Incremental Plastic Deformation Research Articles

Three-dimensional elastoplastic post-buckling analysis of functionally graded plates using a novel meshfree Tchebychev-radial point interpolation approach

This paper presents a three-dimensional (3D) analysis of the post-buckling behavior of functionally graded (FG) plates for the first time using an elastoplasticity-based meshfree formulation. A novel 3D Tchebychev-radial point interpolation approach, which combines radial basis functions with Tchebychev polynomials, is developed to solve the nonlinear post-buckling problem. The incremental plastic deformation is modeled by the Prandtl–Reuss flow rule along the isotropic hardening von Mises criterion. The governing equations are derived using the principle of virtual work by considering the 3D full Green–Lagrange strain components. The Newton–Raphson technique along with the arc-length method is used to determine post-buckling equilibrium paths of FG plates. The effective elastoplastic properties of the functionally graded material are assessed by exploiting the homogenization method, named Tamura–Tomota–Ozawa (TTO) model. It has been demonstrated that the accuracy of the solution is improved by incorporating Tchebychev polynomials into the radial point interpolation method (RPIM) shape function, and the stability and robustness of the results are independent of variations in the shape parameter. Furthermore, it is confirmed that TRPIM, with a slightly higher CPU time compared to RPIM, exhibits a higher convergence rate. The excellent agreement of the results with those existing in the literature shows that the proposed meshfree method can be used as a robust and accurate numerical tool to predict the elastoplastic post-buckling behavior of FG plates. Further numerical assessments indicate that post-buckling paths are significantly affected by factors such as geometric parameters, material gradient, loading ratio, and boundary conditions (BCs).

Effect of Repetitive High-Density Current Pulses on Plastic Deformation of Copper Wires under Stepwise Loading

High-density electric current pulses increase the plasticity and reduce the yield stress of metals with negligible heat generation. This effect has great potential for the development of energy-saving technologies for processing hard-to-deform metallic materials. Despite the long history of the study of electroplasticity, there is still no consensus on the physical nature of this effect. In this paper, the effect of repetitive pulses applied at the same or gradually increasing tensile stress on the plastic deformation of copper wire is investigated using a home-made experimental setup. The electroplasticity of the wire in the delivery state and after annealing is compared. It is shown that for a constant tensile stress, the incremental plastic deformation of the wire decreases with each successive pulse. This effect is stronger for annealed wires because they have a lower dislocation density and therefore a lower plasticity resource. The Joule heat release in the specimen and the heating due to plastic deformation are evaluated. The results obtained will be used to fit the parameters of the atomistic model being developed to describe the interaction of electron flow with dislocations.

Evaluation of nanomechanical and nanoscratch response of Inconel 718 reinforced with graphene nanoplates produced by combined ARB-GTAW processes

An attempt was made to produce graphene reinforced Inconel 718 composite by new combining accumulative roll bonding (ARB) and gas tungsten arc welding (GTAW). The phase composition analysis and wear behavior of the composite were assessed. The microstructure characterization was studied by Raman spectroscopy, scanning and transmission electron microscopy. The results display that integrating ARB with GTAW can be consider as a suitable way to yield superalloy-based composite with enhanced tribological behavior due to carbide and carbonitride formation formed from decomposition of graphene nanoplates (GNPs). The elastic modulus and hardness were initial recorded by nanoindentation and then used to attain the yield stress, and subsequently for characterizing flow behavior parameters like n and K. The obtained results exposed that the load–displacement curve acquired from nanoindentation and Nanoscratching has an excellent potential to investigate microscopic behavior of particle based composites. Evaluation of scratch mechanisms in composite specimens presented that the key failure in specimens are due to tensile state Hertzian cracks. Though, as the applied load rises, the specimen undertakes increasing incremental plastic deformation and failures change to interfacial spallation.

The quantitative relationship between non-linear stress-strain behaviour and dislocation structure in martensitic stainless steel

The reversible behaviour of metals at low applied stresses is more complex than the generally assumed linear behaviour. This is primarily because of the reversible nature of dislocation motion leading to a strain contribution known as anelasticity. This work aims to investigate (a) quantification of dislocation structures in industrial grade stainless steels, (b) unloading behaviour, and (c) the fundamentals of reversible and mechanical behaviour occurring below the yield stress. Mechanical testing of martensitic stainless steel (Stavax ESR) was performed in two different modes: incremental plastic deformation and cyclic loading-unloading below the yield stress with a focus on the measurement of small strains and corresponding stresses, occurring in the pre-yield regime. The non-linear reversible behaviour was quantitatively analysed, as opposed to the common approximation of an empirical determination of apparent Young's modulus. The recently proposed pre-yield model has been refined and, for the first time, successfully applied to a complex microstructure such as stainless steel. The quantification of dislocation structure parameters is shown to be an efficient alternative to the conventional experimental methods of quantifying dislocation structure. Further, a unique representation and quantification of the unloading and hysteresis behaviour provides more insight into the material behaviour. Lastly, the little studied microplasticity occurring below the yield stress upon cyclic loading-unloading was determined. Importantly, the physical basis of the model will allow quantification of plastic deformations in the pre-yield region, large enough to be significant in industrial processes.

Hybrid Manufacturing of Stiffening Grooves in Additive Deposited Thin Parts

This paper is focused on the hybridization of additive manufacturing with single-point incremental forming to produce stiffening grooves in thin metal parts. An analytical model built upon in-plane stretching of a membrane is provided to determine the tool force as a function of the required groove depth and to estimate the maximum allowable groove depth that can be formed without tearing. The results for additively deposited stainless-steel sheets show that the proposed analytical model can replicate incremental plastic deformation of the stiffening grooves in good agreement with experimental observations and measurements. Anisotropy and lower formability caused by the dendritic-based microstructure of the additively deposited stainless-steel sheets justifies the reason why the maximum allowable depth of the stiffening grooves is approximately 27% smaller than that obtained for the wrought commercial sheets of the same material that are used for comparison purposes.

Alexander Revisited: Upper- and Lower-Bound Approaches for Axial Crushing of a Circular Tube

In the classical Alexander model for a rigid, perfectly plastic circular tube under axial progressive crushing, an expression for the average crushing force over one complete folding cycle was given in terms of the folding length while the value of the folding length was determined by minimising the average force. This approach is often misunderstood as a correct upper-bound method and has been widely used for analysing large plastic deformation of structures. In this paper, it is highlighted that Alexander approach is strictly not an upper-bound analysis and alternative analyses are presented. A new initial collapse mechanism involving folding both inwards and outwards of the tube wall is proposed for an upper-bound analysis, which leads to the determination of the folding characteristics such as the folding length. Subsequently, a repeatable mechanism is idealised for the periodic folding process. The upper-bound analysis is performed by minimizing the instant force required for maintaining the folding process, which is equivalent to adopting the energy balance for the incremental plastic deformation rather than the total deformation of one complete folding cycle. Instead of merely obtaining the average force as Alexander did, the present theoretical analysis gives a complete force-displacement curve as well as plastic folding length, etc., which agrees well with the existing knowledge. Furthermore, an equilibrium approach is presented involving detail stress state for a deforming configuration of the tube. The lower-bound results re-produce the variation of the force as obtained from the upper-bound analysis when the folding configurations are the same as those in the assumed collapse mechanisms. The present study conceptually reconciles the upper-bound and low-bound theories in structural plasticity for large deformation analysis.

Dynamic recrystallization and solute precipitation during friction stir assisted incremental forming of AA2024 sheet

Friction stir assisted incremental sheet forming (FS-ISF) has been proved to further improve the formability of aluminum alloy sheets. Under such thermal forming condition, it is quite necessary to explore if the recrystallization and solute precipitation would happen, which might have potential in further improve the strength of aluminum alloy conventionally realized by heat treatment aging. In the present work, FS-ISF experiments are conducted for AA2024 sheet with proper parameters to achieve more solute precipitates and fine recrystallized grains with stable boundaries, of which microstructure evolutions are characterized by Transmission Electron Microscopy (TEM) and Electron Backscattered Diffraction (EBSD). It's found that cyclic and incremental plastic deformation during FS-ISF induces dislocation jogs and dislocation loops, and finally makes solute move into vacancies and generates solute precipitates. And friction stir also contributes to more solute precipitates than conventional incremental sheet forming (CISF) at room temperature. Meanwhile, precipitation zone inside grains helps to resist ductility damage and stable boundary with pinning contributes to higher strength. Besides, irregular sub-boundaries are merged and sub-boundaries consume dislocations to form new boundaries by the slip and arrangement of dislocations during dynamic recrystallization so that fine equiaxed grains with high angle boundaries are obtained, which results in higher yield strength (YS), ultimate tensile strength (UTS) and better ductility than those by CISF. Furthermore, investigations also demonstrate that static recrystallization cannot arise during FS-ISF.

Predictive modelling of longitudinal bow in Chain-die formed AHSS profiles and its experimental verification

Chain-die forming, as a newly developed technology, is considered as an alternative method to fabricate AHSS automotive structural parts. The longitudinal bow is one of the most general geometric deviations of cold-formed materials. This paper utilizes analytical modelling, finite element analysis and experimental verification to disclose the mechanism of the formation of the longitudinal bow of Chain-die forming of AHSS profiles. To improve accuracy, the Chaboche hardening model is adopted in the simulation work to characterize the Bauschinger effect of the AHSS products. A detailed comparison of the mechanisms of the formation of the longitudinal bow of Chain-die-formed and roll-formed AHSS profiles is carried out to emphasize their differences. The analytical model indicates that, in contrast to roll-formed profiles, longitudinal bow in Chain-die-formed profiles is primarily caused by the elastic recovery of the accumulated incremental plastic deformation in the bend corner. It can be understood as a follow-up phenomenon accompanied by springback. With a certain material, its severity is related to the thickness, the bend corner radius and the second moment of area of a product. This is consistent with the simulation and experimental results. Finally, a comprehensive numerical investigation is used to quantify the effect of critical parameters on the longitudinal bow.

Study on mechanical properties of a bimetallic composite produced by explosion welding under incremental plastic deformation

The paper presents the results of the studies of the changes in the mechanical characteristics of the bimetal "08Cr18Ni10Ti – steel 10", subjected to staged plastic deformation by rolling in 5 passes with a reduction of about 10% per pass. Bimetal was obtained by explosion welding. The tensile tests of bimetallic samples after each rolling pass were carried out. It was shown that the relative reduction of individual layers has changed non-proportionally to the magnitude of the relative reduction of the bimetallic strip as a whole. The weld zone obtained as a result of explosion welding was separately considered. To define the size of the welded zone, the values of microhardness distribution in the cross sections of the bimetallic strip after each passage were used. The size of the welded zone decreased from 0.4 mm to 0.1 mm after 5 passes. The values of the yield strength for the weld zone and the individual layers of the bimetal were obtained by the kinetic indentation with processing of loading curves by the original method developed in the IES UB RAS. The value of the yield strength of a bimetal after explosion welding is higher than the values for each material individually. With further plastic strain, the strength properties of the stack do not increase as intensively as the strength properties of stainless steel. A mixture rule can be used in order to calculate the theoretical conventional yield strength for a bimetal after explosion welding.

In-Situ Monitoring of Stress Developments during Electrochemical Lithiation/Delithiation of Amorphous Silicon Films in Presence/Absence of ‘Buffer’ Interlayers

The combination of greater theoretical Li-capacity (~4200 mAhg-1) and improved safety aspects with respect to graphitic carbon renders silicon a potential candidate for replacement of the presently used graphitic carbon based anode materials in Li-ion batteries. However, enormous volume changes that occur during electrochemical cycling (i.e., Li-insertion/removal) lead to severe stress developments, resulting in mechanical degradation of the Si-based anode materials (cracking/fracture/delamination/loss of electric contacts/and continued SEI formation) and concomitantly drastic fade in capacity [1]. It is widely believed that use of ‘buffer’ interlayers may reduce the stresses or at least the impact of such stresses [1-3]. However, the literature base lacked direct experimental investigation/assessment of the stress developments during lithiation/delithiation of Si in the presence/absence of such ‘buffer’ interlayers. Against this backdrop, we have monitored the stress developments in-situ during electrochemical cycling of continuous amorphous Si (a-Si) films, in the presence and absence of suitable ‘buffer’ interlayers between the active electrode film and the current collector. The effects of presence of such interlayers on the mechanical integrity during the course of lithiation/delithiation cycles have also been thoroughly monitored. Such comprehensive experimental work, along with in-depth analysis, has led to better understandings of the mechanistic aspects related to the effects of the presence of ‘buffer’ interlayers and also the interfacial properties. In the present work, two different types of ‘buffer’ interlayers, viz. CVD-grown well-ordered multi-layered graphene (MLG; ~9-10 layers) and NiTi shape memory alloy (SMA; grown via PLD; 150 nm thick), have been used (sandwiched between ~250 nm thick a-Si and ~100 nm thick Ni current collector films). While interlayer sliding of the individual graphene layers may be expected in the case of MLG in response to the expansion/contraction of the a-Si, NiTi SMA is expected to exhibit pseudo-elasticity (viz., reversible stress induced phase transformation; B2 <=> B19’) [3]. The multi-layered film electrodes, on stiff circular quartz substrates (~500 µm thick) were assembled in custom-made electrochemical cell and cycled galvanostatically against Li-metal (counter/reference electrode). Multi-beam optical stress sensor was used for real-time monitoring of the stress developments in the film electrodes, similar to our previously reported works [1,4-8]. The presence of both the buffer interlayers improved not only the cyclic stability, but also the Li-capacity possibly because of reducing the magnitude of compressive stresses developed during lithiation. In addition to reducing the stress magnitudes (when normalized by the corresponding Li-capacities), the stress profiles recorded in real-times tend to indicate that while MLG supressed the ‘flow’ of a-Si during lithiation, stress development was accommodated by preferential plastic deformation of NiTi. Top-view and cross-section SEM observations at different stages of the cycling indicated that, even though the a-Si films cracked in the absence, as well as in the presence of the buffer ‘interlayers’, the cracked ‘islands’ maintained considerably improved integrity upon further cycling in the presence of the ‘buffer’ interlayers (as compared to directly on Ni current collector). Scratch tests indicated weaker interfacial adhesion strengths in the presence of the ‘interlayers’. Along with the reduced magnitudes of the lithiation induced stresses, engineering of the adhesion strengths, in combination with the observed cracked ‘island’ sizes, concomitant suppression of flow of cracked a-Si ‘islands’ (due to weaker adhesion in the presence of the interlayers), and possible incremental plastic deformation of the Ni current collector in the absence of the ‘interlayers’, were associated with the observed stress profiles and improved mechanical integrity in presence of the ‘buffer’ interlayers. Keywords: amorphous Si, patterned film, multi-layered graphene, NiTi shape memory alloy, in-situ stress monitoring.

Special Section on Ratcheting.

The design methods for pressure vessels and piping are based on the avoidance of potential modes of failure, such as collapse, excessive deformation, and cracking. Collapse and excessive deformation from a single load application are addressed by methods such as buckling analysis, primary stress analysis, and plastic limit analysis. For instance, limit load design underlies the evaluation methods for design conditions in most existing pressure vessel design codes. When significant cyclic loading is applied, the evaluation of fatigue and ratcheting effects becomes necessary. Fatigue analysis is concerned with avoiding the initiation and propagation of cracks that could eventually cause a sudden fracture. Ratcheting is a failure mode typically associated with components that are subjected to pressure loading and simultaneously large cyclic thermal stresses. It is characterized by deformations or plastic strains that accumulate with increasing load cycles. Continued deformation can eventually render the component unserviceable and strain accumulation can accelerate fatigue cracking, which is not accounted for in the fatigue analysis. Ratcheting can occur in metals, but also in nonmetallic materials. In order to avoid ratcheting, the cyclic loads must be kept within a specific limit that depends on the level of simultaneously applied mechanical loading (shakedown limit). By maintaining the stresses below the shakedown limit, some incremental plastic deformation may occur during the initial loading cycles, but the deformation in the subsequent cycles will be stable cycling, either in the elastic range (elastic shakedown) or involving alternating plasticity (plastic shakedown). Typical simplified evaluation methods in the design codes are based on perfect (nonhardening) plasticity. Such methods and their extensions, such as direct methods of shakedown analysis, promise simple and efficient solutions and are still being developed. Due to the numerical methods that are now available, a full cyclic plastic simulation that could include work hardening is also becoming feasible. There are, however, some knowledge gaps in the application of hardening plasticity models to shakedown or ratchet analysis. For example, apparently equivalent descriptions of a plastic stress–strain curve by different plasticity models which give comparable results for static loading and even for steady cyclic response can have widely different ratcheting behavior. Depending on the plasticity model, the response may vary from guaranteed shakedown independent of loading to unexpected ratcheting under some stress states. Therefore, there is active research involving experimental studies of ratcheting and development of plasticity models to better describe the material response to various loading combinations. Simultaneously, efforts are underway to identify simple existing plasticity models that include hardening and are suitable for an engineering analysis of shakedown or ratcheting. This special section on ratcheting has a total of 12 papers which represent a good mixture of theoretical, numerical, and experimental research in this area.

Matrix Stress-strain Working Method for Determining the Effective Plastic Strain

A matrix stress and strain implementation is made that becomes simpler than tensor notation as usual. The effective stress is calculated using the indicated matrix notation, starting from a deviatoric stress state. The effective stress defines a functional flow condition which, besides the principle of normality, solves an equation for the incremental plastic deformation. The plastic work is determined, as usual, from the state of stresses and strains. Finally, the effective plastic strain is obtained as a function of the plastic working and the effective stress, both in the case of plastic deformation at constant volume and with variable volume model.

Evaluation of Inelastic Seismic Response of a Piping System Using a Modified Iterative Response Spectrum Method

In pressurized piping systems, strain accumulation may take place due to cyclic loading during a seismic event. This incremental plastic deformation called ratcheting may lead to failure of the piping systems. There is no numerical method available to evaluate this accumulated strain in the piping system using response spectrum as input. In the literature, incremental hinge technique is available to predict the failure level conservatively by considering static collapse as the failure mode. However, it is observed from shake table tests that failure in the piping components, especially in elbows, is due to ratcheting. Considering this failure mode and design input as a response spectrum, a modified incremental hinge technique is developed and validated with experimental results. The strain predicted by this analysis closely matches with that of experimental results which are available up to an excitation of 0.75 g ZPA (zero period acceleration). In the experiment, the pressure boundary rupture occurred at 2 g ZPA, while the analysis predicts the failure of the piping system at 2.37 g ZPA. Details of these investigations are presented in the paper.

Processing‐structure‐mechanical property relationships of semicrystalline polyolefin‐based block copolymers

AbstractThe incremental plastic deformation of the crystals of block copolymers made of semicrystalline polypropylene endblocks and amorphous ethylene‐r‐propylene midblocks occurring during step cycle tensile tests has dramatic effects on the stress‐strain curves. This can be understood from the evolution of the morphology and of the microstructure of the crystalline blocks revealed by X‐ray scattering experiments. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1428–1437, 2010

Rigid plastic model of incremental sheet deformation using second‐order cone programming

AbstractThis paper describes a method for numerically modelling the incremental plastic deformation of shells and applies the method to incremental sheet forming (ISF). An upper bound finite element shell model is developed based on sequential limit analysis under the rigid plastic assumption, which is solved by manipulating the problem into the form of a second‐order cone program (SOCP). Initially, the static upper bound plate problem is investigated and the results are compared with the existing literature. The approach is then extended to a shell formulation using a linearized form of the Ilyushin yield condition and two methods for treating the Ilyushin condition are presented. The model is solved efficiently using SOCP software. The resulting model shows good geometric agreement when validated against an elasto‐plastic model produced using existing commercial software and with measurements from a real product produced using ISF. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Progressive Transformation of Hippocampal Neuronal Representations in “Morphed” Environments

Hippocampal neural codes for different, familiar environments are thought to reflect distinct attractor states, possibly implemented in the recurrent CA3 network. A defining property of an attractor network is its ability to undergo sharp and coherent transitions between pre-established (learned) representations when the inputs to the network are changed. To determine whether hippocampal neuronal ensembles exhibit such discontinuities, we recorded in CA3 and CA1 when a familiar square recording enclosure was morphed in quantifiable steps into a familiar circular enclosure while leaving other inputs constant. We observed a gradual noncoherent progression from the initial to the final network state. In CA3, the transformation was accompanied by significant hysteresis, resulting in more similar end states than when only square and circle were presented. These observations suggest that hippocampal cell assemblies are capable of incremental plastic deformation, with incongruous information being incorporated into pre-existing representations.

Hyperelastic models for elastoplasticity with non-linear isotropic and kinematic hardening at large deformation

This work is concerned with the formulation of hyperelastic-thermodynamic-based models for associated elastoplasticity with non-linear isotropic and kinematic hardening valid for both large elastic and large plastic deformation. On this basis, one can then introduce explicitly the assumptions of (1), small incremental plastic deformation, and (2), small elastic strain, into the general model and obtain special cases whose behaviour corresponds to that of various classical hypoelastic formulations. In particular, these are obtained on the basis of two different thermodynamic formulations for kinematic hardening with respect to the intermediate configuration. The simplest of these, in which the plastic part of the free energy does not depend explicitly on the plastic deformation, leads for example to Jaumann-or Green-Naghdi-hypoelastic-type behaviour for linear kinematic hardening in simple shear. In particular, the former case is obtained in this context when the plastic spin is assumed constant and equal to zero, and the latter case when the plastic rotation is assumed constant and equal to the identity. Allowing the plastic part of the free energy to depend explicitly on the plastic deformation yields the second thermodynamic model for kinematic hardening considered in this work. Here, again in the special case of linear hardening, Oldroyd-like behaviour for the shear stress and back stress, but not for the normal stress, is obtained in simple shear.

Incremental Failure of an Expansion Joint During Combined Pressure and Expansion Loading

Incremental failure was observed when two different loading conditions, pressure and expansion, were applied alternatively to an expansion joint. Neither of the conditions was capable independently of failing the expansion joint. When the conditions occurred together, only a small amount of plasticity was observed. But when the expansion was cycled while holding pressure constant, incremental plastic deformation occurred during each cycle which was cumulative to that of past cycles. The joint was dimensionally unstable over a large number of expansion cycles. Analytical and experimental results are presented in an attempt to explain the observed phenomenon.

The influence of rapid thermal transients on elastic-plastic ratchetting

The ‘Bree diagram’ allows a rapid design assessment of the likelihood of incremental plastic deformation. The diagram was originally developed for plate or beam components subjected to steady mechanical and quasi-steady cyclic thermal loadings. Here, a theoretical investigation shows that a cycle of rapid cooling and quasi-steady heating reduces the combinations of load which do not give rise to ratchetting. This effect approaches an asymptote for large Biot numbers and small Fourier numbers, and is more significant for mechanical loads less than about 30% of yield. Revised interaction diagrams are presented for two load cases of interest and for a worst-case combination of Biot and Fourier numbers. If equal thermal transients are applied to both outer surfaces of a plate, then it is shown that a critical thickness can be found below which ratchetting need not be expected for temperature transients of practical magnitude. This is presented as a function of mechanical load and Fourier number.