Biaxial Ratcheting Research Articles

933 転位密度を考慮した構成式による二軸ラチェット変形シミュレーション

933 転位密度を考慮した構成式による二軸ラチェット変形シミュレーション

Biaxial Ratcheting and Cyclic Plasticity for Bree-Type Loading—Part I: Finite Element Analysis

The Bree diagram has been incorporated in the ASME B&PV Code in the elevated temperature Code Case N47 as a design approach for limiting strain accumulation in cylinders subjected to cyclic thermal loadings under sustained primary stress. Since the Bree diagram is based upon uniaxial-stress model, it is pertinent to examine the influence of biaxial stresses on strain growth and cyclic stress-strain hysteresis response. The results of inelastic analyses presented in this paper showed that ratcheting and hysteresis behavior may also occur in the axial direction in addition to the hoop direction. Results of almost 100 load cases were presented to clarify the influence of biaxial membrane and thermal bending stresses on the structural behavior. A design approach for the assessment of this type of problem was suggested which utilizes these results.

Biaxial Ratcheting and Cyclic Plasticity for Bree-Type Loading—Part II: Comparison Between Finite Element Analysis and Theory

In Part I of this two part paper (Ng and Nadarajah, 1996), the results of an extensive program of finite element analyses were described. The problem being considered is the phenomenon of ratcheting and cyclic stress-strain hysteresis loop behavior in a thin-walled cylinder subject to cyclic thermal stress and sustained internal pressure. The purpose of Part II is to compare the finite element results with two analytical solutions and review the applicability of the latter as a design procedure for assessment of these types of structures. The comparison shows that the ratcheting to shakedown boundaries based on F.E. and analytical models are in close agreement. The hoop ratcheting rates predicted by the uniaxial model enveloped the F.E. and biaxial models, while for the axial ratcheting rates, the F.E. results are upper bound.

On the performance of kinematic hardening rules in predicting a class of biaxial ratcheting histories

It is well known that strain-symmetric axial cycling of thin-walled metal tubes in the presence of pressure results in a progressive accumulation (ratcheting) of circumferential strain. It was previously demonstrated that the prediction of the rate of ratcheting under constant internal pressure, by nonlinear kinematic hardening models, is very sensitive to the hardening rule adopted. It was shown that the Armstrong-Frederick hardening suitably calibrated and used in a class of models can yield reasonably good predictions of the rate of ratcheting for a range of cycle parameters. In this paper, the subject is revisited in the light of further experimental results involving simultaneous cycling of the internal pressure and the axial strain. Experiments and analyses were performed for a family of five such biaxial loading histories. A similar sensitivity to the kinematic hardening rule used in the models was observed in all the new loading histories. Furthermore the hardening rule calibrated in the constant pressure experiments was found to yield accurate predictions for three of the loading histories considered and poor predictions for the other two. The reasons for this varied performance are analyzed and some recommendations for implementation of such models in structural applications are made.

Experimental Observation on Viscoplastic Behavior of SUS 304 : Creep and Ratchetting Behavior

A unified constitutive model which can predict cyclic plasticity, uniaxial and biaxial ratchetting, creep, and stress relaxation is required by designers of aeronautic equipment, nuclear reactors and so on. Detailed experimental observation of considering viscoplastic behavior of materials must be carried out to construct a unified constitutive model. In this paper, uniaxial and biaxial ratchetting tests and creep tests were carried out at room temperature and at 550°C using SUS 304 stainless steel. As a result, it is clarified that uniaxial ratchetting behavior is affected by the viscous deformation of the material, and that biaxial ratchetting behavior is affected by both the viscous deformation of the material and the deformation caused by nonproportional loading.

Constitutive Equation for Cyclic Plasticity Considering Memorization of Back Stress

One of the difficult problems in the study of the constitutive equation for cyclic plasticity is the prediction of ratchetting behavior that is induced by the superposition of a cyclic secondary load to a constant primary load in a biaxial case, or by the mean stress in a uniaxial case. This paper shows the constitutive equation in which the memorization of the back stress is considered for ratchetting behavior, especially for biaxial ratchetting behavior. A biaxial ratchetting test was carried out using SUS 304 stainless steel at room temperature

Biaxial Ratcheting Under Strain or Stress-Controlled Axial Cycling With Constant Hoop Stress

Strain or stress-controlled tension-compression cyclic tests were conducted on pressurized thin-walled tubular specimens of 304 stainless steel. In strain-controlled mode ratcheting strains in hoop direction, and under stress-controlled mode ratcheting in both hoop and axial directions, were observed. To predict the observed ratcheting behavior, an additional evolution rule for the stress memory surface has been introduced in the constitutive model developed recently by the authors. Qualitative and quantitative comparisons with the test results indicate a fairly good agreement in predicting ratcheting deformations.

Creep, Stress Relaxation and Biaxial Ratchetting of Type 304 Stainless Steel After Cyclic Preloading

A series of tests for creep, stress relaxation, and biaxial ratchetting of type 304 stainless steel after cyclic preloading were carried out to investigate their interaction. The interesting fact was pointed out that back stress in cyclic plasticity played an important role to describe creep, relaxation, and biaxial ratchetting following cyclic preloading. Then, the test results showed that the material behavior due to creep after cyclic preloading could be represented by the modified Bailey-Norton law with stress levels evaluated from the current center of the yield surface, i.e., back stress which was determined by the hybrid constitutive model for cyclic plasticity proposed by the authors. In addition, biaxial ratchetting of axial strain induced by cyclic shear straining after cyclic preloading was expressed by the shear stress amplitude, the number of cycle and the axial stress level from the current center.

Ratcheting of cyclically hardening and softening materials: II. Multiaxial behavior

Part II of this study is concerned with ratcheting phenomena of cyclically hardening and softening materials under biaxial, cyclic loading. Two sets of biaxial experiments were performed on carbon steel 1018 and stainless steel 304 thin-walled tubes. In the first tyoe of experiment, a constant internal pressure was prescribed while the tubes were cycled axially in a strain-symmetric fashion. This causes ratcheting in the circumferential direction. In the second type of experiment, the axial cycling was carried out under stress control. This loading history results in simultaneous ratcheting in the axial and circumferential directions. In the case of stainless steel 304, the nonproportionality of these loading histories was found to induce significant hardening in addition to that recorded in unaxial loading. Cyclic hardening was found to reduce the rate of ratcheting. In the case of carbon steel 1018, the nonproportionality of the loading paths was found not to influence the induced softening. Cyclic softening in the axial and circumferential directions were found to be uncoupled. The time-independent cyclic plasticity models developed in Part I, suitably extended to multiaxial loading, were used to simulate the biaxial ratcheting experiments. Two methods for modeling the additional hardening/softening of the material due to nonproportional loading, developed by previous investigators, were incorporated in the models. The prediction of circumferential ratcheting is shown again to be sensitive to the kinematic hardening rule of the yield surface incorporated in the models. The performance of the models in predicting the biaxial ratcheting results was found to be rather poor. Several reasons for this poor performance are identified and suggestions for future improvements are made.

Constitutive Equation for Cyclic Plasticity Considering Memorization of Back Stress.

One of the difficult problems in the study of the constitutive equation for cyclic plasticity is the prediction of ratchetting behavior which is induced by the superposition of a cyclic secondary load to a constant primary load in the biaxial case, or by the mean stress in a uniaxial case. This paper shows the constitutive equation in which the memorization of the back stress was considered for ratchetting behavior, especially for biaxial ratchetting behavior. To verify the applicability of the constitutive equation to ratchetting behavior, biaxial ratchetting tests were carried out using type 304stainless steel at room temperature. As a result, it was found that the simulations based on the constitutive equation had good agreement with the tests.

Effects of grain size on cyclic strain localization in polycrystalline nickel: Morrison, D.J., Chopra, V. and Jones, J.W. Scr. Metall. Mater. June 1991 25, (6), 1299–1304

Kinematic hardening and the associated concept of back-stress and its evolution are fundamental constitutive ingredients of classical plasticity theory used to simulate the inelastic material response under stress reversals. Cyclic plasticity addresses such response under a sequence of repeated stress reversals, which results in plastic strain accumulation, called ratchetting. Biaxial ratchetting occurs whenever the material is loaded in two directions although typically the cyclic loading is only in one direction. The realistic description of the material response during cyclic loading depends strongly on the kind of kinematic hardening used.This paper investigates the performance of some existing and novel kinematic hardening rules in the prediction of ratchetting. The multiplicative AF model by Dafalias et al., 2008a, Dafalias et al., 2008b, which was originally applied to the simulation of uniaxial ratchetting, will be used here to simulate also biaxial ratchetting and will be compared with a model using the concept of a hardening stress threshold. The suggestion of Delobelle et al. (1995) to combine the Armstrong/Frederick and Burlet and Cailletaud (1986) kinematic hardening rules is incorporated in the aforementioned model and used to obtain improved simulations of biaxial ratchetting. After showing a deficiency of the foregoing suggestion which results in the possibility for the back-stress to cross it’s bounding surface and induce a negative plastic modulus, a variation is proposed void of the foregoing deficiency, which is successfully tested in the simulation of multiple biaxial ratchetting experimental results on carbon steel 1026.

Uniaxial and Biaxial Viscoplastic Behavior of SUS304 after Cyclic Preloading.

A series of tests for creep and biaxial ratchetting during cyclic loading were carried out to investigate the interaction between cyclic plasticity and creep or ratchetting of SUS 304 stainless steel. Specimens were subject to intermittent creep or biaxial ratchetting at several stress levels during cyclic tension-compression loading with the constant strain amplitude under the constant stress rate. The test results showed that the creep curve during cyclic loading could be explained by the so-called Bailey-Norton law, with stress levels measured from the current center of the yield surface which was determined by the hybrid constitutive equation for cyclic plasticity proposed by authors. Axial ratchet strain induced by cyclic shear stressing was expressed by the shear stress amplitude, the number of cycles and the axial stress level measured from the current center of the yield surface.

Effects of Variations of the Maximum Stress and Stress Ratio on the Biaxial Ratcheting Behaviors

Effects of Variations of the Maximum Stress and Stress Ratio on the Biaxial Ratcheting Behaviors