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Page 10 of 29 Liu et al. J. Mater. Inf. 2026, 6, 18

JC-P4 model. The primary modification involves replacing the initial segment equation with a fourth-order
polynomial, as expressed in Equation (8) :
[70]
¤ Δ

4
2
3
= [ 0 + 1 + 2 + 3 + 4 ] 1 + ln 1 − (8)
0 −
where σ denotes the flow stress (MPa), and k 0 - k are strain-hardening coefficients. C is the strain rate
4
hardening exponent, and m is the thermal softening coefficient. ε represents the equivalent plastic strain,
while ε and ε 0 denote the equivalent plastic strain rate (s ) and the reference strain rate (s ), respectively. The
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¤
¤
reference strain rate is typically set to 0.01 s . T is the reference temperature (room temperature, 298 K), and
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r
T is the melting temperature of the material. ∆T represents the adiabatic temperature rise, which can be
m
expressed as Equation (9) :
[71]
¹

Δ = = 45° d (9)
0
where C is the specific heat capacity, ρ is the density, and τ = . The thermodynamic software Thermo-Calc

p
45°
2
was used to obtain accurate values of T and C .
p
m
For the TA15 alloy, the JC-P4 parameters k 0 - k , C and m were directly fitted to the experimentally measured
4
stress–strain curves at strain rates of 2,000, 2,500, and 3,000 s . For the newly designed alloy, which has not
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yet been manufactured, an approximate procedure was adopted. The thermal properties (melting
temperature T , specific heat capacity C , and density ρ) were obtained from Thermo-Calc calculations and
m
p
density estimates. The rate-sensitivity parameter C and thermal softening exponent m were assumed to be
similar to those of TA15, reflecting the comparable near-α microstructural class. The strain-hardening
coefficients k 0 - k were then adjusted such that the JC-P4 model reproduces the overall strength level
4
predicted by the ML model at a strain rate of 3,000 s . This approach provides a qualitative estimate of the
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dynamic stress-strain response of the designed alloy.
RESULTS AND DISCUSSION
Feature engineering for knowledge-enabled initial data spaces
To establish a more comprehensive relationship between domain knowledge-based alloy characteristics and
the strength-ductility behavior of titanium alloys under extreme conditions, a database was constructed by
integrating dynamic compressive strength, fracture strain, strain rate, and compositional information of
titanium alloys at high strain rates. On one hand, Figure 2 presents 175 datasets of flow strength and fracture
strain for titanium alloys containing Al, V, Mo, Zr, Fe, Si, Sn, Nb, and Cr. The experimental strain rates
range from 1,000 to 5,000 s [Figure 2A]. Strain rates above 5,000 s often induce premature fracture in
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brittle titanium alloys, thereby limiting the availability of comprehensive data. Figure 2B shows a box plot of
the strength distribution, where most titanium alloys exhibit strengths in the range of 1,100-1,900 MPa. This
range exceeds the typical strength of industrial-scale titanium alloys, which is generally below 1,300 MPa; this
discrepancy may be attributed to the use of small-scale laboratory specimens reported in the literature.
Among the nine principal alloying elements (excluding Ti), Figure 2C shows that Al, V, Mo, Nb, and Cr
exhibit relatively higher concentrations, whereas Fe and Si are present in minor amounts. Figure 2D
illustrates the distribution of alloying elements in typical titanium alloys, which generally contain two to six
elements, as both insufficient and excessive alloying reduce practical applicability. These results indicate a
broad compositional space for titanium alloy design.

On the other hand, a total of 312 datasets reflecting ductility information, including fracture strain and strain
rate, are presented in Figure 3. The strain rates shown in Figure 3A are concentrated between 250 and
5,000 s , indicating that fracture strain rates for commonly used titanium alloys remain below 5,000 s . In
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