Experimental and theoretical characterization of Li 2 TiO 3 and Li 4 SiO 4 pebbles
|
|
- Britton Richard McKinney
- 6 years ago
- Views:
Transcription
1 Experimental and theoretical characterization of Li 2 TiO 3 and Li 4 SiO 4 s D. Aquaro 1 N. Zaccari ABSTRACT Dipartimento di Ingegneria Meccanica Nucleare e della Produzione University of Pisa (Italy) This paper deals with compression tests on one single of Li 2 TiO 3 and Li 4 SiO 4 ( the most promising candidates as breeder materials). Useful information have been obtained from these tests in order to assess a theoretical model developed by the authors. The experimental results have been used in order to implement a numerical model which simulates the mechanical behaviour of the. In the second part of the paper, numerical simulations of oedometer tests on bed, performed with FEM codes, are illustrated.. The experimental results are compared with numerical ones obtained using the Cam-Clay model. The issues derived from the use of the soil model for describing the bed behaviour are described. 1. INTRODUCTION Ceramic materials are investigated in order to develop breeding blanket modules which will be experimentally tested in the ITER reactor. Several research activities are being carried out on ceramic s as well as on beds with the aim to improve the technological processes, to determine the thermal and mechanical properties and to develop suitable models for simulating the behaviour. This paper reports the results of mechanical characterization tests on Lithium Metatitanate and Lithum Ortosilicate spheres. The test is a compression uniaxial test (without radial constraints) on single spheres made of Li 2 TiO 3 and Li 4 SiO 4. This test allows to determine the stiffness in a complete cycle of loading and unloading. The experimental results are compared with those obtained by FEM model which simulate the compression of the. These simulations demonstrate the importance to know very well the material characteristic of the which depend on the production technology. A numerical analysis of a bed in an oedometer test is performed using a model (Cam-clay) which describes the behaviour of the soil. Choosing in appropriate manner the model parameters it is possible to fit very well the experimental results, but the physical meaning of the parameters is not straightforward. 2. EXPERIMENTAL TESTS ON SINGLE PEBBLES Experimental compression tests were performed on Lithium-Metatitanate (Li 2 TiO 3 ) s, mm of diameter, and on Lithium-Orthosilicate s (Li 4 SiO 4 ), mm of diameter. The first s were produced by CEA while the Lithium-Orthosilicate s were produced by Schott- FZK. The s were analyzed by SEM before the test in order to verify the actual shapes and dimensions. These examinations permitted to estimate the average diameter and to normalize the results to a nominal diameter equal to 1 mm for the Li 2 TiO 3 s and.5 mm for the Li 4 SiO 4 s. Moreover the s or their fragments (if the collapsed) were again examined by SEM for evaluating the failure mode and the fracture surfaces. 1 Corresponding author : aquaro@ing.unipi.it
2 T11 T12 T15 T17 T23 T22 Φ=1.1982mm Φ= mm Φ=1.131mm Φ=1.1761mm Φ=1.12 mm Φ=1.2696mm x=1.151mm x=1.1245mm x=1.188mm x=1.28mm x=1.1435mm x=1.2153mm y=1.231 mm y=1.275 mm y=1.74 mm y=1.144 mm y=1.966 mm y=1.324 mm T25 T27 T28 T31 T34 T37 -Φ= mm Φ=1.2362mm Φ=1.197 mm Φ=1.211mm Φ=1.1363mm Φ= mm x=1.1392mm x=1.218mm x=1.194mm x=1.2898mm x=1.1152mm x=1.152mm y=1.118mm y=1.236 mm y=1.2 mm y= mm y=1.1573mm y=1.159 mm Figure 1 Average diameter and bounding box of the tested Li 2 TiO 3 s T42 T43 T44 T45 T48 T412 Φ=.5534mm Φ=.578 mm Φ= mm Φ= mm Φ=.5686 mm Φ=.5822mm x=.532 mm x=.5641 mm x=.5868 mm x= mm x=.5534 mm x= mm y=.5748 mm y=.5775 mm y=.5844 mm y=.5987 mm y=.5838 mm y=.5987 mm Figure 2 Average diameter and bounding box of the tested Li 4 SiO 4 s Figures 1 and 2 show the images of the s obtained by the SEM and reports their average diameters and the dimensions of their bounding box. The maximum variation of the average diameter of the tested s is 7.8% for the Li 2 TiO 3 s and 4% for Li 4 SiO 4 s. Some s were subjected to several loading cycles without reaching the failure while other s were compressed until the collapse. Figures 3 and 4 illustrate for the Li 2 TiO 3 s the curves of the load versus displacement obtained during the loading and unloading phases, respectively. Figures 5 and 6 show the correspondent curves of the Li 4 SiO 4 s. The s calculated with the least square method are expressed by the following equations: a) Lithium-Metatitanate - loading phase: P= s r 2 = unloading phase : P= s r 2 =.9854 b)lithium-orthosilicate - loading phase: P=3613 s r 2 = unloading phase : P=7657 s r 2 =.974
3 where P (N) is the applied load, s (mm) is the vertical displacement and r 2 is the correlation coefficient t37 t23 t22 t28 t11 t12 t15 t34 t t37 t22 t17 t27 t23 t28 t Fig. 3 Loading curve of Lithium-Metatitanate Fig. 4 Unloading curve of Lithium-Metatitanate Before the regression analyses, the values of the experimental displacement were normalized at the nominal diameter assuming according the Hertz theory that the displacement are inversely proportional to the radius t412 t43 t45 t t44 t45 t43 t load( N) Fig. 5 Loading curve of Lithium-Orthosilicate Fig. 6 Unloading curve of Lithium-Orthosilicate
4 Even though the number of the tested is not statistically significative, nevertheless the number of the collapsed s versus the maximum load could give an useful information on the ultimate strength of the s. Figures 7 and 8 show the fraction of the collapsed s versus the maximum load for the Li 2 TiO 3 and Li 4 SiO 4 s, respectively. No Li 2 TiO 3 s collapsed under 25 N while 1 N is the maximum load supported by the Li 4 SiO 4 s without any rupture (Indeed just only one collapsed at 1.6 N while all the other broke for load upper than 7 N..6.7 collapsed fraction fracture collapsed fraction Fig. 7 Collapsed fraction of Lithium-Metatitanate Fig. 8 Collapsed fraction of of Lithium- Orthosilicate 3. NUMERICAL SIMULATION OF THE PEBBLE COMPRESSION The compression tests on single s have been simulated numerically by means of the FEM code MSC- MARC [4]. The aims of the simulations were to implement a model which described correctly the behaviour of the comparing the results with the experimental ones as well as to understand the main phenomena which occur during the compression. 6 5 t22 sy=2mpa-e=3.5gpa-eu=.3-sc=1mpa sy=2mpa-e=5gpa-eu=.15-sc=1mpa Fig. 9- Mesh of the Fig. 1 Compression test on Li 2 TiO 3 :comparison between numerical and experimental results
5 Figure 9 shows the implemented mesh. The mesh is made up of axial symmetric elements. The load is applied by means of a rigid upper plate and the is located on a rigid lower plate. The constraints between the and the plates have been simulated by means of unilateral contacts (reacting only to compression loads) without friction. Being the made of a ceramic material having a low tension resistance but a great compression strength, the implemented model assumes a linear elastic behaviour under tensile stress and an elastic perfectly plastic behaviour under compressive stress. The material fails if the tensile stress overcomes the cracking stress value (σ cr ) or if the plastic strain (under compressive stresses) reaches the crushing strain value (ε u ). Other parameters which characterize the material behaviour are: - the softening module ( Es), which represents the slope of the curve σ-ε after the cracking stress (that is, the manner in which the stress goes to zero), - the shear retention (τ), which means the capability of the material to transmits shear by friction if the crack closure occurs. The material data for the lithium metatitanate and Lithium Ortosilicate are reported in [1]- [3] and are summarize as follows: - Lithium-Metatitanate : E= 2.6 GPa - ν=.27 - σ u = 1113 MPa - Lithium-ortosilicate : E= 9 GPa - ν=.25 - σ u = 88 MPa where E is the Young module, ν, the Poisson coefficient and σ u the ultimate compression stress t44 sy=25mpa-e=5.5gpa-eu=.15- sc=139mpa vertical stress (- MPa) d=.5 mm d=.1 mm d=.125 mm strain Fig. 11- Compression test on Li 4 SiO 4 :comparison between numerical and experimental results Fig. 12 Stress versus strain in different points of the Li 2 TiO 3 Using these data for obtaining the material parameters, the numerical results do not fit the experimental ones. E and σ u seem too high values. In fact considering the average stresses and strains obtained in the single compression tests, the Young modules have to be two or three order of magnitude lower than the above mentioned values. The data reported in [1]- [3] are data collected from different sources and they could not match the material characteristics of the tested s. Indeed for the ceramic material, the thermal mechanical characteristics are strongly dependent on the production technology. This problem was overcame performing a parametric analyses varying the model parameters in manner that the load- displacement curves fitted the experimental ones. Figures 1 and 11 compare the experimental load-displacement curves of the lithium metatitanate and Lithium Ortosilicate with those obtained numerically. In Fig.1, an experimental cycle on a Lithium-
6 Metatitanate (sample T22) fits the numerical results with the following values of the material parameters : E= 5 GPa; σ y =2 MPa; ε u =.15; σ cr =1 MPa; Es=.2 MPa. In the same Figure a cycle built with the s fits the numerical curve assuming E= 5 GPa and ε u =.3. Figure 11 shows the comparison of three cycles of loading and unloading on a Lithium-ortosilicate (sample T44) and the correspondent curves obtained by means of the numerical simulation. A good agreement is obtained assuming the following values of the material parameters: E= 5.5 GPa; σ y =25 MPa; ε u =.15; σ cr =139 MPa; Es=.2 MPa. Figure 12 illustrates the diagrams of the vertical stress ( with the sign changed) versus the total equivalent strain for three points of the, located at different distance from the contact zone (.125mm,.1 mm and.5 mm). The simulation corresponds to the loading phase of the cycle in Fig.1 compared to the. On the centre the vertical stress and the strain are 4 times lower than near the contact zone. For the same case, Figure 13 shows the distribution of the plastic strains and Von Mises stresses on the Lithium Metatitanate. A great part of the is yielded for a load of 47 N. The maximum plastic strain is.19. Plastic strain Von Mises stress 9.5 N 19 N 28 N 47N Fig. 13 Distribution of the plastic strain and Von Mises stress on the Lithium Metatitanate 4 NUMERICAL SIMULATION OF A LITHIUM ORTOSILICATE PEBBLE BED WITH AN HOMOGENEOUS MODEL Several Authors simulate the bed behaviour by means FEM codes using the model developed for the soil ( Cap model of Drucker and Prager[5], Cam-clay model of Roscoe and Burland [6] and so on). These model depend on several soil parameters which have not a precise correspondence with the mechanical
7 characteristics of the s. In the following a numerical simulation of an oedometer test performed on Lithium-ortosilicate bed is illustrated. This simulation is performed using the MSC-Marc FEM code and assuming that the bed behaviour is described by means of the Cam-clay model. The numerical results ( vertical load versus vertical displacement) are compared with the experimental ones obtained by the Authors of this paper [7]. The Cam-clay model depends on several parameters. In order to find a best fit between the numerical and experimental results we have varied the main parameters in reasonable ranges. 6.E+4 M=.5 - k=2e-3 - pc=.9 MPa lbd=5e-3 6.E+4 M=.5 - k=2e-3 lbd=6e-3 load(n) 5.E+4 4.E+4 3.E+4 lbd=6e-3 exp.results lbd=6.5e-3 load(n) 5.E+4 4.E+4 3.E+4 pc=.9mpa exp.results pc=2 MPa pc=.7 MPa 2.E+4 2.E+4 1.E+4 1.E+4.E Fig.14 Influence of the parameter λ.e Fig.15 Influence of the parameter p c 6 5 M=.5 -lbd=6e-3-pc=.9 MPa 6 5 lambda=6e-3 - k=1e-3 - pc=.9 MPa exp.results k=3e-3 k=2e-3 k=.5e-3 load(n) exper. results M=.5 M=.8 M= Fig.16 Influence of the parameter k Fig.17 Influence of the parameter M The main parameters of the Cam-clay model are the following: - M, the slope of the critical state line - p c, preconsolidation pressure ( a stress-like hardening variable) - K, the slope of the over consolidation lines - λ, the slope of the normal consolidation line. M and p c enter in the yield criteria while K and λ enter in the equation which describe the isotropic compression of the soil (K in the elastic range and λ in the elastic plastic range). The isotropic compression
8 constitutive relations give the specific volume ( ratio between the total volume of the soil and the volume of the solid part) as function of the logarithm of the pressure. No influence have in the Cam-clay model the Young module, the Poisson coefficient and the yielding stress. A good agreement between the experimental curve and numerical one was obtained assuming the following values for the four parameters : M=.5; K=.2; λ=.6; p c =.9 MPa. Figures shows the influence of the different parameters on the solution assumed as the best. Obviously several other groups of variable could give a solution which agrees with the experimental curve. A big question is the possibility of the extrapolation of the simple model of the oedometer test at more complex stress states. The stresses in different part of the are very different (Fig.13) but the homogeneous model of the oedometer test gives everywhere a constant stress and a constant strain. It is not easy to relate this effective stress to the actual stress of the. 5. CONCLUSIONS This paper illustrated the experimental results of compression tests on single s. The tests permitted to estimate the fracture load of Lithium-Metatitanate s ( mm of diameter) and of Lithium- Orthosilicate s ( mm of diameter). The numerical simulations of the compression give results which agree very well with the experimental ones assuming values of the material characteristics different from those found in the technical literature for these materials. This fact could be explained considering that the mechanical characteristics of ceramic materials depend strongly on the production technology. An homogeneous model developed for soil has been applied to simulate an oedometer test of a Lithium- Orthosilicate bed. Choosing appropriate values for the several constants it is possible to fit the experimental curve, but the physical meaning of the parameter values is not immediately extrapolate to the bed. REFERENCES [1] W. Dienst, H. Zimmermann, Mechanical properties of ceramics breeder materials, J. of Nucl. Mat., (1998) [2] P. Gierszewski, Review of properties of lithium metatitanate, Fusion Engineering and Design 39 4 (1998) [3] G. Schumacher at alii, Properties of Lithium Ortosilicate, J. of Nuclear Materials, (1998) [4] MSC-MARC Vol. A Theory and User information 23 MSC.Software Corporation [5] Drucker,D.C.,Gibson,R.E., Henkel,D.J. Soil Mechanics and work hardening theories of plasticity Trans. ASCE (1957) 122, [6] Roscoe K.H., Burland J.B. On the generalized stress-strain behaviour of wet clay. Engineering Plasticity, (1968) pp Cambridge Univ. Press, Cambridge [7] D. Aquaro, N. Zaccari, Experimental and numerical analyses on Li4SO4 and Li2TiO3 Pebble beds used in a ITER Test Module Blanket., Journal of Nuclear Materials, in press, 26
Characterization of Thermo-mechanical Performances related to Breeder Pebble Beds by Discrete Element Method
Characterization of Thermo-mechanical Performances related to Breeder Pebble Beds by Discrete Element Method Presented by Zhiyong (John) An With contributions from: A. Ying and M. Abdou Mechanical & Aerospace
More informationApplication of Discrete Element Method to Study Mechanical Behaviors of Ceramic Breeder Pebble Beds. Zhiyong An, Alice Ying, and Mohamed Abdou UCLA
Application of Discrete Element Method to Study Mechanical Behaviors of Ceramic Breeder Pebble Beds Zhiyong An, Alice Ying, and Mohamed Abdou UCLA Presented at CBBI-4 Petten, The Netherlands September
More informationEnhancing Prediction Accuracy In Sift Theory
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS Enhancing Prediction Accuracy In Sift Theory J. Wang 1 *, W. K. Chiu 1 Defence Science and Technology Organisation, Fishermans Bend, Australia, Department
More informationModelling the behaviour of plastics for design under impact
Modelling the behaviour of plastics for design under impact G. Dean and L. Crocker MPP IAG Meeting 6 October 24 Land Rover door trim Loading stages and selected regions Project MPP7.9 Main tasks Tests
More informationEQUIVALENT FRACTURE ENERGY CONCEPT FOR DYNAMIC RESPONSE ANALYSIS OF PROTOTYPE RC GIRDERS
EQUIVALENT FRACTURE ENERGY CONCEPT FOR DYNAMIC RESPONSE ANALYSIS OF PROTOTYPE RC GIRDERS Abdul Qadir Bhatti 1, Norimitsu Kishi 2 and Khaliq U Rehman Shad 3 1 Assistant Professor, Dept. of Structural Engineering,
More informationMechanical Properties of Materials
Mechanical Properties of Materials Strains Material Model Stresses Learning objectives Understand the qualitative and quantitative description of mechanical properties of materials. Learn the logic of
More informationDiscrete Element Modelling of a Reinforced Concrete Structure
Discrete Element Modelling of a Reinforced Concrete Structure S. Hentz, L. Daudeville, F.-V. Donzé Laboratoire Sols, Solides, Structures, Domaine Universitaire, BP 38041 Grenoble Cedex 9 France sebastian.hentz@inpg.fr
More informationModule-4. Mechanical Properties of Metals
Module-4 Mechanical Properties of Metals Contents ) Elastic deformation and Plastic deformation ) Interpretation of tensile stress-strain curves 3) Yielding under multi-axial stress, Yield criteria, Macroscopic
More informationPREPARATION OF HEXCALIBER TESTS AND PRELIMINARY THERMO-MECHANICAL ANALYSES
PREPARATION OF HEXCALIBER TESTS AND PRELIMINARY THERMO-MECHANICAL ANALYSES I. Ricapito a, G. Dell Orco b, P. A. Di Maio c, R. Giammusso c, A. Malavasi a, A. Tincani a, G. Vella c a ENEA C.R. Brasimone
More informationNORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.
NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric
More informationME 2570 MECHANICS OF MATERIALS
ME 2570 MECHANICS OF MATERIALS Chapter III. Mechanical Properties of Materials 1 Tension and Compression Test The strength of a material depends on its ability to sustain a load without undue deformation
More informationUniversity of Sheffield The development of finite elements for 3D structural analysis in fire
The development of finite elements for 3D structural analysis in fire Chaoming Yu, I. W. Burgess, Z. Huang, R. J. Plank Department of Civil and Structural Engineering StiFF 05/09/2006 3D composite structures
More informationA Constitutive Framework for the Numerical Analysis of Organic Soils and Directionally Dependent Materials
Dublin, October 2010 A Constitutive Framework for the Numerical Analysis of Organic Soils and Directionally Dependent Materials FracMan Technology Group Dr Mark Cottrell Presentation Outline Some Physical
More informationConstitutive models: Incremental plasticity Drücker s postulate
Constitutive models: Incremental plasticity Drücker s postulate if consistency condition associated plastic law, associated plasticity - plastic flow law associated with the limit (loading) surface Prager
More informationMECE 3321 MECHANICS OF SOLIDS CHAPTER 3
MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.
More informationPractice Final Examination. Please initial the statement below to show that you have read it
EN175: Advanced Mechanics of Solids Practice Final Examination School of Engineering Brown University NAME: General Instructions No collaboration of any kind is permitted on this examination. You may use
More informationChapter 7. Highlights:
Chapter 7 Highlights: 1. Understand the basic concepts of engineering stress and strain, yield strength, tensile strength, Young's(elastic) modulus, ductility, toughness, resilience, true stress and true
More informationME 243. Mechanics of Solids
ME 243 Mechanics of Solids Lecture 2: Stress and Strain Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil6791@gmail.com Website: teacher.buet.ac.bd/sshakil
More informationON THE FACE STABILITY OF TUNNELS IN WEAK ROCKS
33 rd 33 Annual rd Annual General General Conference conference of the Canadian of the Canadian Society for Society Civil Engineering for Civil Engineering 33 e Congrès général annuel de la Société canadienne
More informationIMPACT RESPONSE ANALYSIS OF LARGE SCALE RC GIRDER WITH SAND CUSHION
-Technical Paper- IMPACT RESPONSE ANALYSIS OF LARGE SCALE RC GIRDER WITH SAND CUSHION Abdul Qadir BHATTI *1, Norimitsu KISHI *2, Shin-ya OKADA *3 and Hisashi KONNO *4 ABSTRACT In order to establish a proper
More informationPlasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur
Plasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 9 Table of Contents 1. Plasticity:... 3 1.1 Plastic Deformation,
More informationLecture 7, Foams, 3.054
Lecture 7, Foams, 3.054 Open-cell foams Stress-Strain curve: deformation and failure mechanisms Compression - 3 regimes - linear elastic - bending - stress plateau - cell collapse by buckling yielding
More informationEFFECT OF STRAIN HARDENING ON ELASTIC-PLASTIC CONTACT BEHAVIOUR OF A SPHERE AGAINST A RIGID FLAT A FINITE ELEMENT STUDY
Proceedings of the International Conference on Mechanical Engineering 2009 (ICME2009) 26-28 December 2009, Dhaka, Bangladesh ICME09- EFFECT OF STRAIN HARDENING ON ELASTIC-PLASTIC CONTACT BEHAVIOUR OF A
More informationFinite Element Solutions for Geotechnical Engineering
Release Notes Release Date: January, 2016 Product Ver.: GTSNX 2016 (v1.1) Integrated Solver Optimized for the next generation 64-bit platform Finite Element Solutions for Geotechnical Engineering Enhancements
More informationTHE BEHAVIOUR OF REINFORCED CONCRETE AS DEPICTED IN FINITE ELEMENT ANALYSIS.
THE BEHAVIOUR OF REINFORCED CONCRETE AS DEPICTED IN FINITE ELEMENT ANALYSIS. THE CASE OF A TERRACE UNIT. John N Karadelis 1. INTRODUCTION. Aim to replicate the behaviour of reinforced concrete in a multi-scale
More informationDynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models
Dynamic Analysis of a Reinforced Concrete Structure Using Plasticity and Interface Damage Models I. Rhee, K.J. Willam, B.P. Shing, University of Colorado at Boulder ABSTRACT: This paper examines the global
More informationUNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich
UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST
More informationA FINITE ELEMENT STUDY OF ELASTIC-PLASTIC HEMISPHERICAL CONTACT BEHAVIOR AGAINST A RIGID FLAT UNDER VARYING MODULUS OF ELASTICITY AND SPHERE RADIUS
Proceedings of the International Conference on Mechanical Engineering 2009 (ICME2009) 26-28 December 2009, Dhaka, Bangladesh ICME09- A FINITE ELEMENT STUDY OF ELASTIC-PLASTIC HEMISPHERICAL CONTACT BEHAVIOR
More informationSTANDARD SAMPLE. Reduced section " Diameter. Diameter. 2" Gauge length. Radius
MATERIAL PROPERTIES TENSILE MEASUREMENT F l l 0 A 0 F STANDARD SAMPLE Reduced section 2 " 1 4 0.505" Diameter 3 4 " Diameter 2" Gauge length 3 8 " Radius TYPICAL APPARATUS Load cell Extensometer Specimen
More informationFailure surface according to maximum principal stress theory
Maximum Principal Stress Theory (W. Rankin s Theory- 1850) Brittle Material The maximum principal stress criterion: Rankin stated max principal stress theory as follows- a material fails by fracturing
More information20. Rheology & Linear Elasticity
I Main Topics A Rheology: Macroscopic deformation behavior B Linear elasticity for homogeneous isotropic materials 10/29/18 GG303 1 Viscous (fluid) Behavior http://manoa.hawaii.edu/graduate/content/slide-lava
More informationA Performance Modeling Strategy based on Multifiber Beams to Estimate Crack Openings ESTIMATE in Concrete Structures CRACK
A Performance Modeling Strategy based on Multifiber Beams to Estimate Crack Openings ESTIMATE in Concrete Structures CRACK A. Medjahed, M. Matallah, S. Ghezali, M. Djafour RiSAM, RisK Assessment and Management,
More informationINTRODUCTION TO STRAIN
SIMPLE STRAIN INTRODUCTION TO STRAIN In general terms, Strain is a geometric quantity that measures the deformation of a body. There are two types of strain: normal strain: characterizes dimensional changes,
More informationTIME-DEPENDENT BEHAVIOR OF PILE UNDER LATERAL LOAD USING THE BOUNDING SURFACE MODEL
TIME-DEPENDENT BEHAVIOR OF PILE UNDER LATERAL LOAD USING THE BOUNDING SURFACE MODEL Qassun S. Mohammed Shafiqu and Maarib M. Ahmed Al-Sammaraey Department of Civil Engineering, Nahrain University, Iraq
More informationTransactions on Engineering Sciences vol 6, 1994 WIT Press, ISSN
Large strain FE-analyses of localized failure in snow C.H. Liu, G. Meschke, H.A. Mang Institute for Strength of Materials, Technical University of Vienna, A-1040 Karlsplatz 13/202, Vienna, Austria ABSTRACT
More informationModule 9 : Foundation on rocks
LECTURE 32 9.3 BEARING CAPCITY contd... 9.3.2 Safe bearing pressure There are different methods are available to determine the safe bearing pressure on rocks. However, the applicability of different methods
More informationStresses Analysis of Petroleum Pipe Finite Element under Internal Pressure
ISSN : 48-96, Vol. 6, Issue 8, ( Part -4 August 06, pp.3-38 RESEARCH ARTICLE Stresses Analysis of Petroleum Pipe Finite Element under Internal Pressure Dr.Ragbe.M.Abdusslam Eng. Khaled.S.Bagar ABSTRACT
More informationSOIL MODELS: SAFETY FACTORS AND SETTLEMENTS
PERIODICA POLYTECHNICA SER. CIV. ENG. VOL. 48, NO. 1 2, PP. 53 63 (2004) SOIL MODELS: SAFETY FACTORS AND SETTLEMENTS Gabriella VARGA and Zoltán CZAP Geotechnical Department Budapest University of Technology
More informationGEO E1050 Finite Element Method Mohr-Coulomb and other constitutive models. Wojciech Sołowski
GEO E050 Finite Element Method Mohr-Coulomb and other constitutive models Wojciech Sołowski To learn today. Reminder elasticity 2. Elastic perfectly plastic theory: concept 3. Specific elastic-perfectly
More informationNumerical modeling of standard rock mechanics laboratory tests using a finite/discrete element approach
Numerical modeling of standard rock mechanics laboratory tests using a finite/discrete element approach S. Stefanizzi GEODATA SpA, Turin, Italy G. Barla Department of Structural and Geotechnical Engineering,
More informationEFFECT OF SHEAR REINFORCEMENT ON FAILURE MODE OF RC BRIDGE PIERS SUBJECTED TO STRONG EARTHQUAKE MOTIONS
EFFECT OF SHEAR REINFORCEMENT ON FAILURE MODE OF RC BRIDGE PIERS SUBJECTED TO STRONG EARTHQUAKE MOTIONS Atsuhiko MACHIDA And Khairy H ABDELKAREEM SUMMARY Nonlinear D FEM was utilized to carry out inelastic
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading
MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Statics
More informationOutline. Tensile-Test Specimen and Machine. Stress-Strain Curve. Review of Mechanical Properties. Mechanical Behaviour
Tensile-Test Specimen and Machine Review of Mechanical Properties Outline Tensile test True stress - true strain (flow curve) mechanical properties: - Resilience - Ductility - Toughness - Hardness A standard
More informationFinite Element Method in Geotechnical Engineering
Finite Element Method in Geotechnical Engineering Short Course on + Dynamics Boulder, Colorado January 5-8, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder Contents Steps
More informationHypoplastic Cam-clay model
Hypoplastic model David Mašín Charles University in Prague corresponence address: David Mašíın Charles University in Prague Faculty of Science Albertov 6 12843 Prague 2, Czech Republic E-mail: masin@natur.cuni.cz
More informationSamantha Ramirez, MSE. Stress. The intensity of the internal force acting on a specific plane (area) passing through a point. F 2
Samantha Ramirez, MSE Stress The intensity of the internal force acting on a specific plane (area) passing through a point. Δ ΔA Δ z Δ 1 2 ΔA Δ x Δ y ΔA is an infinitesimal size area with a uniform force
More informationChapter Two: Mechanical Properties of materials
Chapter Two: Mechanical Properties of materials Time : 16 Hours An important consideration in the choice of a material is the way it behave when subjected to force. The mechanical properties of a material
More informationWellbore stability analysis in porous carbonate rocks using cap models
Wellbore stability analysis in porous carbonate rocks using cap models L. C. Coelho 1, A. C. Soares 2, N. F. F. Ebecken 1, J. L. D. Alves 1 & L. Landau 1 1 COPPE/Federal University of Rio de Janeiro, Brazil
More informationCONTENTS. Lecture 1 Introduction. Lecture 2 Physical Testing. Lecture 3 Constitutive Models
CONTENTS Lecture 1 Introduction Introduction.......................................... L1.2 Classical and Modern Design Approaches................... L1.3 Some Cases for Numerical (Finite Element) Analysis..........
More informationSimulation of the cutting action of a single PDC cutter using DEM
Petroleum and Mineral Resources 143 Simulation of the cutting action of a single PDC cutter using DEM B. Joodi, M. Sarmadivaleh, V. Rasouli & A. Nabipour Department of Petroleum Engineering, Curtin University,
More informationLecture 4 Honeycombs Notes, 3.054
Honeycombs-In-plane behavior Lecture 4 Honeycombs Notes, 3.054 Prismatic cells Polymer, metal, ceramic honeycombs widely available Used for sandwich structure cores, energy absorption, carriers for catalysts
More information6. NON-LINEAR PSEUDO-STATIC ANALYSIS OF ADOBE WALLS
6. NON-LINEAR PSEUDO-STATIC ANALYSIS OF ADOBE WALLS Blondet et al. [25] carried out a cyclic test on an adobe wall to reproduce its seismic response and damage pattern under in-plane loads. The displacement
More informationMODELING OF CONCRETE MATERIALS AND STRUCTURES. Kaspar Willam. Uniaxial Model: Strain-Driven Format of Elastoplasticity
MODELING OF CONCRETE MATERIALS AND STRUCTURES Kaspar Willam University of Colorado at Boulder Class Meeting #3: Elastoplastic Concrete Models Uniaxial Model: Strain-Driven Format of Elastoplasticity Triaxial
More informationME 582 Advanced Materials Science. Chapter 2 Macromechanical Analysis of a Lamina (Part 2)
ME 582 Advanced Materials Science Chapter 2 Macromechanical Analysis of a Lamina (Part 2) Laboratory for Composite Materials Research Department of Mechanical Engineering University of South Alabama, Mobile,
More informationThe Finite Element Method II
[ 1 The Finite Element Method II Non-Linear finite element Use of Constitutive Relations Xinghong LIU Phd student 02.11.2007 [ 2 Finite element equilibrium equations: kinematic variables Displacement Strain-displacement
More informationA Finite Element Study of Elastic-Plastic Hemispherical Contact Behavior against a Rigid Flat under Varying Modulus of Elasticity and Sphere Radius
Engineering, 2010, 2, 205-211 doi:10.4236/eng.2010.24030 Published Online April 2010 (http://www. SciRP.org/journal/eng) 205 A Finite Element Study of Elastic-Plastic Hemispherical Contact Behavior against
More informationEffect of embedment depth and stress anisotropy on expansion and contraction of cylindrical cavities
Effect of embedment depth and stress anisotropy on expansion and contraction of cylindrical cavities Hany El Naggar, Ph.D., P. Eng. and M. Hesham El Naggar, Ph.D., P. Eng. Department of Civil Engineering
More informationTheory at a Glance (for IES, GATE, PSU)
1. Stress and Strain Theory at a Glance (for IES, GATE, PSU) 1.1 Stress () When a material is subjected to an external force, a resisting force is set up within the component. The internal resistance force
More informationPillar strength estimates for foliated and inclined pillars in schistose material
Pillar strength estimates for foliated and inclined pillars in schistose material L.J. Lorig Itasca Consulting Group, Inc., Minneapolis, MN, USA A. Cabrera Itasca S.A., Santiago, Chile ABSTRACT: Pillar
More informationNon-linear and time-dependent material models in Mentat & MARC. Tutorial with Background and Exercises
Non-linear and time-dependent material models in Mentat & MARC Tutorial with Background and Exercises Eindhoven University of Technology Department of Mechanical Engineering Piet Schreurs July 7, 2009
More informationABSTRACT INTRODUCTION
Optimization of soil anchorages M. Teschner, C. Mattheck Kernforschungszentrum Karlsruhe GmbH, Institut fur Materialforschung II, W-7500 Karlsruhe 1, Postfach 3640, Germany ABSTRACT A new optimization
More informationMechanics of Materials Primer
Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus
More informationMicroplane Model formulation ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary
Microplane Model formulation 2010 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary Table of Content Engineering relevance Theory Material model input in ANSYS Difference with current concrete
More informationEngineering Solid Mechanics
}} Engineering Solid Mechanics 1 (2013) 1-8 Contents lists available at GrowingScience Engineering Solid Mechanics homepage: www.growingscience.com/esm Impact damage simulation in elastic and viscoelastic
More informationAn orthotropic damage model for crash simulation of composites
High Performance Structures and Materials III 511 An orthotropic damage model for crash simulation of composites W. Wang 1, F. H. M. Swartjes 1 & M. D. Gan 1 BU Automotive Centre of Lightweight Structures
More informationALGORITHM FOR NON-PROPORTIONAL LOADING IN SEQUENTIALLY LINEAR ANALYSIS
9th International Conference on Fracture Mechanics of Concrete and Concrete Structures FraMCoS-9 Chenjie Yu, P.C.J. Hoogenboom and J.G. Rots DOI 10.21012/FC9.288 ALGORITHM FOR NON-PROPORTIONAL LOADING
More informationNonlinear FE Analysis of Reinforced Concrete Structures Using a Tresca-Type Yield Surface
Transaction A: Civil Engineering Vol. 16, No. 6, pp. 512{519 c Sharif University of Technology, December 2009 Research Note Nonlinear FE Analysis of Reinforced Concrete Structures Using a Tresca-Type Yield
More informationLecture #6: 3D Rate-independent Plasticity (cont.) Pressure-dependent plasticity
Lecture #6: 3D Rate-independent Plasticity (cont.) Pressure-dependent plasticity by Borja Erice and Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering, Chair of Computational Modeling
More informationConstitutive model for quasi-static deformation of metallic sandwich cores
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2004; 61:2205 2238 Published online 18 October 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1142
More informationUNIT I SIMPLE STRESSES AND STRAINS
Subject with Code : SM-1(15A01303) Year & Sem: II-B.Tech & I-Sem SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) UNIT I SIMPLE STRESSES
More informationSSNV221 Hydrostatic test with a behavior DRUCK_PRAGER linear and parabolic
Titre : SSNV221 - Essai hydrostatique avec un comportement[...] Date : 08/08/2011 Page : 1/10 SSNV221 Hydrostatic test with a behavior DRUCK_PRAGER linear and parabolic Summary: The case test proposes
More information5 ADVANCED FRACTURE MODELS
Essentially, all models are wrong, but some are useful George E.P. Box, (Box and Draper, 1987) 5 ADVANCED FRACTURE MODELS In the previous chapter it was shown that the MOR parameter cannot be relied upon
More informationNumerical Modelling of Blockwork Prisms Tested in Compression Using Finite Element Method with Interface Behaviour
13 th International Brick and Block Masonry Conference Amsterdam, July 4-7, 2004 Numerical Modelling of Blockwork Prisms Tested in Compression Using Finite Element Method with Interface Behaviour H. R.
More informationA simple elastoplastic model for soils and soft rocks
A simple elastoplastic model for soils and soft rocks A SIMPLE ELASTO-PLASTIC MODEL FOR SOILS AND SOFT ROCKS by Roberto Nova Milan University of Technology 1. MODEL HISTORY The model is the result of the
More informationCoupling of plasticity and damage in glass fibre reinforced polymer composites
EPJ Web of Conferences 6, 48 1) DOI: 1.151/epjconf/1648 c Owned by the authors, published by EDP Sciences, 1 Coupling of plasticity and damage in glass fibre reinforced polymer composites R. Kvale Joki
More informationExample-3. Title. Description. Cylindrical Hole in an Infinite Mohr-Coulomb Medium
Example-3 Title Cylindrical Hole in an Infinite Mohr-Coulomb Medium Description The problem concerns the determination of stresses and displacements for the case of a cylindrical hole in an infinite elasto-plastic
More informationMATERIAL MECHANICS, SE2126 COMPUTER LAB 2 PLASTICITY
MATERIAL MECHANICS, SE2126 COMPUTER LAB 2 PLASTICITY PART A INTEGRATED CIRCUIT An integrated circuit can be thought of as a very complex maze of electronic components and metallic connectors. These connectors
More informationTensile stress strain curves for different materials. Shows in figure below
Tensile stress strain curves for different materials. Shows in figure below Furthermore, the modulus of elasticity of several materials effected by increasing temperature, as is shown in Figure Asst. Lecturer
More informationThe science of elasticity
The science of elasticity In 1676 Hooke realized that 1.Every kind of solid changes shape when a mechanical force acts on it. 2.It is this change of shape which enables the solid to supply the reaction
More informationLecture #8: Ductile Fracture (Theory & Experiments)
Lecture #8: Ductile Fracture (Theory & Experiments) by Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering, Chair of Computational Modeling of Materials in Manufacturing 2015 1 1 1 Ductile
More informationMechanics of Biomaterials
Mechanics of Biomaterials Lecture 7 Presented by Andrian Sue AMME498/998 Semester, 206 The University of Sydney Slide Mechanics Models The University of Sydney Slide 2 Last Week Using motion to find forces
More informationModelling of ductile failure in metal forming
Modelling of ductile failure in metal forming H.H. Wisselink, J. Huetink Materials Innovation Institute (M2i) / University of Twente, Enschede, The Netherlands Summary: Damage and fracture are important
More informationOn Springback Prediction In Stamping Of AHSS BIW Components Utilizing Advanced Material Models
On Springback Prediction In Stamping Of AHSS BIW Components Utilizing Advanced Material Models Ming F. Shi and Alex A. Konieczny United States Steel Corporation Introduction Origin of Springback AHSS Springback
More informationIntroduction to Engineering Materials ENGR2000. Dr. Coates
Introduction to Engineering Materials ENGR2 Chapter 6: Mechanical Properties of Metals Dr. Coates 6.2 Concepts of Stress and Strain tension compression shear torsion Tension Tests The specimen is deformed
More informationAdvanced model for soft soils. Modified Cam-Clay (MCC)
Advanced model for soft soils. Modified Cam-Clay (MCC) c ZACE Services Ltd August 2011 1 / 62 2 / 62 MCC: Yield surface F (σ,p c ) = q 2 + M 2 c r 2 (θ) p (p p c ) = 0 Compression meridian Θ = +π/6 -σ
More informationSupplementary Figures
Fracture Strength (GPa) Supplementary Figures a b 10 R=0.88 mm 1 0.1 Gordon et al Zhu et al Tang et al im et al 5 7 6 4 This work 5 50 500 Si Nanowire Diameter (nm) Supplementary Figure 1: (a) TEM image
More informationOn Rate-Dependency of. Gothenburg Clay
On Rate-Dependency of Gothenburg Clay Mats Olsson Chalmers/NCC Teknik 1 Background & Introduction Mats Olsson Outline MAC-s model (anisotropic creep model) New K 0 - triaxial cell Results & Simulations
More informationGeology 229 Engineering Geology. Lecture 5. Engineering Properties of Rocks (West, Ch. 6)
Geology 229 Engineering Geology Lecture 5 Engineering Properties of Rocks (West, Ch. 6) Common mechanic properties: Density; Elastic properties: - elastic modulii Outline of this Lecture 1. Uniaxial rock
More informationExercise: concepts from chapter 8
Reading: Fundamentals of Structural Geology, Ch 8 1) The following exercises explore elementary concepts associated with a linear elastic material that is isotropic and homogeneous with respect to elastic
More informationAdapting The Modified Cam Clay Constitutive Model To The Computational Analysis Of Dense Granular Soils
University of Central Florida Electronic Theses and Dissertations Masters Thesis (Open Access) Adapting The Modified Cam Clay Constitutive Model To The Computational Analysis Of Dense Granular Soils 2005
More informationViscoelastic Mechanical Analysis for High Temperature Process of a Soda-Lime Glass Using COMSOL Multiphysics
Viscoelastic Mechanical Analysis for High Temperature Process of a Soda-Lime Glass Using COMSOL Multiphysics R. Carbone 1* 1 Dipartimento di Ingegneria dei Materiali e della Produzione sez. Tecnologie
More informationPowerful Modelling Techniques in Abaqus to Simulate
Powerful Modelling Techniques in Abaqus to Simulate Necking and Delamination of Laminated Composites D. F. Zhang, K.M. Mao, Md. S. Islam, E. Andreasson, Nasir Mehmood, S. Kao-Walter Email: sharon.kao-walter@bth.se
More informationUnified Constitutive Model for Engineering- Pavement Materials and Computer Applications. University of Illinois 12 February 2009
Unified Constitutive Model for Engineering- Pavement Materials and Computer Applications Chandrakant S. Desai Kent Distinguished i Lecture University of Illinois 12 February 2009 Participation in Pavements.
More informationG1RT-CT D. EXAMPLES F. GUTIÉRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE W P 6: TRAINING & EDUCATION
D. EXAMPLES 426 WORKED EXAMPLE I Flat Plate Under Constant Load Introduction and objectives Data Analysis Bibliography/References 427 INTRODUCTION AND OBJECTIVES During a visual inspection of a C-Mn flat
More informationA Notes Formulas. This chapter is composed of 15 double pages which list, with commentaries, the results for:
The modeling process is a key step of conception. First, a crude modeling allows to validate (or not) the concept and identify the best combination of properties that maximize the performances. Then, a
More informationPRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses
OPTIMAT BLADES Page 1 of 24 PRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses first issue Peter Joosse CHANGE RECORD Issue/revision date pages Summary of changes draft 24-10-02
More informationPrediction of the bilinear stress-strain curve of engineering material by nanoindentation test
Prediction of the bilinear stress-strain curve of engineering material by nanoindentation test T.S. Yang, T.H. Fang, C.T. Kawn, G.L. Ke, S.Y. Chang Institute of Mechanical & Electro-Mechanical Engineering,
More informationCHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES
CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric
More informationINCREASING RUPTURE PREDICTABILITY FOR ALUMINUM
1 INCREASING RUPTURE PREDICTABILITY FOR ALUMINUM Influence of anisotropy Daniel Riemensperger, Adam Opel AG Paul Du Bois, PDB 2 www.opel.com CONTENT Introduction/motivation Isotropic & anisotropic material
More informationFinite element analysis of diagonal tension failure in RC beams
Finite element analysis of diagonal tension failure in RC beams T. Hasegawa Institute of Technology, Shimizu Corporation, Tokyo, Japan ABSTRACT: Finite element analysis of diagonal tension failure in a
More information