Unloading-reloading Process Research Articles

Nonlinear unloading-reloading behavior and macro/micro models during multi-pass cyclic hot compression of aluminum alloys

Unloading-reloading behavior is of crucial importance in multi-pass forming of metal materials, the nonlinear of which creates challenges for the analysis of springback and residual stress of the precision manufacture components. Especially for the hot bulk-formed material at elevated temperature, the thermal-mechanical coupling effect makes the unloading-reloading process more complicated and thus more difficult to model and control, which remains to be solved. In this paper, the unloading-reloading behavior dependent on strain rate and deformation temperature and its model of hot compressive deformed aluminum alloys at elevated temperature were studied from the macroscopic and microscopic perspectives. The effect of deformation temperature, strain rate and strain on the unloading-reloading behavior of hot compressive deformed aluminum alloys were revealed, and corresponding micro-mechanism was elucidated and then discussed. Macroscopically, a strain-, strain rate- and temperature-dependent nonlinear macroscopic model describing unloading–reloading process was established, which can be used to describe the unloading stress relaxation and predict springback during multi-pass hot bulk forming. Microscopically, it is suggested that the relaxations of back stress and forest dislocation hardening stress collectively affect the unloading stress relaxation, due to the decrease of mobile and immobile (forest) dislocation density in unloading, while the dislocation-related behavior before yield, i.e. the dislocations’ bowing-out under pinning, affects the reloading behavior. Based on the micro-mechanism, a physically-based micro-model for describing unloading–reloading was constructed which further is used to clarify the physical mechanism of internal stress relaxation and inelastic strain recovery under multi-pass hot compression deformation. The comparison of the calculation results of the models with those of experiments indicated that the established unloading–reloading macroscopic and microscopic models are able to predict the stress–strain response upon the unloading–reloading loop of multi-pass cyclic hot compression deformation.

Study on Explicit–Implicit Simulation and In-Situ Measurement of Floor Failure Law in Extra-Thick Coal Seams

A reliable numerical simulation method and large-scale in-situ test method for super-thick coal seams are very important to determine the failure range of mining floors, which is often the basis to protect Ordovician limestone water, an important drinking water source for people in North China. This paper takes Yushupo Coal Mine as an example; the explicit–implicit coupling simulation method and the corresponding double scalar elastic–plastic constitutive model were established to predict the failure depth of the floor numerically, and verified by the full section borehole stress–strain in-situ testing method. The results show that the explicit–implicit coupling numerical program and the double scalar elastoplastic constitutive model are suitable for predicting the floor failure depth under the condition of extra-thick coal seams. In this condition, the overburden moves violently, resulting in a loading–unloading–reloading process with large stress variation amplitude in the mining floor, which leads to serious rock failure compared with that of medium-thick coal seam conditions. In Yushupo 5105 working face, the floor failure starts to develop from 9.3–24.2 m ahead of the coal wall of working face, and the failure depth no longer increases after 35 m behind the coal wall, with the maximum failure depth of 28 m; the envelope line of the floor failure depth presents an inverted saddle distribution. The above research results lay a foundation for further protecting the Ordovician limestone water, and realizing green coal mining.

Analysis of damage characteristics and energy evolution of salt rock under triaxial cyclic loading and unloading

The gas injection, water-soluble excavation, and gas recovery process in the gas storage salt cavern can be regarded as the loading and unloading process of the surrounding rock stress. By conducting triaxial loading and unloading tests on salt rock samples, several findings are presented: 1) The failure formed in the rock sample is a shear failure mode when confining pressure is below 15 MPa, and after confining pressure exceeds 15 MPa, it is bulging in the middle part of sample. The scientific strain is proved to be more suitable for describing the deformation of salt rock sample than the engineering strain. 2) During the unloading-reloading process, the produced stress difference is small at the beginning of unloading, while the rock undergoes more stress loss in the post-peak stage than that in other stages. 3) When the strain increases to reach a specific value, the dissipative energy difference increases with higher confining pressure. 4) Higher confining pressure improves the initial damage degree to the sample. But under different confining pressures, the damage variable has a similar evolution trend, which reaches a steady growth stage with the loading/unloading cycles gradually.

Unloading and Reloading Process for the Earthquake Damage Repair of Ancient Masonry Columns: The Case of the Basilica di Collemaggio

ABSTRACT The repair of historical masonry columns damaged by earthquakes is a complex engineering procedure. In most cases, these elements support important vertical loads, and, for this reason, the repairing interventions (such as block replacement) could generate critical modifications of the stress pattern and eventually lead to local failures of the masonry material. In order to prevent critical situations, the repair work should account a complete unloading-reloading process of the column. However, at this time, no specific indications are provided by technical codes and guidelines. In the present paper, the unloading-reloading process developed for the stone masonry columns of the Basilica di Collemaggio in L’Aquila (Italy) is presented. Particularly, two specific unloading systems were designed and verified with advanced finite element analyses. A three-dimensional finite element model of the colonnade and supported nave wall was implemented to check if the unloading-reloading process would significantly change the state of stress in the masonry, causing local failures. The geometry of the structure was reconstructed from a complete laser scanner survey of the church, by considering all the intrinsic irregularities of heritage constructions. Finally, a comparison between the numerical results and the corresponding values measured during the worksite intervention was carried out.

Nonlinear anelastic behavior and unloading-reloading constitutive models of severe plastic compressive deformation

The nonlinear anelastic behavior in unloading and unloading‒reloading processes of severe plastic compressive deformation (SPCD) has a decisive impact on the springback of deformed parts. The strain hardening, strain softening and anisotropy affect the anelastic behavior of the deforming material. In this study, the quasi-static single-pass and multi-pass SPCD tests were carried out on the samples along different directions of hot-rolled copper plates. The nonlinear unloading behavior and the variation law of anelastic strain after single-pass and multi-pass compressions and between passes were analyzed, and the effect of the anisotropy on the anelastic strain was clarified. At the micro level, the anelastic strain model in the strain hardening and softening stages was established based on the relationship between anelastic strain and dislocation density, the Hall-Petch and Talor strength models, strain hardening EM model and modified softening constitutive model. Thereby, the nonlinear unloading‒reloading models in an anelastic exponent form and in a modified anelastic hyperbolic sine form were constructed, respectively. At the macro level, the anelastic strain function related to strain were established on the basis of the chord modulus model in a power exponent form and strain hardening and softening constitutive models. Thereby, 1-D ET nonlinear unloading‒reloading constitutive model in a power exponent form was constructed. The nonlinear symmetric relationship between unloading and reloading curves was analyzed. It was found that the 1-D ET model in power exponent form and expression in polynomial form can accurately describe the instantaneous slope of symmetric axis. Finally, the anelastic strain and the unloading‒reloading curves of the single-pass and multi-pass SPCDs and inter passes were predicted using the anelastic strain model and the nonlinear unloading‒reloading model, and compared with the experimental results. The comparison indicated that the established anelastic strain model can accurately predict the anelastic strain in the strain hardening and softening stages of SPCD, and the established unloading‒reloading model can accurately predict the nonlinear relationship between stress and strain in the unloading‒reloading of SPCD.

An Improved Cohesive Zone Model for Interface Mixed-Mode Fractures of Railway Slab Tracks

The interface crack of a slab track is a fracture of mixed-mode that experiences a complex loading–unloading–reloading process. A reasonable simulation of the interaction between the layers of slab tracks is the key to studying the interface crack. However, the existing models of interface disease of slab track have problems, such as the stress oscillation of the crack tip and self-repairing, which do not simulate the mixed mode of interface cracks accurately. Aiming at these shortcomings, we propose an improved cohesive zone model combined with an unloading/reloading relationship based on the original Park–Paulino–Roesler (PPR) model in this paper. It is shown that the improved model guaranteed the consistency of the cohesive constitutive model and described the mixed-mode fracture better. This conclusion is based on the assessment of work-of-separation and the simulation of the mixed-mode bending test. Through the test of loading, unloading, and reloading, we observed that the improved unloading/reloading relationship effectively eliminated the issue of self-repairing and preserved all essential features. The proposed model provides a tool for the study of interface cracking mechanism of ballastless tracks and theoretical guidance for the monitoring, maintenance, and repair of layer defects, such as interfacial cracks and slab arches.

Study on hysteretic deformation characteristics and energy dissipation of granite under cyclic loading

The cyclic load test of granite under different paths is conducted using the strain control method. The nonlinear hysteretic deformation behavior is analyzed, and the energy evolution law in the process is described in detail. Three specific discoveries were made. (1) The skeleton curve shape in the cyclic test is less affected by the increase in the upper load limit and shows good loading memory characteristics. (2) The hysteretic characteristics of the stress-strain curve characterize the energy dissipation process. Dissipated energy is divided into plastic hysteresis and damping energy consumption. Damping energy consumption accounts for a considerable proportion of the total energy consumption at all levels, and the changing trend of the two is positively correlated. The upper limit of the cyclic load can significantly change the plastic hysteretic energy. (3) The loading-unloading process is more prone to large hysteresis deformation, and the unloading-reloading process has an unloading threshold. When the unloading amount is less than the threshold, the unloading-reloading curve linearly coincides, and the energy is dissipated during the process. When the unloading amount is greater than the threshold, damping energy will be generated to increase energy dissipation, and the hysteresis characteristic will appear.

Model for description of nonlinear unloading-reloading stress-strain response with special reference to plastic-strain dependent chord modulus

To describe the nonlinear stress-strain response in the unloading-reloading process, a model was proposed for the variation of the elastic modulus during the process. This model is directly associated with the widely used equation for the plastic-strain dependent chord modulus, and no additional material parameters are needed for modeling. In this model, nonlinearly changing elastic modulus is explicitly determined from the current stress state, instead of using an accumulated-strain measure. Therefore, it is robust against the numerical noise (e.g., stress oscillation) in computation. Based on the same elastic modulus model, two types of calculation models were constructed, namely, a micro-plasticity model and nonlinear-elasticity model. From the numerical simulations of the non-proportional unloading-reloading processes, it was found that the stress-strain responses calculated by the two models were very similar to each other. The model was validated by comparing the calculated stress-strain results with the corresponding experimental observations on a DP980 advanced high-strength steel sheet (AHSS). The influence of the nonlinear unloading behavior on the springback prediction was discussed by performing two cases of springback simulations (a uniform bending-unbending and a hat-shaped draw-bending) on two types of AHSSs (dual-phase DP980 and precipitation strengthen 780 R), by using several types of elastic modulus models. The best choice for springback simulation is to use the nonlinear elastic model to describe the realistic stress-strain responses in the yield surface, along with an appropriate kinematic hardening model of plasticity to express smooth elastic-plastic transition behavior. In comparison with the springback calculation by the nonlinear model, a certain amount of errors were found when using the plastic-strain dependent linear models, however, they were not very large. Thus the second best option in springback simulation would be to use the chord modulus model because of its simple modeling and high computation efficiency.

The Effect of Unloading Positions and Times on Sheet Metal’s Stress-Strain Curve

The loading-unloading-reloading process could affect the tensile deformation of metals with the combined function of stress relaxation and work hardening, which has been reported in multiple experiments. Nevertheless, the effects of different unloading positions and unloading times have not been investigated. In this study, unloading-reloading tests on three materials (AL6061, HSLA and Q195) were conducted. The stress exhibits a rapid rise momentarily upon reloading and stabilizes afterward while the post stress-strain curve deviates up or down from the monotonic tensile curve. The ductility is enhanced by the unloading-reloading process in general. Different unloading positions and unloading times have different degrees of influence on the stretching of these metals. The effect of loading conditions on a medium manganese steel was further studied. The functions to modify the post stress-strain relationship after unloading-reloading were established.

Modeling the Cyclic Response of Perfobond-rib Shear Connectors

In order to predict the shear-slip behavior of steel-concrete hybrid structures under cyclic load, a constitutive model of the unloading and reloading of shear connectors is required. The aim of this study is to develop a constitutive model of perfobond-rib shear connectors (PBL) that includes the description of unloading and reloading paths under single shear force. Static push-out tests with unloading-reloading cycles were carried out under several different restraint conditions to examine the load-displacement relations. The unloading-reloading process was repeated by increasing the maximum load and gradually accumulating the residual displacement and then the total shear displacement of PBL was increased. The experimental results clarified that the relations of load and displacement under cyclic loading can be modeled independently of restraint conditions. Empirical models for unloading and reloading, starting from arbitrary displacements, were successfully formulated.

Laboratory investigation on energy dissipation and damage characteristics of frozen loess during deformation process

For investigating the energy dissipation and damage behavior of frozen loess during deformation process under triaxial compression, besides triaxial compression (TC) tests, a series of static triaxial loading-unloading cyclic (TLUC) tests corresponding to the TC tests were carried out under confining pressures from 0.5MPa to 9.0MPa at temperature of −6°C. It could be found from these two types of tests that the loading stages of TLUC test curves and TC test curves almost coincided under different confining pressure conditions. The influence of confining pressure on stress–strain curves of TC and TLUC tests was similar. The TLUC test results showed that energy dissipation occurred in unloading–reloading process and elastic modulus changed with increase of strain. Dissipative energy value increased at first and then decreased with increase of confining pressure. A damage variable was defined based on the fact of the degeneration of elastic modulus. The experimental results also indicated that there existed an initial damage in frozen loess sample before loading. According to this phenomenon, a method for recognizing undamaged state was proposed. The damage threshold value and damage evolution law under different confining pressures were obtained based on the TLUC test results. The influence of confining pressures on damage characteristics of frozen loess was analyzed. The conclusion can be drawn that damage value of frozen loess decreased with increasing confining pressure under lower confining pressure, but with a further increase in confining pressure, the damage value increased as pressure melting and crushing phenomena caused by higher confining pressure levels.

Influence of unloading–reloading processes on the pullout resistance of geogrid

ABSTRACT: This study presents an evaluation of soil–geogrid interaction mechanisms. Pullout tests were carried out on different types of geogrid to evaluate the effects of transverse ribs and dilatancy characteristics of sand around the geogrid during unload–reload processes. The interaction was observed using particle image velocimetry and analyzed using a spatial discretization scheme in the finite element method to understand the dilatancy mechanism and the shear strain distribution.

Study on compression deformation, damage and fracture behavior of TiAl alloys: Part I. Deformation and damage behavior

The compression deformation, damage and fracture behaviors of TiAl alloys in the fully lamellar and duplex microstructures were systematically studied. The fracture behaviors in compression tests of TiAl specimens are detailed in Part II of this work. In this paper a series of compression preloading–unloading–reloading tests were carried out. Results indicated that the compression engineering stress–strain curves were unchanged and were not affected by the numbers of multiple preloading–unloading processes until the preloading stresses reached the ultimate compression stress. However the tensile strength was significantly reduced by the multiple compression preloading–unloading–reloading processes. At the microscopic scale, the development of the microcracks on the specimen surfaces increases up to ∼1000 cracks/mm 2 with the compression up to the ultimate fracture stress of ∼2200 MPa. The linking of microcracks to form macrocrack damage in the bulk is examined. A preloading–unloading–reloading process with step-by-step observation of the initiation, extension and formation of microcracks on the specimen surface with increasing compression load is described in detail. From these observations, mechanisms of crack linking and propagation are identified in duplex and fully lamellar microstructures.

CENTRIFUGE TESTS ON SEISMIC STABILITY OF THE DAMAGED GEOGRID REINFORCED SOIL WALL

Recent huge earthquakes have caused severe and small damage to a number of geogrid-reinforced soil walls. For proper repair or reconstruction, it is necessary to evaluate degree of damage of those structures. In this research, the pullout test of geogrid subjected to the unloading-reloading process was carried out to learn its effects on the pullout resistance. The results were then used to evaluate the factor of safety and sliding surface of the damaged geogrid reinforced soil wall. GRSW models in centrifuge shaking and tilting table tests under 50G were performed. The damaged GRSW models were first achieved by both shaking and tilting. The damaged GRSW were then subjected to unloading-reloading process until the full collapse occurred. The pullout peak value and residual value using in current design of GRSW were also discussed.

SHEAR STRAIN DISTRIBUTION IN SOIL AROUND GEOGRID DURING THE UNLOADINGRELOADING PULLOUT TEST

The soil-geogrid interaction process was analyzed by the Particle Image Velocimetry furthermore spatial discretization scheme in finite element method to understand about the dilatancy mechanism and shear strain distribution during unloading-reloading process. In this test the geogrid was pushed back and forth at three stages of pullout test: before peak, at peak and at residual part to simulate the seismic activities. Results showed that the shear strain concentrated in front of transverse ribs and upper apart of pullout box. The dilative behavior appears in front of transverse ribs and contractive behavior exits at behind of these bars. The alternative soil dilatancy-contraction distribution in between the two transverse ribs can be seen throughout the length of geogrid.

Effects of repeated loading on the fracture behavior of notched TiAl specimens

Notched specimens of a fully lamellar TiAl alloy and a duplex TiAl alloy were in situ tensile tested with repeated loading–unloading–reloading processes in a scanning electron microscope (SEM). The step-by-step processes of initiation and extension of the main crack were captured by SEM. The fracture surfaces were observed and one-sector-to-one-sector related to the crack extension. Effects of loading–unloading damage on the fracture behavior were evaluated by combining the pictures of propagating crack configurations, corresponding fracture surfaces and the load locus. The results revealed the following events: (1) at the elastic regime, the loading–unloading process had negligible effect on the fracture behavior produced by subsequent reloading; (2) at the plastic regime, even at a value much lower than that of the preload, the reload extended further the existing main crack; (3) after a heavy loading–unloading process, the main crack extended and resulted in final fracture at a value of the reload, which was lower than that of the preload and (4) microcracks produced in the loading–unloading process had minor effects on the fracture behavior.

EFFECTS OF TRANSVERSE RIBS ON PULLOUT RESISTANCE AND DEFORMATION DURING THE UNLOADING-RELOADING PROCESS

It is considered that the pullout resistance is more affected by the transverse elements than the longitudinal elements. In this study a square and a circle opening type and a plate are tested of pullout resistance in Toyoura sand during the unloading-reloading process through a series of laboratory model tests. The results show that unloading-reloading process reduces the pullout resistance of both two types of geogrid and a plate at peak value and at the residual part. But the pullout resistance of the square geogrid type in this study is decreased more as well as less stable than that of the other two. Moreover, the square geogrid type takes larger displacement to reach to the peak values of pullout resistance than the circle and plate ones do. To discuss the effects, all of the deformation of soil around geogrid is observed while it is pulled out. The PIV analysis shows the mechanism and effects of transverse ribs on the pullout resistance.

Effects of microcrack-damage on fracture behavior of TiAl alloy. Part II: load-controlled tensile test

Specimens of a fully lamellar TiAl alloy and a duplex TiAl alloy were tensile tested using load-controlled procedure. The microcracks were measured for each specimen as it was subjected to various preloading–unloading processes. Loading–unloading–reloading processes of in-situ tensile tests were carried out in a scanning electron microscope (SEM). Effects of microcrack damage on the deformation and fracture behavior were evaluated. The following results of microcrack-damage on deformation and fracture behavior of TiAl alloy were found: (1) The apparent plastic elongation resulted mainly from plastic strain. The elongation caused by microcracks is negligible. (2) No appreciable effects of microcrack damage on the apparent elastic modulus could be found. (3) Microcracks damage produced at higher preloading reduced the fracture stress, however, that produced at lower preloading gave diminished effects.

Multi-dimensional consolidation analysis of clay deposits including unloading-reloading process : Matsui, T; Abe, N Proc 5th International Conference on Numerical Methods in Geomechanics, Nagoya, 1–5 April 1985V1, P589–595. Publ Rotterdam: A. A. Balkema, 1985

Multi-dimensional consolidation analysis of clay deposits including unloading-reloading process : Matsui, T; Abe, N Proc 5th International Conference on Numerical Methods in Geomechanics, Nagoya, 1–5 April 1985V1, P589–595. Publ Rotterdam: A. A. Balkema, 1985

Fracture energies of sintered boron nitride

Fracture energies of a sintered boron nitride were measured using chevron-notched compact tension type specimens. During stable crack growth unloading-reloading processes were repeated in order to evaluate the plastic deformation. From load P-loadpoint displacement u diagram, total fracture energy (work of fracture) γWOF was determined as 26.2J/m2 with error of less than 5%, close to a half of which (about 45%) was found to be dissipated by plastic deformation. The results were discussed in the relation with those on graphite materials.