Biaxial Ratcheting Research Articles

Biaxial ratchetting with novel variations of kinematic hardening

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,b), 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.

Biaxial Ratcheting Response of SS 316 Steel

Ratcheting is one of the challenging phenomena that needs to be investigated for the Fast breeder reactor (FBRs), to arrive at the optimum structural dimensions that are safe and yet do not have undue redundancy. Austenitic stainless steel is the principal structural material for Indian FBR. Preliminary assessment indicates that there is a need to demonstrate that the main load carrying vessel made of this material can provide sufficient safety margin against ratcheting under biaxial loading conditions. This exercise calls for carrying out many simulated experiments, particularly with biaxial tension torsion specimens to generate adequate data for developing robust constitutive models to predict ratcheting. Accordingly, many biaxial tension-torsion experiments for austenitic stainless steel pipes were conducted and the best results have been reported here. The mechanical behavior of this material has been reported for a given axial tensile stress superimposed with a given range of cyclic shear stress for many cycles of loading. Rectangular rosette is used for capturing the biaxial response. Important material responses like cyclic hardening and biaxial ratcheting have been experimentally observed. Maximum accumulation of 2700 μ axial strain has been observed for a loading condition of constant axial stress of 102 MPa super imposed with a cyclic variation of shear stress amplitude of 120 MPa over 2450 cycles. The amount of progressive accumulation of axial strain was found to be directly dependent on the number of cycles. The observed rate of axial strain accumulation found decreased with increase in number of cycles. All these results are presented in detail in this paper and important conclusions that are useful in modeling the observed behavior are discussed.

An evaluation for several kinematic hardening rules on prediction of multiaxial stress-controlled ratchetting

This study evaluates the performance of several non-linear kinematic hardening rules in predicting the various biaxial ratchetting experiments of stainless steel (SS) 304L under various stress-controlled histories performed by Hassan et al. (2008). The non-linear kinematic hardening rules proposed by Burlet and Cailletaud (1986), Ohno and Wang (1993, 1994), Abdel-Karim and Ohno (2000), Kang (2004), Chen and Jiao (2004), Chen et al. (2005) and the different rules of Abdel-Karim (2009) are examined and carefully scrutinized. The considered kinematic hardening rules range from the simple classical ones to more detailed rules, which incorporate additional terms and/or parameters to simulate different factors that affect ratchetting. It is shown that none of the examined kinematic hardening rules is general enough to simulate all of the ratchetting responses for the experiments under consideration.

Macro versus micro-scale constitutive models in simulating proportional and nonproportional cyclic and ratcheting responses of stainless steel 304

A recent study by Hassan et al. [Hassan, T., Taleb, L., Krishna, S., 2008. Influences of nonproportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plasticity, 24, 1863–1889.] demonstrated that some of the nonproportional ratcheting responses under stress-controlled loading histories cannot be simulated reasonably by two recent cyclic plasticity models. Two major drawbacks of the models identified were: (i) the stainless steel 304 demonstrated cyclic hardening under strain-controlled loading whereas cyclic softening under stress-controlled loading, which depends on the strain-range and which the existing models cannot describe; (ii) the change in biaxial ratcheting responses due to the change in the degree of nonproportionality were not simulated well by the models. Motivated by these findings, two modified cyclic plasticity models are evaluated in predicting a broad set of cyclic and ratcheting response of stainless steel 304. The experimental responses used in evaluating the modified models included both proportional (uniaxial) and nonproportional (biaxial) loading responses from Hassan and Kyriakides [Hassan, T., Kyriakides, S., 1994a. Ratcheting of cyclically hardening and softening materials. Part I: uniaxial behavior. Int. J. Plasticity, 10, 149–184; Hassan, T., Kyriakides, S., 1994b. Ratcheting of cyclically hardening and softening materials. Part II: multiaxial behavior. Int. J. Plasticity, 10, 185–212.] and Hassan et al. [Hassan, T., Taleb, L., Krishna, S., 2008. Influences of nonproportional loading paths on ratcheting responses and simulations by two recent cyclic plasticity models. Int. J. Plasticity, 24, 1863–1889.] The first model studied is a macro-scale, phenomenological, constitutive model originally proposed by Chaboche et al. [Chaboche, J.L., Dang-Van, K., Cordier, G., 1979. Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. In: Proceedings of the Fifth International Conference on SMiRT, Div. L, Berlin, Germany, L11/3.]. This model was systematically modified for incorporating strain-range dependent cyclic hardening–softening, and proportional and nonproportional loading memory parameters. The second model evaluated is a polycrystalline model originally proposed by Cailletaud [Cailletaud, G., 1992. A micromechanical approach to inelastic behavior of metals. Int. J. Plasticity, 8, 55–73.] based on crystalline slip mechanisms. These two models are scrutinized against simulating hysteresis loop shape, cyclic hardening–softening, cross-effect, cyclic relaxation, subsequent cyclic softening and finally a broad set of ratcheting responses under uniaxial and biaxial loading histories. The modeling features which improved simulations for these responses are elaborated in the paper. In addition, a novel technique for simulating both the monotonic and cyclic responses with one set of model parameters is developed and validated.

Modified kinematic hardening rules for simulations of ratchetting

In order to simulate multiaxial ratchetting, and as a preliminary step, common different variables introduced into the dynamic recovery term of recently developed hardening rules are presented and scrutinized in details. Subsequently, two modified kinematic hardening rules are formulated and presented. The proposed modified rules are based on the Ohno–Wang kinematic hardening rule in which accumulated plastic strain increment is contributed to the dynamic recovery term. The first modified rule is defined by introducing the radial evanescence term of Burlet–Cailletaud [Burlet, H., Cailletaud, G., 1986. Numerical techniques for cyclic plasticity at variable temperature. Eng. Comput. 3, 143–153] into the Ohno–Wang rule powered by specific material parameters. In the second modified rule a multiplying factor, depends on both the unit vector normal to the yield surface ( n ∼ ) and the deviatoric part of back stress ( a ∼ ), is utilized into the Ohno–Wang rule. The modified rules are examined in details to study their characteristics under uniaxial tensile, uniaxial cyclic and multiaxial loading conditions. Then, the validity and accuracy of these rules are scrutinized critically based on simulations of the well-known multiaxial ratchetting experiments of Corona et al. [Corona, E., Hassan, T., Kyriakids, S., 1996. On the performance of kinematic hardening rules in predicting a class of biaxial ratchetting experiments. Int. J. Plast. 12 (1), 117–145] as well as the recently carried out experiments of Chen et al. [Chen, X., Jiao, R., Kim, K.S., 2005. On the Ohno–Wang kinematic hardening rules for multiaxial ratchetting modeling of medium carbon steel. Int. J. Plast. 21, 161–184]. The two modified kinematic hardening rules simulate most of the considered multiaxial ratchetting experiments fairly well; nevertheless, the second one is relatively superior.

Consistency for two multi-mechanism models in isothermal plasticity

A new class of constitutive equations (the multi-mechanism models) devoted to the prediction of ratcheting and of complex material behavior, for instance of steel, has developed during the last years. The main difference between these models and the “Chaboche” type models is the representation of different mechanisms of plastic strain with a possible interaction between them. This sophistication has a cost related to the complexity to understand well how the various parameters act. The identification process thus becomes more difficult as it will be difficult to give reasonable bounds. Two multi-mechanism models have been proposed during the last decade, see Cailletaud and Sai [Cailletaud, G., Sai, K., 1995. Study of plastic/viscoplastic models with various inelastic mechanisms. International Journal of Plasticity 11, 991], Taleb et al. [Taleb, L., Cailletaud, G., Blaj, L., 2006. Numerical simulation of complex ratcheting tests with a multi-mechanism model type. International Journal of Plasticity, 22, 724], and Sai and Cailletaud [Sai, K., Cailletaud, G., 2007. Multi-mechanism models for the description of ratcheting: effect of the scale transition rule and of the coupling between hardening variables. International Journal of Plasticity 23, 1589]. In this paper, we would like to ensure a kind of “after-sales service” by exploring the thermodynamic way in order to see if there exist any restrictions on the parameter values. We prove thermodynamic consistency of some two-mechanism models under suitable conditions. As a result, we obtain conditions for the parameters which ensure the non negativity of the free energy and the fulfilling of the Clausis–Duhem inequality. Besides this, we perform numerical simulations, considering classical histories (monotonic tension, cyclic strain controlled, uniaxial ratcheting, biaxial ratcheting). These simulations show that the violation of the established restrictions may lead to anomalous predictions.

Parameter identification and modeling of large ratcheting strains in carbon steel

In this paper the parameter identification procedure of a material model for large multi-axial ratcheting strains, as proposed in [Johansson G, Ekh M, Runesson K. Computational modelling of inelastic large ratcheting strains. Int J Plast 2005;20:955–80], is demonstrated. In particular, experimental data for uni-axial and bi-axial ratcheting of carbon steel are considered. The bi-axial experimental data are from [Jiang Y, Sehitoglu H. Cyclic ratcheting of 1070 steel under multiaxial stress states. Int J Plast 1994;10:579–608]. The material parameters are identified by means of optimization algorithms, and a sensitivity analysis is performed.

05/00918 Uniaxial and biaxial ratchetting in piping materials — experiments and analysis

05/00918 Uniaxial and biaxial ratchetting in piping materials — experiments and analysis

Biaxial ratcheting deformation of type 304 stainless steel: Effect of memorization of back stress

This paper treats both experiments and simulations of biaxial ratcheting. The experiments are conducted using a tubular specimen of type 304 stainless steel at room temperature. The specimen was subjected to cyclic shear straining under the axial superposed stress. The experiments show that the biaxial ratcheting strain was affected by the cyclic shear strain amplitude, the shear strain rate and the superposed stress level. Larger biaxial ratcheting strain occurred in the case of tensile superposed stress compared with that in the case of the compressive superposed stress. Moreover, even under the zero superposed stress, biaxial ratcheting strain occurred in the axial direction due to the cyclic shearing straining. Finally, the biaxial ratcheting behaviours were simulated by the unified constitutive model proposed by the authors. The characteristic features of the biaxial ratcheting behaviour, especially the axial strain due to the cyclic shear straining superposed on the zero axial stress, are well simulated by the constitutive model.

Uniaxial and biaxial ratchetting in piping materials—experiments and analysis

The performance of the Chaboche kinematic hardening model has been evaluated in this paper to predict the ratchetting responses for a broad set of uniaxial and biaxial loading histories. The investigations have been performed with reference to both uniaxial and biaxial experimental data, viz. (a) strain and stress controlled uniaxial tests on tensile specimens; (b) biaxial tests on straight pipes with constant internal pressure and cyclic bending load; and (c) a shake table test on elbow. The parameters of the Chaboche model have been calculated from the uniaxial strain controlled stable hysteresis loop. Amongst the various parameters in the Chaboche model, it has been found that the selection of the value of γ 3 plays a crucial role in achieving better simulation. The Chaboche model was observed to predict complete shakedown for γ 3=0. On the other hand, the model closely simulated the experimental results for γ 3=9. The same parameters have been used to analyze the biaxial loading condition. Ratchetting simulation studies by the Chaboche model have resulted in reasonably good agreement with experiments.

Uniaxial and biaxial ratchetting study of SA333 Gr.6 steel at room temperature

The phenomenon of ratchetting is defined as constant accumulation of plastic strain or deformation under combined steady state and cyclic loading. It can reduce the fatigue life or can cause failure of piping components or systems subjected to seismic or other cyclic loads. The uniaxial ratchetting characteristics of SA333 Gr.6 steel have been investigated at room temperature in the present paper. The specimens were subjected to cyclic axial stress with a constant mean stress of 200 MPa and a varying amplitude stress of 149, 174, 199 and 224 MPa. Tests were also performed on 203.2 mm, Sch 80, SA333 Gr. 6 carbon steel straight pipe. The pipe was subjected to a constant internal pressure of 18 MPa and a cyclic bending load. The effects of amplitude of load on the rate of ratchetting have also been investigated in the present paper. The uniaxial experiments showed that specimens exhibited shakedown at low stress amplitude after some strain accumulation. However, specimens experienced continuous ratchetting at higher stress amplitudes with no shakedown before failure. Ovalization of the pipe cross-section was observed when the pipe was subjected to constant internal pressure and cyclic point load. Local bulging was observed at higher loading. The pipe did not show any shakedown behaviour for the given cycles of loading and exhibited continuous ratchetting under the varying amplitude loading.

Modeling of uniaxial and biaxial ratcheting behavior of 1026 Carbon steel using the simplified Viscoplasticity Theory Based on Overstress (VBO)

Hassan and Kyriakides [1], Hassan et al. [2], and Corona et al. [3] performed uniaxial and biaxial ratcheting experiments on heat-treated 1026 Carbon steel. The loading histories performed with uniaxial and tubular specimens were selected to simulate those encountered in nuclear reactor vessels. The stress-strain diagram of 1026 Carbon steel was used to determine the material constants in a simplified version of VBO. Small rate dependence was allowed. The model represents some nonlinear rate dependence, kinematic hardening and cyclically neutral behavior. The set of material constants determined only from uniaxial tests was used throughout the paper. Numerical experiments included are: (i) uniaxial stress-controlled cycling with various mean stresses, (ii) strain-controlled axial tests with tubular specimens under constant and variable internal pressure, and (iii) examination and variation of certain material constants of the VBO model that can influence ratcheting. Very good agreement with the experiments is found for the uniaxial case. However the ratchet strain accumulation during biaxial cycling is over-predicted by VBO and other constitutive models.

An advancement in cyclic plasticity modeling for multiaxial ratcheting simulation

In a search for a constitutive model for ratcheting simulations, the models by Chaboche, Ohno–Wang, McDowell, Jiang–Sehitoglu, Voyiadjis–Basuroychowdhury and AbdelKarim–Ohno are evaluated against a set of uniaxial and biaxial ratcheting responses. With the assumption of invariant shape of the yield surface during plastic loading, the ratcheting simulations for uniaxial loading are primarily a function of the plastic modulus calculation, whereas the simulations for multiaxial loading are sensitive to the kinematic hardening rule of a model. This characteristic of the above mentioned models is elaborated in this paper. It is demonstrated that if all parameters of the kinematic hardening rule are determined from uniaxial responses only, these parameters primarily enable a better plastic modulus calculation. However, in this case the role of the kinematic hardening rule in representing the ratcheting responses for multiaxial loading is under-appreciated. This realization motivated many researchers to incorporate multiaxial load dependent terms or parameters into the kinematic hardening rule. This paper evaluates some of these modified rules and finds that none is general enough to simulate the ratcheting responses consistently for the experiments considered. A modified kinematic hardening rule is proposed using the idea of Delobelle and his co-workers in the framework of the Chaboche model. This new rule introduces only one multiaxial load dependent parameter to the Chaboche model, but performs the best in simulating all the ratcheting responses considered.

Simulation of Biaxial Ratchetting by Constitutive Model Based on Dislocation Density.

This paper treated a series of experiments and simulations concerned with biaxial ratcheting behavior. The biaxial ratchetting tests were conducted using SUS304 stainless steel subjected to cyclic torsion with superposed axial tensile or compressive stresses. Experimental results showed that (1) the axial strain occurred due to even zero superposed axial stress, and (2) biaxial ratchetting strain due to the tensile superposed stress was larger than that due to the compressive superposed stress. The biaxial ratchetting behavior was simulated by a constitutive model based on a viscoplastic potential related to dislocation density. To explain the axial strain due to zero or nonzero superposed stresses, a constitutive model was proposed, where the effect of the latent hardening on the back stress was considered in the evolution equation of the back stress. The constitutive model successfully simulated the axial strain due to zero or nonzero superposed stresses. The difference of the biaxial ratchetting strain due to the tensile and compressive superposed stresses was also well explained by the constitutive model.

Simulation of Biaxial Ratchetting Using the Unified Constitutive Model Considering Memorization of Backstress.

In this work, a series of biaxial ratchetting tests and numerical simulations are carried out. Experimental results obtained using the tubular specimen of SUS 304 stainless steel subjected to cyclic shear staining under the superposed axial stress show the dependence of the amount of superposed axial stress, the cyclic shear strain amplitude and the shear strain rate. Even under zero superposed stress, the ratchetting strain is induced in the axial direction. Finally, the unified constitutive model proposed by authors is used for the predictions of these biaxial ratchetting. The characteristic features of biaxial ratchetting are well described by the numerical simulation.

Kinematic hardening rules in uncoupled modeling for multiaxial ratcheting simulation

Abstract An earlier paper by the authors evaluated the performance of several coupled models in simulating a series of uniaxial and biaxial ratcheting responses. This paper evaluates the performance of various kinematic hardening rules in an uncoupled model for the same set of ratcheting responses. A modified version of the Dafalias–Popov uncoupled model has been demonstrated to perform well for uniaxial ratcheting simulation. However, its performance in multiaxial ratcheting simulation is significantly influenced by the kinematic hardening rules employed in the model. Performances of eight different kinematic hardening rules, when engaged with the modified Dafalias–Popov model, are evaluated against a series of rate-independent multiaxial ratcheting responses of cyclically stabilized carbon steels. The kinematic hardening rules proposed by Armstrong–Frederick, Voyiadjis–Sivakumar, Phillips, Tseng–Lee, Kaneko, Xia–Ellyin, Chaboche and Ohno–Wang are examined. The Armstrong–Frederick rule performs reasonably for one type of the biaxial ratcheting response, but fails in others. The Voyiadjis–Sivakumar rule and its constituents, the Phillips and the Tseng–Lee rules, can not simulate the biaxial ratcheting responses. The Kaneko rule, composed of the Ziegler and the prestress directions, and the Xia–Ellyin rule, composed of the Ziegler and Mroz directions, also fail to simulate the biaxial ratcheting responses. The Chaboche rule, with three decomposed Armstrong–Frederick rules, performs the best for the whole set of ratcheting responses. The Ohno–Wang rule performs well for the data set, except for one biaxial response where it predicts shakedown with subsequent reversal of ratcheting.

102 二軸ラチェット変形の粘塑性効果(OS1-1 材料の強度と力学特性)(OS1 材料の力学・疲労・破壊現象)

102 二軸ラチェット変形の粘塑性効果(OS1-1 材料の強度と力学特性)(OS1 材料の力学・疲労・破壊現象)

Study on Multiaxial Inelastic Deformation under Ratcheting and Nonproportional Loading Conditions Based on Viscoplasticity Theory.

Inelastic deformation of 316 FR stainless steel under biaxial ratcheting and nonproportional straining is discussed based on viscoplasticity theory by Krempl. It is pointed out that the multiaxial ratcheting can be regraded as a special case of nonproportional loading and that the simultaneous modeling is necessary for the both behaviors. In the one of the author's previous study a viscoplastic constitutive equation was developed for nonproportional loading based on the viscoplasticity theory proposed by Krempl. An idea similar to Ohno-Wang model for ratcheting is used to extend this previous model and a viscoplastic constitutive model is developed for biaxial ratcheting and nonproportional loading. A critical value is assumed for the dynamic recovery of thekinematic hardening parameter. It is also assumed that the activating the dynamic recovery of the kinematic hardening reduces the additional hardening under nonproportional loading. It is shown that the developed model well reproduces both biaxial ratcheting and stress response under nonproportional loading.

Analysis of Biaxial Ratchetting Deformation Based on Multiple Strata Plasticity Model.

Analysis of Biaxial Ratchetting Deformation Based on Multiple Strata Plasticity Model.

Anatomy of coupled constitutive models for ratcheting simulation

Abstract This paper critically evaluates the performance of five constitutive models in predicting ratcheting responses of carbon steel for a broad set of uniaxial and biaxial loading histories. The models proposed by Prager, Armstrong and Frederick, Chaboche, Ohno-Wang and Guionnet are examined. Reasons for success and failure in simulating ratcheting by these models are elaborated. The bilinear Prager and the nonlinear Armstrong-Frederick models are found to be inadequate in simulating ratcheting responses. The Chaboche and Ohno-Wang models perform quite well in predicting uniaxial ratcheting responses; however, they consistently overpredict the biaxial ratcheting responses. The Guionnet model simulates one set of biaxial ratcheting responses very well, but fails to simulate uniaxial and other biaxial ratcheting responses. Similar to many earlier studies, this study also indicates a strong influence of the kinematic hardening rule or backstress direction on multiaxial ratcheting simulation. Incorporation of parameters dependent on multiaxial ratcheting responses, while dormant for uniaxial responses, into Chaboche-type kinematic hardening rules may be conducive to improve their multiaxial ratcheting simulations. The uncoupling of the kinematic hardening rule from the plastic modulus calculation is another potentially viable alternative. The best option to achieve a robust model for ratcheting simulations seems to be the incorporation of yield surface shape change (formative hardening) in the cyclic plasticity model.