Fracture mechanics fundamentals. Stress at a notch Stress at a crack Stress intensity factors Fracture mechanics based design
|
|
- Lily O’Neal’
- 5 years ago
- Views:
Transcription
1 Fracture mechanics fundamentals Stress at a notch Stress at a crack Stress intensity factors Fracture mechanics based design
2 Failure modes Failure can occur in a number of modes: - plastic deformation - (brittle) fracture - instability (static & dynamic Failure mode will depend on load conditions, material, temperature etc The course focuses on fracture
3 Example fracture of a finger
4 Fracture details A crack normally propagates in mode I (perpendicular to the load) Possible reasons for branching: - altered load direction - anisotropy (path of least resistance) - influence of free edge
5 Stress at a notch!! The elastic stress at the notch edge is defined by the stress concentration factor:! max = K t!! nom! At an elliptic hole in a large plate, the maximum stress is! max = (1+2a/b)!! nom! When b"0, (the case of a crack) we get! max =! (result of elastic mtrl)" and K t =! (useless measure)#! We need something else to charactarize the state of stress! " nom K t = 3 " = 3#" nom " = $" nom % K t = 1+2 a ( ' * & b) 2b $ nom 2a K t " # då b " 0 $ nom 2a " nom $ nom $ nom
6 Crack tip blunting!! Metals: plastic deformation crack tip opening displacement (CTOD) can be used as a (ambiguous) measure of crack loading! Polymers: crazing! Ceramics (e.g. concrete): damage zones
7 Loading of a crack! Three loading modes: " mode I opening " mode II shearing " mode III tearing! In fatigue mode I loading dominates: " often (quasi-)uniaxial loading " shear driven growth more difficult the longer the crack " the crack grows in mode I! Exceptions: " small crack growth " contact fatigue " anisotropic or inhomogenous material
8 Stresses ahead of a crack tip! In mode I, stresses ahead of a crack can be expressed as! xx = K I /($2%r) cos(#/2)[1 " sin(#/2)sin(3#/2)]+ #! yy = K I /($2%r) cos(#/2)[1 " sin(#/2)sin(3#/2)]+ #! xy = K I /($2%r) " cos(#/2)sin(#/2)cos(3#/2)]+ #! K I depends on loading and geometry! The expression is only valid close to the crack tip! Similar expressions are valid for loading in modes II and III
9 Stress intensity factor! The elastic stress field at a crack tip is characterized by K I#! The stress intensity factor K represents how fast the stress goes to infinity at the crack tip! For modes II and III we get similar results (K II and K III )! For the stress directly ahead of the crack tip, we get! xx =! yy = K I /$(2$x)#! The dimension of the stress intensity factor is [N"m/m 2 ] or [MPa"m]! Do not confuse the stress intensity factor K with the stress concentration factor k t [ ].! Some presumptions for K to be valid are: " linear elastic material " isotropic material " ideal crack geometry " loading in one mode
10 How to estimate K! K can be derived from the stress distribution for instance in the following manner: " analytical match K to the stress distribution " FE-simulations employ asymptotic formulas (typically the crack face displacement, %=$, gives the best results) " handbooks of solved cases, K described as K =!$($a) f where " is nominal stress and f a load geometry-factor
11 Superposition of K! Superposition can be used to derive K under combined or two (or more) loads! Demands: " same geometry " load in the same mode
12 Fracture mechanics based design! If K is assumed to reflect the stress at the crack tip, we can assume fracture to occur at a certain magnitude of K K I = K IC! K IC is called the fracture toughness! K IC is valid at plane strain (small plastic zone size)! Criterion for plane strain: a, t, (W-a) & 2.5(K IC /! y ) 2 " must be fulfilled for LEFM to be valid (note that dimensions must agree!)
13 Fracture mechanics design! Determine allowable crack size: " Specify location of the crack " Determine stress intensity factor K a.f.o. {a,!,f(a)}# " from handbooks " from FE-simulations " Find a c that yields K I = K IC " Assure that LEFM is valid a, t, (b-a), h & 2.5(K IC /! y ) 2# " If not, apply corrections " If true, apply safety factors! Determine allowable stress: " Specify crack location " Specify allowable crack size " Determine stress intensity factor K a.f.o. {a,!,f(a)}# " from handbooks " from FE-simulations " Find! that yields K I = K IC " Assure that LEFM is valid a, t, (W-a), h & 2.5(K IC /! y ) 2# " If not, apply corrections " If true, apply safety factors
14 Plastic zone size! The elastic stress is theoretically infinite at the crack tip, but in reality plasticity will occur! The plastic zone must not be so large that it obscures the K-field
15 Plastic zone size continued! The plastic zone must not extend to a free edge! Ensure that the distance towards the free edge is sufficient! Also ensure a small plastic size as compared to the crack length a, (b a), h! 4"(K/" 0 ) 2 /!! Additionally you can assure plane strain conditions (ASTM standard conditions) t, a, (b a), h! 2.5"(K/" 0 ) 2! This is the most usual criterion for static LEFM! Conservative or nonconservative to not follow these?
16 Plane strain vs plane stress! If plane strain conditions are not ensured the fracture toughness will depend on the component geometry
17 Estimation of K! For cases when K is unknown, it can be estimated from known cases
18 Advanced estimation of K! Example: " a hole in the middle of a crack will have a small influence if the crack is long " for a large hole and small crack, the crack will just experience the nearby stress i.e. a two-sided crack will be similar to a one-sided crack " There is no influence of a stress parallel to a long crack " At the hole this stress will give an effect. Why?
19 Leak before break
20 Fracture toughness! Fracture toughness is mainly a material parameter, but dependent on factors as: " geometry (plane stress, plane strain) " ductility " temperature " crack size! Optional methods if LEFM is not valid: " Irwin correction (crack length correction, see book) " J-integral (energy measure)
21 Fracture toughness, continued
22 Fracture toughness, continued
23 Some practical comments! LEFM in static and dynamic loading! Final fracture criterion (and limits of validity) in static and dynamic loading! Plane stress plane strain (also in the same component)! Environmental influence! Elastic vs elastoplastic modelling! Overloads (final fracture vs crack growth)! FE simulations " Derivation of K " J-integral " asymptotic formulas " Crack modelling " mesh " crack face contacts! Handbook solutions " Choice of standard case " approximations " superpositions " Derivation of nominal stresses! Testing and scatter
MMJ1133 FATIGUE AND FRACTURE MECHANICS E ENGINEERING FRACTURE MECHANICS
E ENGINEERING WWII: Liberty ships Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(b), p. 6, John Wiley and Sons, Inc., 1996.
More informationMMJ1133 FATIGUE AND FRACTURE MECHANICS A - INTRODUCTION INTRODUCTION
A - INTRODUCTION INTRODUCTION M.N.Tamin, CSMLab, UTM Course Content: A - INTRODUCTION Mechanical failure modes; Review of load and stress analysis equilibrium equations, complex stresses, stress transformation,
More informationIntroduction to Fracture
Introduction to Fracture Introduction Design of a component Yielding Strength Deflection Stiffness Buckling critical load Fatigue Stress and Strain based Vibration Resonance Impact High strain rates Fracture
More informationTentamen/Examination TMHL61
Avd Hållfasthetslära, IKP, Linköpings Universitet Tentamen/Examination TMHL61 Tentamen i Skademekanik och livslängdsanalys TMHL61 lördagen den 14/10 2000, kl 8-12 Solid Mechanics, IKP, Linköping University
More informationFracture Mechanics, Damage and Fatigue Linear Elastic Fracture Mechanics - Energetic Approach
University of Liège Aerospace & Mechanical Engineering Fracture Mechanics, Damage and Fatigue Linear Elastic Fracture Mechanics - Energetic Approach Ludovic Noels Computational & Multiscale Mechanics of
More informationFCP Short Course. Ductile and Brittle Fracture. Stephen D. Downing. Mechanical Science and Engineering
FCP Short Course Ductile and Brittle Fracture Stephen D. Downing Mechanical Science and Engineering 001-015 University of Illinois Board of Trustees, All Rights Reserved Agenda Limit theorems Plane Stress
More information5. STRESS CONCENTRATIONS. and strains in shafts apply only to solid and hollow circular shafts while they are in the
5. STRESS CONCENTRATIONS So far in this thesis, most of the formulas we have seen to calculate the stresses and strains in shafts apply only to solid and hollow circular shafts while they are in the elastic
More informationExamination in Damage Mechanics and Life Analysis (TMHL61) LiTH Part 1
Part 1 1. (1p) Define the Kronecker delta and explain its use. The Kronecker delta δ ij is defined as δ ij = 0 if i j 1 if i = j and it is used in tensor equations to include (δ ij = 1) or "sort out" (δ
More informationFRACTURE OF CRACKED MEMBERS 1. The presence of a crack in a structure may weaken it so that it fails by fracturing in two or more pieces.
Aerospace Structures Fracture Mechanics: An Introduction Page 1 of 7 FRACTURE OF CRACED MEMBERS 1. The presence of a crack in a structure may weaken it so that it fails by fracturing in two or more pieces.
More informationFracture Mechanics, Damage and Fatigue Non Linear Fracture Mechanics: J-Integral
University of Liège Aerospace & Mechanical Engineering Fracture Mechanics, Damage and Fatigue Non Linear Fracture Mechanics: J-Integral Ludovic Noels Computational & Multiscale Mechanics of Materials CM3
More informationTopics in Ship Structures
Topics in Ship Structures 8 Elastic-lastic Fracture Mechanics Reference : Fracture Mechanics by T.L. Anderson Lecture Note of Eindhoven University of Technology 17. 1 by Jang, Beom Seon Oen INteractive
More informationAdvanced Strength of Materials Prof S. K. Maiti Mechanical Engineering Indian Institute of Technology, Bombay. Lecture 27
Advanced Strength of Materials Prof S. K. Maiti Mechanical Engineering Indian Institute of Technology, Bombay Lecture 27 Last time we considered Griffith theory of brittle fracture, where in it was considered
More informationElastic-Plastic Fracture Mechanics. Professor S. Suresh
Elastic-Plastic Fracture Mechanics Professor S. Suresh Elastic Plastic Fracture Previously, we have analyzed problems in which the plastic zone was small compared to the specimen dimensions (small scale
More informationLecture #7: Basic Notions of Fracture Mechanics Ductile Fracture
Lecture #7: Basic Notions of Fracture Mechanics Ductile Fracture by Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering, Chair of Computational Modeling of Materials in Manufacturing
More informationVideo Lecture on Engineering Fracture Mechanics, Prof. K. Ramesh, IIT Madras 1
Video Lecture on Engineering Fracture Mechanics, Prof. K. Ramesh, IIT Madras 1 (Refer Slide Time: 01:07) Module No. # 01, Lecture No. # 04: LEFM and EPFM In the last class, we had a brief introduction
More informationG1RT-CT A. BASIC CONCEPTS F. GUTIÉRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE W P 6: TRAINING & EDUCATION
A. BASIC CONCEPTS 6 INTRODUCTION The final fracture of structural components is associated with the presence of macro or microstructural defects that affect the stress state due to the loading conditions.
More informationfive Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS
More informationINFLUENCE OF THE LOCATION AND CRACK ANGLE ON THE MAGNITUDE OF STRESS INTENSITY FACTORS MODE I AND II UNDER UNIAXIAL TENSION STRESSES
INFLUENCE OF THE LOCATION AND CRACK ANGLE ON THE MAGNITUDE OF STRESS INTENSITY FACTORS MODE I AND II UNDER UNIAXIAL TENSION STRESSES Najah Rustum Mohsin Southern Technical University, Technical Institute-Nasiriya,
More informationCritical applied stresses for a crack initiation from a sharp V-notch
Focussed on: Fracture and Structural Integrity related Issues Critical applied stresses for a crack initiation from a sharp V-notch L. Náhlík, P. Hutař Institute of Physics of Materials, Academy of Sciences
More informationStress concentrations, fracture and fatigue
Stress concentrations, fracture and fatigue Piet Schreurs Department of Mechanical Engineering Eindhoven University of Technology http://www.mate.tue.nl/ piet December 1, 2016 Overview Stress concentrations
More informationChapter 6: Mechanical Properties of Metals. Dr. Feras Fraige
Chapter 6: Mechanical Properties of Metals Dr. Feras Fraige Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility Toughness
More informationMassachusetts Institute of Technology Department of Mechanical Engineering Cambridge, MA 02139
Massachusetts Institute of Technology Department of Mechanical Engineering Cambridge, MA 02139 2.002 Mechanics and Materials II Spring 2004 Laboratory Module No. 6 Fracture Toughness Testing and Residual
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 informationFatigue calculations in ANSYS Workbench. Martin Eerme
Fatigue calculations in ANSYS Workbench Martin Eerme What is fatigue? In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic
More informationFracture Mechanics, Damage and Fatigue: Composites
University of Liège Aerospace & Mechanical Engineering Fracture Mechanics, Damage and Fatigue: Composites Ludovic Noels Computational & Multiscale Mechanics of Materials CM3 http://www.ltas-cm3.ulg.ac.be/
More informationLecture #2: Split Hopkinson Bar Systems
Lecture #2: Split Hopkinson Bar Systems by Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering, Chair of Computational Modeling of Materials in Manufacturing 2015 1 1 1 Uniaxial Compression
More informationIMECE CRACK TUNNELING: EFFECT OF STRESS CONSTRAINT
Proceedings of IMECE04 2004 ASME International Mechanical Engineering Congress November 13-20, 2004, Anaheim, California USA IMECE2004-60700 CRACK TUNNELING: EFFECT OF STRESS CONSTRAINT Jianzheng Zuo Department
More informationMechanics of Earthquakes and Faulting
Mechanics of Earthquakes and Faulting www.geosc.psu.edu/courses/geosc508 Surface and body forces Tensors, Mohr circles. Theoretical strength of materials Defects Stress concentrations Griffith failure
More informationLinear Elastic Fracture Mechanics
Measure what is measurable, and make measurable what is not so. - Galileo GALILEI Linear Elastic Fracture Mechanics Krishnaswamy Ravi-Chandar Lecture presented at the University of Pierre and Marie Curie
More information2.2 Fracture Mechanics Fundamentals
. Fracture Mechanics Fundamentals Fracture Mechanics is that technology concerned with the modeling of cracking phenomena. Bulk (smooth specimen) properties are not normally useful in design for determining
More informationAVOIDING FRACTURE INSTABILITY IN WEDGE SPLITTING TESTS BY MEANS OF NUMERICAL SIMULATIONS
Damage, Avoiding fracture Fracture instability and Fatigue in wedge splitting tests by means of numerical simulations XIV International Conference on Computational Plasticity. Fundamentals and Applications
More informationCrack Tip Plastic Zone under Mode I Loading and the Non-singular T zz -stress
Crack Tip Plastic Zone under Mode Loading and the Non-singular T -stress Yu.G. Matvienko Mechanical Engineering Research nstitute of the Russian Academy of Sciences Email: ygmatvienko@gmail.com Abstract:
More informationMechanics of Materials
Mechanics of Materials Notation: a = acceleration = area (net = with holes, bearing = in contact, etc...) SD = allowable stress design d = diameter of a hole = calculus symbol for differentiation e = change
More informationCracks Jacques Besson
Jacques Besson Centre des Matériaux UMR 7633 Mines ParisTech PSL Research University Institut Mines Télécom Aγνωστ oς Θεoς Outline 1 Some definitions 2 in a linear elastic material 3 in a plastic material
More informationTreatment of Constraint in Non-Linear Fracture Mechanics
Treatment of Constraint in Non-Linear Fracture Mechanics Noel O Dowd Department of Mechanical and Aeronautical Engineering Materials and Surface Science Institute University of Limerick Ireland Acknowledgements:
More informationIntroduction to fracture mechanics
Introduction to fracture mechanics Prof. Dr. Eleni Chatzi Dr. Giuseppe Abbiati, Dr. Konstantinos Agathos Lecture 6-9 November, 2017 Institute of Structural Engineering, ETH Zu rich November 9, 2017 Institute
More informationThis guide is made for non-experienced FEA users. It provides basic knowledge needed to start your fatigue calculations quickly.
Quick Fatigue Analysis Guide This guide is made for non-experienced FEA users. It provides basic knowledge needed to start your fatigue calculations quickly. Experienced FEA analysts can also use this
More informationStress Concentration. Professor Darrell F. Socie Darrell Socie, All Rights Reserved
Stress Concentration Professor Darrell F. Socie 004-014 Darrell Socie, All Rights Reserved Outline 1. Stress Concentration. Notch Rules 3. Fatigue Notch Factor 4. Stress Intensity Factors for Notches 5.
More informationDelamination Modeling for Power Packages and Modules. Rainer Dudek, R. Döring, S. Rzepka Fraunhofer ENAS, Micro Materials Center Chemnitz
Delamination Modeling for Power Packages and Modules Rainer Dudek, R. Döring, S. Rzepka Fraunhofer ENAS, Micro Materials Center Chemnitz The Micro Materials Center @ Virtual Prototyping Finite Element
More informationFig. 1. Different locus of failure and crack trajectories observed in mode I testing of adhesively bonded double cantilever beam (DCB) specimens.
a). Cohesive Failure b). Interfacial Failure c). Oscillatory Failure d). Alternating Failure Fig. 1. Different locus of failure and crack trajectories observed in mode I testing of adhesively bonded double
More informationChapter 6: Plastic Theory
OHP Mechanical Properties of Materials Chapter 6: Plastic Theory Prof. Wenjea J. Tseng 曾文甲 Department of Materials Engineering National Chung Hsing University wenjea@dragon.nchu.edu.tw Reference: W. F.
More informationFracture Behavior. Section
Section 6 Fracture Behavior In January 1943 the one-day old Liberty Ship, SS Schenectady, had just completed successful sea trials and returned to harbor in calm cool weather when... "Without warning and
More informationGeneralized fracture toughness for specimens with re-entrant corners: Experiments vs. theoretical predictions
Structural Engineering and Mechanics, Vol. 32, No. 5 (2009) 609-620 609 Generalized fracture toughness for specimens with re-entrant corners: Experiments vs. theoretical predictions Alberto Carpinteri,
More informationTensile behaviour of anti-symmetric CFRP composite
Available online at www.sciencedirect.com Procedia Engineering 1 (211) 1865 187 ICM11 Tensile behaviour of anti-symmetric CFRP composite K. J. Wong a,b, *, X. J. Gong a, S. Aivazzadeh a, M. N. Tamin b
More informationAfter lecture 16 you should be able to
Lecture 16: Design of paper and board packaging Advanced concepts: FEM, Fracture Mechanics After lecture 16 you should be able to describe the finite element method and its use for paper- based industry
More informationMechanics of Earthquakes and Faulting
Mechanics of Earthquakes and Faulting Lectures & 3, 9/31 Aug 017 www.geosc.psu.edu/courses/geosc508 Discussion of Handin, JGR, 1969 and Chapter 1 Scholz, 00. Stress analysis and Mohr Circles Coulomb Failure
More informationME 535 Project Report Numerical Computation of Plastic Zone Shapes in Fracture Mechanics. V.V.H. Aditya ( ) Rishi Pahuja ( ) June 9, 2014
ME 535 Project Report Numerical Computation of Plastic Zone Shapes in Fracture Mechanics V.V.H. Aditya (137301) Rishi Pahuja (137303) June 9, 014 Abstract The purpose of this project is to numerically
More informationA novel approach to predict the growth rate of short cracks under multiaxial loadings
A novel approach to predict the growth rate of short cracks under multiaxial loadings F. Brugier 1&2, S. Pommier 1, R. de Moura Pinho 2, C. Mary 2 and D. Soria 2 1 LMT-Cachan, ENS Cachan / CNRS / UPMC
More informationA STUDY ON FATIGUE CRACK GROWTH IN CONCRETE IN THE PRE-PARIS REGION
VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures FraMCoS-8 J.G.M. Van Mier, G. Ruiz, C. Andrade, R.C. Yu and X.X. Zhang (Eds) A STUDY ON FATIGUE CRACK GROWTH IN CONCRETE
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 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 informationFinite Element Investigation on the Stress State at Crack Tip by Using EPFM Parameters
Finite Element Investigation on the Stress State at Crack Tip by Using EPFM Parameters FRANCESCO CAPUTO, ALESSANDRO DE LUCA, GIUSEPPE LAMANNA 1, ALESSANDRO SOPRANO Department of Industrial and Information
More informationSample Questions for the ME328 Machine Design Final Examination Closed notes, closed book, no calculator.
Sample Questions for the ME328 Machine Design Final Examination Closed notes, closed book, no calculator. The following is from the first page of the examination. I recommend you read it before the exam.
More informationEngineering Fracture Mechanics 74 (2007) Elsevier Ltd, doi: /j.engfracmech
Engineering Fracture Mechanics 74 (007) 771-781 Elsevier Ltd, doi: 101016/j.engfracmech.006.06.015 A new fracture mechanics theory of orthotropic materials like wood T.A.C.M. van der Put, TU-Delft, CiTG,
More informationSKIN-STRINGER DEBONDING AND DELAMINATION ANALYSIS IN COMPOSITE STIFFENED SHELLS
SKIN-STRINER DEBONDIN AND DELAMINATION ANALYSIS IN COMPOSITE STIFFENED SHELLS R. Rikards, K. Kalnins & O. Ozolinsh Institute of Materials and Structures, Riga Technical University, Riga 1658, Latvia ABSTRACT
More informationResearch Article Estimation of Fracture Toughness by Testing Notched Fracture Specimens and Applying the Theory of Critical Distances
International Scholarly Research Network ISRN Materials Science Volume, Article ID 689386, 8 pages doi:.54//689386 Research Article Estimation of Fracture Toughness by Testing Notched Fracture Specimens
More informationMechanical properties 1 Elastic behaviour of materials
MME131: Lecture 13 Mechanical properties 1 Elastic behaviour of materials A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Deformation of material under the action of a mechanical
More informationFIS Specifications for Flex Poles (Edition May 2008) Original Text: German
FIS Specifications for Flex Poles (Edition May 2008) Original Text: German 1 Field of Application and Basic Information The following FIS specifications for flex poles are intended to ensure that flex
More informationWeld Fracture. How Residual Stresses Affect Prediction of Brittle Fracture. Outline. Residual Stress in Thick Welds
How Residual Stresses ffect Prediction of Brittle Fracture Michael R. Hill University of California, Davis Tina L. Panontin NS-mes Research Center Weld Fracture Defects provide location for fracture initiation
More information436 A. Barani and G.H. Rahimi assessment models have been employed to investigate the LBB of cracked pipes that are not for combined load [8]. Yun-Jae
Scientia Iranica, Vol. 4, No. 5, pp 435{44 c Sharif University of Technology, October 27 Approximate Method for Evaluation of the J-Integral for Circumferentially Semi-Elliptical-Cracked Pipes Subjected
More informationStudies on the affect of Stress Triaxiality on Strain Energy Density, and CTOD under Plane Stress Condition Subjected to Mixed Mode (I/II) Fracture
Studies on the affect of Stress Triaxiality on Strain Energy Density, and CTOD under Plane Stress Condition... Studies on the affect of Stress Triaxiality on Strain Energy Density, and CTOD under Plane
More informationELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker
THEORY OF ELASTICITY AND FRACTURE MECHANICS y x Vijay G. Ukadgaonker Theory of Elasticity and Fracture Mechanics VIJAY G. UKADGAONKER Former Professor Indian Institute of Technology Bombay Delhi-110092
More informationMODIFIED MONTE CARLO WITH LATIN HYPERCUBE METHOD
MODIFIED MONTE CARLO WITH LATIN HYPERCUBE METHOD Latin hypercube sampling (LHS) was introduced by McKay, Conover and Beckman as a solution to increase the efficiency of computer simulations. This technique
More informationTransactions on Modelling and Simulation vol 10, 1995 WIT Press, ISSN X
Parameters controlling the numerical simulation validity of damageable composite toughness testing S. Yotte, C. Currit, E. Lacoste, J.M. Quenisset Laboratoire de Genie Meanique - IUT 'A\ Domaine Universitaire,
More informationMechanics of Earthquakes and Faulting
Mechanics of Earthquakes and Faulting www.geosc.psu.edu/courses/geosc508 Overview Milestones in continuum mechanics Concepts of modulus and stiffness. Stress-strain relations Elasticity Surface and body
More informationINFLUENCE OF TEMPERATURE ON BEHAVIOR OF THE INTERFACIAL CRACK BETWEEN THE TWO LAYERS
Djoković, J. M., et.al.: Influence of Temperature on Behavior of the Interfacial THERMAL SCIENCE: Year 010, Vol. 14, Suppl., pp. S59-S68 S59 INFLUENCE OF TEMPERATURE ON BEHAVIOR OF THE INTERFACIAL CRACK
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 informationVariational phase field model for dynamic brittle fracture
Variational phase field model for dynamic brittle fracture Bleyer J., Roux-Langlois C., Molinari J-F. EMMC 15, September 8th, 2016 1 / 18 Outline Mechanisms of dynamic fracture Variational phase-field
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 informationDEVELOPMENT OF TEST GUIDANCE FOR COMPACT TENSION FRACTURE TOUGHNESS SPECIMENS CONTAINING NOTCHES INSTEAD OF FATIGUE PRE-CRACKS
Transactions, SMiRT-23 Division II, Paper ID 287 Fracture Mechanics and Structural Integrity DEVELOPMENT OF TEST GUIDANCE FOR COMPACT TENSION FRACTURE TOUGHNESS SPECIMENS CONTAINING NOTCHES INSTEAD OF
More informationFracture mechanics. code_aster, salome_meca course material GNU FDL licence (
Fracture mechanics code_aster, salome_meca course material GNU FDL licence (http://www.gnu.org/copyleft/fdl.html) Why fracture mechanics? 2 - code_aster and salome_meca course material GNU FDL Licence
More information3D Finite Element analysis of stud anchors with large head and embedment depth
3D Finite Element analysis of stud anchors with large head and embedment depth G. Periškić, J. Ožbolt & R. Eligehausen Institute for Construction Materials, University of Stuttgart, Stuttgart, Germany
More informationCourse Notes. Hållfasthetslära Vk MHA100. Fatigue and Fracture Analysis MHA140. General. Teachers. Goals. School of Civil Engineering Period II 1998
Department of Solid Mechanics Course Notes Hållfasthetslära Vk MHA100 Fatigue and Fracture Analysis MHA140 School of Civil Engineering Period II 1998 General Additional and updated information about the
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 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 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 informationElastic and Elastic-Plastic Behaviour of a Crack in a Residual Stress Field
Residual Stresses 2016: IC-10 Elastic and Elastic-Plastic Behaviour of a Crack in a Residual Stress Field Guiyi Wu a, Chris Aird b, David Smith and Martyn Pavier c* Department of Mechanical Engineering,
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 informationPredicting Fatigue Life with ANSYS Workbench
Predicting Fatigue Life with ANSYS Workbench How To Design Products That Meet Their Intended Design Life Requirements Raymond L. Browell, P. E. Product Manager New Technologies ANSYS, Inc. Al Hancq Development
More informationApplication of a non-local failure criterion to a crack in heterogeneous media S. Bavaglia*, S.E. Mikhailov*
Application of a non-local failure criterion to a crack in heterogeneous media S. Bavaglia*, S.E. Mikhailov* University of Perugia, Italy Email: mic@unipg.it ^Wessex Institute of Technology, Ashurst Lodge,
More informationaccounts for both linear and nonlinear material response, whereas the
AN ABSTRACT OF THE THESIS OF Paul Edward Keary for the degree of Master of Science in Mechanical Engineering presented on April 26, 1984 Title: A Comparison of Experimental Mode I Analysis Methods for
More informationComputational Analysis for Composites
Computational Analysis for Composites Professor Johann Sienz and Dr. Tony Murmu Swansea University July, 011 The topics covered include: OUTLINE Overview of composites and their applications Micromechanics
More informationBRIDGING LAW SHAPE FOR LONG FIBRE COMPOSITES AND ITS FINITE ELEMENT CONSTRUCTION
Proceedings of ALGORITMY 2012 pp. 353 361 BRIDGING LAW SHAPE FOR LONG FIBRE COMPOSITES AND ITS FINITE ELEMENT CONSTRUCTION VLADISLAV KOZÁK AND ZDENEK CHLUP Abstract. Ceramic matrix composites reinforced
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 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 informationMECHANICS OF MATERIALS
Third E CHAPTER 2 Stress MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University and Strain Axial Loading Contents Stress & Strain:
More informationFailure from static loading
Failure from static loading Topics Quiz /1/07 Failures from static loading Reading Chapter 5 Homework HW 3 due /1 HW 4 due /8 What is Failure? Failure any change in a machine part which makes it unable
More informationEvolution of Tenacity in Mixed Mode Fracture Volumetric Approach
Mechanics and Mechanical Engineering Vol. 22, No. 4 (2018) 931 938 c Technical University of Lodz Evolution of Tenacity in Mixed Mode Fracture Volumetric Approach O. Zebri LIDRA Laboratory, Research team
More informationMECHANICS OF 2D MATERIALS
MECHANICS OF 2D MATERIALS Nicola Pugno Cambridge February 23 rd, 2015 2 Outline Stretching Stress Strain Stress-Strain curve Mechanical Properties Young s modulus Strength Ultimate strain Toughness modulus
More informationNUMERICAL MODELING OF CRACK PATH PROPAGATION DEPENDING ON STEEL RATIO IN RC BEAMS LECTURE NOTES IRINA KERELEZOVA
NUMERICAL MODELING OF CRACK PATH PROPAGATION DEPENDING ON STEEL RATIO IN RC BEAMS LECTURE NOTES IRINA KERELEZOVA UNIVERSITY OF ARCHITECTURE, CIVIL ENGINEERING AND GEODESY, SOFIA, BULGARIA calculated crack
More informationAutodesk Helius PFA. Guidelines for Determining Finite Element Cohesive Material Parameters
Autodesk Helius PFA Guidelines for Determining Finite Element Cohesive Material Parameters Contents Introduction...1 Determining Cohesive Parameters for Finite Element Analysis...2 What Test Specimens
More informationMaterials and Structures
Journal of Mechanics of Materials and Structures BRITTLE FRACTURE BEYOND THE STRESS INTENSITY FACTOR C. T. Sun and Haiyang Qian Volume 4, Nº 4 April 2009 mathematical sciences publishers JOURNAL OF MECHANICS
More informationAnisotropic modeling of short fibers reinforced thermoplastics materials with LS-DYNA
Anisotropic modeling of short fibers reinforced thermoplastics materials with LS-DYNA Alexandre Hatt 1 1 Faurecia Automotive Seating, Simplified Limited Liability Company 1 Abstract / Summary Polymer thermoplastics
More informationChapter 1 Fracture Physics
Chapter 1 Fracture Physics In this chapter we give a brief account of the theory of fracture, restricting ourselves to brittle fracture. The structure of this chapter is as follows. The first part describes
More informationOn characterising fracture resistance in mode-i delamination
9 th International Congress of Croatian Society of Mechanics 18-22 September 2018 Split, Croatia On characterising fracture resistance in mode-i delamination Leo ŠKEC *, Giulio ALFANO +, Gordan JELENIĆ
More informationInternational Journal of Innovative Research in Science, Engineering and Technology Vol. 2, Issue 7, July 2013
ANALYSIS AND MITIGATION OF STRESS CONCENTRATION FACTOR OF A RECTANGULAR ISOTROPIC AND ORTHOTROPIC PLATE WITH CENTRAL CIRCULAR HOLE SUBJECTED TO INPLANE STATIC LOADING BY DESIGN OPTIMIZATION Shubhrata Nagpal
More informationarxiv:cond-mat/ v1 25 Feb 1994
A Model for Fracture in Fibrous Materials A. T. Bernardes Departamento de Física - ICEB arxiv:cond-mat/9402110v1 25 Feb 1994 Universidade Federal de Ouro Preto Campus do Morro do Cruzeiro 35410-000 Ouro
More informationSingularity characteristics for a lip-shaped crack subjected to remote biaxial loading
International Journal of Fracture 96: 03 4, 999. 999 Kluwer Academic Publishers. Printed in the Netherlands. Singularity characteristics for a lip-shaped crack subjected to remote biaxial loading YU QIAO
More informationFinite Element Analysis of Debonding Propagation in FM73 Joint under Static Loading
Finite Element Analysis of Debonding Propagation in FM73 Joint under Static Loading Reza Hedayati, Meysam Jahanbakhshi Abstract--In this work, Fracture Mechanics is used to predict crack propagation in
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 information