Quantitative Analysis on Light Elements Solution Strengthening in Pure Titanium Sintered Materials by Labusch Model Using Experimental Data
2019 Volume 60 Issue 2 Pages 263-268
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2019 Volume 60 Issue 2 Pages 263-268
Solid solution strengthening effect by oxygen (O) and nitrogen (N) atoms of α-titanium (Ti) materials was quantitatively evaluated using Labusch model by consideration of the experimental data. When using Labusch model to predict solid solution strengthening improvement, an application of the isotropic strains by solute elements is generally assumed to estimate Fm value. It is, however, difficult to exactly calculate Fm value for α-Ti materials with O and N solute atoms because the anisotropic strains are induced in α-Ti crystal with hcp structure by these elements. In this study, Fm value was experimentally derived from the relationship between 0.2% yield stress and solute elements (O and N atoms) content of powder metallurgy Ti materials. As a result, the strengthening improvement was proportional to c2/3/Sf (c: soluted atom content, Sf: Schmid factor), and its factor of proportionality of Ti–O and Ti–N materials was 4.17 × 103 and 3.29 × 103, respectively. According to this analysis, it was clarified that Fm value of Ti–O and Ti–N materials was 6.22 × 10−10 and 5.21 × 10−10, respectively, and then the estimated strengthening improvement by using these values was significantly agreed with the experimental results of PM Ti materials with O and N solution atoms.
This Paper was Originally Published in Japanese in J. Jpn. Soc. Powder Powder Metallurgy 65 (2018) 407–413.
Titanium (Ti) has excellent properties such as high specific strength, excellent corrosion resistance and high biocompatibility due to the osseointegration.1,2) These performances make it possible to apply Ti materials to the medical devices and transport instruments.3–7) From a viewpoint of the strength improvement, there is a serious problem of the conventional Ti–6 Al–4 V alloy (ASTM B348 Gr5) because it contains vanadium element which is one of toxic and expensive rare metals.8) Regarding this issue, recently the ubiquitous element such as oxygen, nitrogen, carbon, silicon, iron etc., are employed instead of rare metals used as the alloying elements to improve the mechanical strength of Ti materials. For instance, there are Ti materials strengthened by TiC particles produced via a reaction between additional carbon particles and titanium matrix,9,10) grains refinement using silicon addition,11,12) and solid solution using oxygen or nitrogen atoms.13–18) In these materials, Orowan mechanism and Hall-Petch relationship are often used to quantitatively estimate the effect of ubiquitous element addition on the increment of their yield strength.19–21) Furthermore, in regard to estimation of solid solution strengthening in metals, Cottrell proposed the model regarding the pinning effect on dislocations movement by solute atoms,22) and Fleischer and Friedel explained the role of obstacles touched by dislocations under the stress applied.23,24) However, no consideration on the interaction between the solute atoms was taken in these models. Mott, Nabarro and others established many theories which overcome this problem,25) and many researchers previously employed these models to quantitatively understand and calculate the solid solution strengthening effect. Labusch also established the similar model regarding the solid solution strengthening behavior.26) In this model, the strengthening increment was predicted by using the premises that solute atoms apply isotropic strain. Therefore, it is difficult to apply Labusch model on α-Ti material having an anisotropic strain due to its hcp structure.27) At this moment, there is no report to show a good agreement between experimental data and calculated results by using above-mentioned models regarding the interstitial solid solution strengthening of α-Ti materials.
This study discussed the effect of the interstitial solid solution elements such as oxygen and nitrogen on the microstructures and mechanical properties of powder metallurgy (PM) Ti materials with oxygen or nitrogen atoms. In particular, the parameters used in Labusch model was obtained from the experimental data, and the solid solution strengthening increment of PM Ti–O and Ti–N materials was quantitatively calculated. As a result, a good agreement between experimental data and calculated results was obtained.
Commercial pure Ti powder (TC-450, TOHO TECHNICAL SERVICE Co., Ltd) and TiO2 particles (KOJUNDO CHEMICAl LABORATORY Co., Ltd) were used as starting materials. Pure Ti powder prepared by the hydride and dehydride (HDH) process, having a mean particle size of 27.8 µm, shows a typical irregular morphology. TiO2 particles with around 3.6 µm mean particle size were employed as oxygen providers to pure Ti materials. In this experiment, each elemental mixture (200 g) of pure Ti and TiO2 powder such as Ti–0.5 mass% TiO2, Ti–1.0 mass% TiO2, Ti–1.5 mass% TiO2 and Ti–2.0 mass% TiO2, was put into the jar, and uniformly mixed by rock milling process (60 Hz, 3.6 ks).
The powder mixture was consolidated using a spark plasma sintering (SPS, SPS-1030, SPS Syntex Inc.). The SPS conditions at 1000 and 1100°C for 1.8 ks in vacuum (6 Pa) were selected, and 30 MPa pressure was applied to the powder in the carbon die. The diameter of each SPSed columned billet was 42 mm.
The homogenization heat treatment at 1000°C for 86.4 ks was applied to the latter billet by using the vacuum furnace (FT-1200R-120, FULL-TECH FURNACE Co., Ltd). The SPSed billets were extruded by a hydraulic direct press machine (SHP-200-450, Shibayama kikai Co., Ltd), where the extrusion speed was 3 mm s−1, the extrusion die diameter was 7 mm and the extrusion ratio was 36. Before hot extrusion, the billet was pre-heated at 1000 and 1100°C for 300 s in Ar gas atmosphere using the image furnace, and immediately supplied to the extrusion process. Each extruded rod was named as Ti1000-O and Ti1100HT-O, respectively as shown in Fig. 1.
Flowchart of specimen preparation of Ti1000-O and Ti1100HT-O materials by powder metallurgy route.
Oxygen (O) and nitrogen (N) contents of the extruded rods were measured using a highly accurate O/N/H analyzer (EMGA-930, HORIBA, Ltd.). The microstructures of final products were characterized using X-ray diffraction (XRD, XRD-6100, SHIMADZU Corp.) and electron back-scatter diffraction (EBSD) that attached to a field emission scanning electron microscopy (FE-SEM, JSM-6500F, JEOL Ltd.). EBSD samples were polished by electro-chemical etching using 95 vol% CH3COOH + 5 vol% HClO4 solution with 20 V for 60∼90 s. The tensile properties of these samples were evaluated at room temperature under a nominal strain rate of 5.0 × 10−4/s using a mechanical tensting machine (Autograph AG-X 50 kN, SHIMADZU CORPORATION). At least two tensile specimens with 15 mm in gauge length and 3 mm in diameter were machined from each extruded rod.
In order to investigate the solid solution strengthening effect by oxygen and nitrogen elements on the mechanical properties of PM titanium materials, each content of Ti1000-O and Ti1100HT-O samples was analyzed. Oxygen and nitrogen contents of raw pure Ti powder, Ti1000-O and Ti1100HT-O materials were shown in Table 1, where the calculated oxygen content from TiO2 addition was also shown. Nitrogen content of each material was 0.07 at%, that is, there was no significant difference in all samples. On the other hand, the oxygen content of each material gradually increased with increase in the TiO2 addition, and agreed well with the calculated value as shown in Table 1. It means that the oxygen content of the extruded materials can be quantitatively controlled by TiO2 particle addition. Ti material with 2 mass% TiO2 addition (Ti1100HT-2.76O) has an extremely high oxygen content of 2.76 at% compared with ASTM/ASME Grade 1 (0.54 at%) and Grade 4 (1.19 at%) pure Ti.
XRD analysis on Ti1000-O and Ti1100HT-O was conducted in order to evaluate the solid solution behavior in α-Ti crystal with a hexagonal close packing (hcp) structure. It is well known that α-Ti crystal lattice is expanded in c-axis direction by the interstitial solid solution elements such as oxygen and nitrogen atoms.27) Figure 2 indicates XRD analysis results of Ti1100HT-O with various oxygen contents. In this study, each XRD profile shows no peak shift at 74.04° corresponding to (200) cylindrical plane which is not affected by the lattice expansion behavior in c-axis direction. On the other hand, α-Ti peaks at 70.66°, 76.22° and 77.55° related to basal and prismatic planes obviously shifted to a lower angle due to the interstitial solid-solution phenomenon. By using the XRD peak shifts shown in Fig. 2 and that of Ti1000-O, the dependence of the lattice parameters of α-Ti hcp structure in a-axis and c-axis directions on the oxygen content were calculated. As shown in Fig. 3, the lattice constant in c-axis direction (b) proportionally increased with increase in oxygen contents while that in a-axis (a) revealed no change in increasing the oxygen content. Previous studies reported that the TiO2 particles were thermally decomposed during sintering with Ti powder.13,14,28) In this study, too, oxygen atoms should be in solid solution, because we applied higher temperature and longer time in the heat treatment to the SPSed billets. Therefore, the additive TiO2 particles were completely decomposed and all oxygen atoms originated from TiO2 particles were soluted into α-Ti crystals of Ti1100HT-O and Ti1000-O materials. It resulted in the lattice expansion in c-axis direction.
XRD profiles of Ti1100HT-O materials with different oxygen contents.
Dependence of lattice parameters in (a) a-axis and (b) c-axis on oxygen content of Ti1000-O and Ti1100HT-O materials.
IPF maps and inverse pole figures of Ti1100HT-O materials with oxygen content of 0.60 at%, 1.68 at% and 2.76 at% are shown in Fig. 4. The matrix of all samples consisted of equiaxial α-Ti grains, not acicular grains. The cooling rate after extrusion was about 6°C/s, and was enough to prevent the formation of martensite phases due to the transformation from β to α-Ti,29) and resulted in the formation of equiaxial α-Ti grains in the extruded materials. All specimens showed strong (10-10) cylindrical textures along the extrusion direction, that is, these texture formation was not related to the oxygen content of Ti1100HT-O materials. Table 2 shows the mean α-Ti grain size and Schmid factor of PM Ti materials prepared in this study. Ti1000-O materials had finer grains compared to Ti1100HT-O materials. This result is interpreted that the higher temperature SPS and heat treatment β phase which were applied to Ti1100HT-O materials resulted in the significant grain coarsening. In all specimens, the oxygen content increment caused α-Ti grains refinement because of the solute drag effect by agglomeration of oxygen soluted atoms at α-Ti grain boundaries.30–32) For example, the grain size decreased from 11.6 µm to 8.2 µm in case of Ti1000-O and from 26.1 µm to 11.3 µm in Ti1100HT-O materials. It is obvious that a small amount of oxygen solution was effective to accelerate the grains refinement. When more than about 1 at% oxygen was soluted in the materials, however, the grain size was constant and never drastically changed because so much oxygen atoms existed at the boundaries and then the above mentioned solute drag effect was saturated. On the other hand, Schmid factor was 0.443∼0.459 and 0.436∼0.455 in Ti1000-O and Ti1100HT-O, respectively. In both materials, this factor was independent of the oxygen content. In general, Schmid factor is affected by the crystal structure and plastic working conditions.33) As shown in Fig. 3(b), however, the oxygen solution in α-Ti grains of these specimens caused the lattice constant change from 4.680 Å to 4.695 Å in c-axis direction, that is, the expansion ratio was only 0.3%. Therefore, the lattice expansion by oxygen solution had very few effects on Schmid factor changes of PM extruded Ti materials, and the extrusion process strongly influenced Schmid factor of each specimen. In general, it is reported that crystal grains induced with plastic strain has multi-color or different shades.34–36) However, IPF maps of extruded Ti1100HT materials with various oxygen contents showed the grains with unicolor. It means that the introduced strains in the matrix during hot extrusion was relieved due to dynamic recrystallization.
IPF maps of Ti1100HT-O materials with (a) 0.60 at%, (b) 1.68 at% and (c) 2.76 at% oxygen.
Figure 5 indicates tensile properties of Ti1000-O and Ti1100HT-O materials. 0.2% yield stress (0.2% YS) and ultimate tensile stress (UTS) increased with increase in the oxygen addition. The 0.2% YS and UTS were 445 and 602 MPa of Ti1100HT-0.60O, 765 and 903 MPa of Ti1100HT-1.68O and 1007 and 1094 MPa of Ti1100HT-2.76O, respectively. On the other hand, the elongation to failure was more than 20% when oxygen content was less than 2.34 at%. while it was 7.5% in case of oxygen content over 2.76 at%. The principal slip plane of hcp metals strongly depends on c/a ratio, where a basal plane slipping is dominant in long hcp structure (c/a > 1.61) and a prismatic plane slipping occurs in short hcp one (c/a < 1.61).37) In addition, it is also reported that α-Ti materials with oxygen solid solution show poor ductility because the principal slip system changes from a prismatic plane to basal plane slipping due to the lattice expansion in c-axis direction by oxygen atoms solution. The strengthening contribution factors on 0.2% YS of Ti1100HT-O materials with different oxygen contents were shown in Fig. 6. As mentioned above, since TiO2 particles were completely dissolved and there was no residual strain in EBSD analysis results, Therefore, it was deduced that there are neither effects of TiO2 particles dispersion nor effects of residual strain on 0.2% YS increment. The major strengthening factors in Ti–O materials were both the grain refinement and the oxygen solid solution. Therefore, the oxygen solid solution strengthening factor could be considered quantitatively after modifying the grain refinement effect by Hall-Petch relationship. Hall-Petch constant of 15.7 MPa/mm2 was used.20) 0.2% YS increment by grain refinement from Ti1100HT-0.60O to Ti1100HT-1.68O and Ti1100HT-2.76O was 50 MPa and 37 MPa, respectively. These values were significantly small compared to oxygen solution strengthening of 269 MPa (Ti1100HT-1.68O) and 525 MPa (Ti1100HT-O-2.76O). It was concluded that the solid solution strengthening by oxygen atoms in α-Ti was the main factor to improve the mechanical strength of Ti–O materials.
Tensile properties dependence on oxygen content of Ti1000-O (closed) and Ti1100HT-O materials (opened).
Strengthening factors contribution to yield stress of Ti1100HT-O materials.
In order to theoretically study the oxygen solution strengthening behavior of PM Ti–O materials, the quantitative evaluation of its strengthening effect by using Labusch model26) dealing with the interaction between edge dislocations and solid solution atoms. In this model, the elastic interaction energy E is given by eq. (1), where Δ is a volume of solid solution atoms and the stress field σ in solute atom is considered to be a constant on the basis of hypothesis that distance between dislocation and solid solute atom is negligibly small compared with radius of solid solute atoms.
| \begin{equation} E = -\varDelta\sigma_{ij}\varepsilon_{ij}. \end{equation} | (1) |
When the solution atoms give isotropic stress, εij is equal to ε δij. δij corresponds to Kronecker’s delta,38) and then δ11, δ22 and δ33 should be 1 and other components are 0. Therefore, eq. (1) could be expressed as the below eq. (2);
| \begin{align} E &= -\varDelta (\sigma_{11}\varepsilon_{11} + \sigma_{22}\varepsilon_{22} + \sigma_{33}\varepsilon_{33}) \\ &= -\varDelta (\sigma_{11} + \sigma_{22} + \sigma_{33})\varepsilon. \end{align} | (2) |
| \begin{equation} E = -\varDelta Gb\frac{(1 + \nu)}{3\pi(1 - \nu)}\frac{y}{(x^{2} + y^{2})} \end{equation} | (3) |
| \begin{equation} F = \frac{\partial E}{\partial x} = \varDelta Gb\frac{(1 + \nu)}{3\pi(1 - \nu)}\frac{2xy}{(x^{2} + y^{2})^{2}}. \end{equation} | (4) |
| \begin{equation} \varDelta\sigma_{YS} = \frac{\tau}{S_{F}} = \frac{c^{2/3}}{S_{F}}\left(\frac{F_{m}{}^{4}w}{4Gb^{9}}\right)^{1/3} \end{equation} | (5) |
Relationship between increment of yield stress by (a) oxygen and (b) nitrogen solid solution strengthening effects and material’s factor in Labusch model.
It is also reported that nitrogen atoms have a solid solution strengthening effect in α-Ti materials in similar to oxygen atoms.27) In Fig. 7(b), 0.2% YS increment was plotted against the factor, c2/3/SF in Ti–N materials. We employed the experimental data in previous study.16) It is obvious that 0.2% YS increment again increased in proportion to the material’s factor, c2/3/SF (R2 = 0.943). It was derived that the constant, (Fm4w/4Gb9)1/3 of Ti–N materials is 3.29 × 103 and the parameter, Fm is 5.21 × 10−10.
In order to evaluate the adequacy of the above Fm values of Ti–O and Ti–N materials, the calculated 0.2%YS increment of three kinds of Ti–O–N materials (Ti1100HT-0.97O-0.78N, Ti1100HT-1.25O-0.53N, Ti1100HT-1.54O-0.30N) by using Fm value was compared with the experimental value. The results are summarized in Table 3. Each Ti–O–N material was fabricated by using the pre-mixed Ti–TiO2–TiN powders. Experimental data of 0.2% YS was 800 MPa for Ti1100HT-0.97O-0.78N, 789 MPa for Ti1100HT-1.25O-0.53N and 795 MPa for Ti1100HT-1.54O-0.30N, respectively. Each calculated 0.2%YS was modified by excluding the grains refinement strengthening effect. In Labusch model, the total increment of 0.2%YS of Ti–O–N materials was a sum of the increment by each solution atom because the interaction between a solid solute atom and dislocation was subscribed as an integrated value. As shown in Table 3, the calculated values of Ti–O–N materials by using Labusch model showed a good agreement with the experimental data. It is concluded that the solid solution strengthening of Ti–O and Ti–N materials can be successfully and quantitatively estimated by Labusch model with a suitable Fm value obtained by the experimental method proposed in this study.
It is difficult to calculate 0.2% YS increment by oxygen or nitrogen solid solution theoretically by Labusch model, since solid solution of oxygen applies anisotropic strain on α-Ti materials having a hcp structure. In this study, thereby, 0.2% YS increment by oxygen or nitrogen solid solution in the α-Ti materials was successfully calculated by the following procedures. At first, material’s factor, c2/3/SF was plotted against 0.2% YS increment by assuming the parameter, (Fm4w/4Gb9)1/3 is a constant. It was shown that linear relationship is obtainable between the 0.2% YS increment and the material’s parameter both in Ti–O and Ti–N materials. Then, the proportion coefficient and hence the maximum force (Fm) between the edge dislocation and solid solution atom was determined from such a linear relationship. Fm was 6.22 × 10−10 for Ti–O materials and 5.21 × 10−10 for Ti–N materials. Finally, the present model was applied to Ti–O–N materials. It was concluded that the calculated 0.2% YS increment shows a good agreement with the experimental results.
This work was partially supported by the Japan Science and Technology Agency (JST) under Industry–Academia Collaborative R&D Program “Heterogeneous Structure Control: Towards Innovative Development of Metallic Structural Materials”.
