After lecture 16 you should be able to
|
|
- Fay Doyle
- 6 years ago
- Views:
Transcription
1 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 illustrate how a finite element model is created discuss the results from finite element analysis of: Compression test of a package Creasing and folding discuss concepts such as the J-integral and the fracture toughness account for the procedures of failure predictions in paper materials 1
2 Literature Pulp and Paper Chemistry and Technology - Volume 4, Paper Products Physics and Technology, Chapters 2 & 12 Östlund, S. and Mäkelä, P., Fracture properties, KTH, 211 Three-dimensional modelling and analysis of paper and board, FEM Adapted from Mikael Nygårds 2
3 Why use numerical methods? Different types of loadings can be investigated. The effect of different material properties can be investigated. More information about damage and deformation mechanisms can be gained. Material behaviour and structural behaviour can be predicted Properties that t are important t for the manufacturer can be linked to properties that are important for the user. Saves costs and enables more efficient product development FEM Process Solutions Material Performance Material performance Establish the important/critical material properties p Converting Packaging Design Delamination 3
4 The Finite Element-Method (FEM) is a method to solve partial differential equations procedure to solve field problems with engineering accuracy In field problems the parameters of interest are described by continuous or discrete field variables, e.g. Continuum mechanics Solid mechanics stress, strain Moisture transport Fluid mechanics Heat transfer, temperature Electro magnetic field theory... Finite element method Assume a deformation (displacement field) N u Calculate displacements N u = N N u Calculate strain N ε = β N u Calculate stress (in general non-linear relations) σ = F ( ) ε Principle of virtual work V σ : εdv = S t T uds + V f T udv 4
5 Way of working 1. Understand the problem (boundary conditions, symmetries, material models, approximations) 2. Modelling, discretisation, input data, selection of elements, Verification (PRE-PROCESSING) 3. Solving of systems of equations and calculation of relevant properties e.g. stress and strain 4. Analysis of output, graphical presentation (POST- PROCESSING) 5. Consequences of analysis Modelling, discretisation, input data, selection of elements, Verification (PRE-PROCESSING) Geometry (discretisation) Boundary conditions Material model σ = f(ε) 5
6 Challenges within paperboard research Constitutive models for paper that involve the through thickness direction, as well as moisture and temperature dependence is still active research Incomplete knowledge of material data for many materials Simulation tools for many applications are still missing Lack of robustness and convergence problems Compression of boxes Experiments 6
7 Compression of cylinders Experiments What is the difference compared to rectangular boxes? FE-analysis of compression of box USE OF PRO- DUCT MATERIAL PROPERTIES ANALYSIS LOADS BOX- MODEL (FEM) LOADS ON DETAILS DETAIL MODEL (FEM) CRITICAL LOADS 7
8 Static compressive load on box FEM and experiment Reference: L. Beldie, Lund University, 21 Top and bottom segments Reference: L. Beldie, Lund University, 2 8
9 Middle segment Reference: L. Beldie, Lund University, 2 Experimental characterization of crease Reference: L. Beldie, Lund University, 21 9
10 Static compressive load on box FEM with crease elements and experiment Test of whole package Reference: L. Beldie, Lund University, 21 Development of a three dimensional paperboard model Real process/object Experimental verification Laws of mechanics Model formulation Solution of mathematical problems Numerical method Mathematical model 1
11 Mechanical behaviour of paperboard Top layer Middle layer/s Bottom layer In-plane behaviour CD 4 MD MD Stress [MPa] CD Anisotropic elasticity The elastic modulus in MD are 2-3 times larger than the elastic modulus in CD Anisotropic initial yield stress The initial yield stress in MD are 2-3 times greater then the initial yield stress in CD Anisotropic plastic strain hardening Strain [%] Paper hardens more in MD than in the CD Reference: Q. Xia, MIT, Boston,
12 Out-of-plane behaviour Nor rmal Stress [MPa] She ear Stress [MPa] Normal displacement [mm] Shear displacement [mm] Reference: N. Stenberg, STFI/KTH, Stockholm, 2. Out-of-plane behaviour Summary Small amount of non-linearity before pre-peakpeak load Dominating softening behavior after the peak load Shear strength is pressure dependent Shearing causes normal dilatation Residual shear-load remains under normal compressive loading. Reference: N. Stenberg, STFI, Stockholm, 2. Q. Xia et. al., MIT, Boston,
13 Model z Constitutive model: damaged region x T x T z T z δ z δ x z T x Continuum model Stresses: σ x, σy, σz, τxy, τzx, τyz Strains: ε x, εy, εz, γxy, γzx, γ yz interface y x Two dimensional view of tractions and displacements at interface Interface model Tractions: Tx, Ty, Tz Displacements: δ, δ, δ x y z In-plane: elastic-plastic continuum Anisotropic elasticity Anisotropic initial yield Anisotropic plastic strain hardening Out-of-plane: interfacial model Post-peak softening tensile and shear behavior. Pressure dependent shear resistance Normal dilation under shearing Existence of shear friction History dependent Reference: Q. Xia et. al., MIT, Boston, 22. Verification Uniaxial tension F F References: N. Stenberg, STFI, Stockholm, 22 Q. Xia, MIT, Boston,
14 Verification Biaxial, compression Out-of-plane compression In-plane compression Reference: N. Stenberg, STFI, Stockholm, 22 Q. Xia, MIT, Boston, 22. Delamination model Failure surface Reference: N. Stenberg, STFI, Stockholm, 22 14
15 Delamination model ZD tension Reference: N. Stenberg, STFI, Stockholm, 22 Q. Xia, MIT, Boston, 22. Delamination model Shear Thickness increase under shear Reference: N. Stenberg, STFI, Stockholm, 22 Q. Xia, MIT, Boston,
16 Creasing and folding Model setup Top ply Middle ply Bottom ply Creasing of Paperboard Reference: H. Dunn, MIT, 2. Reference: STFI-Packforsk/Tetra Pak 24 16
17 Creasing of Paperboard Reference: H. Dunn, MIT, 2. Reference: STFI-Packforsk/Tetra Pak 24 Creasing of Paperboard Reference: H. Dunn, MIT, 2. Reference: STFI-Packforsk/Tetra Pak 24 17
18 Creasing of Paperboard Reference: H. Dunn, MIT, 2. Reference: STFI-Packforsk/Tetra Pak 24 Verification Creasing Measurements Reaction force, F Displacement, u 18
19 Verification Folding Measurements Reaction force, F Rotation ti angle, θ Centre of rotation Specimen Load cell Clamps Creasing and folding Mikael Nygårds, STFI-Packforsk 19
20 Creasing and folding Comparison with experiments MD folding at two different creasing depths Fracture Mechanics Adapted from Petri Mäkelä Innventia AB 2
21 The A4-example Load: 145 N Elongation: 5.2 mm Load: 75 N Elongation: 1.4 mm 1 mm edge crack 48 % reduction of load carrying capacity and 73 % reduction of strain at break Reduced effective width of a paper web 21
22 Corresponding stress distribution Reduced strength Fracture mechanics Geometry Fracture toughness Loading 22
23 Paperboard applications Cut-outs and cracks in corrugated board Failure of sacks Crack Perforation Nicks Crack initiation spots Web breaks K-cracks Web breaks σˆ nom σ nom σ interior crack σ σ edge crack σ R p R p t 2a σ a) b) 23
24 Delamination in printing nips a) b) c) Crack tip modelling FPZ appearance and modes of crack opening 3 4 mm Crack Tip Fracture Process Zone of considerable size Damage Modes I and II are predominant under in-plane loading and mode I is considered most severe. 24
25 Linear elastic fracture mechanics LEFM σ E ε Stress state in the crack tip region σ ij KI = KI k ij r ( ϕ ) = f(material, geometry, loading) Failureprocess zone Singularity dominated zone controlled by K in Equations (6.1) Log (σ yy ) 1 2 Log (r/r p ) Fracture criterion, LEFM Stress Tensile strength K I Critical K I Strain Strain 25
26 Linear elastic fracture mechanics MD CD σ nom /σ b, ε nom /ε b Stress at break, exp. Strain at break, exp. Stress at break, num. Strain at break, num Crack size [mm] σ nom /σ b, ε nom /ε b Stress at break, exp. Strain at break, exp. Stress at break, num. Strain at break, num Crack size [mm] Conclusions, LEFM Does not apply to paper materials in general. Large cracks in very large structures are required in order for LEFM to be applicable to paperboard. 26
27 Non-linear fracture mechanics, NLFM The HRR crack tip fields σ E E, N, ε Stress state in the crack tip region 1 n+ 1 J σ ij = a fij ( n, ϕ ) r J = f(material,geometry,loading) Log (σ yy ) Failure process zone J dominated zone K dominated zone 1 n Log (r/r p ) Hutchinson 1968, Rice, Rosengren 1968 J is the energy release-rate in a non-linear elastic material In the special case of a linear elastic material, J is proportional to K 2 I This means that LEFM is a special case of NLFM. J is defined as a path-independent line- integral around the crack-tip involving expressions containing stress, strain and displacement. 27
28 Fracture criterion, NLFM Stress Tensile strength J Citi Critical ljj Strain Strain NLFM The J-integral method MD CD σ nom /σ b, ε nom /ε b Stress at break, exp. Strain at break, exp. Stress at break, num. Strain at break, num Crack size [mm] σ nom /σ b, ε nom /ε b Stress at break, exp. Strain at break, exp. Stress at break, num. Strain at break, num Crack size [mm] 28
29 Conclusions, NLFM (J-integral method) Does predict failure quantitatively for large cracks and qualitatively ti l for short cracks Numerically cheap Easy calibration What information does J carry? J is a loading parameter J expresses the severity of the stresses at the crack-tip When J reaches a critical value, the crack starts to grow 29
30 Critical value of J (or K) is called fracture toughness 1. In order to formulate a fracture criterion, we need to know how severe stress states the material is able to withstand. 2. We need to know the critical value of J for the material, i.e. the fracture toughness (J c ) of the material. 3. The information from material testing on a test piece with a man-made crack is required to evaluate the fracture toughness. Predictions of failure Generally requires numerical methods 1. Material behaviour Fracture toughness Full-scale predictions of failure FE-analysis FE-analysis 3
31 Verification of transferability J-integral method for 1 m wide paper webs 12 6 Critical elongati ion / mm Fluting Predictions Experiments Critical force / kn Critical elongatio on / mm Sackpaper Predictions Experiments Critical force e / kn Critical elongation / mm Crack length / mm Newsprint Predictions Experiments Critical force / kn Critical elongation / mm Crack length / mm Testliner Predictions Experiments Critical force / kn Critical elongation / mm Crack length / mm MWC 4 Predictions Experiments Crack length / mm Crotical force / kn Critical elongation / mm Crack length / mm SC Predictions Experiments Crack length / mm Critical force / kn Stress state in vicinity of crack tip Model Real material 31
32 Damage behaviour Elastic unloading supports energy Damage evolution consumes energy Elastic unloading supports energy Tensile Stress / M Pa Tensile testing Strain / % Instability when rate of supported energy from elastic unloading exceeds consumed energy during damage evolution Tensile test results Long and short test pieces Ordinary tensile test piece Te ensile Stress [MPa] Short strip Long strip Short tensile test piece Apparant strain [%] 32
33 Modelling of damage cohesive zone w σ σ (w) σ (w) Stress s (σ ) w L+δ δ Elongation (δ ) σ σ δ δ + L E = r Damage zone Stress (σ ) σ( w) = σ e α β w y a v w (r) σ y (r) Widening (w) x Elastic-plastic material + cohesive zone MD CD σ nom /σ b, ε nom /ε b Stress at break, exp. Strain at break, exp. Stress at break, num. Strain at break, num Crack size [mm] σ nom /σ b, ε nom /ε b Stress at break, exp. Strain at break, exp. Stress at break, num. Strain at break, num Crack size [mm] 66 33
34 Conclusions, Cohesive crack model Accurate predictions of failure for all crack sizes Numerically expensive Expensive, cumbersome and Time-consuming calibration No explicit fracture criterion needed Final remarks FPZ size important for the choice of fracture mechanics model. If FPZ is small crack tip fields are singular J-integral method predicts mode I in-plane failure of notched paper structures well. Cohesive stress models excellently predicts mode I inplane failure. Such models are also applicable for out-of-plane failure where the crack tip singularity concept is not unambiguously applicable. Fracture mechanics can be used for damage tolerance analysis of structures containing assumed defects. 34
35 After lecture 16 you should be able to Illustrate the finite element method and its use for paperbased industry Illustrate how a finite element model is created Discuss the results from finite element analysis of: Compression test of a package Creasing and folding Discuss concepts such as the J-integral and the fracture toughness Account for the procedures of failure predictions in paper materials 35
*MAT_PAPER and *MAT_COHESIVE_PAPER: Two New Models for Paperboard Materials
14 th International LS-DYNA Users Conference Session: Constitutive Modeling *MAT_PAPER and *MAT_COHESIVE_PAPER: Two New Models for Paperboard Materials Jesper Karlsson 1, Mikael Schill 1, Johan Tryding
More informationDelamination in the scoring and folding of paperboard
PEER-REVIEWED CONVERTING Delamination in the scoring and folding of paperboard DOEUNG D. CHOI, SERGIY A. LAVRYKOV, and BANDARU V. RAMARAO ABSTRACT: Delamination between layers occurs during the creasing
More information*MAT_PAPER - a new orthotropic elastoplastic model for paper materials
*MAT_PAPER - a new orthotropic elastoplastic model for paper materials Jesper Karlsson, Dynamore Nordic Mikael Schill, Dynamore Nordic Johan Tryding, Tetra Pak *MAT_PAPER (*MAT_274) A new orthotropic elastoplastic
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 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 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 informationPackaging Materials, SE2127 Problems with Solutions
Packaging Materials, SE2127 Problems with Solutions Compiled by Mikael S. Magnusson and Sören Östlund Department of Solid Mechanics Royal Institute of Technology - KTH, Stockholm, Sweden 2010 Contents
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 informationFracture mechanics fundamentals. Stress at a notch Stress at a crack Stress intensity factors Fracture mechanics based design
Fracture mechanics fundamentals Stress at a notch Stress at a crack Stress intensity factors Fracture mechanics based design Failure modes Failure can occur in a number of modes: - plastic deformation
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 informationStatic and Time Dependent Failure of Fibre Reinforced Elastomeric Components. Salim Mirza Element Materials Technology Hitchin, UK
Static and Time Dependent Failure of Fibre Reinforced Elastomeric Components Salim Mirza Element Materials Technology Hitchin, UK Introduction Fibre reinforced elastomers are used in many applications,
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 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 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 informationNumerical simulation of delamination onset and growth in laminated composites
Numerical simulation of delamination onset and growth in laminated composites G. Wimmer, C. Schuecker, H.E. Pettermann Austrian Aeronautics Research (AAR) / Network for Materials and Engineering at the
More informationThis is the accepted version of a paper presented at 2014 IEEE Electrical Insulation Conference (EIC).
http://www.diva-portal.org Postprint This is the accepted version of a paper presented at 2014 IEEE Electrical Insulation Conference (EIC). Citation for the original published paper: Girlanda, O., Tjahjanto,
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 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 informationAbstract. 1 Introduction
Contact analysis for the modelling of anchors in concrete structures H. Walter*, L. Baillet** & M. Brunet* *Laboratoire de Mecanique des Solides **Laboratoire de Mecanique des Contacts-CNRS UMR 5514 Institut
More informationA Constitutive Model for DYNEEMA UD composites
A Constitutive Model for DYNEEMA UD composites L Iannucci 1, D J Pope 2, M Dalzell 2 1 Imperial College, Department of Aeronautics London, SW7 2AZ l.iannucci@imperial.ac.uk 2 Dstl, Porton Down, Salisbury,
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 informationThe objective of this experiment is to investigate the behavior of steel specimen under a tensile test and to determine it's properties.
Objective: The objective of this experiment is to investigate the behavior of steel specimen under a tensile test and to determine it's properties. Introduction: Mechanical testing plays an important role
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 informationDesign of paper and board packages
Lecture 14: Design of paper and board packages Design of paper and board packaging: stacking, analytical methods. Software such as Billerud Box Design, EUPS, Model PACK & Korsnäs After lecture 14 you should
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 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 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 informationImpact and Crash Modeling of Composite Structures: A Challenge for Damage Mechanics
Impact and Crash Modeling of Composite Structures: A Challenge for Damage Mechanics Dr. A. Johnson DLR Dr. A. K. Pickett ESI GmbH EURO-PAM 99 Impact and Crash Modelling of Composite Structures: A Challenge
More informationLimit analysis of brick masonry shear walls with openings under later loads by rigid block modeling
Limit analysis of brick masonry shear walls with openings under later loads by rigid block modeling F. Portioli, L. Cascini, R. Landolfo University of Naples Federico II, Italy P. Foraboschi IUAV University,
More informationNon-linear fracture mechanics in LS-DYNA and LS-PrePost
Non-linear fracture mechanics in LS-DYNA and LS-PrePost Per Lindström 1,, Anders Jonsson 3, Anders Jernberg 3, Erling Østby 1 Department of Engineering Science, University West, Trollhättan, Sweden DNV
More informationCOMPARISON OF COHESIVE ZONE MODELS USED TO PREDICT DELAMINATION INITIATED FROM FREE-EDGES : VALIDATION AGAINST EXPERIMENTAL RESULTS
COMPARISON OF COHESIVE ZONE MODELS USED TO PREDICT DELAMINATION INITIATED FROM FREE-EDGES : VALIDATION AGAINST EXPERIMENTAL RESULTS A. Uguen 1, L. Zubillaga 2, A. Turon 3, N. Carrère 1 1 Laboratoire Brestois
More informationAn investigation of the mechanical behaviour of carbon epoxy cross ply cruciform specimens under biaxial loading
An investigation of the mechanical behaviour of carbon epoxy cross ply cruciform specimens under biaxial loading A. Makris, C. Ramault, D. Van Hemelrijck Department of Mechanics of Materials and Constructions,
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 informationNUMERICAL SIMULATION OF DAMAGE IN THERMOPLASTIC COMPOSITE MATERIALS
5 th European LS-DYNA Users Conference Composites NUMERICAL SIMULATION OF DAMAGE IN THERMOPLASTIC COMPOSITE MATERIALS Kevin Brown 1, Richard Brooks, Nicholas Warrior School of Mechanical, Materials and
More informationExperimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives
Experimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives Mark Oliver October 19, 2016 Adhesives and Sealants Council Fall Convention contact@veryst.com www.veryst.com Outline
More informationStrength of GRP-laminates with multiple fragment damages
Strength of GRP-laminates with multiple fragment damages S. Kazemahvazi, J. Kiele, D. Zenkert Kungliga Tekniska Högskolan, KTH 100 44 Stockholm, Sweden sohrabk@kth.se SUMMARY The strength of glass fibre
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 informationAdhesive Joints Theory (and use of innovative joints) ERIK SERRANO STRUCTURAL MECHANICS, LUND UNIVERSITY
Adhesive Joints Theory (and use of innovative joints) ERIK SERRANO STRUCTURAL MECHANICS, LUND UNIVERSITY Wood and Timber Why I m intrigued From this to this! via this Fibre deviation close to knots and
More informationELASTICITY (MDM 10203)
ELASTICITY () Lecture Module 3: Fundamental Stress and Strain University Tun Hussein Onn Malaysia Normal Stress inconstant stress distribution σ= dp da P = da A dimensional Area of σ and A σ A 3 dimensional
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 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 informationModelling the nonlinear shear stress-strain response of glass fibrereinforced composites. Part II: Model development and finite element simulations
Modelling the nonlinear shear stress-strain response of glass fibrereinforced composites. Part II: Model development and finite element simulations W. Van Paepegem *, I. De Baere and J. Degrieck Ghent
More informationA rate-dependent Hosford-Coulomb model for predicting ductile fracture at high strain rates
EPJ Web of Conferences 94, 01080 (2015) DOI: 10.1051/epjconf/20159401080 c Owned by the authors, published by EDP Sciences, 2015 A rate-dependent Hosford-Coulomb model for predicting ductile fracture at
More informationTHREE DIMENSIONAL STRESS ANALYSIS OF THE T BOLT JOINT
THREE DIMENSIONAL STRESS ANALYSIS OF THE T BOLT JOINT Víctor Martínez 1, Alfredo Güemes 2, Norbert Blanco 1, Josep Costa 1 1 Escola Politècnica Superior. Universitat de Girona. Girona, Spain (17071) 2
More informationExperiments and Numerical Simulations on Stress-State-Dependence of Ductile Damage Criteria
Experiments and Numerical Simulations on Stress-State-Dependence of Ductile Damage Criteria Michael Brünig, Steffen Gerke and Daniel Brenner Abstract The paper deals with a series of new experiments and
More informationIntroduction and Background
Introduction and Background Itasca Consulting Group, Inc. (Itasca) has been participating in the geomechanical design of the underground 118-Zone at the Capstone Minto Mine (Minto) in the Yukon, in northwestern
More informationModeling of Interfacial Debonding Induced by IC Crack for Concrete Beam-bonded with CFRP
Proceedings of the World Congress on Engineering 21 Vol II WCE 21, June 2 - July 1, 21, London, U.K. Modeling of Interfacial Debonding Induced by IC Crack for Concrete Beam-bonded with CFRP Lihua Huang,
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 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 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 informationNUMERICAL INVESTIGATION OF DELAMINATION IN L-SHAPED CROSS-PLY COMPOSITE BRACKET
NUMERICAL INVESTIGATION OF DELAMINATION IN L-SHAPED CROSS-PLY COMPOSITE BRACKET M.Gümüş a*, B.Gözlüklü a, D.Çöker a a Department of Aerospace Eng., METU, Ankara, Turkey *mert.gumus@metu.edu.tr Keywords:
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 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 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 informationCHAPTER 4: BENDING OF BEAMS
(74) CHAPTER 4: BENDING OF BEAMS This chapter will be devoted to the analysis of prismatic members subjected to equal and opposite couples M and M' acting in the same longitudinal plane. Such members are
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 informationMAE 322 Machine Design. Dr. Hodge Jenkins Mercer University
MAE 322 Machine Design Dr. Hodge Jenkins Mercer University What is this Machine Design course really about? What you will learn: How to design machine elements 1) Design so they won t break under varying
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 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 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 informationKeywords: CFRP, compressive failure, kink-band, cohesive zone model. * Corresponding author
THE 19 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS AN EXPERIMENTAL METHOD TO DETERMINE THE CRITICAL ENERGY RELEASE RATE ASSOCIATED WITH LONGITUDINAL COMPRESSIVE FAILURE IN CFRP D. Svensson 1 *,
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 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 informationBending Load & Calibration Module
Bending Load & Calibration Module Objectives After completing this module, students shall be able to: 1) Conduct laboratory work to validate beam bending stress equations. 2) Develop an understanding of
More informationTHEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?
CIE309 : PLASTICITY THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT? M M - N N + + σ = σ = + f f BENDING EXTENSION Ir J.W. Welleman page nr 0 kn Normal conditions during the life time WHAT HAPPENS DUE TO
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 informationA RESEARCH ON NONLINEAR STABILITY AND FAILURE OF THIN- WALLED COMPOSITE COLUMNS WITH OPEN CROSS-SECTION
A RESEARCH ON NONLINEAR STABILITY AND FAILURE OF THIN- WALLED COMPOSITE COLUMNS WITH OPEN CROSS-SECTION H. Debski a*, J. Bienias b, P. Jakubczak b a Faculty of Mechanical Engineering, Department of Machine
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 informationCHAPER THREE ANALYSIS OF PLANE STRESS AND STRAIN
CHAPER THREE ANALYSIS OF PLANE STRESS AND STRAIN Introduction This chapter is concerned with finding normal and shear stresses acting on inclined sections cut through a member, because these stresses may
More informationMODELING DYNAMIC FRACTURE AND DAMAGE IN A FIBER-REINFORCED COMPOSITE LAMINA WITH PERIDYNAMICS
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Mechanical & Materials Engineering Faculty Publications Mechanical & Materials Engineering, Department of 011 MODELING DYNAMIC
More informationMechanics PhD Preliminary Spring 2017
Mechanics PhD Preliminary Spring 2017 1. (10 points) Consider a body Ω that is assembled by gluing together two separate bodies along a flat interface. The normal vector to the interface is given by n
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 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 informationMulti Disciplinary Delamination Studies In Frp Composites Using 3d Finite Element Analysis Mohan Rentala
Multi Disciplinary Delamination Studies In Frp Composites Using 3d Finite Element Analysis Mohan Rentala Abstract: FRP laminated composites have been extensively used in Aerospace and allied industries
More informationTowards Efficient Finite Element Model Review Dr. Richard Witasse, Plaxis bv (based on the original presentation of Dr.
Towards Efficient Finite Element Model Review Dr. Richard Witasse, Plaxis bv (based on the original presentation of Dr. Brinkgreve) Journée Technique du CFMS, 16 Mars 2011, Paris 1/32 Topics FEA in geotechnical
More informationCOMPRESSIVE BEHAVIOR OF IMPACT DAMAGED COMPOSITE LAMINATES
16 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS COMPRESSIVE BEHAVIOR OF IMPACT DAMAGED COMPOSITE LAMINATES Hiroshi Suemasu*, Wataru Sasaki**, Yuuichiro Aoki***, Takashi Ishikawa**** *Department of
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 informationEvaluation of in-plane orthotropic elastic constants of paper and paperboard
Evaluation of in-plane orthotropic elastic constants of paper and paperboard T. Yokoyama and K. Nakai Department of Mechanical Engineering, Okayama University of Science - Ridai-cho, Okayama 7-5, Japan
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 informationFRACTURE MECHANICS FOR MEMBRANES
FRACTURE MECHANICS FOR MEMBRANES Chong Li, Rogelio Espinosa and Per Ståhle Solid Mechanics, Malmö University SE 205 06 Malmö, Sweden chong.li@ts.mah.se Abstract During fracture of membranes loading often
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 informationAdvanced Numerical Study of the Effects of Road Foundations on Pavement Performance
Advanced Numerical Study of the Effects of Road Foundations on Pavement Performance X. Liu Section of Structural Mechanics, Faculty of Civil Engineering and Geosciences, Delft University of Technology,
More informationCalibration and Experimental Validation of LS-DYNA Composite Material Models by Multi Objective Optimization Techniques
9 th International LS-DYNA Users Conference Optimization Calibration and Experimental Validation of LS-DYNA Composite Material Models by Multi Objective Optimization Techniques Stefano Magistrali*, Marco
More informationConstitutive Equations (Linear Elasticity)
Constitutive quations (Linear lasticity) quations that characterize the physical properties of the material of a system are called constitutive equations. It is possible to find the applied stresses knowing
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 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 informationEXPERIMENTAL CHARACTERIZATION AND COHESIVE LAWS FOR DELAMINATION OF OFF-AXIS GFRP LAMINATES
20 th International Conference on Composite Materials Copenhagen, 19-24 th July 2015 EXPERIMENTAL CHARACTERIZATION AND COHESIVE LAWS FOR DELAMINATION OF OFF-AXIS GFRP LAMINATES Esben Lindgaard 1 and Brian
More informationAnálisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas
San Miguel de Tucuman, Argentina September 14 th, 2011 Seminary on Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas Antonio Caggiano 1, Guillermo Etse 2, Enzo
More informationFINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS
FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS Ever J. Barbero Department of Mechanical and Aerospace Engineering West Virginia University USA CRC Press Taylor &.Francis Group Boca Raton London New York
More informationOpen-hole compressive strength prediction of CFRP composite laminates
Open-hole compressive strength prediction of CFRP composite laminates O. İnal 1, A. Ataş 2,* 1 Department of Mechanical Engineering, Balikesir University, Balikesir, 10145, Turkey, inal@balikesir.edu.tr
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 informationStress-Strain Behavior
Stress-Strain Behavior 6.3 A specimen of aluminum having a rectangular cross section 10 mm 1.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.
More informationCHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS
CHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS Concepts of Stress and Strain 6.1 Using mechanics of materials principles (i.e., equations of mechanical equilibrium applied to a free-body diagram),
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 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 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 informationMMJ1133 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 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 information6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa ( psi) and
6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 10 6 psi) and an original diameter of 3.8 mm (0.15 in.) will experience only elastic deformation when a tensile
More informationSize effect in the strength of concrete structures
Sādhanā Vol. 27 Part 4 August 2002 pp. 449 459. Printed in India Size effect in the strength of concrete structures B L KARIHALOO and Q Z XIAO Division of Civil Engineering School of Engineering Cardiff
More information