Unloading Behavior Research Articles

Evaluation of creep mechanical behavior of deep-buried marble under triaxial cyclic loading

Triaxial compression experiments were carried out on deep-buried marble specimens to investigate their short-term and creep mechanical behavior under cyclic loading. First, based on the results of short-term triaxial experiments, the elastic, plastic, and strength behaviors of marble were analyzed. The results show that for the same confining pressure, the elastic modulus of marble remains basically constant at the lower axial deviatoric level but decreases slowly after yielding strength; in contrast, the plastic modulus reduces rapidly with the increase of axial deviatoric stress. However, the elastic and plastic moduli of the tested marble were quite independent of the confining pressure. The relationship between axial deviatoric stress and plastic deformation of marble can be described well by the interface model. The peak strength of marble under higher stress increases with the confining pressure, which can be better described in accordance with the Mohr–Coulomb criterion. And then, in accordance with the experimental results of marble creep under triaxial cyclic loading, the instant elastic and plastic strains, and the visco-elastic and visco-plastic strains were all separated successfully, which provided a better foundation for constructing a visco-elasto-plastic creep model of rock. The creep strain rate of marble under different deviatoric stresses is analyzed, which shows that the steady-state creep rate of marble increases nonlinearly with the increase of axial deviatoric stress. In the end, the creep mechanical behavior of marble under cyclic loading is theoretically analyzed using the creep model. The results show that Burgers creep model can describe the creep behavior of marble under the loading condition satisfactorily but is inadequate to describe the creep behavior of marble under the unloading condition. Therefore, by adopting the fundamental hypothesis of visco-plastic mechanics, a visco-elasto-plastic creep model of rock material is constructed, which can describe the unloading creep behavior of marble better than Burgers creep model. The creep model curve agrees very well with the experimental results, which verifies the proposed visco-elasto-plastic creep model.

Modeling rate-independent hysteresis in large deformations of preconditioned soft tissues

A phenomenological model is proposed for characterizing rate-independent hysteresis exhibited by preconditioned soft tissues. The preconditioned tissue is modeled as an isotropic composite of a hyperelastic component and a dissipative (inelastic) component. Specifically, the constitutive equations are hyperelastic in the sense that the stress is determined by derivatives of a strain energy function. Inelasticity of the dissipative component is controlled by a yield function with different functional forms for the hardening variable during deformation loading and unloading. The constitutive equations proposed in this paper are simple. In particular, they depend on only seven material constants: three controlling the response of the elastic component and the remainder controlling the response of the dissipative component. More importantly, the material constants can be determined to match rather general loading and unloading behavior. It is observed that the hysteretic response of the model compares well with experimental data for passive uniaxial loading/unloading of Manduca muscle. Moreover, the present model treats partial loading and reloading of preconditioned tissue as elastic–plastic response, which is different from the treatment of pseudo-elastic models used in the literature.

Nanoindentation characterization of tetragonal zirconia polycrystalline implanted by titanium ions with MEVVA sources

The applicability and the reliability of the traditional power-law proposed by Oliver and Pharr in describing the nanoindentation unloading behavior of the ion-implanted samples were examined in this paper. Nanoindentation tests were conducted on a tetragonal zirconia polycrystalline (TZP) ceramic implanted by titanium ions with metal vapor vacuum-arc (MEVVA) sources. Both the power law (a paraboloid punch approximation) and the quadratic polynomial (conical indenter approximation) were employed to analyze the unloading portions of the resultant load-displacement curve. It was found that, when the examined contact depth is smaller then the thickness of the ion-implanted layer, the determined power law exponent, m, is much larger than 1.5, the theoretical value for a paraboloid punch. This phenomenon may be attributed mainly to the effect of the residual surface stresses associated with the ion implantation. The hardness and Young's modulus of the ion-implanted sample were found to exhibit a graded distribution and have maxima when the contact depth is comparable to the average projected range of the implanted ions.

Plastic Deformation Influence on Material Properties of Autofrettaged Tubes Used in Diesel Engines Injection System

According to the DIN2391 standard, the DIN1.0406 steel is used to manufacture high-pressure injection tubes of diesel engines. The parts are autofrettaged during the manufacturing process to increase operating pressure and fatigue life. The autofrettage process is affected by loading–unloading cycle. In Bauschinger effect (BE) phenomenon, plastic deformation causes a loss in unloading yield strength. The ratio of unloading yield strength to the loading yield strength is called Bauschinger effect factor, BEF. In this paper, plastic deformation influence on the loading and unloading behaviors of DIN1.0406 steel is studied considering the BE. Uniaxial tension–compression experimental data are used to figure out a suitable model to study the BE. To carry out these experiments, a servohydraulic Instron machine is used. The sample tubes having inside diameter of 2.4 mm and outside diameter of 6 mm were made based on the standard ASTM E8M-97a. The tests were carried out using the total strain of 4.31%. Another important purpose of this paper is to investigate the effect of the amount of plastic strain on loading–unloading Young's modulus. Finally, the behavior of DIN1.0406 steel is compared with the steels such as DIN1.6959, HY 180, and PH 13-8Mo used in tubes.

Unloading behavior of clays measured by CRS test

The unloading behavior of clays was studied by the Constant Rate of Strain (CRS) test, for three clays: two of them are reconstituted and the other was intact. In the conventional CRS test where the stress monotonically increases, the distribution of the pore water pressure in a specimen is assumed to be parabolic, the effective stress is calculated and then the compression behavior is evaluated. However, this assumption cannot be directly applied the unloading condition. In this study, the pore pressure distribution under unloading was simulated by a cubic polynomial under the assumption that hydraulic conductivity does not change in the unloading process. A unique relation in the e–logσ′v relation was found, irrespective of both the magnitude of stress or strain and the compression index, Cc, at the unloading test, when the consolidation pressure is normalized by σ′vmax, which is the consolidation pressure before the unloading test. In addition, the creep strain, which is gained by constant loading before the unloading test, was shown to have a great effect on the unloading behavior: that is, the soil behaves stiffly when subjected to a constant load for a prolonged period of time. A strain rate dependency in the unloading process was also observed particularly for heavily unloaded specimens. The unloading behavior was also investigated by the conventional constant load test. The test results show reasonable agreement with those obtained from the CRS test.

A phenomenological constitutive model for the pseudoelastic behavior of shape memory alloys

Shape memory alloys (SMAs) possess the distinctive ability to recover large mechanically-induced inelastic strains upon unloading, which is known as the pseudoelastic behavior. This paper deals with an extension of the phenomenological viscoplasticity theory, which has been developed by the author to depict the negative strain rate sensitivity, to model the macroscopic behavior of the phase transformation. Unlike most phenomenological models for the pseudoelasticity, the proposed model does not employ a kinetic law describing the evolution of the martensitic volume fraction and the transformation loading and unloading conditions but introduces two internal state variables concerned with the evolution of the elastic modulus and the back stress. The applicability of the constitutive model to SMAs is validated by comparing simulation results with experimental data on uniaxial and torsional loading reported in the literature. And then it is demonstrated that the same constitutive equations can be applied to model the highly nonlinear unloading behavior of solid polymer.

A study of the unloading behaviour of dual phase steel

It is important to understand the strain recovery of a steel sheet in order to predict its springback behaviour. During strain recovery, the stress–strain relation is non-linear and the resulting unloading modulus is decreased. Moreover, the unloading modulus will degrade with increasing plastic pre-straining. This study aims at adding new knowledge on these phenomena and the mechanisms causing them. The unloading behaviour of the dual-phase steel DP600 is characterised experimentally and finite element (FE) simulations of a representative volume element (RVE) of the microstructure are performed. The initial stress and strain state of the micromechanical FE model is found by a simplified simulation of the annealing processes. It is observed from the experimental characterisation that the decrease of the initial stiffness of the unloading is the main reason for the degrading unloading modulus. Furthermore, the developed micromechanical FE model exhibits non-linear strain recovery due to local plasticity caused by interaction between the two phases.

Polymer reinforced by flax fibres as a viscoelastoplastic material

Flax fibre reinforced polymers are at the heart of current scientific and societal concerns. However their mechanical behaviour is still poorly known despite significant scientific efforts, in particular the non-linear behaviour observed under tensile tests. In this paper, results of hardening, creep and repeated progressive tests under uniaxial loading performed on various quasi-unidirectional flax fibre reinforced composites are analysed in terms of the volume fraction of fibre, the titration of yarn reinforcement and temperature testing. To identify the respective parts of pure elastic, viscoelastic and viscoplastic components in the global mechanical response, a phenomenological model is built based on eight independent parameters. The parameter identification based on experimental data and checked by a sensitivity analysis shows that the viscoelastic effects are non-significant at room temperature. The non-linear behaviour can mainly be attributed to viscoplastic effects. Viscoplastic modelling is based on a combination of two hardenings; the first classical (linear) one describes the translation of the elastic domain; the second (non-linear) one describes a translation coupled with a contraction of the elastic domain during loading that improves the unloading behaviour during repeated progressive loading tests.

On the polymeric foams: modeling and properties

Polymeric foams are now widely used and researched. The physical properties of polymeric foam can be related to a set of independent structural parameters or variables of the foam. Study of these variables and correlation with commercial FE packages is essential for reliable and faster product development. Some aspects of foam behavior are widely studied while some are little less, like correlation of physical unloading behavior. For example, a lot of work in the area of phenomenological constitutive modeling of uniaxial loading was done, though research in areas of unloading–reloading and their correlation still demands more attention. Increasing number of OEMs and suppliers are moving to computer simulations in the design phase to assess their future products. Hence, different parameters within FE packages play a significant role and also affect the results. Appropriate use of these parameters will narrow down error band and automatically reduce the cycle time and development cost. This brief review is expected to set the perspective for major research work done so far in terms of FE modeling correlation and constitutive modeling of polymeric foam vis-a-vis to its properties.

Bauschinger Effect During Unloading of Cold-rolled Copper Alloy Sheet and its Influence on Springback Deformation after U-bending

Tension, cyclic tension-compression and partial unloading tests for two types of cold rolled brass sheet (i.e. JIS C2600R-H, C2600R-1/2H) were carried out in order to investigate cyclic plasticity and unloading behavior, and to determine the plastic dependency on Young's modulus. The Young's moduli for the pre-strained materials were determined in different two ways. For the first case, unlading stress-strain data from σ0 to 0.0MPa was used, and data from σ0 to (σ0 - 2Y0) was used for the second case, where σ0 and Y0 denote 90% of the stress at the beginning of unloading and the initial yield stress used in a constitutive equation, respectively. The saturated Young's moduli were significantly different on C2600R-H sheet, but similar plastic strain dependency on Young's modulus relationship was found on C2600R-1/2H sheet. Subsequently, U-bending experiments and the corresponding finite element simulations using several combinations of plastic strain dependent Young's moduli and isotropic and kinematic hardening rules were conducted. The simulation results indicated that Young's moduli measured using σ0 to (σ0 - 2Y0) data with elasto-plastic unloading is the best choice for springback simulation of the cold rolled sheets.

Irreversible mixed mode interface delamination using a combined damage-plasticity cohesive zone enabling unloading

Delamination is often identified as an important failure mechanism in structures with a high interface density, such as modern microelectronic systems and advanced composite materials. Delamination tests performed on different interface structures reveal complex failure mechanisms (crack bridging, fibre pull out, micro-void coalescence, fibrilation, crack meandering, etc.) in the fracture process zone that lead to an irreversible unloading response of the interface, ranging from full damage to full plasticity. Modeling the unloading response of an interface is important for predicting phenomena such as crack branching and crack propagation at multiple interfaces. This paper presents a 2D irreversible combined plasticity-damage unloading model, which can be used to extend the cohesive zone (loading) models with a proper unloading description that is suitable for modeling the entire loading-unloading response in the process zone. The presented model is able to capture changes in unloading behavior as a function of mode mixity, whereas it introduced only two additional model parameters that can be determined from dedicated delamination experiments. As a demonstration, the improved Xu–Needleman cohesive zone law has been extended with the proposed combined damage-plasticity unloading formulation. Numerical simulations with this extended model are performed for a glue interface system, recovering the typical observed behavior in delamination experiments. Finally, a complete procedure to extract all CZ model parameters is presented and illustrated for the glue interface system.

Evaluating the significance of hardening behavior and unloading modulus under strain reversal in sheet springback prediction

Abstract Springback is one of the most important problems that should be compensated in sheet metal forming process with the increasing application of advanced high strength steels and light-weight alloys. In the finite element analyses for the springback, accurate modeling of Bauschinger effect, transient behavior and permanent softening under cyclic loading has been recognized as the most critical hardening behavior in the constitutive modeling aspect. However, if parts of these hardening behavior are not well modelled, is the accuracy of springback prediction seriously deteriorated? To answer this question, in this paper the significance of Bauschinger effect and transient behavior, permanent softening and unloading modulus in springback prediction were estimated using the springback problem of U-draw/bending simulations proposed at Numisheet2011 Benchmark. A recent anisotropic non-linear kinematic (ANK) model [Zang S, Guo C, Thuillier S, Lee M. A model of one-surface cyclic plasticity and its application to springback prediction. Int J Mech Sci 2011;53:425–35.] was adopted to estimate the significance of hardening behavior and unloading modulus because of its special feature. The ANK model can predict exactly the same monotonous stress–strain curves for different hardening schemes, while different Bauschinger effect and transient behavior under one-dimensional cyclic loading can be also modelled. This feature is quite suitable to quantitatively evaluate the effects of the aforementioned hardening behaviors in springback prediction. Initial anisotropy is described by the anisotropic yield function Yld2000-2d. The unloading behavior is also considered by defining Young's modulus as a function of equivalent plastic strain. Several quantitative analyses were carried out to distinguish the effect of each hardening component and unloading elastic modulus scheme. Finally, the predicted springback by different models were compared with experiments for both as-received and pre-strained DP780 steel sheets.

Unloading Behavior Study on FRP-Concrete Interface under an Exponential Softening Law

Loading behavior studies on FRP-concrete interface are refined enough. Because of the complexity of the problem, there exist relatively few unloading behavior studies. Occurrence mechanism of unloading needs to be clarified. Through a combination of theory and finite element method, this paper studied the unloading behavior involved in interfacial failure process under an exponential softening law, clarified when and where unloading occurred and estimated the effect of unloading.

Comparison of Loading and Unloading Behavior of Commercial and Locally Made Copper-Nickle-Titanium (NiTiCu) Orthodontic Archwire

Background: Copper-nickel-titanium (NiTiCu) archwire has been favoured in clinical orthodontic practice because of its superior superelasticity (SE) and shape memory effect (SME) properties. Objective: To compare the loading and unloading behavior of commercial NiTiCu orthodontic archwire and locally made NiTiCu orthodontic archwire based on composition and mechanical properties especially in relation to percentage recovery, stress plateau, stress hysteresis, and loading and unloading slope. Materials and Methods: The materials used were divided into two categories: the NiTiCu (40°C) commercial Ormco brand (USA) archwires and the locally made NiTiCu archwires produced at King Mongkut University of Technology Thonburi (KMUTT). The samples were examined using an Electron Probe Microanalysis (EPMA) to test their chemical composition. For loading and unloading behavior the Universal Testing Machine (Instron) was used for the three-point bending test. The Mann-Whitney U test was employed to analyze and compare the data. Results: Chemical composition, there were significant differences in at.% of Ni, Ti, and Cr composition between commercial and locally made archwire. There was no significant difference in at.% in Cu. In terms of percentage recovery, there was a significant decrease in locally made archwire. For stress plateau and stress hysteresis, there were also significant increases in Thai-made archwire when compared with commercial archwires. In addition NiTiCu (Ormco) showed significantly less inclination than locally made NiTiCu archwire in both loading and unloading slopes. Conclusion: Based on the results of this study, the mechanical properties of the locally made archwires were not as suitable as the commercial archwires. This preliminary study provides useful information for the further development of locally made NiTiCu archwires. Therefore, the use of the NiTiCu should be considered on a case by case basis. This experiment was useful in comparing locally made NiTiCu wire and commercial orthodontic wire.

속도 의존적인 폴리머 거동에 대한 구성적 모델

Abstract Solid polymers exhibit rate-dependent deformation behavior such as nonlinear strain rate sensitivity and stress relaxation like metallic materials. Despite the different microstructures of polymeric and metallic materials, they have common properties with respect to inelastic deformation. Unlike most metallic materials, solid polymers and shape memory alloys (SMAs) exhibit highly nonlinear stress-strain behavior upon unloading. The present work employs the viscoplasticity theory [K. Ho, 2011, Trans. Mater. Process. 20, 350-356] developed for the pseudoelastic behavior of SMAs, which is based on unified state variable theory for the rate-dependent inelastic deformation behavior of typical metallic materials, to depict the curved unloading behavior of polyphenylene oxide (PPO). The constitutive equations are characterized by the evolution laws of two state variables that are related to the elastic modulus and the back stress. The simulation results are compared with the experimental data obtained by Krempl and Khan [2003, Int. J. Plasticity 19, 1069-1095].

Influence of computational parameters and nonlinear unloading behavior on springback simulation

The advanced high-strength steels (AHSS) have become an interesting alternative to the automotive industry that aims to reduce the thickness of the components without compromising the structural performance and absorption capacity of impact. However, their mass utilization is still limited due to computational problems to predict the occurrence of the phenomenon of springback. Nonlinear unloading behavior following plastic deformation is identified as the factor that compromises the computational prediction of AHSS sheet forming. Moreover, it is observed sensitive dependence on correct choice of numerical parameters on the quality of the springback prediction such as the number of through-thickness integration points (NIP), coefficient of friction, the number of element on tool radius and simulation punch velocity. The aim of this study is to evaluate the degradation of elastic modulus and how the choice of numerical parameters can affect the computational prediction of AHSS springback. For this purpose, a user subroutine has been implemented in ABAQUS to describe the degradation of the modulus of elasticity during unloading, and several numerical parameters have been evaluated. It was possible to observe the influence of considering the degradation of elastic modulus during simulation and the large or small influence of some computational parameters.

Residual Stress Analysis of the Autofrettaged Thick-Walled Tube Using Nonlinear Kinematic Hardening

Recent research indicates that accurate material behavior modeling plays an important role in the estimation of residual stresses in the bore of autofrettaged tubes. In this paper, the material behavior under plastic deformation is considered to be a function of the first stress invariant in addition to the second and the third invariants of the deviatoric stress tensor. The yield surface is assumed to depend on the first stress invariant and the Lode angle parameter which is defined as a function of the second and the third invariants of the deviatoric stress tensor. Furthermore for estimating the unloading behavior, the Chaboche's hardening evolution equation is modified. These modifications are implemented by adding new terms that include the effect of the first stress invariant and pervious plastic deformation history. For evaluation of this unloading behavior model a series of loading-unloading tests are conducted on four types of test specimens which are made of the high-strength steel, DIN 1.6959. In addition finite element simulations are implemented and the residual stresses in the bore of a simulated thick-walled tube are estimated under the autofrettage process. In estimating the residual stresses the effect of the tube end condition is also considered.

Transportation of market-weight pigs: I. Effect of season, truck type, and location within truck on behavior with a two-hour transport1

There is evidence that season and truck/trailer design play important roles in pig welfare during transportation although little is known about their interaction and effect on pig behavior. This experiment was designed to examine the influence of season and truck/trailer design on the behavior during loading, transit, unloading, and lairage of market-weight pigs transported to slaughter. A total of 3,756 pigs were transported on either a 3-deck pot-belly trailer (PB; n = 181 pigs/wk in 8 experimental compartments) or a double-decker hydraulic truck (DD; n = 85 pigs/wk in 4 compartments) for 2 h to a commercial abattoir in summer and winter (6 wk in each season). Density on both vehicles was 0.40 m(2)/pig. Accounting for the number of pigs, loading took longer (P = 0.033) onto the DD than the PB, but season did not (P = 0.571) influence loading time. Pigs loaded onto the PB moved backward more (P = 0.003) frequently than those loaded onto the DD. The frequency of tapping by handler was the lone handling intervention affected by truck type, with more (P = 0.014) tapping needed to move pigs on and off DD than PB. During loading, pigs made more (P < 0.001) slips and falls, overlaps, 180° turns, underlaps, and vocalizations in winter compared with summer. On truck, more (P < 0.001) pigs were standing on the DD at the farm and in transit than on the PB whereas more (P = 0.012) pigs were lying in transit in summer than in winter. Pigs took longer to unload (P < 0.001) from the PB than the DD, but no difference between vehicles (P = 0.473) in latency to rest in lairage was found. Pigs slipped and fell more (P < 0.001) during unloading, took longer (P < 0.001) to unload, and had a shorter (P = 0.006) latency to rest in lairage in winter than summer. Vehicle design, in particular the presence of ramps, influenced pig behavior before, during, and after transportation, regardless of the season. Season affected loading and unloading behavior, especially in terms of slips and falls on the ramp, and differences in truck/trailer designs were also partly to blame for unloading times and lairage behavior. Ramps and changes in direction during unloading appear to slow down the handling process.

Stress wave transmission across a filled joint with different loading/unloading behavior

This paper presents a theoretical study of stress wave propagation across a rock joint with different loading/unloading behavior. Two Bandis–Barton (B–B) models are introduced to describe the stress–closure relationships of a rock joint under loading and unloading situations, respectively. A characteristics method is proposed to investigate the stress wave transmission. Amplitude-dependence and frequency-dependence of unloading effect on the energy transmission are analyzed. The unloading effect on stress waves with different waveforms and stress waves with multiple pluses are evaluated. The results show that the characteristics method can be used to investigate the wave propagation across a rock joint with different loading/unloading behavior. The effect of unloading behavior on energy transmission is amplitude- and frequency-dependent. The stress wave with a rectangular waveform is less influenced by the unloading behavior than the stress waves with other waveforms. Unloading behavior has a significant effect on the energy transmission for the stress wave with both single pulse and multiple pulses. However, unloading behavior has an effect on the wave attenuation provided that the time interval of multiple pulses stress wave is sufficiently small.

New Load Transfer Hyperbolic Model for Pile-Soil Interface and Negative Skin Friction on Single Piles Embedded in Soft Soils

A proper load transfer model describing the pile and surrounding soil interaction is important for accurately predicting the behavior of piles. In this paper, a new load transfer hyperbolic model for the pile-soil interface is developed based on soil-structure interface tests reported in the literature, which consider the characteristics of increasing initial shear stiffness, the development of shear strength at the pile-soil interface, the loading, step by step loading, unloading, and reverse loading shearing behavior of the pile-soil interface with consolidation. The proposed model was validated by the close agreement between the computed results and published case histories. Further studies based on the proposed model considering negative skin friction on single piles under pile head load and/or surcharge were subsequently conducted. It was found that the pile-soil interface undergoes complicated shearing, and the depth of the neutral plane (NP) and the skin friction along the pile shaft vary during consolidation. The magnitude of the pile head load and pile installation time has a significant impact on the depth of the NP and the dragload. Pile capacity was shown to decrease with consolidation.