Recently, the team of Professor Da Shu and Academician Baode Sun from the School of Materials Science and Engineering at Shanghai Jiao Tong University, in collaboration with Professor Yao Shen, has made important progress in studying the high-temperature deformation behavior of nickel-based superalloys during solidification processing. They revealed the mechanism transition from creep to viscoplasticity in the extremely high-temperature regime of 0.8 Tm~1.0 Tm, and established a unified creep-viscoplasticity constitutive model coupling the γ′ phase evolution effect. The related work, titled “A unified creep-viscoplasticity model for high temperature distortion prediction of nickel-based superalloys during solidification processing,” was published in International Journal of Plasticity, a leading authoritative journal in the mechanics of plasticity. The first author of the paper is postdoctoral researcher Jiayu Cui, and the corresponding authors are Professor Da Shu, Professor Yao Shen, and Academician Baode Sun.

Nickel-based superalloys are one of the most extensively used groups of heat-resistant materials for the hot-end components of aero engines and gas turbines. Through investment casting, net shape or near-net shape manufacturing of components such as turbine blades with intricate cooling channels and thin-walled structural components like aero-engine casings can be achieved. Casting distortion begins as early as the alloy cools down to the dendrite coherency temperature (slightly above the solidus temperature), at which point dendrites have just established interconnections as a continuous skeletal structure capable of transmitting stress, allowing the material to be treated and described using solid constitutive equations. Subsequently, during solidification and cooling within a low-strength (< 10 MPa) and low-modulus (< 5 GPa) thin-thickness (~10 mm) ceramic shell mold in contact, complex and massive unexpected plastic deformation (termed distortion below) emerges in the superalloy. Nevertheless, current distortion prediction methods predominantly rely on plastic models (typically at a strain rate of 10⁻³ s⁻¹) or simple phenomenological viscoplastic models (typically with strain rates exceeding 10⁻³ s⁻¹), where time-dependent deformation behavior is neglected or oversimplified. Moreover, long-duration high-temperature tensile experiments near the melting point face technical challenges such as maintaining high vacuum and oxidation protection, resulting in a scarcity of systematic experimental data in this temperature range. This bottleneck leads to inconsistent prediction accuracy in both shape and residual stress of complex components.

Leveraging a high-vacuum environment (< 0.01 Pa) and a specialized molybdenum fixture, with synchronized temperature monitoring and control ensured through thermocouples and photoelectric colorimeters, the research team systematically conducted high-temperature tensile experiments and strain-rate jump tests, across the temperature range of 950~1220 ℃ and strain rates of 10⁻⁵~10⁻² s⁻¹. This revealed the creep-to-viscoplasticity transition, which is uniquely temperature-controlled within the measured strain-rate domain, of nickel-based superalloys in the extremely high-temperature regime. This temperature-controlled mechanism transition is directly related to γ′ precipitation, unlike the temperature- and strain-rate-dependent behavior reported in some other alloys (e.g., Ti alloys, Cu alloys), thereby providing a unique physical picture for the high-temperature deformation of nickel-based superalloys (Fig. 1).

Fig. 1 | Schematic of the evolution of deformation mechanisms in the extremely high-temperature regime of 0.8 Tm~1.0 Tm for nickel-based superalloys

Above the γ′ solvus (> 1080 ℃), the alloy exhibits typical five-power-law creep (stress exponent N ≈ 5) controlled by dislocation climb and rate-limited by solute-retarded vacancy diffusion, and this behavior persists up to near the melting point. Below the γ′ solvus, as the γ′ phase precipitates and its volume fraction f increases, linear increases in both the stress exponent N and the apparent activation energy Qc with the γ′ volume fraction are identified (Fig. 2a). Furthermore, the stress versus (strain rate)^(1/N) relationships show all extrapolated fits converging to near zero stress (R² > 0.9996) (Fig. 2b), confirming the absence of a threshold stress (σth) under these conditions. This trend is contrary to predictions from existing local climb and general climb models, suggesting that under extremely high-temperature conditions, the thermally activated dislocation climb may become sufficiently rapid to bypass the particles at the coherent γ/γ′ interface.

Fig. 2 | Temperature-dependent stress–strain rate relationships obtained by fitting the experimental results

Based on the above deformation mechanism analysis, the evolution laws of the apparent activation energy and stress exponent with respect to the γ′ volume fraction were further embedded into the power-law model to construct a unified creep–viscoplasticity constitutive model covering the range from 950 ℃ to 1220 ℃ and strain rates of 10⁻²~10⁻⁵ s⁻¹, with high accuracy (R² = 0.9998). Based on a finite-element prediction method and the Abaqus numerical simulation platform, the model was applied to simulate the solidification distortion of a typical thin-walled investment casting. Validated by industrial-scale computed tomography and blue light scanning experiments, the displacement prediction error is less than 0.1 mm (against a total distortion on the order of 3 mm). Radial enlargement of the casting differs by approximately 13% from the prediction of the traditional elastoplastic model that neglects time dependence, indicating that creep-viscoplastic strain offsets approximately 13% of the total shrinkage induced by radial thermal strain. The study quantifies, for the first time, the dominant role of creep in the dimensional distortion of nickel-based superalloy castings: during the cooling process of the casting on the order of a thousand seconds, creep can still significantly affect the final distortion, in which creep deformation exerts a decisive influence on the total plastic deformation (Fig. 3).

Fig. 3 | Creep strain distribution and mechanism analysis at different characteristic locations of the ring-shaped casting

This work was financially supported by the National Science and Technology Major Project of China (No. 2025ZD0609500) and the National Natural Science Foundation of China (Nos. 52090042, 52575417). The research results offer a high-accuracy constitutive model to improve the distortion prediction accuracy of many high-temperature forming processes for superalloys, such as investment casting, 3D printing, welding, and even hot isostatic pressing, supporting the net-shape manufacturing of key complex components of aero engines. The article link address is: https://doi.org/10.1016/j.ijplas.2026.104754.