Joint Inclination Effect on Strength, Stress-Strain Curve and Strain Localization of Rock in Plane Strain Compression

2005 ◽  
Vol 495-497 ◽  
pp. 69-76 ◽  
Author(s):  
X.B. Wang
Keyword(s):  
Plane Strain ◽  
Strain Softening ◽  
Strain Curve ◽  
Plane Strain Compression ◽  
Peak Strength ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Softening Behavior ◽  
Ideal Plastic ◽  
Joint Inclination

Peak strength, mechanical behavior, and shear band (SB) of anisotropic jointed rock (JR) were modeled by Fast Lagrangian Analysis of Continua (FLAC). The failure criterion of rock was a composite Mohr-Coulomb criterion with tension cut-off and the post-peak constitutive relation was linear strain-softening. An inclined joint was treated as square elements of ideal plastic material beyond the peak strength. A FISH function was written to find automatically elements in the joint. For the lower or higher joint inclination (JI), the higher peak strength and more apparent strain-softening behavior are observed; the failure of JR is due to the slip along the joint and the new generated SBs initiated at joint’s two ends. For the lower JI, the slope of softening branch of stress-strain curve is not concerned with JI since the new and longer SBs’s inclination is not dependent on JI, as can be qualitatively explained by previous analytical solution of post-peak slope of stress-strain curve for rock specimen subjected to shear failure in uniaxial compression based on gradient-dependent plasticity. For the higher JI, the post-peak stress-strain curve becomes steeper as JI increases since the contribution of the new SBs undergoing strain-softening behavior to axial strain of JR increases with JI. For the moderate JI, the lower strength and ideal plastic behavior beyond the elastic stage are found, reflecting that the inclined joint governs the deformation of JR. The present numerical prediction on anisotropic peak strength in plane strain compression qualitatively agrees with triaxial experimental tests of many kinds of rocks. Comparison of the present numerical prediction on JI corresponding to the minimum peak strength of JR and the oversimplified theoretical result by Jaeger shows that Jaeger’s formula has overestimated the value of JI.

Effects of Joint Width on Strength, Stress-Strain Curve and Strain Localization of Rock Mass in Uniaxial Plane Strain Compression

2007 ◽  
Vol 353-358 ◽  
pp. 1129-1132 ◽  
Author(s):  
X.B. Wang
Keyword(s):  
Plane Strain ◽  
Inclination Angle ◽  
Rock Specimen ◽  
Strain Curve ◽  
Plane Strain Compression ◽  
Intact Rock ◽  
Peak Strength ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Joint Width

Effects of joint width (JW) on the macroscopic stress-strain curve, the failure process and mode of jointed rock specimen (JRS) in plane strain compression are modeled by use of FLAC. The failure criterion of intact rock outside the inclined joint is a composite Mohr-Coulomb criterion with tension cut-off and the linear strain-softening post-peak constitutive relation is adopted. The joint is treated as quadrate elements of ideal plastic material beyond the peak strength. A written FISH function is used to automatically find elements in the joint. Numerical results show that the peak strength of JRS depends on JW and is lower than that of intact rock specimen without joint. For JRS, the shear strains are concentrated into the joint or the new generated shear bands (NGSBs); the peak strength decreases with an increase of JW. At lower or higher joint inclination angle (JIA), the failure mode and pattern of NGSBs are not related to JW. The post-peak response becomes ductile at wider JW and higher JIA. The post-peak slope of stress-strain curve at lower JIA is not dependent on JW since the width and inclination angle of NGSBs are not affected by JW.

Model for predicting the variation of shear stress in unsaturated soils during strain-softening

2020 ◽  
Author(s):  
Xiuhan Yang ◽  
Sai Vanapalli
Keyword(s):  
Shear Stress ◽  
Large Deformation ◽  
Unsaturated Soils ◽  
Strain Softening ◽  
Strain Curve ◽  
Published Data ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Relationship ◽  
State Stress

Several of the geotechnical structures constructed with unsaturated soils undergo a large deformation prior to reaching failure conditions (e.g. progressive failure of a soil slope). During this process, the shear stress in soils typically increases initially and then reduces with an increase in the shear strain. The prediction of the stress-strain relationship is critical for reasonable interpretation of the mechanical behavior of those geo-structures that undergo large deformation. This paper introduces a model based on the disturbed state concept (DSC) to predict the variation of shear stress in unsaturated soils during strain-softening process under consolidated drained triaxial compression condition. In this model, the apparent stress-strain relationship is formulated as a weighted average of a hyperbolic hardening response extending the pre-peak state stress-strain curve and a linear response extending the critical state stress-strain curve with an assumed disturbance function as the weight. The prediction procedure is described in detail and the proposed model is validated using several sets of published data on unsaturated soils varying from coarse- to fine-grained soils. Finally, a comprehensive error analysis is undertaken based on an index of agreement approach.

scholarly journals An Improved Statistical Damage Constitutive Model for Granite under Impact Loading

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Zhenwei Zhao ◽  
Bo Wu ◽  
Xin Yang ◽  
Zhenya Zhang ◽  
Zhantao Li
Keyword(s):  
Constitutive Model ◽  
Elasticity Modulus ◽  
Strain Curve ◽  
Peak Strength ◽  
Peak Strain ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Statistical Damage

To study the impact properties of granite, the parameters (including the stress-strain curve, elasticity modulus, peak strength, and peak strain) of the test pieces in each group were determined via standard split-Hopkinson pressure bar tests. The results revealed that the prepeak stress-strain curves are approximately linear; the postpeak stress-strain curve declined sharply and exhibited the characteristics of brittle material failure after the stress exceeded the peak strength. In terms of the specimen form following failure, for increasing strain rate, the granite specimen became increasingly fragmented after failure. In addition, the single-parameter statistical damage constitutive model was improved, and a double-parameter statistical damage constitutive model for describing the total stress-strain curve of granite under the action of impact loading was proposed. The parameters of the statistical damage model, m and a, were obtained via fitting. The results revealed that the parameter m decreases with increasing elasticity modulus, whereas the parameter a increases. Similarly, the peak strength and the peak strain increased (in general) with increasing strain rate.

The Stress-Strain Behavior of Densified Mix Design of Concrete

2002 ◽  
Vol 18 (4) ◽  
pp. 185-192
Author(s):  
Ping-Kun Chang
Keyword(s):  
High Performance ◽  
Strain Softening ◽  
High Performance Concrete ◽  
Strain Curve ◽  
Type I ◽  
Peak Strain ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Behavior ◽  
Slump Flow

ABSTRACTThis paper investigates the compressive strength and workability of High-Performance Concrete (HPC) which yields a slump at 250 ± 20mm and a slump flow at 650 ± 50mm. From the complete stress-strain curve, it shows the peak strain will be higher while the strength increases. Two kinds of the post failure models can be distinguished. The first type (Type I) is called strain softening and the second type (Type II) is called strain snapping back. Also, it is found that the modulus of elasticityEcdecreases as the volume of cementitious pasteVpincreases. On the other hand, Poisson's ratio ν increases asVpincreases.

Failure Process and Stress-Strain Curve of Plane Strain Rock Specimen with Initially Random Material Imperfections

2007 ◽  
Vol 353-358 ◽  
pp. 1133-1136 ◽  
Author(s):  
X.B. Wang
Keyword(s):  
Rock Specimen ◽  
Failure Process ◽  
Shear Bands ◽  
Strain Curve ◽  
Peak Stress ◽  
Plastic Behavior ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Initial Imperfections ◽  
Ideal Plastic

The failure process of heterogeneous rock specimen with initially random material imperfections in uniaxial plane strain compression and the macroscopically mechanical response are numerically modeled by using FLAC (Fast Lagrangian Analysis of Continua). A FISH function is generated to prescribe the initial imperfections within the heterogeneous specimen by using Matlab. The imperfection is weaker than the intact rock. Beyond the failure of the imperfection, it undergoes ideal plastic behavior, while intact rock exhibits linear strain-softening behavior and then ideal plastic behavior once failure occurs. The specimen with smooth ends is loaded at a constant strain rate and is divided into 3200 elements. The maximum numbers of the initial imperfections in five schemes are 100, 300, 500, 700 and 900. The effects of the number of the imperfections on the fracture process, the final fracture pattern and the complete stress-strain curve are investigated. Prior to the peak stress, some imperfections extend in the axial direction and then a part of them coalesce to form inclined shear bands. Beyond the peak stress, shear bands progressively intersect the specimen; in the process the number of the yielded elements approximately remains a constant. With an increase of the number of the initial imperfections, the spacing of shear fractures decreases, the peak stress and corresponding axial strain decrease; the post-peak branch of stress-strain curve becomes steeper; much more elements fail in tension; the number of the yielded elements in tension in the vicinity of the two lateral edges of the specimen remarkably increases.

Softening of Rubber by Deformation

1969 ◽  
Vol 42 (1) ◽  
pp. 339-362 ◽  
Author(s):  
L. Mullins
Keyword(s):  
Steady State ◽  
Strain Curve ◽  
Hardness Test ◽  
Simple Extension ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Softening Behavior ◽  
Reinforcing Fillers ◽  
Conventional Test

Abstract It has been known for many years that deformation results in softening of rubber and that the initial stress-strain curve determined during the first deformation is unique and cannot be retraced. Further the effect of repeated deformation is to cause rubber asymptotically to approach a steady state with a constant or equilibrium stress-strain curve. Softening in this way occurs in vulcanizates either with or without fillers although the effect appears to be much more pronounced in vulcanizates containing high proportions of reinforcing fillers. After the hardness test the simple extension stress-strain test is the test most widely used by rubber technologists. The conventional stress-strain curve is obtained on samples which have not been previously deformed and for design purpose the unique value of stiffness given by this curve may be of little significance. Thus it appears that the values of stress—strain properties determined after “conditioning” cycles of deformation would be of more practical use than the unique value obtained in the conventional test. In recent years much interest has been shown in the factors responsible for this softening behavior particularly in regard to the implications of the loss of the stiffening action of reinforcing fillers on the mechanism of reinforcement.

Plane-strain Bulge Test for Thin Films

2005 ◽  
Vol 20 (9) ◽  
pp. 2360-2370 ◽  
Author(s):  
Y. Xiang ◽  
X. Chen ◽  
J.J. Vlassak
Keyword(s):  
Thin Films ◽  
Residual Stress ◽  
Finite Element ◽  
Plane Strain ◽  
Strain Curve ◽  
Bulge Test ◽  
Stress And Strain ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Cu Film

The plane-strain bulge test is a powerful new technique for measuring the mechanical properties of thin films. In this technique, the stress–strain curve of a thin film is determined from the pressure-deflection behavior of a long rectangular membrane made of the film of interest. For a thin membrane in a state of plane strain, film stress and stain are distributed uniformly across the membrane width, and simple analytical formulae for stress and strain can be established. This makes the plane-strain bulge test ideal for studying the mechanical behavior of thin films in both the elastic and plastic regimes. Finite element analysis confirms that the plane-strain condition holds for rectangular membranes with aspect ratios greater than 4 and that the simple formulae are highly accurate for materials with strain-hardening exponents ranging from 0 to 0.5. The residual stress in the film mainly affects the elastic deflection of the membrane and changes the initial point of yield in the plane-strain stress–strain curve, but has little or no effect on further plastic deformation. The effect of the residual stress can be eliminated by converting the plane-strain curve into the equivalent uniaxial stress–strain relationship using effective stress and strain. As an example, the technique was applied to an electroplated Cu film. Si micromachining was used to fabricate freestanding Cu membranes. Typical experimental results for the Cu film are presented. The data analysis is in good agreement with finite element calculations.

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