Mitsutoshi Kuroda

The permanent strengths of interstitial-free (IF) steels with different grain sizes and dislocation densities processed by severe plastic deformation (SPD) and subsequent annealing are systematically investigated. Permanent strength, which is athermal and time-independent, corresponds to the fundamental capability to bear stresses caused by external forces. Sufficiently long-time (24 h) stress relaxation tests were carried out and experimental stress–relaxation time relationships were extrapolated to estimate the permanent strength that remained after an infinite time passed. The flow stresses observed in standard uniaxial tension tests increased with repeated SPD processes, and the fraction of permanent strength to the observed flow stress was mostly above 65%. The permanent strength also increased with repetition of SPD processes, and subsequent low-temperature annealing further augmented the permanent strength. During SPD processes, the dislocation-related strengthening was dominant, while the grain-size-related strengthening was minor, i.e., the Hall–Petch relation does not hold. On the other hand, after low-temperature annealing, the grain-size-related strengthening became dominant, quickly replacing the dislocation-related strengthening. In a coarse-grain region, the grain-size-related strength was consistent with the classical Hall–Petch relation. It was confirmed that the original Hall–Petch relation holds only in the coarse-grain region and it indicates “softening with grain coarsening due to annealing”, not “strengthening by grain refinement due to SPD”.

A previously proposed strain gradient plasticity theory is extended to incorporate a non-quadratic power law function of the plastic strain gradient in the free energy expression with an exponent of N + 1. The values of N are taken to vary from N = 1 to N = 0. A simple shear problem of a metal layer between rigid boundaries is analyzed. Two stages of plastic deformation are considered. In stage I, the plastic strain is taken to be zero at the boundaries. Stage I ends when a specified magnitude of the plastic strain gradient is attained at the boundaries. In stage II, the magnitude of the plastic strain gradient at the boundaries is fixed at the specified value. With N = 0, a critical plastic strain gradient cannot be specified at the boundaries because the plastic strain gradient is infinite at the boundaries. The theory with N = 0 predicts a constant plateau stress immediately after initial yield, and the dependence of the plateau stress on the layer thickness can fit experimentally observed plateau stress values. However, with N = 0, a stress gap occurs between the initial yield stress and the plateau stress. The theory with 0 < N ≤ 1 and with stage II also can reproduce the experimentally observed dependence of the plateau stress on the layer thickness for any value of N in that range, with an appropriate value of critical plastic strain gradient at the boundaries. The solution for 0 < N ≤ 1 includes that for N = 0 as a limiting case.

Characteristic material behaviors in obtuse‐angled conical indentation for elasto‐viscoplastic solids are explored and discussed. Finite element calculations are carried out for indentation of a rigid sharp conical indenter into a cylindrical body that models a pseudo‐half space, considering the friction between the indenter and the solid. Under low‐friction conditions, it is assumed that breakage of the material by the sharp tip of the indenter occurs and a new surface emerges along the contact interface during indentation. It is revealed that the load required for indentation does not necessarily reach its maximum at the perfect sticking condition, which shows a nonlinear variation from the frictionless condition to the perfect sticking condition. The increase in strain hardening and the decrease in elastic modulus relative to yield strength both reduce the difference between the required loads for different friction conditions. For perfect sticking, the indenter tip is covered by an elastically deforming material cap during indentation similarly to the case of the plane strain wedge indentation. Similarity and discrepancy between the behavior in the conical indentation and that in the plane strain wedge indentation, which is well described by the classical slip‐line field theory, are clarified in detail.

The permanent strengths of interstitial-free (IF) steels with different grain sizes and dislocation densities processed by severe plastic deformation (SPD) and subsequent annealing are systematically investigated. Permanent strength, which is athermal and time-independent, corresponds to the fundamental capability to bear stresses caused by external forces. Sufficiently long-time (24 h) stress relaxation tests were carried out and experimental stress–relaxation time relationships were extrapolated to estimate the permanent strength that remained after an infinite time passed. The flow stresses observed in standard uniaxial tension tests increased with repeated SPD processes, and the fraction of permanent strength to the observed flow stress was mostly above 65%. The permanent strength also increased with repetition of SPD processes, and subsequent low-temperature annealing further augmented the permanent strength. During SPD processes, the dislocation-related strengthening was dominant, while the grain-size-related strengthening was minor, i.e., the Hall–Petch relation does not hold. On the other hand, after low-temperature annealing, the grain-size-related strengthening became dominant, quickly replacing the dislocation-related strengthening. In a coarse-grain region, the grain-size-related strength was consistent with the classical Hall–Petch relation. It was confirmed that the original Hall–Petch relation holds only in the coarse-grain region and it indicates "softening with grain coarsening due to annealing", not "strengthening by grain refinement due to SPD".

For a plane strain wedge indentation problem, detailed comparisons between slip-line field theory (SLFT) solutions, experimental observations and finite-element analysis results are carried out. Several past remaining questions on this problem are explored. The finite-element computations appear to account for the nature of a modified slip-line field solution (Petryk H. 1980 Journal de Mécanique Appliquée 4 , 255–282) that assumes the existence of an additional fan-shaped slip-line field just above the boundary between yielding and unyielding regions. For obtuse-angled wedges, finite-element computations show that the indentation load could be smaller for a rough wedge than for a smooth wedge. The question that was raised in the literature with respect to the reversed order of required loads for smooth and rough wedges is not necessarily a paradox. It is revealed that with increasing friction coefficient, a distinct deformation mode resembling the dead metal cap solution in the SLFT is established immediately after passing the critical friction coefficient value at which the contact mode theoretically changes from frictional sliding to perfect sticking. The profiles of the bulged-out lip material remain straight in all the finite-element computations for non-hardening materials. Nonlinearity of the lip profiles frequently observed in experiments appears in the presence of strain hardening or strain-rate sensitivity.