Guozheng Kang

A visco-plastic constitutive model for ratcheting of cyclically stable materials and its finite element implementation

Abstract A visco-plastic constitutive model was proposed to simulate the uniaxial/multiaxial ratcheting of cyclically stable materials (such as U71Mn rail steel), and its finite element implementation was also achieved. The kinematic hardening rule used in the proposed model is similar to that developed by Abdel-Karim and Ohno [Int. J. Plast. 16 (2000) 225], except for a modification to the dynamic recovery term. The proposed model is verified by simulating the uniaxial/multiaxial ratcheting of U71Mn rail steel at room temperature. In the finite element implementation of the proposed model, based on radial return method and backward Euler integration, a new implicit stress integration algorithm is proposed by combining the successive substitution method developed by Kobayashi and Ohno [Int. J. Numer. Meth. Engng. 53 (2002) 2217] with Newton–Raphson solving method of non-linear scalar equation. Simultaneously, a new expression of consistent tangent modulus is also derived for rate-dependent plasticity. Numerical examples are given to verify the advantage of the implementation and the capability of the model in simulating ratcheting and cyclic stress relaxation.

A visco–plastic constitutive model incorporated with cyclic hardening for uniaxial/multiaxial ratcheting of SS304 stainless steel at room temperature

Abstract In the framework of unified visco–plastic constitutive theory, the strain-controlled cyclic characteristics and uniaxial/multiaxial ratcheting of cyclically hardening materials, such as SS304 stainless steel, were analyzed and modeled. A constitutive model was developed on the base of Ohno–Wang kinematic hardening model (Int. J. Plast. 9 (1993) 375, 391). In the developed model, the rate dependence of the material was reflected by a viscous term; the steady cyclic flow was reflected by the evolution of kinematic hardening rules with critical state of dynamic recovery developed by Ohno and Wang (Int. J. Plast. 9 (1993) 375, 391); the cyclic hardening was only characterized by the evolution of isotropic hardening and an evolution rule of isotropic hardening with a term of dynamic recovery was used; the effect of loading history on the ratcheting was also considered by introducing a fading memorization function for maximum plastic strain amplitude into the model. Comparing with experimental results of SS304 stainless steel at room temperature, the predicted results of the developed model were proved to be reasonable.

Constitutive modeling of strain range dependent cyclic hardening

Abstract In this paper, a new approach for constitutive modeling of strain range dependent cyclic hardening is proposed by extending the kinematic hardening model based on the critical state of dynamic recovery. It is assumed that isotropic, as well as kinematic, hardening consists of several parts, and that each part of isotropic hardening evolves when the corresponding part of kinematic hardening is in the critical state of dynamic recovery. The extended model is capable of simulating the cyclic hardening behavior in which different characteristics of cyclic hardening appear depending on strain range. The model is verified by simulating the relatively large cyclic straining tests of 304 stainless steel at ambient temperature, in which cyclic hardening does not stabilize before rupture if strain range exceeds a certain value. The model is further verified by predicting the history dependence of cyclic hardening under incremental cyclic loading and the maximum plastic strain dependence of strain hardening in cyclic tension.

Uniaxial and non-proportionally multiaxial ratcheting of SS304 stainless steel at room temperature: experiments and simulations

Abstract The uniaxial and non-proportionally multiaxial ratcheting behaviors of SS304 stainless steel at room temperature were initially researched by experiment and then were theoretically described by a cyclic constitutive model in the framework of unified visco-plasticity. The effects of cyclic stress amplitude, mean stress, and their histories on the ratcheting were experimentally investigated under uniaxial and different multiaxial loading paths. The shapes of non-proportional loading paths were linear, circular, elliptical and rhombic, respectively. In the constitutive model, the rate-dependent behavior of the material was reflected by a viscous term; the cyclic flow and cyclic hardening behaviors of the material under asymmetrical stress-controlled cycling were reflected by the evolution rules of kinematic hardening back stress and isotropic deforming resistance, respectively. The effect of loading history on the ratcheting was also considered by introducing two fading memorization functions for maximum inelastic strain amplitude and isotropic deformation resistance, respectively, into the constitutive model. The effect of multiaxial loading path on the ratcheting was reflected by a non-proportional factor defined in this work. The predicting ability of the developed model was proved to be good by comparing the simulations with corresponding experiments.

Uniaxial and non-proportionally multiaxial ratcheting of U71Mn rail steel: experiments and simulations

Abstract The ratcheting and strain cyclic characteristics of U71Mn rail steel were experimentally researched under uniaxial and non-proportionally multiaxial cyclic loading at room temperature. The effects of cyclic strain, stress and their histories on strain cyclic characteristics and ratcheting were studied, respectively. It is shown that: U71Mn rail steel exhibits a cyclic stabilization and non-memorization for previous loading history under strain cycling; however, the ratcheting of the material depends greatly not only on the current values of mean stress and stress amplitude, but also on their histories; the non-proportionality of multiaxial loading path only causes a negligible additional hardening for the material. Based on the Ohno–Wang non-linear kinematic hardening model [Int. J. Plast. 9 (1993) 375, 391], the uniaxial and multiaxial ratcheting behaviours of the material were simulated by a visco-plastic constitutive model. The simulated results are in good consistence with the experimental ones.

Uniaxial cyclic ratcheting and plastic flow properties of SS304 stainless steel at room and elevated temperatures

An experimental study was carried out for the uniaxial ratcheting of SS304 stainless steel subjected to cyclic stress at room and elevated temperatures. The effects of stress amplitude, mean stress and their histories on the ratcheting of SS304 stainless steel were analyzed at room and elevated temperatures. The interaction of uniaxial strain cycling and stress cycling was also discussed at variable temperatures. On the basis of the experimental data under uniaxial strain and stress cycling, the plastic flow properties of the material were analyzed. The evolution rules of plastic modulus vs. accumulated plastic strain during cyclic loading were investigated under the condition of variable loading processes. The discussion was focused on the relation of uniaxial ratcheting rate and such plastic flow properties as plastic modulus and accumulated plastic strain. It is shown that the uniaxial cyclic properties of the material depend not only on the current loading case and temperature, but also greatly on the previous loading history. The plastic flow properties of strain cycling are apparently different from those of asymmetrical stress cycling; the ratcheting of asymmetrical stress cycling at room and elevated temperature is greatly influenced by the evolution of plastic modulus and accumulated plastic strain. These conclusions are very useful to the development of constitutive model for ratcheting.

Uniaxial ratcheting of SS304 stainless steel at high temperatures: visco-plastic constitutive model

The uniaxial ratcheting of SS304 stainless steel at high temperatures (300, 600 and 700 °C) were analyzed experimentally, and described by a cyclic constitutive visco-plasticity model. The rate dependence of the material was accounted for by introducing a viscous term. The cyclic hardening and cyclic flow behavior of the material under asymmetrical stress-controlled cycling were described by the evolution rules of kinematic hardening back stress and isotropic deforming resistance. Under the isothermal condition, temperature effect was included by terms involving temperature in the evolution equations of isotropic deforming resistance. The effect of load history on ratcheting was also considered by introducing a fading memory function of the maximum inelastic strain amplitude and isotropic deformation resistance. After the material constants were determined from the experimental data, the uniaxial ratcheting of SS304 stainless steel was numerically simulated and compared with the corresponding experimental results at high temperatures. The predicted results agree well with the experimental ones.

Uniaxial Ratcheting Behaviors of Metals with Different Crystal Structures or Values of Fault Energy: Macroscopic Experiments

The uniaxial ratcheting behaviors of several metals with different crystal structures or values of fault energy were observed by the stress-controlled cyclic tests at room temperature. The prescribed metals included 316L stainless steel, pure copper, pure aluminum, and ordinary 20# carbon steel. The effects of applied mean stress, stress amplitude and stress ratio on the uniaxial ratcheting were also investigated. The observations show that different crystal structures or values of fault energy result in more or less different ratcheting behaviors for the prescribed metals. The different ratcheting behaviors are partially caused by the variation of dislocation mobility.

Ratchetting of porcine skin under uniaxial cyclic loading.

Skin soft tissue (e.g., porcine skin) was tested in vitro under uniaxial cyclic loading, and its biomechanical responses were investigated to realize some basic properties which are very significant in assessing the fatigue life of skin soft tissue. The results show that a cyclic accumulation of peak and valley strain, which can be terminologically called as ratchetting in terms of material science of metals, occurs in the porcine skin during cyclic tension-unloading, tension-tension and compression-unloading tests. Observed ratchetting of porcine skin depends on load level and loading orientation greatly and also presents remarkable rate dependence due to the viscosity of skin soft tissue. The ratchetting is much more remarkable during the test at lower loading rate than that at higher loading rate. Moreover, some basic properties of porcine skin were also investigated by monotonic tension, compression and creep tests in order to address the ratchetting more comprehensively. Finally, collagen fiber bundles in the porcine skin and their variation during monotonic and cyclic tension tests were observed microscopically in term of standard iron-hematoxylin staining method. The observations are useful to realize the micro-mechanism of ratchetting deformation.

Experimental study on the cyclic deformation and plastic flow of U71Mn rail steel

Abstract The strain cyclic characteristics and ratcheting behaviour of U71Mn rail steel were experimentally investigated under uniaxial cyclic loading at room temperature. The effects of cyclic strain amplitude, mean strain, strain rate and their histories on strain cyclic characteristics were studied. The effects of stress amplitude, mean stress and their histories on the ratcheting under asymmetrical stress cycling were also analysed. Then, the interaction between strain cycling and stress cycling was discussed, too. Based on the experimental stress–strain data, the plastic flow properties of U71Mn rail steel under cyclic loading were analysed. Plastic modulus and its evolution rule were calculated from experimental data and were discussed under strain and stress cycling, respectively. It is shown that both the strain cyclic characteristics and ratcheting depend not only on current loading state, but also greatly on previous loading history. Under asymmetrical stress cycling, the evolution rule of plastic modulus is different from that under strain cycling. The strain cyclic characteristics and ratcheting behaviour of the material can be described essentially by the evolution of plastic flow.