High-temperature plastic flow is the underlying process that governs the product quality in many advanced metal manufacturing technologies, such as extrusion, rolling, and welding. Data and models on the high-temperature flow behavior are generally desired in the design of these manufacturing processes. In this paper, quantitative constitutive analysis is carried out on 3Cr-1Si-1Ni ultra-high strength steel, which sheds light on the mathematic relation between the flow stress and the thermal-mechanical state variables, such as temperature, plastic strain, and strain rate. Particularly, the hyperbolic-sine equation in combination with the Zener-Hollomon parameter is shown to be successful in representing the effect of temperature and strain rate on the flow stress of the 3Cr-1Si-1Ni steel. It is found that the flow stress of the 3Cr-1Si-1Ni steel is significantly influenced by strain. The strain-dependence on flow stress is not identical at different temperatures and strain rates. In the constitutive model, the influence of strain in the constitutive analysis is successfully implemented by introducing strain-dependent constants for the constitutive equations. Fifth-order polynomial equations are employed to fit the strain-dependence of the constitutive constant. The proposed constitutive equations which considers the compensation of strain is found to accurately predict flow stress of the 3Cr-1Si-1Ni steel at the temperatures ranging from 800 °C to 1250 °C, strain rate ranging from 0.01/s to 10/s, and strain ranging from 0.05 to 0.6.

I nternal crack of an ingot is frequently encountered in casting practice, which directly leads to scrapping the whole product. From many studies [1][2][3][4][5][6][7] , it appears that hot crack initiates in the brittle temperature range and propagates in the interdendritic liquid film. An extension of the two-phase model, which includes plasticity of the porous network, is reported, considering the void as the crack nucleus, although the pores should not necessarily develop into a crack [8] . The crack may nucleate or develop from other defects and then propagate through a chain of pores. The excessive stress and strain developing during the brittle temperature range are the main reasons for hot crack formation. A coherent dendritic network can sustain and transmit stress. Above the coherency temperature, continuous liquid film still exists as the solid dendrite arms have not yet coalesced. Deformation induced by thermal stress can pull these Abstract: P91 is a new kind of heat-resistant and high-tensile steel. It can be extruded after ingot casting and can be widely used for different pipes in power plants. However, due to its mushy freezing characteristics, a lack of feeding in the ingot center often generates many defects, such as porosity and crack. A six-ton P91 ingot was cast and sliced, and a representative part of the longitudinal section was inspected in more detail. The morphology of crack-like defects was examined by X-ray high energy industrial CT and reconstructed by 3D software. There are five main portions of defects larger than 200 mm 3 , four of which are interconnected. These initiated from continuous liquid film, and then were torn apart by excessive tensile stress within the brittle temperature range (BTR). The 3D FEM analysis of thermo-mechanical simulation was carried out to analyze the formation of porosity and internal crack defects. The results of shrinkage porosity and Niyama values revealed that the center of the ingot suffers from inadequate feeding. Several criteria based on thermal and mechanical models were used to evaluate the susceptibility of hot crack formation. The Clyne and Davies' criterion and Katgerman's criterion successfully predicted the high hot crack susceptibility in the ingot center. Six typical locations in the longitudinal section had been chosen for analysis of the stresses and strains evolution during the BTR. Locations in the defects region showed the highest tensile stresses and relative high strain values, while other locations showed either low tensile stresses or low strain values. In conclusion, hot crack develops only when stress and strain exceed a threshold value at the same time during the BTR.

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