Resolved shear stress in elastically anisotropic polycrystals

Kneer’s analysis was used to calculate the fraction of a tensile stress applied along the rolling or transverse direction, which is resolved as a shear stress on the various slip systems of an α titanium crystallite as a function of crystallite orientation. The crystallite was assumed to be imbedded in a sheet for which the crystallite orientation distribution had been previously determined. The maximum resolved shear stress was found to increase in the order \(\left\{ {10\bar 10} \right\} - \left\langle {1\bar 210} \right\rangle \) , \(\left\{ {10\bar 11} \right\} - \left\langle {1\bar 210} \right\rangle \) , \(\left\{ {0001} \right\} - \left\langle {1\bar 210} \right\rangle \) in the ratio 1∶1.04∶1.17 for the material studied. This seems to be a direct consequence of single crystal anisotropy, and should be relatively insensitive to changes in crystallite orientation distribution. For a given slip system, the maximum resolved shear stress was found to be higher for a tensile stress applied along the rolling direction than for an equivalent stress along the transverse direction in the ratio 1.04∶1 for the material studied. This is a result of the type of preferred orientation present, which is typical for titanium sheet continuously rolled in the α phase.     

The precipitation of epsilon-carbide in twinned martensite

Tempering of martensite has been investigated by means of thin foil electron microscopy in a high carbon steel, a high nickel steel, and a silicon steel. ε carbide has been unambiguously identified in each steel. It was found that the carbide was precipitated with the Jack orientation relationship: $$\begin{gathered} \left( {0001} \right)_\varepsilon \parallel \left( {011} \right)_{\alpha '} \hfill \\ \left( {10\bar 10} \right)_\varepsilon \parallel \left( {2\bar 11} \right)_{\alpha '} \hfill \\ \end{gathered} $$ In the silicon steel the ε carbide precipitated in the form of needles which grew with a \(\left[ {01\bar 10} \right]_\varepsilon \) close to \(\left[ {21\bar 1} \right]_{\alpha '} \) . This growth direction minimizes the surface energy of the needles, yet allows growth in a direction of low mismatch.     

Anomalous Strain Rate Sensitivity of \{ 10\overline{1}2\} \langle 10\overline{1}\overline{1}\rangle Twinning in a Magnesium Alloy at High Temperature

Anomalous strain rate sensitivity of $ \{ 10\overline{1} 2\} $ { 10 1 ¯ 2 } $ \langle 10\overline{1}\overline{1}\rangle $ 〈 10 1 ¯ 1 ¯ 〉 twinning was observed in a Mg-Al-Mn magnesium alloy during extrusion around 723 K (450 °C). The density of $ \{ 10\overline{1}2\} $ { 10 1 ¯ 2 } $ \langle 10\overline{1}\overline{1}\rangle $ 〈 10 1 ¯ 1 ¯ 〉 twins decreases as the ram speed increases. At 10 mm min^?1, relatively high density twins are activated, but much fewer twins were observed at 30 mm min^?1; at 50 mm min^?1, twins were hardly seen. The negative strain rate sensitivity was ascribed to the interaction of $ \{ 10\overline{1}2\} $ { 10 1 ¯ 2 } $ \langle 10\overline{1}\overline{1}\rangle $ 〈 10 1 ¯ 1 ¯ 〉 twinning with defects.     

Study of \{ 11\bar{2} 1\} Twinning in α-Ti by EBSD and Laue Microdiffraction

Activity of the $ \{ 11\bar{2} 1\} \langle \bar{1} \bar{1} 26 \rangle $ extension twinning (T2) mode was analyzed in a commercial purity Ti sample after 2 pct tensile strain imposed by four-point bending. The sample had a moderate c-axis fiber texture parallel to the tensile axis. Compared with the many $ \{ 10\bar{1} 2\} \langle \bar{1} 011 \rangle $ extension (T1) twins that formed in 6 pct of the grains, T2 twins were identified in 0.25 pct of the grains by scanning electron microscopy (SEM) and electron backscattered diffraction (EBSD) maps. Most of the T2 twins exhibited irregular twin boundaries (TBs) on one side of the twin. High-resolution EBSD revealed both intermediate orientations at some matrix/twin interfaces and substantial lattice rotation within some T2 twins. Interactions between matrix 〈c + a〉 dislocations $ \frac{1}{3} \langle 1\bar{2} 13 \rangle $ and a $ \{ 11\bar{2} 1\} $ T2 twin were investigated by combining SEM/EBSD slip trace characterization and Laue microdiffraction peak streak analysis. 〈c + a〉 dislocations that originally glided on a pyramidal plane in the matrix were found on other planes in both the matrix and the twin, which was attributed to extensive cross-slip of the screw component, whose Burgers vector was parallel to the twinning plane. On the other hand, thickening of the twin could engulf some pile-up edge components in front of the TB. During this process, these 〈c + a〉 dislocations transmuted from a pyramidal plane $ (0\bar{1} 11) $ in the matrix to a prismatic plane $ (\bar{1} 010)_{\text{T}} $ in the twin lattice. Finally, possible mechanisms for the nucleation and growth of T2 twins will be discussed.     

Stress-strain behavior and the dislocation structure at small strains in iron deformed in tension,torsion and combined tension-torsion

Commercial iron specimens of 40 μm grain size were deformed to small strains in tension, torsion and combined tension-torsion at 300 K and the resulting dislocation structures, distributions and densities determined using transmission electron microscopy. Employing the von Mises yield criterion and the total plastic-work hypothesis, good agreement was obtained for the three testing conditions for: a) equivalent stress vs equivalent strain curves, b) the dislocation structure, distribution and densityρ as a function of and c) as a function ofρ ^1/2. Furthermore, upon comparing the vsρ ^1/2 curve for polycrystalline iron with theτ _RSS vsρ ^1/2 curve for single crystals of polyslip orientations, it appears that the theoretical value of 2.9 for the average Taylor factor for bcc metals is appropriate. Almost equally good correlations were obtained on the basis of maximum shear strain and therefore a positive decision between the von Mises andτ _max-γ _ρ ^max yield criteria could not be made. A single test in which the direction of straining in torsion was reversed yielded a density and distribution of dislocations (and a corresponding value of ) equivalent to that developed at a smaller strain in unidirectional straining. Formerly with the Department of Metallurgical Engineering and Materials Science, University of Kentucky, Lexington, Ky. Formerly with the Department of Metallurgical Engineering and Materials Science, University of Kentucky, Lexington, Ky.     

Nonmetallic inclusions in 13XΦA steel for reliable oil-line pipe

Nonmetallic inclusions in low-alloy 13XΦA steel mass-produced at OAO Severskii Trubnyi Zavod are studied. Corrosive nonmetallic inclusions of two types, identified by etching, are found to consist of two phases: MgO · Al₂O₃; and CaS with some quantity of Mn. The orientations identified are \(\{ 111\} _{CaS} \left\| {\{ 110\} _{MgO \cdot Al_2 O_3 } } \right.\) and \(\left\langle {1\bar 10} \right\rangle _{CaS} \left\| {\left\langle {1\bar 11} \right\rangle _{MgO \cdot Al_2 O_3 } } \right.\) .     

Dependence of the lattice parameter of {\gamma '} iron nitride,Fe4N1−x,on nitrogen content; Accuracy of the nitrogen absorption datairon nitride,Fe4N1−x,on nitrogen content; Accuracy of the nitrogen absorption data

Pure iron foils were converted into { \(\gamma ' - Fe_4 N_{1 - x} \) } foils of various compositions by means of nitriding in selected NH₃/H₂ gas mixtures at 803 and 843 K. The lattice parameter and the linear thermal expansion coefficient of { \(\gamma ' - Fe_4 N_{1 - x} \) } nitride and the surrounding gas atmosphere.     

The thermodynamic properties of liquid Fe−Si alloys

The thermodynamic properties of liquid Fe?Si alloys have been determined electrochemically by use of the following galvanic cells: $$\begin{gathered} Cr - Cr_2 O_3 (s)|ZrO_2 (CaO)|Fe - Si(l), SiO_2 (s) \hfill \\ Cr - Cr_2 O_3 (s)|ThO_2 (Y_2 O_3 )|Fe - Si(l), SiO_2 (s) \hfill \\ \end{gathered} $$ The free energy of formation of SiO₂ was measured and is ?139.0 and ?134.3 kcals per mole at 1500° and 1600°C, respectively. The activity coefficients of iron and silicon for the atom fraction of siliconN _Si<0.35 at 1600° and 1500°C can be represented by the quadratic formalism. $$\begin{gathered} \left. {\begin{array}{*{20}c} {log \gamma _{Fe} = - 2.12 N_{Si}^2 } \\ {log \gamma _{Si} = - 2.12 N_{Fe}^2 - 0.22} \\ \end{array} } \right\}1600^ \circ C (2912^ \circ F) \hfill \\ \left. {\begin{array}{*{20}c} {log \gamma _{Fe} = - 2.50 N_{Si}^2 } \\ {log \gamma _{Si} = - 2.50 N_{Fe}^2 - 0.13} \\ \end{array} } \right\}1500^ \circ C (2732^ \circ F) \hfill \\ \end{gathered} $$ The results indicate that an excess stability peak occurs at about the equimolar composition. Combining the heats of solution determined in this study with previous data indicates that the heats also follow the quadratic formalism. The partial molar heats, \(\bar L_{Si} \) and \(\bar L_{Fe} \) , are represented by $$\begin{gathered} \bar L_{Si} = - 31 N_{Fe}^2 - 4 kcals per mole \hfill \\ \bar L_{Fe} = - 31 N_{Si}^2 kcals per mole \hfill \\ \end{gathered} $$ ForN _Si less than 0.35 and by $$\begin{gathered} \bar L_{Si} = - 22 N_{Fe}^2 \hfill \\ \bar L_{Fe} = - 22 N_{Fe}^2 - 7.0 \hfill \\ \end{gathered} $$ forN _Fe less than 0.35. There is an inflection point in the transition region similar to an excess stability peak for the excess free energies. At 1600°C the ThO₂(Y₂O₃) electrolyte exhibited insignificant electronic conductivity at oxygen partial pressures as low as that in equilibrium with Si?SiO₂ (2×10^?16 atm).     

Effect of Environment on Fatigue Crack Wake Dislocation Structure in Al-Cu-Mg

Fatigue-induced dislocation structure was imaged at the crack surface using transmission electron microscopy (TEM) of focused ion beam (FIB)-prepared cross sections of naturally aged Al-4Cu-1.4Mg stressed at a constant stress intensity range (7?MPa??m) concurrent with either ultralow (~10^?8?Pa?s) or high-purity (50?Pa?s) water vapor exposure at 296?K (23?°C). A 200-to-600-nm-thick recovered-dislocation cell structure formed adjacent to the crack surface from planar slip bands in the plastic zone with the thickness of the cell structure and slip bands decreasing with increasing water vapor exposure. This result suggested lowered plastic strain accumulation in the moist environment relative to the vacuum. The previously reported fatigue crack surface crystallography is explained by the underlying dislocation substructure. For a vacuum, $ \left\{ { 1 1 1} \right\} $ facets dominate the crack path from localized slip band cracking without resolvable dislocation cells, but cell formation causes some off- $ \left\{ { 1 1 1} \right\} $ features. With water vapor present, the high level of hydrogen trapped within the developed dislocation structure could promote decohesion manifest as either low-index $ \left\{ { 100} \right\} $ or $ \left\{ { 1 10} \right\} $ facets, as well as high-index cracking through the fatigue-formed subgrain structure. These features and damage scenario provide a physical basis for modeling discontinuous environmental fatigue crack growth governed by both cyclic strain range and maximum tensile stress.     

Evolution of Strain and Microstructure During Creep of Wrought AE42 and ZE10 Magnesium Alloys

Wrought magnesium alloys have been extensively used in the aerospace, electronics and automotive industries, where component weight is of concern and ambient temperatures remain below 100 °C. Undesirable creep relaxation of the wrought alloys above this temperature has been generally attributed to grain boundary sliding and plastic deformation leading to intergranular failure. The objective of this study was to investigate the compressive creep performance and microstructure of two wrought magnesium alloys (AE42 and ZE10) developed for high temperature applications. The total deformation of the AE42 and ZE10 alloys was 2.4 and 0.2 %, respectively, after 24 h creep test at 175 °C and 50 MPa. The poor creep performance of the AE42 alloy was explained via neutron diffraction studies which revealed that the elastic compressive response of $ (10\bar{1}0),\;(10\bar{1}1)\;{\text{and}}\;(2\bar{1}\bar{1}0) $ planes was significantly more anisotropic in the AE42 than in the ZE10 alloy. Further, microstructural analysis revealed ~10 % increase in grain size due to creep, with additional $ (10\bar{1}2) $ and $ (11\bar{2}1) $ twinning in the AE42 alloy. Precipitation of β-Mg₁₇Al₁₂ phase in the AE42 alloy possibly contributed to grain boundary sliding and high plastic strain during creep testing.     

Inhomogeneity of plastic flow in constrained deformation

Crystals of copper, Cu+6 wt pct Al, and Ag+4 wt pct Sn were compressed along [111] with flow restricted to [ \(\bar 1\bar 12\) ]. After deformation, four differently oriented regions were observed. Their origin is explained by the instability of the (111)[ \(\bar 1\bar 12\) ] orientation which can rotate to either (112) \(\bar 1\bar 11\) or (110)[001] during the imposed shape change. The direction of rotation is determined by which of two initially equally favored pairs of slip systems operate. Surface friction produces shear stresses which favor one pair over the other (depending on the sign of the shear stress) and thus one of the final orientations. Since the sign of the frictional stress varies systematically with position in the deforming crystal, a systematic variation of orientation results. Another orientation (001)[110] has also been observed to behave similarly. During rolling, the frictional forces drawing the crystal into the roll gap are also expected to lead to the division of the crystal into two misoriented regions. The predictions are generalized to include bcc metals of ( \(\bar 1\bar 12\) )[111] and (110)[001] orientations. Previously reported observations of rolled crystals of FeNi₃, Fe-3.5 pct Si, and Fe-2 pct Al are in accord with the present analysis.     

Observations of the Atomic Structure of Tensile and Compressive Twin Boundaries and Twin–Twin Interactions in Zirconium

The boundary structures of twins in the hexagonal close-packed metal zirconium were studied. High-resolution transmission electron microscopy was used to characterize the boundary structure of \(\{10\bar{1}2\}\) (T1), \(\{\bar{1}\bar{1}21\}\) (T2), and \(\{\bar{1}\bar{1}22\}\) (C1) twins on the atomic level. Basal–prismatic (B–P) plane faceting is observed along the T1 twin boundaries, matching previous observations of T1 twins in magnesium. C1 twins are observed to form basal–pyramidal (B–Py) facets along otherwise perfect twin planes. T2 twins exhibit faceting that aligns prism planes with second-order pyramidal planes across the boundary (P–Py facets). As a function of the crystallography, T2 twins appear less likely to accommodate large deviations from perfect twin planes by P–Py faceting alone, and may rely on small dislocation-accommodated facets to achieve arbitrary boundary planes. The structure of these boundaries, specifically the modes by which faceting is permitted, has a direct impact on boundary mobility. In addition, the boundary structure of two C1 twins during a twin–twin interaction event is observed, and is compared to previous observations of tensile twin–twin interactions in magnesium.     

Thermodynamic properties of the Zn−Pb−In ternary system in dilute liquid zinc solutions

Electromotive force measurements were conducted on ternary Zn?Pb?In solutions having zinc concentrationsX _Zn=0.03, 0.05, 0.07, and 0.1. Special attention was paid to the effect of the addition of indium and lead on the Ln γ_Zn value at 714°, 757°, and 805°K. These data served to determine the interaction parameters ∈ _Zn ^In and ∈ _Pb ^Zn from the \((ln\gamma _{Zn} )_{X_{Zn} } \to _0 vs X_{Pb} \) plots over the indicated ranges of temperatures. The end points in ln γ_Zn vs X_Pb and \((ln\gamma _{Zn} )_{X_{Zn} } \to _0 vs X_{Pb} \) plots were taken from previous measurements on the Zn?In and Zn?Pb systems. The values of ln γ_Zn and \((ln\gamma _{Zn} )_{X_{Zn} } \to _0 \) in Zn?Pb?In dilute solutions were carried out by means of Krupkowski’s formulae. The influence of the Zn?Pb system in Zn?Pb-Me ternary solutions with a preponderant content of lead was analyzed whenMe=Bi, Cd, Sn, and Sb.     

Atomic Structures of [0\bar{1}10] Symmetric Tilt Grain Boundaries in Hexagonal Close-Packed (hcp) Crystals

Molecular dynamics simulation and interface defect theory are used to determine the relaxed equilibrium atomic structures of symmetric tilt grain boundaries (STGBs) in hexagonal close-packed (hcp) crystals with a $ [0\bar{1}10] $ tilt axis. STGBs of all possible rotation angles ?? from 0?deg to 90?deg are found to have an ordered atomic structure. They correspond either to a coherent, defect-free boundary or to a tilt wall containing an array of distinct and discrete intrinsic grain boundary dislocations (GBDs). The STGBs adopt one of six base structures, $ P_{B}^{(i)} $ , i?=?1, ??, 6, and the Burgers vector of the GBDs is related to the interplanar spacing of the base structure on which it lies. The base structures correspond to the basal plane (???=?0?deg, $ P_{B}^{(1)} $ ); one of four minimum-energy, coherent boundaries, $ (\bar{2}111),\;(\bar{2}112),\;(\bar{2}114) $ , and $ (\bar{2}116)\;\left( {P_{B}^{(2)} - P_{B}^{(5)} } \right) $ ; and the $ \left( {11\bar{2}0} \right) $ plane (???=?90?deg, $ P_{B}^{(6)} $ ). Based on these features, STGBs can be classified into one of six possible structural sets, wherein STGBs belonging to the same set i contain the same base boundary structure $ P_{B}^{(i)} $ and an array of GBDs with the same Burgers vector $ b_{\text{GB}}^{(i)} $ , which vary only in spacing and sign with ??. This classification is shown to apply to both Mg and Ti, two metals with different c/a ratios and employing different interatomic potentials in simulation. We use a simple model to forecast the misorientation range of each set for hcp crystals of general c/a ratio, the predictions of which are shown to agree well with the molecular dynamics (MD) simulations for Mg and Ti.     

Fabrication and Characterization of Naturally Selected Epitaxial Fe-{111} Y2Ti2O7 Mesoscopic Interfaces: Some Potential Implications to Nano-Oxide Dispersion-Strengthened Steels

The smallest features of ≈2 to 3 nm in nanostructured ferritic alloys (NFA), a variant of oxide dispersion-strengthened steels, include the Y₂Ti₂O₇ complex oxide cubic pyrochlore phase. The interface between the bcc Fe-Cr ferrite matrix and the fcc nanometer-scale Y₂Ti₂O₇ plays a critical role in the stability, strength, and damage tolerance of NFA. To complement other characterization studies of the actual nanofeatures (NF) themselves, mesoscopic interfaces were created by electron beam deposition of a thin Fe layer on a 5 deg miscut {111} Y₂Ti₂O₇ bulk single crystal surface. While the mesoscopic interfaces may differ from those of the embedded NF, the former facilitate characterization of controlled interfaces, such as interactions with point defects and helium. The Fe-Y₂Ti₂O₇ interfaces were studied using scanning electron microscopy, including electron backscatter diffraction, atomic force microscopy, X-ray diffraction, and transmission electron microscopy (TEM). The polycrystalline Fe layer has two general orientation relationships (OR) that are close to (a) the Nishiyama–Wasserman (NW) OR $ \left\{ {110} \right\}_{\text{Fe}} ||\left\{ {111} \right\}_{{{\text{Y}}_{2} {\text{Ti}}_{2} {\text{O}}_{7} }} $ 110 Fe | | 111 Y 2 Ti 2 O 7 and $ \left\langle {100} \right\rangle_{\text{Fe}} ||\left\langle {110} \right\rangle_{{{\text{Y}}_{2} {\text{Ti}}_{2} {\text{O}}_{7} }} $ 100 Fe | | 110 Y 2 Ti 2 O 7 and (b) $ \left\{ {100} \right\}_{\text{Fe}} ||\left\{ {111} \right\}_{{{\text{Y}}_{2} {\text{Ti}}_{2} {\text{O}}_{7} }} $ 100 Fe | | 111 Y 2 Ti 2 O 7 and $ \left\langle {100} \right\rangle_{\text{Fe}} ||\left\langle {110} \right\rangle_{{{\text{Y}}_{2} {\text{Ti}}_{2} {\text{O}}_{7} }} $ 100 Fe | | 110 Y 2 Ti 2 O 7 . High-resolution TEM shows that the NW interface is near-atomically flat, while the {100}_Fe grains are an artifact associated with a thin oxide layer. However, the fact that there is still a Fe-Y₂Ti₂O₇ OR is significant. No OR is observed in the presence of a thicker oxide layer.     

Effect of Tungsten on Primary Creep Deformation and Minimum Creep Rate of Reduced Activation Ferritic-Martensitic Steel

Effect of tungsten on transient creep deformation and minimum creep rate of reduced activation ferritic-martensitic (RAFM) steel has been assessed. Tungsten content in the 9Cr-RAFM steel has been varied between 1 and 2 wt pct, and creep tests were carried out over the stress range of 180 and 260 MPa at 823 K (550 °C). The tempered martensitic steel exhibited primary creep followed by tertiary stage of creep deformation with a minimum in creep deformation rate. The primary creep behavior has been assessed based on the Garofalo relationship, \( \varepsilon = \varepsilon_{\text{o}} + \varepsilon_{\text{T}} [1-\exp (-r^{\prime} \cdot t)] + \dot{\varepsilon }_{\text{m}} \cdot t \) , considering minimum creep rate \( \dot{\varepsilon }_{\text{m}} \) instead of steady-state creep rate \( \dot{\varepsilon }_{\text{s}} \) . The relationships between (i) rate of exhaustion of transient creep r′ with minimum creep rate, (ii) rate of exhaustion of transient creep r′ with time to reach minimum creep rate, and (iii) initial creep rate \( \dot{\varepsilon }_{\text{i}} \) with minimum creep rate revealed that the first-order reaction-rate theory has prevailed throughout the transient region of the RAFM steel having different tungsten contents. The rate of exhaustion of transient creep r′ and minimum creep rate \( \dot{\varepsilon }_{\text{m}} \) decreased, whereas the transient strain ? _T increased with increase in tungsten content. A master transient creep curve of the steels has been developed considering the variation of \( \frac{{\left( {\varepsilon - \varepsilon_{\text{o}} } \right)}}{{\varepsilon_{\text{T}} }} \) with \( \frac{{\dot{\varepsilon }_{\text{m}} \cdot t}}{{\varepsilon_{\text{T}} }} \) . The effect of tungsten on the variation of minimum creep rate with applied stress has been rationalized by invoking the back-stress concept.     

Crystallographic Reconstruction Study of the Effects of Finish Rolling Temperature on the Variant Selection During Bainite Transformation in C-Mn High-Strength Steels

The effect of finish rolling temperature on the austenite-(γ) to-bainite (α) phase transformation is quantitatively investigated in high-strength C-Mn steels using an alternative crystallographic γ reconstruction procedure, which can be directly applied to experimental electron backscatter diffraction mappings. In particular, the current study aims to clarify the respective contributions of the γ conditioning during the hot rolling and the variant selection during the phase transformation to the inherited texture. The results confirm that the sample finish rolled at the lowest temperature [1102 K (829 °C)] exhibits the sharpest transformation texture. It is shown that this sharp texture is exclusively due to a strong variant selection from parent brass {110} \( \left\langle {1\bar{1}2} \right\rangle \) , S {213} \( \left\langle {\bar{3}\bar{6}4} \right\rangle \) and Goss {110}〈001〉 grains, whereas the variant selection from the copper {112} \( \left\langle {\bar{1}\bar{1}1} \right\rangle \) grains is insensitive to the finish rolling temperature. In addition, a statistical variant selection analysis proves that the habit planes of the selected variants do not systematically correspond to the predicted active γ slip planes using the Taylor model. In contrast, a correlation between the Bain group to which the selected variants belong and the finish rolling temperature is clearly revealed, regardless of the parent orientation. These results are discussed in terms of polygranular accommodation mechanisms, especially in view of the observed development in the hot-rolled samples of high-angle grain boundaries with misorientation axes between 〈111〉γ and 〈110〉γ.