A hardening load transfer function for rock bolts and its calibration using distributed fiber optic sensing

Confinement of rock bolts by the surrounding rock formation has long been recognized as a positive contributor to the pull-out behavior,yet only a few experimental works and analytical models have been reported,most of which are based on the global rock bolt response evaluated in pull-out tests.This paper presents a laboratory experimental setup aiming to capture the rock formation effect,while using distributed fiber optic sensing to quantify the effect of the confinement and the reinforcement pull-out behavior on a more local level.It is shown that the behavior along the sample itself varies,with certain points exhibiting stress drops with crack formation.Some edge effects related to the kinematic freedom of the grout to dilate are also observed.Regardless,it was found that the mid-level response is quite similar to the average response along the sample.The ability to characterize the variation of the response along the sample is one of the many advantages high-resolution fiber optic sensing allows in such investigations.The paper also offers a plasticity-based hardening load transfer function,representing a"slice"of the anchor.The paper describes in detail the development of the model and the calibration/determination of its parameters.The suggested model captures well the coupled behavior in which the pull-out process leads to an increase in the confining stress due to dilative behavior.

Hardening effects of sheared precipitates on {1121} twinning in magnesium alloys

The interactions between a plate-like precipitate and two twin boundaries(TBs)({1012},{1121}) in magnesium alloys are studied using molecular dynamics(MD) simulations. The precipitate is not sheared by {1012} TB, but sheared by {1121} TB. Shearing on the(110) plane is the predominant deformation mode in the sheared precipitate. Then, the blocking effects of precipitates with different sizes are studied for {1121} twinning. All the precipitates show a blocking effect on {1121} twinning although they are sheared, while the blocking effects of precipitates with different sizes are different. The blocking effect increases significantly with the increasing precipitate length(in-plane size along TB) and thickness, whereas changes weakly as the precipitate width changes. Based on the revealed interaction mechanisms, a critical twin shear is calculated theoretically by the Eshelby solutions to determine which TB is able to shear the precipitate. In addition, an analytical hardening model of sheared precipitates is proposed by analyzing the force equilibrium during TB-precipitate interactions. This model indicates that the blocking effect depends solely on the area fraction of the precipitate cross-section, and shows good agreement with the current MD simulations. Finally, the blocking effects of plate-like precipitates on the {1012} twinning(non-sheared precipitate), {1121} twinning(sheared precipitate) and basal dislocations(non-sheared precipitate) are compared together. Results show that the blocking effect on {1121} twinning is stronger than that on {1012} twinning, while the effect on basal dislocations is weakest. The precipitate-TB interaction mechanisms and precipitation hardening models revealed in this work are of great significance for improving the mechanical property of magnesium alloys by designing microstructure.

Improved shape hardening function for bounding surface model for cohesive soils

A shape hardening function is developed that improves the predictive capabilities of the generalized bounding surface model for cohesive soils, especially when applied to overconsolidated specimens. This improvement is realized without any changes to the simple elliptical shape of the bounding surface, and actually reduces the number of parameters associated with the model by one.

Applicability of discrete element method with spherical and clumped particles for constitutive study of granular materials

Discrete element method(DEM)has been intensively used to study the constitutive behaviour of granular materials.However,to what extent a real granular material can be reproduced by virtual DEM simulations remains unclear.This study attempts to answer this question by comparing DEM simulations with typical features of experimental granular materials.Three groups of models with spherical and clumped particles are investigated from four perspectives:(i)deviatoric stress and volumetric behaviour;(ii)critical state behaviour;(iii)stress-dilatancy relationship;and(iv)the evolution of principal stress ratio against axial strain.The results demonstrate that DEM with spherical or clumped particles is capable of qualitatively describing macroscopic deviatoric stress responses,volumetric behaviour,and critical state behaviour observed in experiments for granular materials.On the other hand,some qualitative deviations between experiments and the investigated DEM simulations are also observed,in terms of the stress-dilatancy behaviour and principal stress ratio against axial strain,which are proven to be critical for constitutive modelling.The results demonstrate that DEM with spherical or clumped particles may not necessarily fully capture experimental features of granular materials even from a qualitative perspective.It is thus encouraged to thoroughly validate DEM with experiments when developing constitutive models based on DEM observations.

Comparison Study of Constitutive Models for Overconsolidated Clays

Widely distributed in natural deposits,the overconsolidated(OC)clays have attracted extensive experimental investigations on their mechanical behaviors,especially in the 1960s and 1970s.Based on these results,numerous constitutive models have also been established.These models generally fall into two categories:one based on the classical plasticity theory and the other the bounding surface(BS)plasticity theory,with the latter being more popular and successful.The BS concept and the subloading surface(SS)concept are the two major BS plasticity theories.The features of these two concepts and the representative models based on them are introduced,respectively.The unified hardening(UH)model for OC clays is also based on the BS plasticity theory but distinguishes itself from other models by the integration of the reference yield surface,unified hardening parameter,potential failure stress ratio,arid transformed stress tensor.Modification is made to the Hvorslev envelop employed in the UH model to improve its capability of describing the behaviors of clays with extremely high overconsolidation ratio in this paper.The comparison among the BS model,SS model,and UH model is performed.Evidence shows that all these three models can characterize the fundamental behaviors of OC clays,such as the stress dilatancy,strain softening and attainment of the critical state.The UH model with the revised Hvorslev envelop has the fewest parameters which are identical to those of the modified Cam-Clay model.

Loading-unloading judgement for advanced plastic UH model

The unified hardening(UH)model proposed by Yao et al.(Geotechnique 2009)is the constitutive model which can consider the influence of the complex stress path and stress history on the deformation and strength of clays reasonably.Firstly,the loading-unloading criterion of material model is defined as the change law of the intersection of current yield surface and the p axis,which makes the loading-unloading in the process of hardening and softening can be unified considered in UH model.Then,the Newton-Raphson method is adopted to attain the nonlinear problems solution in the finite element method of UH model,and the semi-implicit return mapping method is adopted to update stress.The application of the UH model in the finite element is realized.And then,the analyses of triaxial test are performed using the unit prediction and finite element method.The results of the unit prediction method are compared with the experimental results to illustrate the rationality of the UH model.Comparing the results with the unit prediction method and the finite element method,the correctness of the finite element program of the UH model is iUusttated.Further,Ae three-dimensional firdte element andysis of embankment on soft soil is performed by the program.The comparison between the results calculated by the UH model and the modified Cam-clay(MCC)model and the experimental data shows that the UH model is rational in analyzing the actual embankment engineering on soft soil.

Effect of tempering temperature on strain hardening exponent and flow stress curve of 1000MPa grade steel for construction machinery

To study the effect of tempering temperature on strain hardening exponent and flow stress curve,one kind of 1000 MPa grade low carbon bainitic steel for construction machinery was designed,and the standard uniaxial tensile tests were conducted at room temperature.A new flow stress model,which could predict the flow behavior of the tested steels at different tempering temperatures more efficiently,was established.The relationship between mobile dislocation density and strain hardening exponent was discussed based on the dislocation-stress relation.Arrhenius equation and an inverse proportional function were adopted to describe the mobile dislocation,and two mathematical models were established to describe the relationship between tempering temperature and strain hardening exponent.Nonlinear regression analysis was applied to the Arrhenius type model,hence,the activation energy was determined to be 37.6kJ/mol.Moreover,the square of correlation coefficient was 0.985,which indicated a high reliability between the fitted curve and experimental data.By comparison with the Arrhenius type curve,the general trend of the inverse proportional fitting curve was coincided with the experimental data points except of some fitting errors.Thus,the Arrhenius type model can be adopted to predict the strain hardening exponent at different tempering temperatures.

Bauschinger-Like Effect of AZ31 Magnesium Alloy Wide Sheet During the Straightening Process

The Bauschinger-like effect, which showed up in the straightening process of the AZ31 magnesium alloy wide sheet, was investigated through the multi-pass discrete three-point bending–unloading–bending(BUB) experiments. The stress variable, anisotropy, and asymmetry of tension and compression on the straightening process were corresponding to the Bauschingerlike effect. The Bauschinger-like effect in the initial, intermediate, and end of the straightening process was dominated by the twinning, detwinning, and dislocation induced by pyramidal < c + a > slip, respectively. Also, they were responsible for the transformation of the Bauschinger stress parameter(BSP) and Bauschinger energy parameter(BEP). Later, the anisotropic nonlinear kinematic hardening model(ANK model) to describe the Bauschinger-like effect was optimized and simplified.

Numerical Study of the Forming Process of High Frequency Welded Pipe

The roll forming process is applied to the manufacturing of high frequency welded (HFW) pipes,section steels,etc. In this paper,the roll forming process of the HFW pipe is simulated with the finite element method (FEM). A user-defined material routine of the commercial finite element code ABAQUS/Explicit is developed,and the mixed hardening constitution model is realized through the user-defined material routine. Based on the mixed hardening constitutive equation,the numerical simulation of roll forming process of HFW pipe is performed. The evolutions of equivalent stress and strain are analyzed,and the calculated results are also compared between different hardening models. The results show that the different material hardening models have some important effects on the variation of equivalent stress and strain of strip steel during the simulation of the roll forming process.