About the Alloy Strength - Ti Property Model

The Alloy Strength - Ti Property Model, available with the Property Model Calculator and the Titanium Model Library, calculates the strength and hardness for Ti-base alloys.

To run calculations with the Titanium Models requires a valid maintenance license plus a license for the TCTI (version 6 and newer) database. For some Property Models, additional recommendations for the database version to use is indicated in its description. Also see our website to learn more about the Titanium Model Library.

The various forms of alpha martensite HCP (alpha, alpha, or alpha double prime) are not explicitly distinguished and are collectively described by the phase HCP_A3 in terms of thermodynamic properties.

The Alloy Strength - Ti model is built from individual models for four strength contributions. The effect of impurities on the strength of Ti-base alloys is very strong [1981Con; 1998Ouc] and this model has therefore been equipped with a functionality to select base grades, according to the ASTM definitions of purity, for cases where the exact impurity content is not known.

Intrinsic Strength

The intrinsic strength is calculated as the combination of the strength for the pure elements in the system, weighted by the mole fraction of each element. In the Alloy Strength - Ti model you can choose the Titanium base grade, which are base grades of “commercially pure” titanium and represent the impurity elements allowed in each grade. The compositions defined for the available grades are as listed:

  • Iodide Titanium: Pure Ti with no impurity elements (the default)
  • Grade 1 (35A): Ti-0.2Fe-0.18O-0.08C-0.03N-0.015H (wt%)
  • Grade 2 (50A): Ti-0.3Fe-0.25O-0.08C-0.03N-0.015H (wt%)
  • Grade 3 (65A): Ti-0.3Fe-0.35O-0.08C-0.05N-0.015H (wt%)
  • Grade 4 (75A): Ti-0.5Fe-0.4O-0.08C-0.05N-0.015H (wt%)

The intrinsic strength for the different grades is given as the linear combination of the strength for the elements in the system plus the calculated strengthening contribution from solid solution of the impurity elements.

Grain Boundary Strengthening

For the grain boundary strengthening, after selecting the Grain boundary strengthening checkbox you can include an effect of Grain size on the strength/hardness. This contribution is given by the Hall-Petch equation [2016Cor]. When setting up the model, you can either specify a User-defined Hall-Petch coefficient or otherwise it is calculated by default.

For additional background information, see About the Yield Strength Property Model.

Solid Solution Strengthening

The solid solution strengthening contribution is evaluated as per the model by Walbrühl et al. [2017Wal], where the parameters for each Ti binary system are optimized against a compiled collection of experimental studies on titanium. There is no specific input required for solid solution strengthening when setting up the model. This calculation uses the composition of the alpha and/or beta phase of the system, which is automatically calculated in the model.

For additional background information, see About the Yield Strength Property Model.

Precipitation Strengthening

After selecting the Precipitation strengthening checkbox on the Configuration window, there are several settings you can define. One phase can be chosen to contribute to the alloy strength by precipitation strengthening, which in this Property Model is given by the model by Deschamps et al. [1998Des].

On the Configuration window for this setting, the following input parameters can be defined:

  • Precipitate radius: The mean radius of the precipitates.
  • Critical radius: The mean precipitate radius where the mechanism that dislocations pass precipitates changes from shearing () to looping ().
  • Taylor factor: The Taylor factor accounts for the texture of the material, normally the value is between 2.24 and 3.06 for randomly oriented grains.
  • Shear modulus: The shear modulus of the matrix phase, given in Pascal (Pa).
  • Burgers vector: The burgers vector of the matrix phase, given in meters (m).

Starting with TCS Ti/TiAl-based Alloys Database (TCTI) version 6, it is possible to calculate the Shear modulus of individual phases. The option is enabled by default for the precipitation strengthening contribution. See the settings information or the tooltip.

Constant Strength Addition

The Constant strength addition contribution can be used to displace the calculated result in the y-direction.

Settings, Example, and References

The input parameters are entered on the Configuration window for the Property Model Calculator. There are also settings on the Plot Renderer where you can choose from the available and relevant axis variables.

See Alloy Strength - Ti Property Model Settings.

For an example see PM_Ti_02: Alloy Strength for Ti-O.

[1981Con] H. Conrad, Effect of interstitial solutes on the strength and ductility of titanium. Prog. Mater. Sci. 26, 123–403 (1981).

[1998Des] A. Deschamps, Y. Brechet, Influence of predeformation and ageing of an Al–Zn–Mg alloy—II. Modeling of precipitation kinetics and yield stress. Acta Mater. 47, 293–305 (1998).

[1998Ouc] C. Ouchi, H. Iizumi, S. Mitao, Effects of ultra-high purification and addition of interstitial elements on properties of pure titanium and titanium alloy. Mater. Sci. Eng. A. 243, 186–195 (1998).

[2000Tan] X. Tang, T. Ahmed, H. J. Rack, Phase transformations in Ti-Nb-Ta and Ti-Nb-Ta-Zr alloys. J. Mater. Sci. 35, 1805–1811 (2000).

[2016Cor] Z. C. Cordero, B. E. Knight, C. A. Schuh, Six decades of the Hall–Petch effect – a survey of grain-size strengthening studies on pure metals. Int. Mater. Rev. 61, 495–512 (2016).

[2017Wal] M. Walbruhl, D. Linder, J. Ågren, A. Borgenstam, Modelling of solid solution strengthening in multicomponent alloys. Mater. Sci. Eng. A. 700, 301–311 (2017).

[2022Sal] C. A. F. Salvador, E. L. Maia, F. H. Costa, J. D. Escobar, J. P. Oliveira, A compilation of experimental data on the mechanical properties and microstructural features of Ti-alloys. Sci. Data. 9, 188 (2022).

[2024Sal] A. Salmasi. Internal report. Thermo-Calc Software AB (2024).