Mechanical Behavior of Ion-Irradiated Fe-Cr alloys Investigated by Spherical Indentation

2012 ◽  
Vol 1424 ◽  
Author(s):  
Christopher D. Hardie ◽  
Steve G. Roberts ◽  
Andrew J. Bushby
Keyword(s):  
Plastic Zone ◽  
Strain Softening ◽  
Strain Curve ◽  
Spherical Indentation ◽  
Stress Strain Curve ◽  
Damage Layer ◽  
Dual Beam ◽  
Tip Radius ◽  
Fe Ions

ABSTRACTFe12%Cr was irradiated with 2MeV and 0.5MeV Fe+ ions at 320°C, to create a layer with a mean level of displacement damage of 6.18dpa to a depth of ∼800nm. Spherical indentation, with a nominal tip radius of 10μm, was used to investigate the mechanical properties of the damage layer. Indents produced with loads of 2mN, 3mN, 5mN and 10mN were cross-sectioned and fabricated into TEM foils using an in situ lift-out technique in a dual beam FIB-SEM microscope. The extent of the plastic zone beneath the indent was observed in the TEM for each indentation. The indentation results were analysed so as to give an indentation stress-strain curve, in which strain softening was found to occur beyond the yield point. At loads up to 3mN the plastic zone remained entirely within the damage layer, implying strain-softening of the damaged material. At higher indentation loads the plastic zone was observed to extend into the softer un-irradiated substrate, giving rise to a further fall in flow stress with increasing strain.

Determining engineering stress–strain curve directly from the load–depth curve of spherical indentation test

2010 ◽  
Vol 25 (12) ◽  
pp. 2297-2307 ◽  
Author(s):  
Baoxing Xu ◽  
Xi Chen
Keyword(s):  
Indentation Test ◽  
Strain Curve ◽  
Spherical Indentation ◽  
Displacement Curve ◽  
Large Set ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Constraint Factors ◽  
Engineering Stress ◽  
Depth Curve

The engineering stress–strain curve is one of the most convenient characterizations of the constitutive behavior of materials that can be obtained directly from uniaxial experiments. We propose that the engineering stress–strain curve may also be directly converted from the load–depth curve of a deep spherical indentation test via new phenomenological formulations of the effective indentation strain and stress. From extensive forward analyses, explicit relationships are established between the indentation constraint factors and material elastoplastic parameters, and verified numerically by a large set of engineering materials as well as experimentally by parallel laboratory tests and data available in the literature. An iterative reverse analysis procedure is proposed such that the uniaxial engineering stress–strain curve of an unknown material (assuming that its elastic modulus is obtained in advance via a separate shallow spherical indentation test or other established methods) can be deduced phenomenologically and approximately from the load–displacement curve of a deep spherical indentation test.

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.

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.

Application of Damp Newton Algorithm on FEPG Platform

2015 ◽  
Vol 744-746 ◽  
pp. 437-441
Author(s):  
Shi Wei Hou ◽  
Yi Fang Zhang ◽  
Jin Hong Qu ◽  
Xiu Li Du
Keyword(s):  
Finite Element ◽  
Shear Band ◽  
Strain Softening ◽  
Strain Curve ◽  
Weak Form ◽  
Yield Function ◽  
Stress Strain Curve ◽  
First Order ◽  
Newton Algorithm ◽  
Order Element

Damp Newton algorithm based on FEPG system is developed for calculating strain softening problem. The algorithm can solve displacement and yield surface equation simultaneously. Soften modulus is introduced into D-P yield function. The example result shows that, the algorithm with damp factor can be used to solve softening problems. The plastic theory described by finite element weak form has no requirement of continuity, so appropriate outcome can be obtained by first-order element. Descent segment of stress-strain curve and cloud picture of finite shear band are presented.

Influence of Uniaxial Stress on the Stress-Strain Curve Measured by Nanoindentation

2014 ◽  
Vol 597 ◽  
pp. 17-20
Author(s):  
Ikuo Ihara ◽  
Kohei Ohtsuki ◽  
Iwao Matsuya
Keyword(s):  
Compressive Stress ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Local Area ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Compressive Stresses ◽  
Multiple Loading ◽  
Tip Radius ◽  
Uniaxial Compressive Stress

A nanoindentation technique with a spherical indenter of tip radius 10 μm is applied to the evaluation of stress-strain curve at a local area of a pure iron under the uniaxial compressive stress exerted through the iron, and the influence of the compressive stress on the estimated stress-strain curve has been examined. A continuous multiple loading method is employed to determine the stress-strain curve. In the method, a set of 21 times of loading/unloading sequences with increasing terminal load are made and load-displacement curves with the different terminal loads from 0.1 mN to 100 mN are then continuously obtained and converted to a stress-strain curve. To examine the stress dependence of the stress-strain curve, the estimation by the nanoindentetion is performed under different uniaxial compressive stresses up to 250 MPa. It has been found that the stress-strain curve determined by the nanoindentation shifts upward as the compressive stress increases and the quantity of the shift is almost equal to the uniaxial stress acting on the iron specimen. It is also noted that the yield stress (0.2 % proof stress) estimated from the stress-strain curve increases almost proportionally to the uniaxial stress and the increase ratio tends to decrease as the stress reaches around 200 MPa.

Tenth Canadian Geotechnical Colloquium: Recent developments in consolidation of natural clays

1988 ◽  
Vol 25 (1) ◽  
pp. 85-107 ◽  
Author(s):  
Serge Leroueil
Keyword(s):  
Global Analysis ◽  
Strain Curve ◽  
The Self ◽  
Permeability Measurement ◽  
Stress Strain Curve ◽  
Consolidation Process ◽  
Recent Developments ◽  
Natural Clays ◽  
Excellent Tool

A global analysis of the consolidation of natural clays is realized considering the consolidation process to be a combination of the effects of compressibility and of permeability. The compressibility or stress–strain curve followed is strongly influenced, both in the laboratory and in situ, by the strain rate. The self-boring permeameter appears to be an excellent tool for permeability measurement; however, in homogeneous clays direct measurement in the laboratory also gives representive results. The coefficients of consolidation determined graphically strongly underestimate the in situ coefficient. The consolidation must thus be analysed by considering compressibility and permeability parameters measured separately. Key words: consolidation, clay, compressibility, permeability.

Study on Post-Failure Deformation and Residual Strength of Rock Mass Based on Hoek-Brown Criterion

2012 ◽  
Vol 170-173 ◽  
pp. 121-124
Author(s):  
Jian Xin Han ◽  
Xing Hua Tong ◽  
Lei Wang ◽  
Guo Fu Sun
Keyword(s):  
Rock Mass ◽  
Residual Strength ◽  
Strain Softening ◽  
Strain Curve ◽  
Strength Criterion ◽  
Stress Strain Curve ◽  
Strength Parameters ◽  
Softening Parameter ◽  
Residual Values ◽  
The Stability

In order to predict the stability of surrounding rock mass in geotechnical engineering, it is important to study the post-failure deformation property and residual strength of rock mass. Based on evolutional behavior of strength parameters, aiming at generalized Hoek-Brown strength criterion, selecting major principal strain as strain softening parameter, this paper presents the method of solving post-failure stress-strain curve . In numerical case, the effect of evolutional law of strength parameters ， and to deformation and residual strength is discussed and we can draw the following conclusions: the greater the residual values of ， are and the smaller the residual value of is, the post-failure strain softening curve falls more gently and the greater the residual strength is.

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