The Studies of Rock Damage Softening Statistical Constitutive Model under True Triaxial Stress State

2014 ◽  
Vol 580-583 ◽  
pp. 312-315
Author(s):  
Hui Mei Zhang ◽  
Xiang Miao Xie ◽  
Geng She Yang
Keyword(s):  
Constitutive Model ◽  
Strain Curve ◽  
Stress Path ◽  
Complex Stress ◽  
Model Parameters ◽  
Stress Strain ◽  
Deformation And Failure ◽  
True Triaxial ◽  
Complex Stress Path ◽  
The Impact

From the feature of rock micro-unit failure obeys Poisson random distribution, the damage softening statistical constitutive of was established under true triaxial confinement based on D-P criterion, so the impact of the intermediate principal stress on rock deformation and failure was considered in theory, and the actual engineering rock complex stress path evolution was reflected more realistically. Furthermore, according to the geometrical conditions of stress-strain relationship, the theoretical relationship between constitutive model parameters and the stress-strain curve characteristic parameters during the process of rock softening and deforming, which enhance the adaptability of the model. Finally, the rationality of the model verified by the measured data.

scholarly journals Study of Damage Constitutive Model of Brittle Rocks considering Stress Dropping Characteristics

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Fei Li ◽  
Shuang You ◽  
Hongguang Ji ◽  
Hao Wang
Keyword(s):  
Constitutive Model ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Brittle Rock ◽  
Model Parameters ◽  
Deformation And Failure ◽  
Brittle Rocks ◽  
Whole Process ◽  
Confining Pressures ◽  
Damage Constitutive Model

Deep brittle rock exhibits characteristics of rapid stress dropping rate and large stress dropping degree after peak failure. To simulate the whole process of deformation and failure of the deep brittle rock under load, the Lemaitre strain equivalent theory is modified to make the damaged part of the rock has residual stress. Based on the damage constitutive model considering residual strength characteristics, a correction factor reflecting stress dropping rate is added, the Weibull distribution is used to describe the inhomogeneity of rock materials, and Drucker–Prager criterion is used to quantitatively describe the influence of stress on damage; a damage constitutive model of deep brittle rock considering stress dropping characteristics is established. According to the geometric features of the rock stress-strain curve, the theoretical expressions of model parameters are derived. To verify the rationality of the model, triaxial compression experiments of deep brittle rock under different confining pressures are conducted. And the influence of model parameters on rock mechanical behaviour is analysed. The results show that the model reflects the stress dropping characteristics of deep brittle rock and the theoretical curve is in good agreement with the experimental results, which indicates that the proposed constitutive model is scientific and feasible.

scholarly journals Study on Damage Statistical Constitutive Model of Triaxial Compression of Acid-Etched Rock under Coupling Effect of Temperature and Confining Pressure

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7414
Author(s):  
Youliang Chen ◽  
Peng Xiao ◽  
Xi Du ◽  
Suran Wang ◽  
Zhoulin Wang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Coupling Effect ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Confining Pressure ◽  
Effect Of Temperature ◽  
Acid Etching ◽  
Model Parameters ◽  
Stress Strain Curve ◽  
Stress Strain

Based on Lemaitre’s strain equivalence hypothesis theory, it is assumed that the strength of acid-etching rock microelements under the coupling effect of temperature and confining pressure follows the Weibull distribution. Under the hypothesis that micro-element damage meets the D-P criterion and based on continuum damage mechanics and statistical theory, chemical damage variables, thermal damage variables and mechanical damage variables were introduced in the construction of damage evolution equations and constitutive models for acid-etching rocks considering the coupled effects of temperature and confining pressure. The required model parameters were obtained by theoretical derivation, and the model was verified based on the triaxial compression test data of granite. Comparing the experimental stress-strain curve with the theoretical stress-strain curve, the results show that they were in good agreement. By selecting reasonable model parameters, the damage statistical constitutive model can accurately reflect the stress-strain curve characteristics of rock in the process of triaxial compression. The comparison between the experimental and theoretical results also verifies the reasonableness and reliability of the model. This model provides a new rock damage statistical constitutive equation for the study of rock mechanics and its application in engineering, and has certain reference significance for rock underground engineering.

Effect of high differential stress and mineral properties on deformation and failure mechanism of hard rocks

2020 ◽  
Author(s):  
Xia-Ting Feng ◽  
Jun Zhao ◽  
Zhaofeng Wang ◽  
Cheng-Xiang Yang ◽  
Qiang Han ◽  
...  
Keyword(s):  
Triaxial Compression ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Differential Stress ◽  
Deformation And Failure ◽  
True Triaxial ◽  
Elastic Plastic ◽  
Hard Rocks ◽  
True Triaxial Compression

In order to study the deformation and failure mechanism of hard rocks, true triaxial compression tests were conducted on four type of hard rocks to obtain the complete stress-strain curve and failure modes. Under true triaxial compression condition, the shape of the complete stress-strain curve can be divided into three types: elastic-brittle (EB), elastic-plastic-brittle (EPB), and elastic-plastic-ductile (EPD) types. According to the different post-peak deformation behaviours, the stress-strain curves of elastic-plastic-brittle (EPB) type can be subdivided into three sub-categories: post-peak instantaneous brittle (EPB-I) type, post-peak multi-stage brittle (EPB-M) type, and post-peak delayed brittle (EPB-D) type. The stress-strain curves change from EPD to EPB-D to EPB-M to EPB-I to EB with increasing differential stress (σ2-σ3). The deformation characteristics are dependent on the σ2, σ3, mineral composition and mineral texture to the rock sample. An increase in σ3 leads to an increased ductility, while an increase in σ2 leads to an increased brittleness. Moreover, rocks with regular mineral texture and low mineral hardness are more prone to ductility. When the deformation curve is transformed from EPD to EPB to EB, the tensile crack is gradually dominant, and the macroscopic failure angle is gradually steeper.

scholarly journals A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1393
Author(s):  
Xiaochang Duan ◽  
Hongwei Yuan ◽  
Wei Tang ◽  
Jingjing He ◽  
Xuefei Guan
Keyword(s):  
Composite Materials ◽  
Constitutive Model ◽  
Model Parameters ◽  
Temperature Dependent ◽  
Stress Strain ◽  
Proposed Model ◽  
Single Temperature ◽  
Testing Data ◽  
Bonded Composite ◽  
Tension And Compression

This study develops a general temperature-dependent stress–strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from −40 ∘C to 75 ∘C is performed. The testing data reveal that the stress–strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg–Osgood relationship is proposed to build the stress–strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress–strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

scholarly journals Effect of Nanopores on Mechanical Properties of the Shape Memory Alloy

Micromachines ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 529
Author(s):  
Chunzhi Du ◽  
Zhifan Li ◽  
Bingfei Liu
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Shape Memory ◽  
Young’S Modulus ◽  
Residual Strain ◽  
Surface Effect ◽  
Young's Modulus ◽  
Strain Curve ◽  
Stress Strain ◽  
Strength Limit

Nanoporous Shape Memory Alloys (SMA) are widely used in aerospace, military industry, medical and health and other fields. More and more attention has been paid to its mechanical properties. In particular, when the size of the pores is reduced to the nanometer level, the effect of the surface effect of the nanoporous material on the mechanical properties of the SMA will increase sharply, and the residual strain of the SMA material will change with the nanoporosity. In this work, the expression of Young’s modulus of nanopore SMA considering surface effects is first derived, which is a function of nanoporosity and nanopore size. Based on the obtained Young’s modulus, a constitutive model of nanoporous SMA considering residual strain is established. Then, the stress–strain curve of dense SMA based on the new constitutive model is drawn by numerical method. The results are in good agreement with the simulation results in the published literature. Finally, the stress-strain curves of SMA with different nanoporosities are drawn, and it is concluded that the Young’s modulus and strength limit decrease with the increase of nanoporosity.

Stress-strain curve of paper revisited

2012 ◽  
Vol 27 (2) ◽  
pp. 318-328 ◽  
Author(s):  
Svetlana Borodulina ◽  
Artem Kulachenko ◽  
Mikael Nygårds ◽  
Sylvain Galland
Keyword(s):  
Three Dimensional ◽  
Strain Curve ◽  
Failure Behavior ◽  
Three Dimensional Model ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Fiber Network ◽  
Bonding Parameters ◽  
Particle Level ◽  
The Impact

Abstract We have investigated a relation between micromechanical processes and the stress-strain curve of a dry fiber network during tensile loading. By using a detailed particle-level simulation tool we investigate, among other things, the impact of “non-traditional” bonding parameters, such as compliance of bonding regions, work of separation and the actual number of effective bonds. This is probably the first three-dimensional model which is capable of simulating the fracture process of paper accounting for nonlinearities at the fiber level and bond failures. The failure behavior of the network considered in the study could be changed significantly by relatively small changes in bond strength, as compared to the scatter in bonding data found in the literature. We have identified that compliance of the bonding regions has a significant impact on network strength. By comparing networks with weak and strong bonds, we concluded that large local strains are the precursors of bond failures and not the other way around.

Dynamic Stress-Strain Relations for Annealed 2S Aluminum Under Compression Impact

1953 ◽  
Vol 20 (4) ◽  
pp. 523-529
Author(s):  
J. E. Johnson ◽  
D. S. Wood ◽  
D. S. Clark
Keyword(s):  
Dynamic Stress ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Impact Stress ◽  
Stress Strain Relation ◽  
Final Strain ◽  
Dynamic Relations ◽  
Single Stress ◽  
The Impact

Abstract This paper presents the results of an experimental study of the stress-strain relation of annealed 2S aluminum when subjected to compression impact. Two methods of securing a dynamic stress-strain curve are considered, namely, from the measurement of impact stress as a function of maximum plastic strain, and impact stress as a function of the impact velocity. The dynamic stress-strain curves obtained by these methods lie considerably above the static curve. The elevation in stress of the dynamic relations above the static relation increases progressively from zero at the elastic limit to about 20 per cent at a strain of 4.5 per cent. However, the two dynamic relations are not coincident which indicates that the behavior of the material cannot be described by a single stress-strain curve for all impact velocities. A family of stress-strain curves which differ slightly from each other and which depend upon the final strain is postulated in order to correlate both sets of data adequately.

A finite-deformation constitutive model of particle-binder composites incorporating yield-surface-free plasticity

2021 ◽  
pp. 1-32
Author(s):  
Ankit Agarwal ◽  
Marcial Gonzalez
Keyword(s):  
Constitutive Model ◽  
Yield Surface ◽  
Finite Deformation ◽  
Large Strain ◽  
Elastic Response ◽  
Rate Equations ◽  
Internal Variables ◽  
Model Parameters ◽  
Stress Strain ◽  
Stress Softening

Abstract We present a constitutive model for particle-binder composites that accounts for finite-deformation kinematics, nonlinear elasto-plasticity without apparent yield, cyclic hysteresis, and progressive stress-softening before the attainment of stable cyclic response. The model is based on deformation mechanisms experimentally observed during quasi-static monotonic and cyclic compression of mock Plastic-Bonded Explosives (PBX) at large strain. An additive decomposition of strain energy into elastic and inelastic parts is assumed, where the elastic response is modeled using Ogden hyperelasticity while the inelastic response is described using yield-surface-free endochronic plasticity based on the concepts of internal variables and of evolution or rate equations. Stress-softening is modeled using two approaches; a discontinuous isotropic damage model to appropriately describe the softening in the overall loading-unloading response, and a material scale function to describe the progressive cyclic softening until cyclic stabilization. A nonlinear multivariate optimization procedure is developed to estimate the elasto-plastic model parameters from nominal stress-strain experimental compression data. Finally, a correlation between model parameters and the unique stress-strain response of mock PBX specimens with differing concentrations of aluminum is identified, thus establishing a relationship between model parameters and material composition.

Uniaxial Mechanical Properties of Sandstone under Cyclic of Drying and Wetting

2011 ◽  
Vol 243-249 ◽  
pp. 2310-2313 ◽  
Author(s):  
Hua Yan Yao ◽  
Zhen Hua Zhang ◽  
Zhao Hui Zhu
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Test Results ◽  
Stress Strain ◽  
Deformation And Failure ◽  
Deformation Behaviors ◽  
Uniaxial Strength

Water is an important factor that influences the mechanical properties of rock. Uniaxial compressive experiments have been carried out on sandstone under different cyclic times of drying and wetting. The corresponding complete stress-strain curves are obtained, and characteristics of deformation and failure are analyzed. Test results show that when sandstone samples are submitted to cyclic of drying and wetting, the uniaxial strength and Young's modulus of sandstone obviously decrease. Then, the improved Duncan constitutive model is developed, which can do better in describing sample’s deformation behaviors subject to different cyclic times of drying and wetting. Introduction

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