Plastic Strain Range Research Articles

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.

Cold pilgering of duplex steel tubes: The response of austenite and ferrite to excessive cold deformation up to high strains

Duplex stainless steels are not easily formable due to the different deformation behaviour of austenite and ferrite. The seamless tube making process cold pilgering provides deformation conditions that enable enormous plastic strains at room temperature. The favourable stress state makes axial elongations of 400 to 600% at cross-sectional reductions of about 80% possible for hollows made of Super duplex steel grades. Upon reaching the final dimensions, a range of equivalent plastic strains of up to approximately 3 is covered varying between the transition zone's in- and outside. In this work the cold working behaviour and textural evolution of Super duplex steel 2507 during cold pilgering under these conditions are investigated. An industrial tube's transition zone is considered. The microstructural response to deformation is studied at different axial positions. The impact of the different forming conditions through the wall thickness on the final properties is analyzed. A unique combination of Electron Backscatter Diffraction, finite element modelling and nanoindentation is used to correlate the microstructure with the deformation behaviour before, during and after the cold pilger process.

Cyclic deformation behaviors of AZ31B magnesium alloy in two different asymmetric loading manners

The low cycle fatigue (LCF) behavior of AZ31B magnesium alloy with fiber texture was investigated in two asymmetric loading manners with strain ratios of Rε=0 (named as T-T loading manner) and Rε=-∞(named as C-C loading manner), respectively. It was found that {10–12}<10–11> extension twinning-detwinning occurred in the samples in both the manners. Although the characteristics of twinning-detwinning alternations in the two manners exhibited little difference, the mechanical behaviors were quite different. Detwinning was induced during tensile unloading in the T-T manner and resulted in an evident Bauschginer effect, and cyclic softening in the tension was observed. The LCF life in this case was 68 cycles. In contrast, cyclic hardening occurred in both the tension and compression in the C-C manner with a life of 53 cycles. The twinning-detwinning contribution to the plastic strain-range was reduced especially in the C-C manner. The difference of twinning-detwinning contribution to the plastic strain-range between the two loading manners was responsible for the different LCF lives.

High temperature deformation mechanisms in the 14% Cr ODS alloy

The stress relaxation behavior of the ODM401 ODS steel is tested at the temperature range 400–800°C in order to investigate the deformation mechanisms. The repeated relaxation tests are performed on the tensile specimens within the plastic strain range 10−4–10−1. The deformation mechanisms are analyzed in terms of an activation volume, dislocation density and velocity, a thermal stress component and a strain rate hardening. The deformation is driven by the dislocation glide and climb. Dispersed particle-dislocation interactions is a dominant effect at temperatures 400–600°C. Short-range interactions between dislocations and a lattice are most significant at 600°C. The non-conservative motion of dislocations becomes active at temperatures above 600°C. The majority of the mobile dislocations is not trapped and is able to move freely in the microstructure.

A Strain Range Dependent Cyclic Plasticity Model

Hysteresis loop curves are highly important for numerical simulations of materials deformation under cyclic loadings. The models mainly take account of only the tensile half of the stabilized cycle in hysteresis loop for identification of the constants which don’t vary with accumulation of plastic strain and strain range of the hysteresis loop. This approach may be quite erroneous particularly if the mean stress is not small and the effect of isotropic hardening is large. A strain dependent cyclic plasticity model which considers the variation of material constants versus strain range and accumulation of plastic strain has been proposed and experimentally investigated by the authors. In this paper it is proved that their proposed model is accurate for simulating all cycles of the hysteresis loop regardless of the strain range of the test. It is shown in this work that artificial neural network (ANN) model, if designed and trained properly, can be used for interpolating and extrapolating the experimental data. The results of this work are compared with two well-known cyclic plasticity models. The results also indicate that there is a remarkable agreement between the proposed model and ANN within and outside the strain ranges used in the experiments.

Mechanical properties determination of dual-phase steels using uniaxial tensile and hydraulic bulge test

Numerical simulations of sheet metal forming processes need the establishment of highly reliable results, which in turn need the accurate identification of mechanical properties. In this paper a study is presented on the choice of the characterization function of flow stress-strain curve of sheet metal materials, as well as the selection of the best yield locus, based on experimental uniaxial tensile and biaxial hydraulic bulge tests performed on dual-phase steels of industrial interest. To obtain a better characterization of the hardening curve, a combination is made using the uniaxial tensile test data with biaxial hydraulic bulge test results, since bulge test covers a larger range of plastic strain when compared to tensile test. Since the two flow curves have different strain paths, they can’t be directly compared or combined. Therefore, it is necessary a transformation of flow stress-strain curve provided from biaxial bulge test into equivalent stress-strain curve. Different methodologies were applied to transform biaxial stress-strain curve to an equivalent one and the different results are compared and evaluated.

P‐version finite elements and finite cells for finite strain elastoplastic problems

AbstractIn this paper, the p‐version finite element method and its fictitious domain extension, the finite cell method, are extended to the finite strain J2 plasticity. High‐order shape functions are used for the finite element approximation of volume‐preserving plastic dominated deformations. The accuracy and efficiency of p‐version elements and cells in the finite plastic strain range are evaluated by the computation of two benchmark problems. It is shown that they provide locking free behavior and simplified meshing. These results are verified in comparison with the results of h‐version elements in F‐bar formulation. (© 2016 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A new ultra-low cycle fatigue model applied to the X60 piping steel

Fatigue damage under extreme cyclic plastic loading conditions (ultra-low-cycle fatigue (ULCF)) has been increasingly investigated motivated by several applications involving structures and mechanical components, such as pipelines, that may be, during operation, likely exposed to severe cyclic loading regimes (e.g. accidental loads, earthquakes, pipeline reeling). ULCF corresponds to a transition damage mechanism between the monotonic ductile damage and the low-cycle-fatigue (LCF), both widely investigated in the literature, using independent approaches. Investigation in this transition damage mechanism is still scarce covering a reduced number of materials and few models are available. The main goal of this paper is to investigate the cyclic behavior of the X60 piping steel under cyclic extreme loading conditions, also covering the respective monotonic ductile and low-cycle fatigue behaviors. A unified model to describe the three damage regimes will be also proposed. This investigation is supported by an experimental program covering tests of smooth and notched specimens to derive monotonic and elastoplastic cyclic/fatigue data under a diversity of multiaxial stress conditions. Data reduction schemes based on each individual test simulation, by non-linear elastoplastic finite element models, is performed. In detail, the monotonic fracture strain, the average stress triaxiality and the average Lode angle parameters were obtained and considered for the calibration of 3D ductile fracture locus in accordance with Bai and Wierzbicki formulation, a satisfactory agreement being found. Afterwards, cyclic test data is used to calibrate a modified Xue model that is made explicitly sensitive to the stress triaxiality and Lode angle parameters. This model relates the equivalent plastic strain range, normalized by the fracture strain with the number of cycles to failure. Aiming the determination of the strain fracture of each specimen, two distinct methods are proposed. The first one consists of a direct method, based on the simulation of each ULCF specimen under monotonic conditions and in the other one is based on the use of the previously generated 3D monotonic ductile fracture locus.

Estimating the plastic strain with the use of acoustic anisotropy

Experimental verification is used to show that reference specimens and structure unloading do not permit obtaining an adequate estimate of plastic strain by measuring the acoustic anisotropy. Analytic estimates of the speed of propagation of a plane acoustic wave of various polarizations in an elastoplastic material in the direction orthogonal to the action of preliminary uniaxial stress are obtained. An analysis of the obtained relations reveala an advantage of using absolute values of the velocity of longitudinal and transverse waves for the plastic strain identification. In contrast to acoustic anisotropy, the velocities vary monotonically in a wider range of plastic strains. At the same time, the elastic strain does not affect the longitude wave velocity, which allows one to use the measurement results to estimate the character of strains.

Behavior of 321 stainless steel under engineering stress and strain controlled fatigue

Cyclic deformation and fracture behavior of the 321 stainless steel are investigated at 633K under engineering-stress and strain controlled low cycle fatigue (LCF) cycling, and the fatigue life data are compared with ASME section-III Division-1 S-N curve. In stress-controlled LCF tests, ratcheting-strain accumulation is observed even under zero mean-stress, and the direction of ratcheting is found to strongly depend on initial-ramp direction of first-cycle. In addition, plastic-strain range and striation width are observed to be higher than those in strain-controlled tests. The stress-life curve obtained from stress-controlled tests is 2–3 orders of magnitude lower in comparison to stress-life curve derived from strain-controlled LCF tests as per the ASME procedure. The discrepancy is attributed to the differences in deformation and damage development in stress and strain-controlled cycling.

Study of Influence of Heat Treatment on Cyclic Properties of L21HMF Cast Steel

This work presents the results of studies of CrMoV cast steel after long-term service and after regenerative heat treatment (RHT). The cast steel was investigated in the conditions of static and changeable load. The tests were carried out at room temperature and 550 °C. The fatigue lifetime curves were determined and described using the Basquin-Manson-Coffin relationship. It has been shown that the cast steel after RHT is characterized by smaller range of plastic strain and bigger range of stress amplitude, with the same value of total strain, compared with the cast steel after service. For the cast steel after RHT, the observed fatigue properties were different in comparison with the cast steel after service at small and large strains. At room temperature (20 °C) and at elevated temperature (550 °C), there is an increase in the life of samples of the cast steel after RHT in comparison with the samples of the cast steel after service only in the area of large strains (e ac > 1.2%). For small strains e ac < 0.50%, the life of the cast steel after RHT at the examined temperatures is shorter than that of the cast steel after service. The paper shows that regardless of an explicit improvement in the strength properties (the static and cyclic ones), as a result of the performed RHT, a complete improvement in the fatigue properties of the cast steel does not occur.

A model of one-surface cyclic plasticity with Lemaitre damage criterion for plastic instability prediction in the incremental forming process

The precise prediction of plastic deformation instabilities during the incremental forming process is quite complex because of the complex stress state and extremely large plastic strain. Until now, most elasto-plastic constitutive models are only suitable within a small strain range and describe the isotropic behavior. However, for extremely large plastic deformation under complex loading processes such as an incremental forming process, these models are ineffective and ill-conceived. This paper presents an elasto-plastic constitutive model which combines a mixed isotropic-kinematic hardening model with the Lemaitre damage model. This model can predict the Bauschinger effect, transient behavior, permanent softening and fractures over a large plastic strain range. By using explicit integration schemes, an integration algorithm of numerical implementation is proposed using simple expressions. A cyclic loading test comparison between experiments and numerical analysis is carried out to validate these models. The model is also applied to FE analysis of incremental forming. The deformation and the prediction of thickness are consistent with experimental results and thus verify the accuracy of the model.

Evolution of free volume and shear band intersections and its effect on hardness of deformed Zr64.13Cu15.75Ni10.12Al10 bulk metallic glass

Introduction of shear bands in metallic glasses is usually regarded as being responsible for softening metallic glasses. Here we present that hardness of deformed Zr64.13Cu15.75Ni10.12Al10 bulk metallic glass (BMG) exhibits an initial decrease and a subsequent increase with plastic strain. This extraordinary variation of hardness was studied by investigating evolution of shear band intersections and free volume with plastic strain. As plastic strain increases from 6% to 83%, the density of shear bands increases from 0.04 to 0.92 μm−1. Meanwhile, the distribution width of shear band spacings gradually narrows, and the number of intersections between shear bands increases. When plastic strain is larger than 47%, the number of intersections increases faster. Free volume in the deformed BMG at room temperature increases with plastic strain increasing from 6% to 83%. Both free volume induced softening and shear band interaction induced hardening may affect the hardness of the deformed BMG. In the plastic strain range of 0%–47%, free volume induced softening mainly contributes to the initial decrease in hardness with plastic strain. In the plastic strain range of 47%–83%, shear band interaction induced hardening may lead to the increase in hardness with plastic strain, after counteracting free volume induced softening.

Numerical validation of crack closure concept using non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Numerical models with and without contact of crack flanks were built for a wide range of loading parameters. The non-linear crack tip parameters studied were the range of cyclic plastic strain, the crack tip opening displacement (CTOD) and the size of reversed plastic zone. Well defined relations between non linear parameters and K were obtained without contact of crack flanks which reinforces the validity of linear elastic fracture mechanics. When the CTOD with contact is plotted versus ΔKeff the values are coincident with those obtained without contact, which shows that the crack closure concept is valid and able to explain the influence of mean stress. The analysis of overloads and high-low load blocks demonstrated the validity of crack closure concept for variable amplitude loading.

True stress and shakedown analysis of pressure vessel under repeated internal pressure

This study aims to investigate the true stress and the plastic shakedown behavior of a cyclically loaded pressure vessel. To serve this study, an experimental platform has been built up, which comprised of a self-made thin-wall cylinder pressure vessel, a water pressure loading system to simulate the actual working loading condition, and strain gauge sets for strain measurement. A number of experiments have been done by cyclically loading and unloading the vessel at different strain levels of plastic deformation to shakedown state in different experiments respectively. The relationship between plastic strain and shakedown range has therefore been obtained. The true stress-strain constitutive model of the vessel under large deformation condition has also been derived. The experiments lead to three observations: (1) the strain hardening technology can effectively reduce the residual stress of stainless steel pressure vessel. (2) The shakedown range is less than 2000 μe for a total strain under 4%, and yet the shakedown range increases fast to more than 3000 μe for a total strain higher than 6%. (3) It is also found that the true stress-strain constitutive model given in this paper describes the multi-axial stress-strain state of pressure vessels, and validates the engineering practicability of conventional uniaxial tensile shakedown constitutive curve.

Damage Analysis of a Ferritic SiMo Ductile Cast Iron Submitted to Tension and Compression Loadings in Temperature

Tensile and compression tests were carried out on a ductile cast iron for temperatures up to 1073 K. The damage caused inside and around graphite nodules was evaluated as a function of the local equivalent plastic strain by using microstructural quantifications. The mechanical properties are strongly dependent on a temperature above 773 K. Concerning tensile behavior, an evolutional law issued from the Gurson model representing the void growth as a function of the deformation and temperature was successfully employed. It is demonstrated that the strain state and the temperature have a strong influence on the void growth function. In the case of compression tests, the temperature has a weak influence on the nodule deformation for temperatures lower than 773 K, and the mechanical behavior is driven by the viscoplastic properties of the ferrite. For higher temperatures, the mechanical properties in compression are progressively modified, since graphite nodules tend to remain spherical, and ferrite grains are severely deformed. A synthesis of the damage mechanisms is proposed in the studied range of temperature and plastic strain. It appears that the graphite nodule aspect ratio can be used as an indicator of the deformation under compression loading for temperatures ranging from room temperature to 673 K.

Linear matching method for design limits in plasticity

In this paper a state-of-the-art numerical method is discussed for the evaluation of the shakedown and ratchet limits for an elastic-perfectly plastic body subjected to cyclic thermal and mechanical load history. The limit load or collapse load, i.e. the load carrying capacity, is also determined as a special case of shakedown analysis. These design limits in plasticity have been solved by characterizing the steady cyclic state using a general cyclic minimum theorem. For a prescribed class of kinematically admissible inelastic strain rate histories, the minimum of the functional for these design limits are found by a programming method, the Linear Matching Method (LMM), which converges to the least upper bound. By ensuring that both equilibrium and compatibility are satisfied at each stage, a direct algorithm has also been derived to determine the lower bound of shakedown and ratchet limit using the best residual stress calculated during the LMM procedure. Three practical examples of the LMM are provided to confirm the efficiency and effectiveness of the method: the behaviour of a complex 3D tubeplate in a typical AGR superheater header, the behaviour of a fiber reinforced metal matrix composite under loading and thermal cycling conditions, and effects of drilling holes on the ratchet limit and crack tip plastic strain range fora centre cracked plate subjected to constant tensile loading and cyclic bending moment.

Length scales and scaling laws for dislocation cells developed during monotonic deformation of (001) nickel single crystal

An extensive collection of experimental data was gathered to improve the well-known self-organization process of dislocation resulting from a tensile strain. Statistical analyses by Transmission Electronic Microcopy were performed over a large area in order to obtain additional insights into the different relationships between the structural parameters and the flow stress. A scaling behaviour was established for the size of quasi equiaxed dislocation cells over a large plastic strain range. Additionally, the dislocation organization reveals a variety of scaling laws relative to shear stress, cell size, dislocation wall thickness and dislocation densities in dislocation walls and cells. The physical bases of these laws were demonstrated and their consequences on plastic strain behaviour are discussed.

Effect of Intermetallic Compounds on the Thermomechanical Fatigue Life of Three-Dimensional Integrated Circuit Package Microsolder Bumps: Finite Element Analysis and Study

Currently, intermetallics (IMCs) in the solder joint are getting much attention due to their higher volume fraction in the smaller thickness interconnects. They possess different mechanical properties compared to bulk solder. Large volume fraction of IMCs may affect the mechanical behavior, thermomechanical and mechanical fatigue life and reliability of the solder interconnects due to very brittle nature compared to solder material. The question that this study is seeking to answer is how degrading IMCs are to the thermomechanical reliability of the microbumps used in three-dimensional (3D) integrated circuits (ICs) where the microsolder bumps have only a few microns of bond thicknesses. Several factors such as “squeezed out” solder geometry and IMC thickness are studied through a numerical experiment. Fatigue life is calculated using Coffin–Manson model. Results show that, though undesirable because of high likelihood of creating short circuits, squeezed out solder accumulates less inelastic strains under thermomechanical cyclic load and has higher fatigue life. The results show that with the increase of IMCs thickness in each model, the inelastic strains accumulation per cycle increases, thus decreasing the fatigue life. The drop in fatigue life tends to follow an exponential decay path. On the other hand, it was observed that plastic strain range per cycle tends to develop rapidly in Cu region with the increase in IMC thickness which calls for a consideration of Cu fatigue life more closely when the microbump contains a higher volume fraction of the IMCs. Overall, by analyzing the results, it is obvious that the presence of IMCs must be considered for microsolder bump with smaller bond thickness in fatigue life prediction model to generate more reasonable and correct results.

Effect of compressive loads on plasticity induced crack closure

Compressive stresses play an important role on tension–compression fatigue which can be attributed to plasticity induced crack closure (PICC). The objective here is to study numerically the effect of compressive stresses on PICC and to discuss the applicability of PICC to explain the effect of negative stress ratios on fatigue crack growth rate. The compression produces reversed plastic deformation at the crack tip, reducing linearly the crack opening level. The incursion to negative stress ratios did not produce sudden changes in the behavior of PICC and no saturation with the decrease of minimum load was observed for ΔKeff. Crack closure was able to collapse da/dN–ΔK curves with negative stress ratios, indicating the applicability of the crack closure concept to explain the effect of negative R. The analysis of crack tip plastic strain range with and without contact of crack flanks confirmed the validity of crack closure concept.