Unloading Modulus Research Articles

Mechanical properties and failure modes of stratified backfill under triaxial cyclic loading and unloading

Multiple filling of gobs will lead to a layered structure of the backfill. To explore the influence of layering structure on the mechanical properties and failure modes of backfill, different backfill specimens were prepared with a cement/sand ratio of 1:4, a slurry concentration of 75%, and backfilling times of 1, 2, 3 and 4, separately. Triaxial cyclic loading and unloading experiments were carried out. The results show that with an increase in backfilling time, the peak strength of backfill decreases as a polynomial function and the peak strain increases as an exponential function. The cyclic load enhances the linear characteristic of backfill deformation. The loading and unloading deformation moduli have a linear negative correlation with the backfilling time. The unloading deformation modulus is always slightly higher than the loading deformation modulus. The failure modes of stratified backfill are mainly characterized by conjugate shear failure at the upper layer and tensile failure across the layer plane, and there is usually no damage in the lower layer away from the loading area.

Finite Element Analysis on the Unloading Elastic Modulus of Aluminum Foams by Unit-cell Model

This paper presents finite element analyses (FEA) on the unloading elastic moduli of aluminum foams under uniaxial loading and bending conditions. The unit-cell model of Gibson and Ashby was utilized in the FEA with elasto-perfectly plastic material. Compression, tension, and bending tests simulations were carried out using Abaqus software. The non-linearity effect caused by structural imperfection/buckling of unit-cell was incorporated. From the compressive test simulation, it was confirmed that the results showed good agreement with the referred experimental data. This means that the developed FE model can be regarded as an RVE model of aluminum foams. Then, the deformation characteristic and elastic modulus obtained from all simulations were compared and examined. As the results, the elastic modulus obtained from bending test demonstrated higher value than that of under uniaxial loads. This discrepancy increases gradually as the relative density decreases. The mechanism responsible for generating the discrepancy in stiffness was discussed. Furthermore, this work points out the necessity of measuring both Young’s and flexural moduli for designing an engineering structure using foam materials especially when accuracy and precision are demanded.

Loading‐Rate Dependence of Rocks in Postfailure Region under Triaxial Compression

To study the loading‐rate dependence of four types of rocks in the peak and postfailure regions, the alternative strain rate test method is employed in conducting triaxial compressive tests under different confining pressure and moisture conditions. An index of the loading‐rate dependence in the postfailure region is proposed, and the effects of confining pressure and moisture condition on the index are analyzed. The reliability of the test results is verified by comparing the experimental and calculated results of stress relaxation. Following are the results. (1) The peak strength and postfailure behavior significantly depend on the loading rate. The indices (nc and nd) of the loading‐rate dependence in the postfailure region obtained based on the elastic and unloading moduli show a good linear relationship. It is feasible to use nc to evaluate the loading‐rate dependence of rocks in the postfailure region. (2) The loading‐rate dependence of the rock strength increases with the increase in the confining pressure. The effect of confining pressure on the loading‐rate dependence in the postfailure region is related to the moisture condition state. (3) Water‐saturation treatment will increase the loading‐rate dependence in the peak and postfailure regions, and the effect of water is greater than that of the confining pressure. (4) The experimental and calculated results of stress relaxation in the postfailure region are in good agreement, thus validating the experimental results.

Applying 2<sup>k</sup> Factorial Design to Study on Parameters Affecting Springback of Forming of Advanced High Strength Steel Sheets (AHSS)

Advanced high strength steels (AHSS) are widely used in the automotive industry due to their appropriate strength to weight ratio. This alloy has unique hardening behavior and variable unloading elastic modulus; however, the unavoidable obstacle of AHSS sheet metal forming is springback. The springback is a result of elastic recovery and residual stress. The aim of this study is to determine the proper process parameters enabling the reduction of the springback defects in AHSS forming process. This work was divided into two parts, regarding to the effects of numerical parameters and process parameter on forming AHSS. In this paper, a U-shape forming was used to examine the springback behaviors, such as springback angle, sidewall curl, and thickness, through an experiment. To achieve this purpose, 2k factorial statistical experimental design has been employed to investigate the parameters affecting the springback of forming in AHSS to find out the main effect in the springback reduction focusing on using as a guideline for die design. It showed that the blank holder force is the most influential parameter. The second is the punch radius. However, the blank holder force and punch radius is not simple to adjust in die design, the die radius becomes the important parameter to be used to reduce the springback angle.

Dynamic behavior of remolded loess under planar shock conditions

Utilizing a single-stage light gas gun the plane shock-wave experiments were performed in order to determine the dynamic behavior of the remolded loess whose density was 1.8 g/cm3 and saturation degree was 22% at stress levels between 0.2 and 1.6 GPa. Wave motions were detected by four electromagnetic particle velocity sensors embedded into the samples directly. The typical waveforms of particle velocity and the Hugoniot data of the experiments were presented in this paper. The dynamic stress–strain relation that was critical in researching the shock propagation in the sample could be obtained when the Lagrangian analysis method was utilized to the four particle velocity waveforms. Shock speed versus particle velocity was linear correlation. The speed of follow rarefaction wave was several times the speed of loading shock wave, corresponding, the unloading modulus was greater than the loading modulus, and the hysteresis effect was exhibited in the dynamic stress–strain relation.

Investigation of the variable elastic unloading modulus coupled with nonlinear kinematic hardening in springback measuring of advanced high-strength steel in U-shaped process

Advanced high strength steels are widely used in the automotive industry due to their appropriate strength to weight ratio. This alloy has unique hardening behavior and variable unloading elastic modulus. In this paper, an analytical model is introduced to predict springback in U-shaped bending process of normal and pre-strained DP780 dual phase steel stripes. It is based on the Hill48 yield criterion and plane strain condition. In this model, the effect of forming history, sheet thinning and the motion of the neutral surface on the springback is taken into account. The anisotropic nonlinear kinematic hardening model (ANK) is used to consider the impact of complex deformation including stretching, bending and reverse bending. This model is able to investigate the Bauschinger effect, transient behavior and permanent softening. Also, a nonlinear function of plastic strain is implemented to capture the variable unloading elastic modulus. This model is used for the Numisheet2011 benchmark U-shaped bending problem. The effect of the sheet holder force, the coefficient of friction, thickness, material anisotropy, hardening parameters, pre-strain and variable elastic modulus on the sheet springback is studied. It can be seen that analytical model with constant young's modulus has better accuracy in predicting springback angles than FEM solutions. Also in the case of variable young's modulus, FEM solution has better agreement with experiments in comparison with the analytical model.

The variation in elastic modulus throughout the compression of foam materials

We present a comprehensive experimental study of the variation in apparent unloading elastic modulus of polymer (largely elastic), aluminium (largely plastic) and fibre-reinforced cement (quasi-brittle) closed-cell foams throughout uniaxial compression. The results show a characteristic “zero-yield-stress” response and thereafter a rapid increase in unloading modulus during the supposedly “elastic” regime of the compressive stress–strain curve. The unloading modulus then falls with strain due to the localised cell-wall yielding or failure in the pre-collapse stage and the progressive cell crushing in the plateau stage, before rising sharply during the densification stage which is associated with global cell crushing and foam compaction. A finite element model based on the actual 3D cell structure of the aluminium foam imaged by X-ray computed tomography (CT) predicts an approximately linear fall of elastic modulus from zero strain until a band of collapsed cells forms. It shows that the subsequent gradual decrease in modulus is caused by the progressive collapse of cells. The elastic modulus rises sharply after the densification initiation strain has been reached. However, the elastic modulus is still well below that of the constituent material even when the “fully” dense state is approached. This work highlights the fact that the unloading elastic modulus varies throughout compression and challenges the idea that a constant elastic modulus can be applied in a homogenised foam model. It is suggested that the most representative value of elastic modulus may be obtained by extrapolating the measured unloading modulus to zero strain.

Unloading Elastic Behavior of Sand in Cyclic Triaxial Tests

In this paper, digital image technology was used in the surface-deformation measurement of soil, making it possible to monitor the axial, radial, and volumetric deformations and the deformation distribution over the entire surface of specimens in triaxial tests. A series of cyclic triaxial tests on silica powder and Fujian sand were conducted to investigate the stress-strain behavior of sand in pre-failure deformation, particularly in the unloading elastic behavior. The sand gradually tended toward the stable state of deformation after it was subjected to a certain number of cyclic loadings. The sand appeared to be entirely nonlinear elastic, with unchanged and closed hysteresis loops of the stress-strain curve. In addition, the elastic parameters—Young's modulus and Poisson's ratio—of the specimens during the unloading process of the stable state of deformation were carefully studied. The test results suggested that the unloading tangent Young's modulus of sand was determined by the stress state and void ratio but was not affected by the stress amplitude of cyclic loading. However, Young's modulus depended more definitely on the axial stress than on the lateral stress when the deviatoric stress increment was applied in the triaxial stress condition. Moreover, the unloading average Poisson's ratio was dependent on the stress state and void ratio.

Constitutive model for cyclic behaviour of cohesionless sands

ABSTRACTThis paper presents a constitutive model for describing the stress-strain response of sands under cyclic loading. The model, formulated using the critical state theory within the bounding surface plasticity framework, is an upgraded version of an existing model developed for monotonic behaviour of cohesionless sands. With modification of the hardening law, plastic volumetric strain increment and unloading plastic modulus, the original model was modified to simulate cyclic loading. The proposed model was validated against triaxial cyclic loading tests for Fuji River sand, Toyoura sand and Nigata sand. Comparison between the measured and predicted results suggests that the proposed modified model can capture the main features of cohesionless sands under drained and undrained cyclic loading.

Damage evolution in compacted graphite iron during thermomechanical fatigue testing

Thermomechanical fatigue properties of a compacted graphite iron in an out of phase configuration are investigated for different maximum temperatures and mechanical strain ranges. Furthermore, the stress–strain hysteresis loops are analysed, and, in particular, the unloading modulus, i.e. the elastic modulus measured during specimen unloading, is obtained from each cycle. This material parameter has earlier been explicitly related to the amount of microcracking in cast irons. The results show that the unloading modulus linearly declines with the numbers of cycles in all tests performed. In addition, the rate of change of the unloading modulus is closely related to the number of cycles to failure. Accordingly, it is concluded that microcracks are independently propagated by fatigue until a point of rapid crack linking resulting in ultimate failure. This is supported by microstructural analyses consisting of optical microscope images taken at different stages throughout the life of a specimen.

Effects of Microstructure on the Variation of the Unloading Behavior of DP780 Steels

The nonlinear unloading behavior of three different commercial dual-phase steels (DP780 grade equivalent) was examined. These steels exhibited small variations in chemical composition (0.07 to 0.10 mass percent carbon) and martensite volume fraction (0.23 to 0.28), and they demonstrated similar hardening behavior. Uniaxial loading-unloading-loading tests were conducted at room temperature and quasi-static strain rates between engineering strains of 0.5 and 8%. Steel microstructures were examined using electron backscatter diffraction and nanoindentation techniques. The microplastic component of the unloading strain exhibited no dependence on the martensite volume fraction or the ferrite grain size within the small range encountered in this investigations. Instead, the magnitude of the microplastic component of the unloading strain increased as the strength ratio between the martensite and ferrite phases increased. Correspondingly, the apparent unloading modulus, or chord modulus, exhibited a greater reduction for equivalent increments of strain hardening as the strength ratio increased. These results suggest that springback can be reduced in structures containing two ductile phases if the strength ratio between the harder and softer phases is reduced.

Determining of parameters of nonisothermal cyclic curve model

It was proposed methodology of determining parameters of model of nonisothermal cyclic stress-strain curve. Algorithm of pattern recognition was implemented. It was based on minimization of function of mismatch between experimental results and calculation of three-parameter model curve which depends on Bauchinger’s effect, elastic unloading modulus and scale of transformation of nonlinear part of stress-strain curve. Odkvist’s parameter was used for measure of plastic deformation. Simulation of cyclic stress strain curve was carried out. Results of simulation were compared with experimental data.

Constitutive and friction modeling for accurate springback analysis of advanced high strength steel sheets

The present work aims to analyze the influences of the material and friction models and to suggest the optimum selection of the models for springback simulations. Firstly, a transformation-induced plasticity (TRIP) steel was characterized using the conventional and advanced models for the springback prediction in U-draw/bending. A special attention was paid to the friction model, which was derived based on the macroscopically observed frictional behavior and interpreted with the microscopic contact mechanism. The combination of advanced constitutive and friction models could predict springback and punch load quite well. It was found that the hardening law and elastic unloading modulus had the major influences, while the friction model also had a major influence in the case of high blank holding force. A specific value of constant friction coefficient could provide similar predictions as the variable friction coefficient, but the former could not describe a non-uniform distribution of friction coefficient. Next, the analysis was extended to the sensitivity studies that considered wider ranges of material and frictional behaviors. These studies suggested that (1) the plastic anisotropy has to be modeled using an anisotropic yield function if the yield stresses or r-values affecting the relevant stress state are far from the isotropic assumption; (2) the reverse loading behavior has to be characterized using a hardening model that can precisely describe the transient hardening and permanent softening; (3) the elastic modulus should be defined using an advanced model if the material shows a visible reduction of elastic modulus; and (4) the friction coefficient should be carefully defined using an advanced friction model if the blank holding force is high.

Production of recycled concrete and its material properties

To research durability and dynamic properties of recycled concrete, we had made lots of tests and experiments. Tests results showed that impermeability of recycled concrete enlarged with the increasing of the water–cement ratio. Anti cl− ion permeability of recycled concrete was lower than that of ordinary concrete. Sulphate resistance of recycled concrete was slightly lower than that of ordinary concrete. Freezing-thawing resistance of recycled concrete were not lower than that of ordinary concrete. Experiments results showed unloading modulus of recycled concrete were larger than their corresponding loading modulus. When replacement rate of recycled concrete was less than 20%, their unloading modulus enlarged with the increasing of their replacement rate, whereas the replacement rate of recycled concrete was more than 20%, their unloading modulus reduced with the increasing of their replacement rate. Both loading modulus and unloading modulus of recycled concrete enlarged with the increasing of their water–cement ratio.

Experimental study of elastic properties of different constituents of partially saturated argillite using nano-indentation tests

Callovo-Oxfordian argillite, obtained from the ANDRA underground research laboratory in Meuse/Haute-Marne (France), is characterized as a multiphase material. The argillite is composed of carbonate inclusions (10–50μm) embedded in an argillaceous matrix (representing expanding clay minerals, such as smectites). The matrix itself is also multiphase, composed of clay aggregates of 1μm-size carbonate and quartz inclusions. The high sensitivity of the mechanical behaviour of argillite to saturation is an important characteristic of this material as it has been previously demonstrated in macro-scale mechanical experiments performed under varying degrees of humidity.The study presented here consists of grids of nano-indentation tests performed under controlled saturation conditions. The influence of the load hold time before unloading has been studied. Series of indentations were performed without or with load hold, which led to consider instantaneous or deferred unloading moduli respectively. The experimental procedure employed allows the micro-mechanical properties of the different phases (matrix and inclusions) to be determined under controlled hydration and therefore under partially saturated conditions. Several series of measurements were performed at relative humidity levels of 50%, 85%, 90% and 95%, and at a constant temperature of 20°C. A statistical analysis enabled to discriminate the deferred unloading modulus of the different phases. At 50% humidity, we measured a mean deferred unloading modulus of 16GPa for the clay matrix (a mean instantaneous unloading modulus of 13GPa was observed for the clay matrix and moduli higher than 70GPa were measured for the carbonate macro-inclusions). The mean deferred unloading modulus of the matrix appears to decrease with increasing saturation; at 95% humidity (near-saturation) it is less than 5GPa. However, it was impossible to verify the instantaneous unloading modulus of the carbonate macro-inclusions at this high-level of saturation.

Unloading‐Based Stiffness Characterisation of Cement Pastes During the Second, Third and Fourth Day After Production

AbstractThe stiffness evolution of binder ‘cement paste’ is triggering the stiffness of concrete. In the engineering practice, concrete formworks are typically removed 24 h after production. This underlines that knowledge on mechanical properties of cementitious materials during the second, third and fourth day after production is of high relevance for the ongoing construction process. This provides the motivation to perform early‐age stiffness characterisation on hydrating cement pastes, by means of the following three test methods. Unloading modulus is determined using a novel setup for non‐destructive uniaxial compression testing including overdetermined deformation measurements. Dynamic Young's moduli are obtained from ultrasonics experiments. Isothermal differential calorimetry allows for linking the observed temporal evolution of early‐age stiffness to the hydration degree of cement. Pastes with three different compositions are investigated, defined in terms of the initial water‐to‐cement mass ratio w/c and the initial water‐to‐solid (binder) mass ratio w/s. Pure cement pastes exhibit w/c = w/s = 0.50 and w/c = w/s = 0.42, respectively. A fly ash‐blended cement paste refers to a cement mass replacement level of 16%, and this is related to w/c = 0.50 and w/s = 0.42. Both unloading moduli and dynamic Young's moduli of all three materials increase practically linearly with increasing hydration degree, in the investigated regime of hydration degrees ranging from 40 to 60%. Fly ash does not contribute significantly to the early‐age hydration of the material, i.e. it represents a quasi‐inert part of the material's microstructure, exhibiting a significant stiffening effect.

OS1301-376 対称アングルプライCFRP積層板の高温におけるサイクル軟化挙動

Strain-controlled cyclic behavior of angle-ply CFRP laminates [±θ] at high temperature has been studied. Strain-controlled symmetric tension-compression cyclic tests for different strain amplitudes were carried out on coupon specimens with different fiber orientations (θ = 30°, 35° and 45°), respectively. On the basis of the cyclic tests, the changes of stress amplitude, mean stress, non-elastic strain amplitude, maximum and minimum stress levels and loading and unloading tangent moduli with cyclic straining are examined. The experimental results showed that hysteretic stress-strain response to cyclic straining appears, regardless of the fiber orientation. The stress amplitude decreased with increasing number of cycles, and accordingly the non-elastic strain amplitude increased with cyclic straining. These observations reveal that the cyclic softening occurs in the angle-ply CFRP laminates tested in this study. The cyclic softening terminates rapidly in a small number of cycles, and a cyclic saturation stage is reached in all the strain-controlled cyclic tests, except some cases of large strain amplitude or small fiber orientation angle.

Mechanical Properties of Sialic Foamed Ceramic and Applications in Defense Structure

Mechanical properties of a closed-cellular sialic foamed ceramic are investigated by compressive tests. The sialic foamed ceramic under uniaxial stress compression shows brittleness and the flow stress increases with the strain rate. The engineering stress-engineering strain curve under uniaxial strain compression could be divided into three stages: linear elasticity, collapsed plateau and densification. The unloading elastic modulus, Poisson ratio and energy absorption ability are discussed. Shelly cellular material made by sialic foamed ceramic is applied into the stress distribution layer in the defense structure. Field explosion experiments are performed for the sand based stress distribution layer and shelly cellular material based layer. Compared with sand, the shelly cellular material reduces the peak stress of the blast wave.

Low Cycle Fatigue Evaluation of NiTi SESMA Thin Wires

This paper presents experimental studies on low cycle fatigue (LCF) life of super-elastic shape memory alloy (SESMA) wires. The effect of frequency of the loading and amplitude of the strain on the fatigue life has been studied individually. Various loading frequencies have been considered to study the effect of frequency, by keeping the amplitude constant. From the experimental data, it was found that the LCF life of the SESMA reduces with increase in the frequency. The effect of amplitude on the LCF life of SESMA has also been studied, and it was found that the SESMA cycled at lower net strain has more fatigue life than the one cycled at higher net strain. Further, the plastic strain accumulation is also more in the samples tested at the higher net strain loadings. The modulus of austenite is found to be by and large independent of the frequency and amplitude of the loading. Further, martensitic unloading modulus is same for all the minimum strain amplitudes.

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.