中村 俊哉

The ratcheting behavior of the "unsymmetric two bar system" was investigated by numerical experiments. The two bars are restrained to the same length and are subjected to a constant load. One bar sees cyclic temperature variations while the other bar is kept a: constant temperature. The material models employed are rate-independent plasticity (kinematic hardening) and the Viscoplasticity Theory based on Overstress (VBO) matched to represent the cyclic neutral 6061 T6 Aluminum alloy elastic and inelastic deformation behavior. For simplicity temperature independent material properties were assumed. Numerical analyses were performed to investigate the effects of rate of thermal loading and temperature range. Elastic-inelastic shakedown is ultimately achieved due to work hardening. There is a strain range increase until it reaches a steady value. Kinematic hardening and VBO predict almost the same strain range which for the case of VBO is nearly rate independent. The behavior for both material models is very different for the mean strain For VBO. the number of cycles to shakedown is rate-dependent and is considerably larger than for kinematic hardening. Finally, the steady state mean strain and strain range are computed directly for VBO.

A loading history effect on biaxial mechanical ratchetting under the interaction of creep and plasticity has been experimentally investigated with Modified 9Cr-1Mo steel. The experiments were conducted at 873K under the biaxial loading of a steady torsional shear stress superposing upon a cyclic push-pull straining. In the first series of experiments it has been found that the slower cyclic straining and/or the larger steady shear stress result in the larger accumulation of ratchet strain. The second series of experiments includes changes in the cyclic strain rate and the ″steady″ shear stress to investigate the loading history effect. Simple empirical equations were derived. Additional analysis has been done with inelastic constitutive equations of creep-plasticity superposition type and Chaboche type.

A series of creep-fatigue experiments has been conducted with 304 stainless steel, 2 1/4Cr-1Mo steel and modified 9Cr-1Mo steel at in both air and very high vacuum environment of 0.1μPa. The damage model developed by the authors to evaluate the creep-fatigue damage in vacuum is applied to the data obtained in air and a separate evaluation of the environmental effect of air on the creep-fatigue interaction is made. Fatigue damage is highly affected with the air environment which results in a time/rate-dependent life reduction being mainly controlled by a strain rate. The air environment has different effect to the different material on the evolution of creep damage. It accelerates the creep damage in 304 stainless steel, gives no effect on it in modified 9Cr-1Mo steel and reduces it in 2 1/4Cr-1Mo steel.

The stability analysis of the one-step Euler method in numerical time integration of a viscoplastic constitutive equation is discussed by applying the theory of nonlinear discrete dynamic system. The algorithm is represented as a discrete dynamic system which has a fixed point. The behavior of the system is classified into three types based on the eigen value of the Jacobian at the fixed point. Some numerical experiments are conducted and it is shown that the calculations meet the present theory.

A series of creep-fatigue tests has been conducted with modified 9Cr-1Mo steel at 600°C in a high vacuum environment of 0.1 mPa to assess an accumulation of creep-fatigue damage. In these tests, each test specimen has been subjected to prior creep-fatigue loading followed by subsequent fatigue loading or prior fatigue loading followed by subsequent creep-fatigue loading. A linear summation of cumulative damage of fatigue and creep life faction was smaller then unity for the former case, and larger than unity for the latter case. SEM observation showed that in the case of prior creep-fatigue loading, a crack propagated from inclusions around which cavities were observed and its appearance transformed from transgranular to intergranular type with the increase of the number of cycles of prior creep-fatigue loading, while crack mode was predominantly intergranular in the case of prior fatigue loading. It was suggested that in the case of prior creep-fatigue loading, the fatigue life becomes shorter than that predicted by the linear rule due to early initiation of a crack caused from the cavity creation. In the case of prior fatigue loading, the crack propagates different courses in each loading to lead to the life fraction which is ″larger than unity″.

A series of creep-fatigue tests have been conducted with Modified 9Cr-1Mo steel at 600°C in air and in a very high vacuum environment of 10-9 torr. Strain wave forms employed include symmetric continuous cycle, unsymmetric continuous cycle, and tension or compression hold-time cycle with a strain rate from 10-6 to 10-3 1/8 and a hold-time up to 600 s. Creep-fatigue life was reduced by about one order of amgnitude in air than in vacuum, however, the life reduction decreased as the creep component of damage increased. Data were analyzed based on the overstress concept to separate the environmental effect of air from the creep-fatigue interaction behavior. The environmental effect of air decreases the fatigue life, however, it does not affect the creep component of life.

A unified inelastic constitutive equation is suggested for 2 1/4Cr-1Mo steel at the elevated temperature of 550°C. In the present study, an evolution of the overstress is discussed, where the overstress is a difference between the applied stress and the internal stress. Another significant point suggested in this study is the distinction of the inelastic deformation depending on the evolution of the overstress. A mathematical model is developed based on these assumptions. Many numerical experiments have been conducted to examine the validity of the present model. In comparison with the experimental results, the present model is shown to give good descriptions for a wide variety of loading conditions, including time-dependent plasticity, stress relaxation, creep and cyclic softening.

Tension-torsion biaxial creep-fatigue tests have been conducted with 304 stainless steel at 650°C under a proportional biaxial strain condition. An overstress and an internal stress were analyzed under the biaxial strain condition. Peak stress components were well prepared with Von Mises equivalent stress. However, the overstress and internal stress showed a dominant anisotropy. A long term stress relaxation test was examined under biaxial proportional straining. The result suggested that a time-dependent inelastic strain is composed of at least two origins. One is caused from a relaxation of the overstress and the other is caused from a relaxation of the internal stress. The former is much faster than the latter. The relaxation of the internal stress indicates a recovery of the anisotropy.