DOCSLIB.ORG

MAE 456 FINITE ELEMENT ANALYSIS Truss Buckling Analysis – LAB INSTRUCTIONS LAB ASSIGNMENT 3

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
MAE 456 FINITE ELEMENT ANALYSIS Truss Buckling Analysis – LAB INSTRUCTIONS LAB ASSIGNMENT 3 MAE 456 FINITE ELEMENT ANALYSIS Truss Buckling Analysis – LAB INSTRUCTIONS LAB ASSIGNMENT 3 Lab Objectives Perform a FEA Eigenvalue buckling analysis of a simple column. Perform a FEA Eigenvalue buckling analysis of a 3D truss structure. Verify the buckling analyses with hand calculations. Write‐up the FEA in an Engineering Report. Lab Tasks The analyses of the truss structure from Lab Assignments 1 and 2 did not account for buckling of members in compression. For slender shapes with heavy axial compressive loads, the structure will fail by buckling before it fails by yielding in axial compression. An “Eigenvalue” buckling analysis can be performed to determine the force level at which the buckling will occur.1 To perform a buckling FEA, beam elements must be used for members in compression. 1. First, a simple column buckling test case will be performed to test the capability of SolidWorks to perform a beam buckling analysis, as part of the verification. A pipe is cast into a concrete floor and used to support an axial load as shown in Figure 1. The top of the pipe may move vertically but may not move horizontally. (It may also rotate at the top as shown.) The cross section of the column has a 1.8 in. outside diameter and a wall thickness of 0.15 in. as shown. The pipe is made of AISI 1020 steel. Apply a force P = 1000 lbf. P D = 1.8 in 10 ft t = 0.15 in Figure 1. Pipe column and cross section 1 A non‐linear FEA stress analysis with slightly off‐center loading can also be used and may be more accurate. Perform an FEA Eigenvalue buckling analysis for this test case to verify that the FEA results agree closely with Euler’s critical buckling load as given by the equation: 2EI P . cr 0.7L 2 Here Pcr is the load at which buckling failure will occur if the load P is increased gradually. The “Buckling Load Factor” (BLF) is given by BLF = Pcr/P. It gives the factor by which the load(s) can be increased before buckling occurs. Thus the BLF also gives the Factor of Safety (FS) for a buckling analysis. Graph the BLF as a function of the number of elements. Determine the minimum number of beam elements that can accurately represent the solution to 2 decimal places. To perform an Eigenvalue buckling analysis of a truss structure in SolidWorks: a) Create a CAD model of the structure by drawing lines and using a “Weldment” to define “Structural Members” based on the lines. Be sure to orient the cross‐section correctly using the angle input at the bottom of the “Structural Member” dialog box. Alternatively, use regular solid modeling operations like extrude or sweep to model truss members. Ensure that a material has been assigned to the CAD model. b) Perform hand calculations to determine the approximate BLF. c) Create a new Simulation Study. Choose “Buckling” as the type of study. d) For the structural members of the study, ensure that beam elements are being used: For members not‐created using “Structural Members,” in the Simulation Manager, right‐click on the solid () and select “Treat as Beam…” so that the member is treated as a 1‐D element. Ensure that the icon changes to . For members created using “Structural Members”, under the cut‐list (), under the list of structural members (), ensure that the member appears as a beam () and not as a truss element (). If necessary, right‐click on the icon, select “Edit Definition …” and select “Beam” as the Type. e) Set the analysis to give the first ten buckling modes. Right‐click on the buckling study () and select “Properties…” Set the number of buckling modes to 10 and press OK. f) Apply the boundary conditions to the joints and run the study in the usual way. You will notice that it gives a “Mode Shape” number and “Load Factor” in the information at the top left. This information can also be obtained by right‐clicking on the Results and selecting “List Buckling Factor of Safety”. The displayed mode shape can be changed by right‐clicking on the mode shape amplitude result () and clicking on “Edit Definition…” Each mode has an Eigenvalue which can be directly interpreted as the Buckling Load Factor. If the loads are increased gradually and proportionately, the structure will fail at the mode with the lowest positive BLF. (If the directions of all the loads are reversed and increased proportionately, then the lowest negative BLF may apply.) Note that the displacements and stresses from an Eigenvalue analysis are scaled arbitrarily. In real‐life the structure will just continue a sudden deflection according to the mode shape until the structure yields fully or fractures. g) Repeat the analysis with fewer and fewer elements to observe when the BLF converges. In SolidWorks, this can be accomplished by right‐clicking on the Mesh in the Simulation Manager and selecting “Apply Mesh Control.” Select the Structural Member and set the “Number of elements” as desired. Create a graph to show the convergence. Make a conclusion about the minimum number of elements needed to achieve the desired accuracy. 2. Perform a buckling analysis of your structure and boundary conditions from Lab Assignment 2. The only difference in setting up the buckling analysis is selecting “Buckling” instead of “Static” when creating a new study. For the check calculations, calculate the BLF for the member or section of the structure that is anticipated to buckle first. This will be the BLF (and safety factor) for the entire structure. See the Appendix for more detailed information. Remember that for an FEA buckling analysis: P FS cr BLF Eigenvalue P Remember that the displacements and stresses shown in an Eigenvalue analysis are scaled arbitrarily. Do not quote any actual stress values from the buckling FEA. 3. Complete a report on the truss buckling analysis. The column buckling analysis does not need to be written up. The report should include the following sections: 1) Summary (What is this report about? What structure did you analyze? What kind of failure did you study? What were the conclusions?) 2) Introduction (What were the objectives and constraints on the design? What kind of failures needed to be considered?) 3) Description of design (including geometric and material information, and mass) 4) Description of failure scenario and the FE model . Describe the overall situation. What types of failure are studied? What assumptions are made? . Describe the actual physical boundary conditions (loads and supports) for each load case. Show the mesh and types of elements used. What simplifications did you make for your model? . Show how the supports and loading conditions were applied. Which degrees‐of‐freedom were restrained at each support? 5) Discussion of results of FE analysis . For each load case, for the first positive buckling mode, show how the structure would buckle. What is the factor of safety with respect to the given loads? . Compare the factor of safety with that from Assignment 2. Which one is the true factor of safety? Which failure would happen first? 6) Description of verification of FE analysis . Does the buckling mode seem reasonable? Is it as expected? Are the support conditions maintained as intended? Is it evident that rotation was restrained or allowed as intended? . By hand, calculate Euler’s buckling load (Pcr) for the most critical member (or sub‐structure). The most critical member (or sub‐structure) is the one that experiences the buckling first. The Appendix has notes on how to identify the most critical member or they can be identified by looking at which members (or sub‐structure) are most highly displaced in the first positive mode of the buckling FEA. The Appendix also shows how to calculate Euler’s buckling load for different end conditions. Compute the Buckling Load Factor (BLF) for the critical member (BLF = Pcr / P), where P is the actual load that is expected for that member. The actual load can be obtained from the hand calculations from Assignment 1 or by multiplying the stress from the Assignment 1 FEA by the cross‐sectional area. Compare the BLF for the critical member (which is also the BLF for the entire structure) with the BLF from the FEA. 7) Conclusions (Will the structure fail? What is the safety factor? Will it fail first by yielding or buckling? How heavy is the structure?) Be sure there is no confusion about units. The report should be about 15 pages long, having mostly figures and calculations. A template is provided on the course web page. 4. Submit the report electronically via eCampus. The PDF document file name must start with your name and include the assignment number. Due date/time: April 5. Appendix – Practical Aspects of Using Euler’s Buckling Formula .
Load more

Recommended publications
  • The Effect of Yield Strength on Inelastic Buckling of Reinforcing
    Mechanics and Mechanical Engineering Vol. 14, No. 2 (2010) 247{255 ⃝c Technical University of Lodz The Effect of Yield Strength on Inelastic Buckling of Reinforcing Bars Jacek Korentz Institute of Civil Engineering University of Zielona G´ora Licealna 9, 65{417 Zielona G´ora, Poland Received (13 June 2010) Revised (15 July 2010) Accepted (25 July 2010) The paper presents the results of numerical analyses of inelastic buckling of reinforcing bars of various geometrical parameters, made of steel of various values of yield strength. The results of the calculations demonstrate that the yield strength of the steel the bars are made of influences considerably the equilibrium path of the compressed bars within the range of postyielding deformations Comparative diagrams of structural behaviour (loading paths) of thin{walled sec- tions under investigation for different strain rates are presented. Some conclusions and remarks concerning the strain rate influence are derived. Keywords: Reinforcing bars, inelastic buckling, yield strength, tensil strength 1. Introduction The impact of some exceptional loads, e.g. seismic loads, on a structure may re- sult in the occurrence of post{critical states. Therefore the National Standards regulations for designing reinforced structures on seismically active areas e.g. EC8 [15] require the ductility of a structure to be examined on a cross{sectional level, and additionally, the structures should demonstrate a suitable level of global duc- tility. The results of the examinations of members of reinforced concrete structures show that inelastic buckling of longitudinal reinforcement bars occurs in the state of post{critical deformations, [1, 2, 4, 7], and in some cases it occurs yet within the range of elastic deformations [8].
    [Show full text]
  • Lecture 42: Failure Analysis – Buckling of Columns Joshua Pribe Fall 2019 Lecture Book: Ch
    ME 323 – Mechanics of Materials Lecture 42: Failure analysis – Buckling of columns Joshua Pribe Fall 2019 Lecture Book: Ch. 18 Stability and equilibrium What happens if we are in a state of unstable equilibrium? Stable Neutral Unstable 2 Buckling experiment There is a critical stress at which buckling occurs depending on the material and the geometry How do the material properties and geometric parameters influence the buckling stress? 3 Euler buckling equation Consider static equilibrium of the buckled pinned-pinned column 4 Euler buckling equation We have a differential equation for the deflection with BCs at the pins: d 2v EI+= Pv( x ) 0 v(0)== 0and v ( L ) 0 dx2 The solution is: P P A = 0 v(s x) = Aco x+ Bsin x with EI EI PP Bsin L= 0 L = n , n = 1, 2, 3, ... EI EI 5 Effect of boundary conditions Critical load and critical stress for buckling: EI EA P = 22= cr L2 2 e (Legr ) 2 E cr = 2 (Lreg) I r = Pinned- Pinned- Fixed- where g Fixed- A pinned fixed fixed is the “radius of gyration” free LLe = LLe = 0.7 LLe = 0.5 LLe = 2 6 Modifications to Euler buckling theory Euler buckling equation: works well for slender rods Needs to be modified for smaller “slenderness ratios” (where the critical stress for Euler buckling is at least half the yield strength) 7 Summary L 2 E Critical slenderness ratio: e = r 0.5 gYc Euler buckling (high slenderness ratio): LL 2 E EI If ee : = or P = 2 rr cr 2 cr L2 gg c (Lreg) e Johnson bucklingI (low slenderness ratio): r = 2 g Lr LLeeA ( eg) If : =−1 rr cr2 Y gg c 2 Lr ( eg)c with radius of gyration 8 Summary Effective length from the boundary conditions: Pinned- Pinned- Fixed- LL= LL= 0.7 FixedLL=- 0.5 pinned fixed e fixede e LL= 2 free e 9 Example 18.1 Determine the critical buckling load Pcr of a steel pipe column that has a length of L with a tubular cross section of inner radius ri and thickness t.
    [Show full text]
  • 28 Combined Bending and Compression
    CE 479 Wood Design Lecture Notes JAR Combined Bending and Compression (Sec 7.12 Text and NDS 01 Sec. 3.9) These members are referred to as beam-columns. The basic straight line interaction for bending and axial tension (Eq. 3.9-1, NDS 01) has been modified as shown in Section 3.9.2 of the NDS 01, Eq. (3.9-3) for the case of bending about one or both principal axis and axial compression. This equation is intended to represent the following conditions: • Column Buckling • Lateral Torsional Buckling of Beams • Beam-Column Interaction (P, M). The uniaxial compressive stress, fc = P/A, where A represents the net sectional area as per 3.6.3 28 CE 479 Wood Design Lecture Notes JAR The combination of bending and axial compression is more critical due to the P-∆ effect. The bending produced by the transverse loading causes a deflection ∆. The application of the axial load, P, then results in an additional moment P*∆; this is also know as second order effect because the added bending stress is not calculated directly. Instead, the common practice in design specifications is to include it by increasing (amplification factor) the computed bending stress in the interaction equation. 29 CE 479 Wood Design Lecture Notes JAR The most common case involves axial compression combined with bending about the strong axis of the cross section. In this case, Equation (3.9-3) reduces to: 2 ⎡ fc ⎤ fb1 ⎢ ⎥ + ≤ 1.0 F' ⎡ ⎛ f ⎞⎤ ⎣ c ⎦ F' 1 − ⎜ c ⎟ b1 ⎢ ⎜ F ⎟⎥ ⎣ ⎝ cE 1 ⎠⎦ and, the amplification factor is a number greater than 1.0 given by the expression: ⎛ ⎞ ⎜ ⎟ ⎜ 1 ⎟ Amplification factor for f = b1 ⎜ ⎛ f ⎞⎟ ⎜1 − ⎜ c ⎟⎟ ⎜ ⎜ F ⎟⎟ ⎝ ⎝ E 1 ⎠⎠ 30 CE 479 Wood Design Lecture Notes JAR Example of Application: The general interaction formula reduces to: 2 ⎡ fc ⎤ fb1 ⎢ ⎥ + ≤ 1.0 F' ⎡ ⎛ f ⎞⎤ ⎣ c ⎦ F' 1 − ⎜ c ⎟ b1 ⎢ ⎜ F ⎟⎥ ⎣ ⎝ cE 1 ⎠⎦ where: fc = actual compressive stress = P/A F’c = allowable compressive stress parallel to the grain = Fc*CD*CM*Ct*CF*CP*Ci Note: that F’c includes the CP adjustment factor for stability (Sec.
    [Show full text]
  • “Linear Buckling” Analysis Branch
    Appendix A Eigenvalue Buckling Analysis 16.0 Release Introduction to ANSYS Mechanical 1 © 2015 ANSYS, Inc. February 27, 2015 Chapter Overview In this Appendix, performing an eigenvalue buckling analysis in Mechanical will be covered. Mechanical enables you to link the Eigenvalue Buckling analysis to a nonlinear Static Structural analysis that can include all types of nonlinearities. This will not be covered in this section. We will focused on Linear buckling. Contents: A. Background On Buckling B. Buckling Analysis Procedure C. Workshop AppA-1 2 © 2015 ANSYS, Inc. February 27, 2015 A. Background on Buckling Many structures require an evaluation of their structural stability. Thin columns, compression members, and vacuum tanks are all examples of structures where stability considerations are important. At the onset of instability (buckling) a structure will have a very large change in displacement {x} under essentially no change in the load (beyond a small load perturbation). F F Stable Unstable 3 © 2015 ANSYS, Inc. February 27, 2015 … Background on Buckling Eigenvalue or linear buckling analysis predicts the theoretical buckling strength of an ideal linear elastic structure. This method corresponds to the textbook approach of linear elastic buckling analysis. • The eigenvalue buckling solution of a Euler column will match the classical Euler solution. Imperfections and nonlinear behaviors prevent most real world structures from achieving their theoretical elastic buckling strength. Linear buckling generally yields unconservative results
    [Show full text]
  • Buckling Failure Boundary for Cylindrical Tubes in Pure Bending
    Brigham Young University BYU ScholarsArchive Theses and Dissertations 2012-03-14 Buckling Failure Boundary for Cylindrical Tubes in Pure Bending Daniel Peter Miller Brigham Young University - Provo Follow this and additional works at: https://scholarsarchive.byu.edu/etd Part of the Mechanical Engineering Commons BYU ScholarsArchive Citation Miller, Daniel Peter, "Buckling Failure Boundary for Cylindrical Tubes in Pure Bending" (2012). Theses and Dissertations. 3131. https://scholarsarchive.byu.edu/etd/3131 This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. Buckling Failure Boundary for Cylindrical Tubes in Pure Bending Daniel Peter Miller A thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science Kenneth L. Chase, Chair Carl D. Sorenson Brian D. Jensen Department of Mechanical Engineering Brigham Young University April 2012 Copyright © 2012 Daniel P. Miller All Rights Reserved ABSTRACT Buckling Failure Boundary for Cylindrical Tubes in Pure Bending Daniel Peter Miller Department of Mechanical Engineering Master of Science Bending of thin-walled tubing to a prescribed bend radius is typically performed by bending it around a mandrel of the desired bend radius, corrected for spring back. By eliminating the mandrel, costly setup time would be reduced, permitting multiple change of radius during a production run, and even intermixing different products on the same line. The principal challenge is to avoid buckling, as the mandrel and shoe are generally shaped to enclose the tube while bending.
    [Show full text]
  • Column Analysis and Design
    Chapter 9: Column Analysis and Design Introduction Columns are usually considered as vertical structural elements, but they can be positioned in any orientation (e.g. diagonal and horizontal compression elements in a truss). Columns are used as major elements in trusses, building frames, and sub-structure supports for bridges (e.g. piers). • Columns support compressive loads from roofs, floors, or bridge decks. • Columns transmit the vertical forces to the foundations and into the subsoil. The work of a column is simpler than the work of a beam. • The loads applied to a column are only axial loads. • Loads on columns are typically applied at the ends of the member, producing axial compressive stresses. • However, on occasion the loads acting on a column can include axial forces, transverse forces, and bending moments (e.g. beam-columns). Columns are defined by the length between support ends. • Short columns (e.g. footing piers). • Long columns (e.g. bridge and freeway piers). Virtually every common construction material is used for column construction. • Steel, timber, concrete (reinforced and pre-stressed), and masonry (brick, block, and stone). The selection of a particular material may be made based on the following. • Strength (material) properties (e.g. steel vs. wood). • Appearance (circular, square, or I-beam). • Accommodate the connection of other members. • Local production capabilities (i.e. the shape of the cross section). Columns are major structural components that significantly affect the building’s overall performance and stability. • Columns are designed with larger safety factors than other structural components. 9.1 • Failure of a joist or beam may be localized and may not severely affect the building’s integrity (e.g.
    [Show full text]
  • Local Buckling Analysis of Steel Truss Bridge Under Seismic Loading
    LOCAL BUCKLING ANALYSIS OF STEEL TRUSS BRIDGE UNDER SEISMIC LOADING Eiki Yamaguchi1, Keita Yamada2 Abstract In the 2004 Mid Niigata Prefecture Earthquake, a steel truss bridge was damaged: the lower chord member underwent local buckling. The axial force in that member is not necessarily compression-dominant: tensile axial force is also expected. Since many steel bridge piers were subjected to local buckling in the 1995 Kobe Earthquake, the criterion for local bucking in the member under axial compression has been studied rather extensively. However, the local buckling in the member under the other states of axial force has not. In the present study, the local buckling in the lower chord member of a truss bridge is to be looked into. To that end, the existing criterion for local buckling in terms of average strain is tested for the case when tensile yielding precedes compression, failing to confirm its applicability. Then the criterion is modified by introducing the updated average strain. The seismic response analysis is then conducted to show the significance of the proposed criterion. Introduction One of the largest earthquakes in the recorded history, the Tohoku Earthquake, just hit Japan in March, 2011, causing very serious damage in the eastern part of Japan. Yet the memory of the damage to structures in the 1995 Kobe Earthquake is still fresh and vivid for many structural engineers. Between the two large earthquakes, numerous earthquakes occurred as well, some of which were quite large and comparable to the 1995 Kobe Earthquake. The damage in each big earthquake has posed a new challenge for engineers; some of them are yet to be solved.
    [Show full text]
  • Impact of Ballast Fouling on the Mechanical Properties of Railway Ballast: Insights from Discrete Element Analysis
    Impact of Ballast Fouling on the Mechanical Properties of Railway Ballast: Insights from Discrete Element Analysis By Luyu Wang Department of Civil Engineering and Applied Mechanics McGill University Montréal, Québec, Canada July 2020 A thesis submitted to McGill University in partial fulfillment of the requirements for the degree of Master of Engineering © Luyu Wang, 2020 Abstract Ballast fouling is a major factor that contributes to the reduction of the shear strength of railway ballast, which can further influence the stability of railway equipment. Depending on the railway function and location, the major sources of ballast fouling are the infiltration of foreign fine material and ballast material degradation. The discrete element method (DEM) is an efficient way to capture the mechanical behavior of particles under various loading conditions. It has been successfully applied to investigate the mechanical behavior of ballast assembly and fouled ballast in the previous practices. In this study, a discrete element model is developed in PFC3D to simulate the stress-strain behavior of fresh ballast assembly tested in the direct shear test. A series of sensitivity analyses of the different parameters are conducted to better understand the corresponding effect on the stress- strain behavior of ballast assembly. An efficient approach to simulate the foreign material induced fouling of ballast and capture the mechanical behavior of the material at various levels of void contamination index (VCI) is proposed. The approach is based on the concept that the foreign fouling material will not only change the inter-particle friction angle but also the inter-particle contact stiffness. Therefore, both the effective modulus and the inter-particle friction coefficient are adjusted based on the validated fresh ballast contact model.
    [Show full text]
  • Residual Ultimate Buckling Strength of Steel Stiffened Panels Subjected
    RESIDUAL ULTIMATE BUCKLING STRENGTH OF STEEL STIFFENED PANELS SUBJECTED TO CORROSION DAMAGE A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment Of the Requirements for the Degree Master of Science Elijah Fox May, 2017 RESIDUAL ULTIMATE BUCKLING STRENGTH OF STEEL STIFFENED PANELS SUBJECTED TO CORROSION DAMAGE Elijah Fox Thesis Approved: Accepted: Advisor Department Chair Dr. Anil Patnaik Dr. Wieslaw K. Binienda Committee Member Interim Dean of the College Dr. Craig Menzemer Dr. Donald J. Visco Committee Member Dean of the Graduate School Dr. Ping Yi Dr. Chand Midha Date 2 ACKNOWLEDGEMENTS I would like to thank my mother, Janice, and my siblings, Kivie and Nakita. Without my families support over all of these years, I would not have been able to complete my degree. My mother has always been strong and has taught me so many fundamentals which I live by; I just want to thank her for making me the man I am today. My family has always been so supportive, loving, and has done anything they could to help me succeed and because of this, I am forever grateful. I owe a special thank you to my amazing life partner, Marisa. She has been in my life since my first day of college and I would not have been able to make it without her love and support throughout these years. She is still by my side through all of the trials and tribulations life has thrown at me over the past seven years and words could not express how appreciative I am of all of her help.
    [Show full text]
  • Buckling Analysis of a Column
    Buckling Analysis of a Column Title Euler Buckling Analysis of a pin-ended column Description A column with both ends pinned has to be checked for buckling instability i) Find out the buckling mode shapes, ii) Find the critical buckling compressive load on the column Assume Column to be an I-section i.e. a Universal Column UC 203x203x60. The material of the column is S355 as per Eurocode. Height of the column, L= 5 m. Vertical Load acting on the column, P= 1000 kN. Structural geometry and analysis model 1 Finite Element Modelling: Analysis Type: 2-D static analysis (X-Z plane) Step 1: Go to File>New Project and then go to File>Save to save the project with any name Step 2: Go to Model>Structure Type to set the analysis mode to 2D (X-Z plane) Unit System: kN,m Step 3: Go to Tools>Unit System and change the units to kN and m. 2 Geometry generation: Step 4: Go to Model>Structure Wizard>Column and enter Distance as 0.50 m and Repeat times = 10. Press Add. This will create a column of height 5 m which is composed of 10 finite elements. A column should be divided into several finite elements before performing the buckling analysis in the software. Select pin as the boundary condition. Enter Material and Section ID as 1. Click OK. Switch to the Front view by clicking on as shown below. 3 Material: S355 (Eurocode). E=2.1x108 kN/m2 Step 7: Go to Model>Properties>Material>Add. Select Steel in the Type of Design and select Standard as EN(05)S.
    [Show full text]
  • Fracture, Delamination, and Buckling of Elastic Thin Films on Compliant Substrates
    FRACTURE, DELAMINATION, AND BUCKLING OF ELASTIC THIN FILMS ON COMPLIANT SUBSTRATES Haixia Mei, Yaoyu Pang, Se Hyuk Im, Rui Huang Department of Aerospace Engineering and Engineering Mechanics University of Texas at Austin 1 University Station, C0600 Austin, Texas 78712 Phone: (512) 471-7558 Fax: (512) 471-5500 Email: [email protected] ABSTRACT Greek symbols A series of studies have been conducted for mechanical fracture toughness (J/m2) behavior of elastic thin films on compliant substrates. Under first Dundurs parameter (dimensionless) tension, the film may fracture by growing channel cracks. The second Dundurs parameter (dimensionless) driving force for channel cracking (i.e., the energy release opening displacement (m) rate) increases significantly for compliant substrates. phase angle of mode mix (radian) Moreover, channel cracking may be accompanied by Poisson’s ratio (dimensionless) interfacial delamination. For a film on a relatively compliant 2 substrate, a critical interface toughness is predicted, which stress (N/m ) separates stable and unstable delamination. For a film on a relatively stiff substrate, however, a channel crack grows with Subscripts no delamination when the interface toughness is greater than a f film critical value. An effective energy release rate for the steady- i interface state growth of a channel crack is defined to account for the s substrate influence of interfacial delamination on both the fracture ss steady state driving force and the resistance, which can be significantly higher than the energy release rate assuming no delamination. Alternatively, when the film is under compression, it tends to INTRODUCTION buckle. Two buckling modes have been observed, one with interfacial delamination (i.e., buckle-delamination) and the Integrated structures with mechanically soft components have other without delamination (i.e., wrinkling).
    [Show full text]
  • DNVGL-CG-0128 Buckling
    CLASS GUIDELINE DNVGL-CG-0128 Edition October 2015 Buckling The electronic pdf version of this document, available free of charge from http://www.dnvgl.com, is the officially binding version. DNV GL AS FOREWORD DNV GL class guidelines contain methods, technical requirements, principles and acceptance criteria related to classed objects as referred to from the rules. © DNV GL AS Any comments may be sent by e-mail to [email protected] If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of DNV GL, then DNV GL shall pay compensation to such person for his proved direct loss or damage. However, the compensation shall not exceed an amount equal to ten times the fee charged for the service in question, provided that the maximum compensation shall never exceed USD 2 million. In this provision "DNV GL" shall mean DNV GL AS, its direct and indirect owners as well as all its affiliates, subsidiaries, directors, officers, employees, agents and any other acting on behalf of DNV GL. CHANGES – CURRENT This is a new document. Changes - current Class guideline — DNVGL-CG-0128. Edition October 2015 Page 3 Buckling DNV GL AS CONTENTS Changes – current...................................................................................................... 3 Contents Section 1 Introduction............................................................................................... 7 1 Objective.................................................................................................7 2 Buckling methods..................................................................................
    [Show full text]