General Analytical Shakedown Solution for Structures with Kinematic Hardening Materials

The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems： a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.

AN EXPERIMENTAL STUDY ON THE KINEMATIC HARDENING RULES FOR NONPROPORTIONAL CYCLIC PLASTICITY

An experimental investigation was cawted out of the cyclic saturated kinematic hardening of the solution treatment stainless steel 316L subjected to cyclic loading for seveml strain paths, such as uniaxial cycling, cireulan elliPtic, diamond, rectangular shapes. The evoluting tndectories of back stresses in deviatoric stress space were obtained, and the evolution of back stress mtes during cyclic saturuted loading was analyzed under the assumption that the yield sudece rudius at cyclic saturation is constant and the direction of plastic stmin rute coincides with the one of the out normal vector Of the yield sudece. Some significant results were obtained.

THE KINEMATIC HARDENING RULES UNDER NONPROPORTIONAL CYCLIC LOADING

A discussion of several kinematic hardening rules based on nonproportional cyclic experiments of 42CrMo steel is presented. They include Prager, Ziegler, Chaboche, Mroz and Tseng Lee hardening rules. It shows that Mroz and Tseng Lee rule related to a two surface model has the latent potentiality to describe the nonproportional cyclic hardening behaviors, and a simple two surface model is presented.

SHAKEDOWN ANALYSIS OF SHELL STRUCTURES OF KINEMATIC HARDENING MATERIALS

It is of great practical importance to analyze the shakedown of shell structures under cyclic loading, especially of those made of strain hardening materials.In this paper, same further understanding of the shakedown theorem for kinematic hardening materials has been made, and it is applied to analyze the shakedown of shell structures Though the residual stress of a real stale is related to plastic strain, the time-independent residual stress field as we will show in the theorem may be unrelated to the time-independent kinematically admissible plastic strain field For the engineering application, it will lie much more convenient to point this out clearly and definitely, otherwise it will be very difficult. Also, we have proposed a new method of proving this theorem.The above theorem is applied to the shakedown analysis of a cylindrical shell with hemispherical ends. According to the elastic solution, various possible residual sfcss and plastic strain Jlelds, the shakedown analysis of the structure can be reduced to a mathematical programming problem.The results of calculation show that the shakedown load oj strain hardening materials is about 30-40% higher than that of ideal plastic materials. So it is very important to consider the hardening of materials in the shakedown analysis,for it can greatly increase the structure design capacity, and meanwhile provide ascicntific basis to improve the design of shell structures.

A refined deviatoric hardening plastic model for sand

The classical deviatoric hardening models are capable of characterizing the mechanical response of granular materials for a broad range of degrees of compaction.This work finds that it has limitations in accurately predicting the volumetric deformation characteristics under a wide range of confining/consolidation pressures.The issue stems from the pressure independent hardening law in the classical deviatoric hardening model.To overcome this problem,we propose a refined deviatoric hardening model in which a pressure-dependent hardening law is developed based on experimental observations.Comparisons between numerical results and laboratory triaxial tests indicate that the improved model succeeds in capturing the volumetric deformation behavior under various confining/consolidation pressure conditions for both dense and loose sands.Furthermore,to examine the importance of the improved deviatoric hardening model,it is combined with the bounding surface plasticity theory to investigate the mechanical response of loose sand under complex cyclic loadings and different initial consolidation pressures.It is proved that the proposed pressure-dependent deviatoric hardening law is capable of predicting the volumetric deformation characteristics to a satisfactory degree and plays an important role in the simulation of complex deformations for granular geomaterials.

A unified plasticity methodology for rate-and temperature-sensitive alloys exhibiting a non-linear kinematic hardening behavior

In this paper, a novel unified plasticity methodology is proposed to allow the coupling of rate-and temperature-sensitivity of engineering alloys as well as the non-linear kinematic hardening behavior often observed during cyclic loading. The proposed methodology is general in the sense that an arbitrary constitutive model may be chosen for the viscoplastic part, as well as the cyclic part. We adapt our model with a physically-motivated viscoplasticity flow rule and a nonlinear kinematic hardening model. In contrast with other unified plasticity models, the simplified theory involves few material parameters that can be readily calibrated from standard mechanical tests. The capabilities of the proposed theory are demonstrated for a hot rolled annealed 304 L stainless steel supplied by Vimetal Peckover. The model is tested with stress–strain curves obtained from standard tensile and cyclic uniaxial tests at various strain amplitudes and strain-rates, and good accuracy of the response is obtained for strains up to 15%, within a temperature range of 293–673 K. We note that the cyclic plasticity model in our adapted theory can be readily enhanced with ratchetting, mean stress relaxation, strain amplitude history, Masing effects or other complex capabilities.

Parameters Calibration of the Combined Hardening Rule through Inverse Analysis for Nylock Nut Folding Simulation

Locking nuts are widely used in industry and any defects from their manufacturing may cause loosening of the connection during their service life.In this study,simulations of the folding process of a nut’s flange made from AISI 1040 steel are performed.Besides the bilinear isotropic hardening rule,Chaboche’s nonlinear kinematic hardening rule is employed with associated flow rule and Hill48 yield criterion to set a plasticity model.The bilinear isotropic hardening rule’s parameters are determined by means of a monotonic tensile test.The Chaboche’s parameters are determined by using a low cycle tension/compression test by applying curve fitting methods on the low cycle fatigue loop.Furthermore,the parameter calibrations are performed in the finite element simulations by using an optimization approach based on the inverse analysis.Dimensional accuracy for the nut is of primary concern due to the tolerance constraints of the nut manufacturers.Experimental diameter and height measurements of the folded locking nut are compared with those obtained from the optimized model.The results reveal that the folding dimensions can be predicted more accurately when the model parameters are determined by using the combined hardening rule.The calibrated parameters are presented for the folding and cycling deformation processes.

Constitutive Model for Multiaxial Ratcheting Predictions of Cyclic Softening Weld Metal

A series of fully reversed axial, torsional strain-controlled cyclic tests and two multiaxial ratcheting tests were conducted on weld metal specimens using an Instron8521 tension-torsional servo-controlled testing machine. The weld metal showed clear cyclic softening under axial, torsional and multiaxial loading. A modified kinematic hardening rule was proposed in which a multiaxial-loading-dependent parameter incorporated the radial evanescence term of the Burlet-Cailletaud mode with the Ohno-Wang kinematic hardening rule to predict the multiaxial ratcheting effects. The introduction of yield stress evolved with accumulated plasticity strain enables the model to predict cyclic plasticity behavior of cyclic softening or cyclic hardening materials. Thus modified model considers the isotropic hardening as well as kinematic hardening of yield surface, and it can present description of plasticity behavior and ratcheting of cyclic softening and cyclic hardening materials well under multiaxial loading.

Cyclic behavior of soils and numerical analyses in cold regions and seismic zones

The solutions of boundary value problems involving strain-softening material property contain serious difficulties from both modeling of strain-localization and a viewpoint of numerical procedure. Mesh size-dependent hardening modulus is considered to alleviate the mesh size-dependency of the solution. The elasto-plastic soil model with kinematic hardening model considering the cumulative deformation by cyclic loading is developed. In finite element analyses, the dynamic relaxation method combined with the generalized return-mapping algorithm is applied to the static drained and un-drained tri-axial tests and plane strain tests. The cyclic behavior of retaining wall problems by freeze and thaw in cold regions is also analyzed. Finally the dynamic progressive failure analysis of rockfill dam is carried out.

APPLICATION AND THEORETICAL ANALYSIS OF C/SiC COMPOSITES BASED ON CONTINUUM DAMAGE MECHANICS

Based on the thermodynamic theory, an orthotropic damage constitutive model was developed to describe the nonlinear mechanical behavior of C/SiC composites. The different nonlinear kinematic and isotropic hardening functions were adopted to describe accurately the damage evolution processes. The damage variables were defined with the damaged modulus and the initial undamaged modulus on energy equivalence principle. The initial orthotropy and damage coupling were presented in the damage yield function. Tensile and in-plane shear loading and unloading tests were performed, and a good agreement between the model and the experimental results was achieved.

Bauschinger-Like Effect of AZ31 Magnesium Alloy Wide Sheet During the Straightening Process

The Bauschinger-like effect, which showed up in the straightening process of the AZ31 magnesium alloy wide sheet, was investigated through the multi-pass discrete three-point bending–unloading–bending(BUB) experiments. The stress variable, anisotropy, and asymmetry of tension and compression on the straightening process were corresponding to the Bauschingerlike effect. The Bauschinger-like effect in the initial, intermediate, and end of the straightening process was dominated by the twinning, detwinning, and dislocation induced by pyramidal < c + a > slip, respectively. Also, they were responsible for the transformation of the Bauschinger stress parameter(BSP) and Bauschinger energy parameter(BEP). Later, the anisotropic nonlinear kinematic hardening model(ANK model) to describe the Bauschinger-like effect was optimized and simplified.

Ratcheting behavior of notched stainless steel samples subjected to asymmetric loading cycles

The ratcheting response of 316 stainless steel samples at the vicinity of notch roots under single-and multi-step loading conditions is evaluated.Multi-step tests were conducted to examine local ratcheting at different low–high–high and high–low–low loading sequences.The stress levels over loading steps and their sequences highly influenced ratcheting magnitude and rate.The change of stress level from low to high promoted ratcheting over proceeding cycles while ratcheting strains dropped in magnitude for opposing sequence where stress level dropped from high to low.Local ratcheting strain values at the vicinity of notch root were found noticeably larger than nominal ratcheting values measured at farer distances from notch edge through use of strain gauges.Ratcheting values in both mediums of local and nominal were promoted as notch diameter increased.To assess progressive ratcheting response and stress relaxation concurrently,the Ahmadzadeh-Varvani(A-V)kinematic hardening rule was coupled with Neuber’s rule enabling to calculate local stress at notch root of steel samples.Local stress/strain values were progressed at notch root over applied asymmetric stress cycles resulting in ratcheting buildup through A-V model.The relaxation of stress values at a given peak-valley strain event was governed through the Neuber’s rule.Experimental ratcheting data were found agreeable with those predicted through the coupled framework.