Based on the invariant theory of continuum mechanics by Spencer, the strain energy depends on deformation, fiber direction, and the gradients of the fiber direction in the deformed configuration. The resulting extended theory is very complicated and brings a nonsymmetric stress and couple stress. By introducing the gradient of fiber vector in the current configuration, the strain energy function can be decomposed into volumetric, isochoric, anisotropic, and bending deformation energy. Due to the particularity of bending deformation, the reinforced material has tensile deformation and compression deformation. The bending stiffness should be taken into consideration, and it is further verified by the bending simulation.

The deformation and damage mechanisms of a single crystal nickel-based superalloy containing 6.0%Re/5.0%Ru were studied through creep performance tests at 800 °C/860–880 MPa, microstructure and morphology observation, and dislocation configuration analyzation. It was found that, during the creep process at the intermediate temperature, the γ′ phase does not form a raft-like structure. After a creep fracture, the distortion degree of the cubic γ′ phase becomes greater when the observation region is closer to the fracture. The alloy has a long creep life at 800 °C, and the dislocation slipping or climbing in the γ matrix is the deformation mechanism at the early and middle creep stages. At the later creep stage, the γ′ phase is sheared by dislocations. Because of the low stacking-fault energy of the alloy, the superdislocation shearing into the γ′ phase can decompose on the {111} plane to form a (1/3) partial dislocation and stacking-fault configuration or cross-slip to the {100} plane to form the Kear–Wilsdorf (K-W) lock, which greatly improves the creep resistance of the alloy. At the later creep stage, the primary/secondary slip systems in the alloy are activated alternately, resulting in micro-cracks at the intersection of the two slip systems. As the creep progresses, the initiated cracks spread and propagate in the γ matrix phase along a direction normal to the stress axis and connect with each other until creep fracture occurs. This is the fracture mechanism of the alloy during creep at the medium temperature.

Through room-temperature tensile testing, microstructural observation, and comparative analysis of dislocation configurations, this study investigates the deformation and damage behavior of a high-concentration Re/Ru single-crystal alloy. The results show that the alloy possesses excellent mechanical properties at room temperature, with a tensile strength of 875 MPa and a yield strength of 847 MPa. During tensile deformation, plastic strain primarily occurs through dislocation slip within the γ matrix and dislocation shear into the γ′ phase. Dislocations sheared into the γ′ phase exhibit distinct decomposition patterns. Microcracks initiate at γ′/γ interfaces where two slip systems intersect. As tensile loading continues, these microcracks coalesce, leading to increased local stress and unstable crack propagation along the γ/γ′ interfaces, ultimately resulting in fracture. This process constitutes the deformation and damage mechanism of the alloy during room-temperature tensile deformation. These findings suggest that high Re/Ru concentrations fundamentally alter low-temperature deformation pathways, which may improve resistance to brittle fracture during cold start or handling conditions.