Wang models, which are used to identify effective elements to counteract the GB-decohesion by S segregation, such as B and W. For verification, electrodeposited Ni, Ni–B, and Ni–W alloys, containing the same S content, were prepared and their tensile behavior after annealing was examined. Although thermal embrittlement occurred in all electrodeposited samples, microstructure observation and fracture surface analysis indicated differences in grain size and S concentration at the GBs, resulting in embrittlement. These results revealed that W alloying in Ni-based electrodeposits has a high ability to suppress thermal embrittlement.

A key property for the design of new shape memory alloys is their working temperature range that depends on their transformation temperature T0. In previous works, T0 was predicted using a simple linear regression with respect to the energy difference between the parent and the martensitic phases, [Formula: see text]E[Formula: see text]. In this paper, we developed an accurate method to predict T0 based on machine learning assisted by the first-principles calculations. First-principles calculations were performed on 15 shape memory alloys; then, we proposed an artificial neural network method that used not only computed [Formula: see text]E[Formula: see text] but also bulk moduli as input variables to predict T0. The prediction error of T0 was improved to 49 K for the proposed artificial neural network compared with 188 K for simple linear regression.

Enthalpies of solutions and misfit strains for the Al–X (X = H, B, C, N, and O) binary alloys were determined by first-principles calculations to estimate the strengthening of solid solutions caused by interstitial atoms. The results indicate that interstitial solute atoms produced large misfit strains. Electrodeposited Al containing 0.12–1.32 at.% C was used to assess the validity of solid-solution strengthening by interstitial solute atoms. The role that interstitial carbon plays in strengthening electrodeposited Al is discussed.

Al was electrodeposited from a dimethylsulfone (DMSO 2 ) bath using a new pre-electrodeposition process to investigate the effect of sulfur and chlorine on the tensile ductility. Al electrodeposited from a DMSO 2 bath contains sulfur and chlorine, which are impurities are incorporated into the electrodeposits as sulfide and chloride, respectively. By pre-electrodeposition, the sulfur and chlorine contents of electrodeposited Al decreased from approximately 0.64 and 0.71 at% to 0.15 and 0.17 at%, respectively. This reduction in the sulfur and chlorine contents affects the microstructure, hardness, and ductility of the electrodeposits. The grain size increased from approximately 200 nm to 4 μm, and the microhardness decreased from 1.67 to 0.24 GPa. In tensile tests, electrodeposited Al before pre-electrodeposition exhibited failure even in the elastic regime, while electrodeposited Al after pre-electrodeposition exhibited good tensile ductility of approximately 30%.

To gain insight into accommodation mechanisms for local stress concentrations produced by grain boundary sliding (GBS), we systematically examined texture evolution within a superplastic magnesium alloy undergoing deformation at a relatively low deformation temperature (at which basal slip is known to be the preferred slip system in magnesium). Although we did observe an overall weakening of the initial basal texture during superplastic deformation, we also observed within the interior of the specimen a convergent evolution that depends on loading direction. We attribute this texture evolution within the bulk to the competing effects of (a) orientation divergence due to grain rotation accompanied by GBS and (b) convergent evolution due to slip, which acts primarily as an accommodation mechanism for GBS. In contrast, at the near-surface, we found the initial orientation to be preserved, indicating that slip accommodation is less important near the surface than within the bulk.

Effect of orientation on tensile ductility of electrodeposited bulk nanocrystalline Ni–W alloys was studied. Bulk nanocrystalline Ni–W alloys with different textures were prepared by electrodeposition, varying the amount of saccharin sodium and the bath temperature. An elongation of 0–13.4% was obtained in a tensile test. Although there was no relationship between tensile ductility and the grain size or W content, there was the relationship between tensile ductility and the orientation index for the (200) plane in the bulk nanocrystalline Ni–W alloys. In fact, no plastic deformability was observed when the index was below 1, while the tensile ductility increased with increasing orientation index above a value of 1. The cross-sectional TEM observations indicate the colony structure of electrodeposits varied in orientation. The results of this study point to that the colony structure of electrodeposits has an effect on the tensile ductility.