Kinematic Hardening Plasticity Research Articles

Partitioned coupling framework to combine a kinematic hardening plasticity model and a creep model for structures in a high‐temperature environment

AbstractThe present study proposes a partitioned coupling framework for the implementation of a combined kinematic hardening plasticity and creep model. In the present framework, plastic and creep implicit stress integrations are performed alternately and iteratively until convergence in a partitioned coupling manner. This approach enables us to tractably implement a constitutive model that combines a plasticity model and a creep model in the program. The present framework was applied to the combination of the Ohno–Wang plasticity model and the Norton–Bailey creep model for numerical examples. The numerical examples demonstrated the capability of the present framework in analyzing realistic structures at high temperature with the consideration of both plasticity and creep.

Analysis of thruster nozzle in a high-temperature environment using partitioned coupling framework to combine a kinematic hardening plasticity model and a creep model

A framework based on a partitioned stress integration technique was proposed by the present authors for a general combined elastic-plastic and creep constitutive model. It was developed to analyze a structure used in a high temperature environment. In the present study, a thruster nozzle model subjected to thermal strain is analyzed using the framework to verify it. The Ohno-Wang model and the Norton-Bailey model are used for the elastic-plastic model and the creep model, respectively. This combined model is also verified..

Micro-mechanical modeling of irreversible hygroscopic strain in paper sheets exposed to moisture cycles

Paper is a complex material consisting of a network of cellulose fibres at the micro-level. During manufacturing, the network is dried under restraint conditions due to tension in the paper web in machine direction. This gives rise to internal strains that are stored in the produced sheet. Upon exposure to a moisture cycle, these strains may be released. This results in permanent shrinkage that may cause instabilities such as curl or waviness of the sheet. The prime objective of this paper is to model this irreversible shrinkage and to link its magnitude to the properties of the fibres and of the network. For this purpose, randomly generated fibrous networks of different coverages (i.e.ratio of the area occupied by fibres and that of the sheet) are modeled by means of a periodic representative volume element (RVE). Within such RVEs, a finite element method combined with a kinematic hardening plasticity model at the scale of the fibres is used to capture the irreversible response. The computational results obtained demonstrate that the magnitude of the irreversible strains increases with coverage until a certain coverage and beyond that coverage decreases in magnitude. This phenomenon is explained by considering the area fraction of free-standing fibre segments relative to bonded fibre segments in the network. A structure–property dependency of irreversible strains at the sheet-level on the micro-structural parameters of the network is thereby established.

Finite Element Analysis of RC Beams by the Discrete Model and CBIS Model Using LS-DYNA

There are several techniques to simulate rebar reinforced concrete, such as smeared model, discrete model, embedded model, CLIS (constrained Lagrange in solid) model, and CBIS (constrained beam in solid) model. In this study, however, the interaction between the concrete elements and the reinforcement beam elements is only simulated by the discrete model and CBIS (constrained beam in solid) model. The efficiency and accuracy comparisons are investigated with reference to the analysis results by both models provided by LS-DYNA explicit finite element software. The geometric models are created using LS-PrePost, general purpose preprocessing software for meshing. The meshed models are imported to LS-DYNA where the input files are then analyzed. Winfrith and CSCM concrete material options are employed to describe the concrete damage behavior. The reinforcement material model is capable of isotropic and kinematic hardening plasticity. The load versus midspan deflection curves of the finite element models correlate with those of the experiment. Under the conditions of the same level of accuracy, the CBIS model is evaluated to have the following advantages over the discrete model. First, it has the advantage of reducing the time required for FE modeling; second, saving computer CPU time due to a reduction in total number of nodes; and third, securing a good aspect ratio of concrete elements.

Effect of Foreign Object Damage at Different Impact Parts for TC4 Titanium Alloy Blades

The effect of foreign object damage at different impact parts of TC4 Titanium Alloy blades is studied in this paper and impact damage from common foreign objects at different parts of the inlet side of the blade has been simulated in the process of aircraft skidding using the ANSYS/LS-DYNA software based on the Kinematic hardening plastic constitutive model. The results show that the damage depth of the sandstone increases linearly with the increase of relative kinetic energy when the same foreign object strikes different parts, but there is a critical relative kinetic energy of 2.54J and 2.50J for the steel ball and screw, respectively. When the relative kinetic energy is less than the critical value, the damage depth increases continuously with the relative kinetic energy, and when the relative kinetic energy is greater than the critical value, the damage depth decreases continuously with the relative kinetic energy.

Numerical modelling of blast-induced fractures in coal masses under high in-situ stresses

Borehole blasting is a technique widely applied to form fracture networks in coal masses. There are many original cracks in coal masses, such as bedding planes and cleat planes. Coal masses are also subjected to high in-situ stress deep underground. However, the effects of pre-existing cracks and in-situ stress on blast-induced fractures are not well understood. In this paper, the isotropic and kinematic hardening plasticity model considering compression and tensile failure is introduced to numerical models, and the contact interface is used to simulate the effect of jointed planes on coal-mass blasting. The effects of jointed plane, constant in-situ stress and lateral pressure coefficient on blast-induced cracks are explored, and the relative peak displacement (Δup) of jointed planes is considered as the basis for determining jointed plane failure. The results indicate that blast-induced cracks tend to expand along jointed planes in the coal mass; the in-situ stress enhances the compression effect and weakens the tension effect in the radial direction of the borehole; and the jointed plane failure zone in coal masses decreases with increasing in-situ stress. The lateral pressure coefficient also has a distinctive influence on blast-induced crack expansion.

Characterization of the super-short shock pulse generated by an exploding foil initiator

Exploding foil initiator (EFI) uses a thin flyer to initiate an explosive pellet. The shock pulse generated by EFI is very difficult to measure and calculate accurately, which is crucial to the operation of EFI. The velocity of the thin flyer driving by electrical explosion was obtained in order to quantitate the input of the impact process. Replacing the explosive pellet by a LiF window, the super-short shock pulse generated by a thin flyer (25 μm) was measured using the interface particle velocity method by a Photonic Doppler Velocimetry (PDV). The maximum particle velocity is 1.716 km/s in the experimental condition, meanwhile the shock duration is 4.5 ns. The impedance matching technique and the shock Hugoniot data were used to calculate the shock pressure and shock duration of the impact process, however the calculation results have distinct error comparing to the experimental ones. Utilizing the elastic-plastic model of flyer which considers the kinematic hardening plasticity effect, the simulations were carried out to predict the particle velocity and shock duration. The results show good consistency of the experimental and simulated particle velocities, which infers that the material model of flyer can describe its impact behaviours accurately.

On Residual Stress and Relief for an Ultra-Thick Cylinder Weld Joint Based on Mixed Hardening Model: Numerical and Experimental Studies

Residual stress distributions as welded and after local postwelding heat treatment (PWHT) of butted weld joint of a huge cylinder with ultra-thick wall were investigated by finite element (FE) simulations and measurement. Sequential coupling thermal-mechanical analyses were conducted with a generalized plane strain two-dimensional (2D) model to simulate the welding procedure bead by bead, combining with three-dimensional (3D) double-ellipsoid moving heat source and mixed isotropic–kinematic hardening plastic model. The simulation was validated by X-ray diffraction (XRD) measurements. Simulation results showed that local PWHT with heated band width of 0.5Rt can significantly reduce the residual stress on the outer surface of weld joint, but bring about harmful high tensile stress on inner surface due to bending moment induced by local radial thermal distortion. For the purpose to find out the appropriate heated band width of local PWHT, relations between stress relief and size of heated band were studied. Results show that the stresses on the inner surface reach a maximum value when the heated band width is less than 1Rt. Based on the simulation results and from the view point of lowering the stress level on the inner surface, the optimum width of 3Rt for heated band was proposed.

Model Verification for Material Parameters of Titanium Alloy Ti-6AL-4V and Steel

To carry out numerical simulation of TC4 titanium alloy blade impacted by foreign objects effectively, this paper takes the test results of steel ball and sandstone impacting titanium alloy flat blade inlet and blade surface as the benchmark, and uses ANSYS/LS-DYNA software to adopt kinematic hardening plasticity model to simulates the impact results and inverts the contact stiffness factor and the other three parameters were obtained by the way of inversion reasoning.

Deformation Behavior of Press Formed Shell by Indentation and Its Numerical Simulation

Deformation behavior and energy absorbing performance of the press formed aluminum alloy A5052 shells were investigated to obtain the basic information regarding the mutual effect of the shell shape and the indentor. Flat top and hemispherical shells were indented by the flat- or hemispherical-headed indentor. Indentation force in the rising stage was sharper for both shell shapes when the flat indentor was used. Remarkable force increase due to high in-plane compressive stress arisen by the appropriate tool constraint was observed in the early indentation stage, where the hemispherical shell was deformed with the flat-headed indentor. This aspect is preferable for energy absorption performance per unit mass. Less fluctuation in indentation force was achieved in the combination of the hemispherical shell and similar shaped indentor. The consumed energy in the travel length of the indentor equal to the shell height was evaluated. The increase ratio of the energy is prominent when the hemispherical indentor is replaced by a flat-headed one in both shell shapes. Finite element simulation was also conducted. Deformation behaviors were successfully predicted when the kinematic hardening plasticity was introduced in the material model.

Three-Dimensional Finite Element Elastic–Plastic Model for Subsurface Initiated Spalling in Rolling Contacts

In this investigation, a three-dimensional (3D) finite element (FE) model was developed to study subsurface initiated spalling observed in rolling line contact of tribo components such as bearings. An elastic–kinematic hardening–plastic material model is employed to capture the material behavior of bearing steel and is coupled with the continuum damage mechanics (CDM) approach to capture the material degradation due to fatigue. The fatigue damage model employs both stress and accumulated plastic strain based damage evolution laws for fatigue failure initiation and propagation. Failure is modeled by mesh partitioning along unstructured, nonplanar, intergranular paths of the microstructure topology represented by randomly generated Voronoi tessellations. The elastic–plastic model coupled with CDM was used to predict both ratcheting behavior and fatigue damage in heavily loaded contacts. Fatigue damage induced due to the accumulated plastic strains around broken intergranular joints drive the majority of the crack propagation stage, resulting in a lower percentage of life spent in propagation. The 3D FE model was used to determine fatigue life at different contact pressures ranging from 2 to 4.5 GPa for 33 different randomly generated microstructure topology models. The effect of change in contact pressure due to subsurface damage and plastic strain accumulation was also captured by explicitly modeling the rolling contact geometry and the results were compared to those generated assuming a Hertzian pressure profile. The spall shape, fatigue lives, and their dispersion characterized by Weibull slopes obtained from the model correlate well with the previously published experimental results.

Fatigue Modeling of a Notched Flat Plate Under Variable Amplitude Loading Supported by Elastoplastic Finite Element Method Analyses

Although intensive research has been carried out to understand the fatigue behavior of steel notched components, under variable amplitude loading, no definite and general robust models have been derived so far. Therefore, every effort to augment the knowledge in this topic is welcomed. Within this context, existing variable amplitude data, derived by the authors for a notched low carbon pressure vessel steel (P355NL1) flat plate, is used to assess a local approach to fatigue. A linear damage summation framework, supported by elastoplastic finite element analyses, is used. Several variable amplitude loadings were selected and analyzed, using alternative configurations of kinematic hardening plasticity models (e.g., Chaboche’s model with distinct constants superposition). The predictions are assessed using available experimental data and data derived with simplified empirical elastoplastic tools. This paper highlights the difficulties of performing such elastoplastic analysis and compares the obtained results with those obtained using more classical tools for elastoplastic analysis (Glinka and Seeger–Heuler). It was found that fatigue predictions based on an elastoplastic finite element analysis, made using the Chaboche’s model, were significantly more accurate than predictions based on simplified elastoplastic analysis. These results have important practical relevance.

Numerical Simulation for Failure Modes of Reinforced Concrete Beams under Blast Loading

The reinforced concrete (RC) beams have three failure modes using large-scale finite element procedure LS-DYNA to simulate dynamic responses and failure modes of RC beams under blast loading. Holmquist-Johnson-Cook material model was used in concrete, the damage and strain rate effects were considered the kinematic hardening plasticity material model was used in reinforcing bars. With different rebar ratios and charges of weight TNT equivalent and stand-off distance were investigated and discussed. The numerical simulation can predict responses and flexure, flexure-shear and direct shear of the RC beams under different blast loading. The influence of the several factors have been identified and provided a theoretical basis for blast resistant design and retrofitting of the RC beam.

Singular value decomposition of the compliance response matrix for the triaxial stress condition

Performance-based design demands accurate prediction of soil deformation under a working load condition. The nonlinear stress–strain behavior needs to be analyzed quantitatively to advance the understanding of complex soil behavior in the pre-failure condition. The singular value decomposition technique is introduced to quantitatively analyze the compliance matrix representing the strain response envelope (SRE). The rotation of the ellipse of the SRE relates to the anisotropic response of the soil deformation. The off-centered SRE provides evidence of the kinematic hardening plasticity. Quantitative data on the movement of SREs provide us with crucial information to investigate the effect of stress history and the evolution of stiffness anisotropy in soil deformation.

A study on the interaction between fretting wear and cyclic plasticity for Ti–6Al–4V

The fretting wear behaviour of Ti–6Al–4V is experimentally investigated using a cylinder-on-flat specimen arrangement for different loads, strokes and numbers of fretting cycles, including partial slip and gross sliding conditions. An elastic–plastic, finite element (FE) based, incremental wear simulation approach is employed to study the evolution of the surface and sub-surface fretting variables, using a kinematic hardening (continuum) plasticity model to represent the cyclic plasticity behaviour. The predicted evolution of plastic deformation and fretting variables, such as contact pressure, relative slip, sub-surface stresses and critical-plane Smith–Watson–Topper (multiaxial) fatigue parameter, due to the simulated wear are compared with the observed wear scar characteristics and locations of crack initiation. It is shown that the characteristics of predicted plastic strain and damage accumulation are significantly different for the gross sliding and the partial slip cases and that the differences can be correlated with the observed differences in surface morphology and surface cracking. It is shown that the location of plasticity due to shear yielding at the surface promotes wear across the contact region for the gross sliding case and at the stick–slip interface for the partial slip case.

Calculated and observed behaviour of clayey soil under cyclic loading beneath preloading embankments for oil tanks

Two accurately monitored preloading embankments built to reduce the settlement of two oil tanks for a thermoelectric power plant near Mantova, Italy, were analysed using the finite element method and different constitutive assumptions. The most prominent feature of the proposed case study is that it involved two major loading cycles (preloading embankment construction–removal and oil tank filling–emptying) of different amplitudes (embankment heights of 8.60 and 12.50 m and a tank level of 14.00 m). Further minor loading cycles were also applied due to changes (of up to 6–7 m) in the hydrometric levels of the Po River. Because of the cyclic nature of the loading and the detailed measurements (of pore pressures and horizontal and vertical movements on the ground surface and in depth), this case study proves very useful for validating advanced features of modern constitutive models. The effects of elastic anisotropy, plastic anisotropy, and destructuration are considered in two different bounding-surface, kinematic-hardening plasticity models specific to clays and sands. The effects of permeability and Poisson’s ratio are also analysed. The conclusions have a general applicability and are not specific to the selected constitutive models.

Implicit integration of a mixed isotropic–kinematic hardening plasticity model for structured clays

AbstractIn recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non‐trivial problems in their numerical integration in finite elements codes.The paper describes a fully implicit stress‐point algorithm for the numerical integration of a single‐surface mixed isotropic–kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid‐shaped yield function, inside which a stress‐dependent reversible stiffness is accounted for by a non‐linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam‐Clay one to include plastic strain‐driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space.The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global‐level Newton–Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd.

General Formulation of Two Kinematic Hardening Constitutive Models with a Smooth Elastoplastic Transition

Two new constitutive models formulated within the framework of kinematic hardening plasticity are presented and their implementation into a finite-element program is described. The models are extensions of two existing constitutive models for reconstituted clays and introduce a number of kinematic surfaces within the modified CAM clay bounding surface. The new key feature of the models is a hardening modulus which results in a smooth variation of stiffness with strain, from the high elastic value, within the first kinematic surface, to the value on the bounding surface. Other features include a mathematical formulation of the models in general stress space to facilitate their implementation into a finite-element program, a variety of shapes of the yield and plastic potential surfaces in the deviatoric plane, and the novel concept of changing the active yield surface, which is necessary for the consistent formulation and implementation of the models into a finite-element code. The models are shown to have the ability to reproduce realistically the observed nonlinear prefailure behavior of overconsolidated clays in the small strain range.

Optimization-based material parameter identification in indentation testing for finite strain elasto-plasticity

The calculation of the derivatives of the state variables with respect to material parameters using the direct differentiation method is developed for the case of a finite strain finite element analysis in corotational formulation for material behaviour including hypo-elasticity and non-linear isotropic and kinematic hardening plasticity. The sensitivity analysis for the case of flexible-to-flexible contact, required in indentation testing, has been included. The derivatives obtained in a rotating-stretching bar problem are compared to results obtained by the finite difference method in order to verify the suitability of the corotational formulation in sensitivity analysis for dealing with rigid body rotations. Material parameter identification using a gradient-based numerical optimization procedure is assessed with respect to stability by using pseudo-experimental indentation curves, obtained from modelling with known material parameters, and superposed with artificial noise. The effect of the load history on parameter identification is investigated.

Multiscale Thermodynamic Significance of the Scale Invariance Approach in Continuum Inelasticity

AbstractIn this paper, the scale invariance approach from micro- to macro-plasticity by Aifantis (1995, “From Micro- to Macro-plasticity: The Scale Invariance Approach,” ASME J. Eng. Mater., 117, pp. 352–355) and Ning and Aifantis (1996, “Anisotropic Yield and Plastic Flow of Polycristalline Solids,” Int. J. Plasticity, 12, pp. 1221–1240) is investigated within Rice’s normality structure (1971, “Inelastic Constitutive Relations for Solids: An Integral Variable Theory and its Application to Metal Plasticity,” J. Mech. Phys. Solids, 19, pp. 433–455; 1975, “Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms,” Constitutive Equations in Plasticity, A. S. Argon, ed., MIT Press, Cambridge, MA, pp. 23–79). The normality structure provides a minimal framework of multiscale thermodynamics, and the dissipation equivalence between the microscale and macroscale is ensured by a variational equation which can be further formulated into principle of maximum equivalent dissipation. It is revealed in this paper that within the framework of normality structure, the so-called hypothesis of generalized scale invariance holds for the kinetic rate laws, flow rules, and orthogonality conditions in the sense of Aifantis (1995, “From Micro- to Macro-plasticity: The Scale Invariance Approach”). Stemming from Rice’s kinetic rate laws, the generalized scale invariance reflects the inherent self-consistent character of the normality structure. If the plastic work rate is assumed to be equal to the intrinsic dissipation rate, the kinematic hardening plasticity as a demonstration of the scale invariance approach by Aifantis (1995, “From Micro- to Macro-plasticity: The Scale Invariance Approach”), can be well accommodated within the framework of normality structure. Therefore, the scale invariance approach is justified from a multiscale thermodynamic viewpoint. It is further shown that the maximization procedure in this approach just corresponds to the principle of maximum equivalent dissipation.