# Finite-Element Analysis of Stress Concentration in ASTM D 638 Tension Specimens

Save this PDF as:

Size: px
Start display at page:

Download "Finite-Element Analysis of Stress Concentration in ASTM D 638 Tension Specimens"

## Transcription

2 2 JOURNAL OF TESTING AND EVALUATION Finite-Element Modeling The two-dimensional plane stress six-node and twelve degreeof-freedom triangular linear elastic element was selected to model the flat-plate tension specimens. The commercially available AN- SYS finite-element analysis software and its mesh generator were used. Figure 2 shows the finite-element meshes used to model the four types of ASTM D 638 tension specimens. Due to the symmetry of the specimen geometry, only one quarter of the specimen is modeled. Point O is the center of the specimen. Lines OA and OE are the symmetry planes of the specimen. Point O is fixed in both the X- and Y-directions. Nodes on Line OA have zero displacement in the X-direction and are free to move in the Y-direction. Nodes on Line OE have zero displacement in the Y-direction and are free to move in the X-direction. Nodes on Line ED are prescribed a uniform 0.1-mm displacement in the X-direction and zero displacement in the Y-direction. This is intended to simulate the holding of both ends in the wide section of the tension specimen using perfectly rigid grips. The extension of the specimen under this condition is 0.2 mm. In actual tensile tests, the specimen is clamped and pulled using a set of mechanical or hydraulic grips. The actual loading condition near the gripped area is therefore the combination of the normal compressive stress and in-plane tensile and shear stresses. Dimensions of finite-element meshes and the number of elements and nodes are summarized in the table in Fig. 2 for each type of ASTM D 638 specimen. OA is one half of the width of the gage FIG. 1 Pictures of ASTM D Type IV tension specimens: (a) Nylon-11 bonded Nd-Fe-B (59.7 vol%) material tested with at 100 C, and (b) pure Nylon-11 tested at 100 C. FIG. 3 Geometric model of the single and double radius transitional area. FIG. 2 Finite-element mesh for four types of specimen in ASTM D

3 GARRELL ET AL. ON ASTM 638 TEST SPECIMENS 3 FIG. 4 Distribution of von Mises stress in ASTM D 638 tensile test specimens. (Value by the node represents the ratio of nodal von Mises stress relative to the maximum von Mises stress at node MX in Pa.) section, DE is one half of the width of the wide section, OE is one half of the length of the specimen, and AB is one half of the length of the gage section. Between Points B and C, the specimen changes from the narrow to the wide section. As shown in Figs. 2a, 2b, and 2c, Type I, II, and III specimens consist of a circular arc of radius r 1 between Points B and C. These are known as single-arc specimens. As shown in Fig. 2d, two radii, r 1 and r 2, are used to blend two arcs in the transitional region between Points B and C for the Type IV specimen. This is designated as the double-arc specimen. The geometrical relationships of the single- and double-arc shape between Points B and C are shown in Fig. 3; w 1 and w 2 are widths of the narrow and wide section, respectively. As shown in Fig. 3a, the single-radius specimen has a continuous slope at Point B and a discontinuous slope at Point C. The double-arc specimen, as shown in Fig. 3b, has a continuous slope at all three transitional points: B, F, and C. Arcs BF and FC have the same angle, indicated by. The center of Arc BF, denoted as C 1 in Fig. 3a, has the same X-coordinate as Point B. Similarly, the center of Arc CF, denoted as C 2, has the same X-coordinate as Point C. These geometrical constraints together ensure a continuous slope at Points B, F, and C for the double-arc specimen. A hydrostatic stress-dependent yield criterion is usually used to analyze stress concentrations in plastics [12,13]. The yield criterion for magnetic particle reinforced plastics has not yet been studied. The maximum von Mises stress was used to calculate the stress concentration factor and to identify the location that possibly initializes the fracture. In addition to the von Mises stress, the maximum principal stress, which is more suitable for the analysis of brittle materials, was also applied to calculate the stress concentration factor. The finite-element analysis provided results of stress components and the von Mises and principal stress for each node. The nodal stress was used to calculate the stress concentration factor, K f. max K f (1) nominal where max is either the maximum nodal von Mises stress or maximum first principal stress, and nominal is either the average von Mises stress or the average first principal stress on nodes in the gage section. Finite-element analysis results show that the variation of von Mises stress among nodes in the gage section is very small, less than 1.5%. An elastic modulus of 130 MPa and Poisson s ratio of 0.3 were used in the finite-element analysis.

4 4 JOURNAL OF TESTING AND EVALUATION Finite-Element Analysis of Four Types of Tension Specimens Figure 4 shows the distribution of von Mises stress for ASTM D 638 Type I, II, III, and IV standard tension specimens. For each specimen, an overview and another enlarged view of the von Mises TABLE 1 The stress concentration for different single- and doubleradius tension specimen geometry. Designation r 1 (mm) r 2 (mm) w 1 /r 1 K f ASTM Type I D 638 Type II Type III Type IV Single S-I radius S-II tension S-III specimen S-IV S-V S-VI S-VII Double D-I radius D-II* tension D-III specimen D-IV D-V D-VI D-VII * The same geometry as Type IV. stress distribution is presented. The enlarged view is centered about Point B to identify the increase in von Mises stress. In Fig. 4, MX and MN mark the nodes with maximum and minimum von Mises stress, respectively. As shown in the overview of the specimen, Node MN is close to Point C. In the enlarged view, the location of Node MX relative to Node B can be seen. Node MX is next to Node B, as in Type I and II, or a node away from Node B, as in Type III and IV. It is noted that the mesh shown in the enlarged view represents the exaggeratedly deformed finite-element mesh from the ANSYS output. Node B, originally located at the intersection of a straight line and an arc, can be seen on a slightly curved region after deformation. The ratio of nodal von Mises stress relative to the maximum von Mises stress at Node MX is also presented in the enlarged view on nodes around Points B and MX in Fig. 4. For Type I, II, and III specimens, the overview of von Mises stress distribution does not show the stress concentration. Upon closely examining the distribution of von Mises stress around Point MX in the enlarged view, all four types of ASTM D 638 tension specimens demonstrate different levels of stress concentration at Node MX. The von Mises stress at Node MX ( max ) and at nodes in the gage section ( nominal ) were extracted from the finite-element output and substituted into Eq 1 to calculate the stress concentration factor, K f. Results of K f are listed in Table 1. Type IV and II specimens have the highest and lowest K f, and 1.014, respectively. It was found that K f has an almost linear relationship versus the parameter w 1 /r 1, as shown in Fig. 5, for the four types of ASTM D 638 specimen. FIG. 5 The stress concentration factor versus ratio of gage section width and radius for five types of ASTM D 638 specimens and the single- and double-radius specimens.

5 GARRELL ET AL. ON ASTM 638 TEST SPECIMENS 5 Tension specimens with low w 1 /r 1 ratio usually have large arc radius and are longer than specimens with high w 1 /r 1. For example, as shown in Fig. 2 and Table 1, Type II and IV specimens have the same width in the gage section and different radius r 1. The Type II specimen has a larger arc radius, which makes the specimen longer and has lower w 1 /r 1 and K f. Longer and bigger tension specimens are unattractive because they require more material and a bigger die for injection molding and cost more to produce. Instead of using the von Mises stress, the maximum principal stress and nominal principal stress were extracted from the finiteelement output and substituted into Eq 1 to calculate K f. For all four types of specimens, the difference in K f based on von Mises and maximum principal stresses is very small, less than Finite-Element Analysis of Single- and Double-Arc Tension Specimens In this section, the investigation of stress distribution in alternative tension specimen geometries that maintain the same overall size as the Type IV specimen is discussed. The objective is to identify the geometric parameters that would reduce the magnitude of K f. The width (w 1 ) and length of the gage section are 6 and 13 mm, respectively. The width of the wide section, w 2, is 19 mm. Two groups of sample geometry were studied. One group consists of single-arc specimens, similar to those in Type I, II, and III. Another group has the double-arc geometry, similar to the Type IV specimen. Single-Arc Specimens As shown in Table 1, seven single radius curves are used to blend between Points B and C. The minimum radius of Arc BC is 6.5 mm ( (w 2 w 1 )/2). The specimens with radii of 6.5, 9, 13, 19, 28, 39, or 52 mm at Arc BC were designated as S-I to S-VII, respectively. The shape and finite-element mesh of three selected specimens, S-I, S-IV, and S-VII, are shown in Fig. 6. For specimens with arc radius equal to or less than 39 mm, the overall length of the original Type IV specimen can be maintained. The K f of the 39-mm radius single-arc specimen (S-VI), as shown in Table 1, is This is significantly lower than K f of of the Type IV specimen. Plots of K f versus w 1 /r 1 for these seven specimens are shown in Fig. 5. The larger radius of arc BC lowers both w 1 /r 1 and K f. Figure 5 also shows that the relationship between K f and w 1 /r 1 is almost linear and matches the trend of Type I to IV specimens. Double-Arc Specimens Seven double-arc specimens, denoted as D-I to D-VII, were studied as well. As shown in Fig. 3, the values of r 1 and r 2 in the doublearc geometry can be reversed and still maintain the continuity of both position and slope at Points B, F, and C. This special geometrical characteristic of the double-arc shape was used to define conjugate pairs of specimens. As shown in Table 1, D-I (r 1 9 mm, r 2 30 mm) and D-VII (r 1 30 mm, r 2 9 mm) form a conjugate pair of double-arc specimens. D-II (r 1 14 mm, r 2 25 mm) and D-VI (r 1 25 mm, r 2 14 mm) as well as D-III (r 1 17 mm, r 2 22 mm) and D-V (r 1 22 mm, r 2 17 mm) are another two sets of conjugate double-arc specimens. It is noted that the D-II specimen has the same geometry as the ASTM D 638 Type IV specimen. The intent is to investigate the change in K ƒ of a conjugate doublearc specimen. The D-III specimen has the same r 1 and r 2, both equal to 19.5 mm. The shape and finite-element mesh of three selected specimens, D-I, D-IV, and D-VII, are shown in Fig. 6. Finite-element analysis results of K f versus w 1 /r 1 for seven double-arc specimens are listed in Table 1 and plotted in Fig. 5. It is important to note that the value of r 2 does not affect K f. By just switching the two arcs of the original Type IV specimen, the K f was reduced from to By further increasing r 1 to 30 mm without changing the overall size of the Type IV specimen, K f was reduced to Modeling of the Stress Concentration Factor As shown in Fig. 5, a straight line can be used to determine K f for various w 1 /r 1. Linear regression analysis was performed on all 17 data points, including the four types of specimen specified by ASTM D 638 and the seven single-arc and six double-arc specimens. The following model is obtained: K f (w 1 /r 1 ) (2) Equation 2 can be used to predict the K f based on w 1 /r 1 and may be useful for new tension specimen design. FIG. 6 Finite-element meshes for selected single- and double-arc specimens (3 mm half-width in the gage section for all specimens).

6 6 JOURNAL OF TESTING AND EVALUATION The linear trend indicates the possibility that an analytical solution for the stress distribution in this geometrical configuration may exist. This requires further investigation. Concluding Remarks The stress distribution of four types of tension specimens recommended in ASTM D 638 was investigated through the use of the finite-element technique. It was found that the location of maximum von Mises stress for Type IV geometry coincided with the location of experimentally observed failures in brittle specimens made of Nylon-11 bonded Nd-Fe-B particles. This study identified a solution to reduce the magnitude of stress concentration by increasing the radius of the arc in the transitional area. A linear correlation of stress concentration factor K f versus w 1 /r 1 was identified and a linear model was established to predict the K f based on w 1 /r 1. Results obtained in this research can help establish standards and aid in the design of specimen geometry for tension testing of brittle particle-reinforced composites. Acknowledgments A portion of this research was sponsored by the User program of the High Temperature Material Laboratory of Oak Ridge National Laboratory and by National Science Foundation Grant (Dr. K. P. Rajurkar, Program Director). References [1] ASTM D : Standard Test Method for Tensile Strength of Plastics, Annual Book of ASTM Standards, ASTM International, West Conshohocken, PA, [2] Garrell, M. G., Ma, B. M., Lara-Curzio, E., Shih, A. J., and Scattergood, R. O., Mechanical Properties of Nylon Bonded Nd-Fe-B Permanent Magnets, Journal of Magnetism and Magnetic Materials, accepted for publication. [3] Garrell, M. G., Ma, B. M., Lara-Curzio, E., Shih, A. J., and Scattergood, R. O., Mechanical Properties of Polyphenylene-Sulfide (PPS) Bonded Nd-Fe-B Permanent Magnets, Materials Science and Engineering: A, submitted. [4] Garrell, M. G., Mechanical Properties of Injection Molded Permanent Magnets, M.S. thesis, North Carolina State University, Raleigh, NC, April [5] Pilkey, W. D., Peterson s Stress Concentration Factors, 2nd ed., John Wiley & Sons, New York, [6] Wilson, L. H. and White, D. J. Stress-Concentration Factors for Shoulder Fillets and Grooves in Plates, Journal of Strain Analysis, Vol. 8, 1973, pp [7] Frocht, M. M. Factor of Stress Concentration Photoelastically Determined, Transactions of ASME, 1935, Vol. 57, pp. A-67 A-68. [8] Worthem, D. W., Flat Tension Specimen Design for Advanced Composites, NASA Technical Report CR , NASA Lewis Research Center, Cleveland, OH, [9] Shi, J., Brady, L., and Ireson, A., Design of Room Temperature Tension Specimen Made of Ceramic Matrix Composites, Key Engineering Materials, Vol , Trans Tech Publications, 1999, pp [10] Wang, Z, Chiang, C. K., and Chuang, T.-J., Optimum Design of a Ceramic Tensile Creep Specimen Using a Finite Element Method, Journal of Research of the National Institute of Standards and Technology, Vol. 102, 1997, pp [11] Oplinger, D. W., Parker, B. S., Gandhi, K. R., Lamothe, R., and Foley, G., On the Streamline Specimen for Tension Testing of Composite Materials, Recent Advances in Composites in the United States and Japan, ASTM STP 864, J. R. Vinson and M. Taya, Eds., ASTM International, West Conshohocken, PA, 1985, pp [12] McCrum, N. G., Buckley, C. P., and Bucknall, C. B., Principles of Polymer Engineering, 2nd ed., Oxford University Press, Oxford, [13] Courtney, T. H., Mechanical Behavior of Materials, 2nd ed., McGraw-Hill, New York, 2000.

### Structural Metals Lab 1.2. Torsion Testing of Structural Metals. Standards ASTM E143: Shear Modulus at Room Temperature

Torsion Testing of Structural Metals Standards ASTM E143: Shear Modulus at Room Temperature Purpose To determine the shear modulus of structural metals Equipment Tinius-Olsen Lo-Torq Torsion Machine (figure

### 5. 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

### Outline. 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

### Testing and Analysis

Testing and Analysis Testing Elastomers for Hyperelastic Material Models in Finite Element Analysis 2.6 2.4 2.2 2.0 1.8 1.6 1.4 Biaxial Extension Simple Tension Figure 1, A Typical Final Data Set for Input

### ME 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

### IMECE 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

### Burst pressure estimation of reworked nozzle weld on spherical domes

Indian Journal of Engineering & Materials Science Vol. 21, February 2014, pp. 88-92 Burst pressure estimation of reworked nozzle weld on spherical domes G Jegan Lal a, Jayesh P a & K Thyagarajan b a Cryo

### Stress-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.

### Practice 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

### Size Effects In the Crushing of Honeycomb Structures

45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference 19-22 April 2004, Palm Springs, California AIAA 2004-1640 Size Effects In the Crushing of Honeycomb Structures Erik C.

### Chapter 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

### BIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS

BIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS H. Kumazawa and T. Takatoya Airframes and Structures Group, Japan Aerospace Exploration Agency 6-13-1, Ohsawa, Mitaka,

### NORMAL 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

### SIZE EFFECTS IN THE COMPRESSIVE CRUSHING OF HONEYCOMBS

43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Con 22-25 April 2002, Denver, Colorado SIZE EFFECTS IN THE COMPRESSIVE CRUSHING OF HONEYCOMBS Erik C. Mellquistand Anthony M.

### Stress and Displacement Analysis of a Rectangular Plate with Central Elliptical Hole

Stress and Displacement Analysis of a Rectangular Plate with Central Elliptical Hole Dheeraj Gunwant, J. P. Singh mailto.dheerajgunwant@gmail.com, jitenderpal2007@gmail.com, AIT, Rampur Abstract- A static

### Nonlinear FE Analysis of Reinforced Concrete Structures Using a Tresca-Type Yield Surface

Transaction A: Civil Engineering Vol. 16, No. 6, pp. 512{519 c Sharif University of Technology, December 2009 Research Note Nonlinear FE Analysis of Reinforced Concrete Structures Using a Tresca-Type Yield

### MECHANICS 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:

### Stresses Analysis of Petroleum Pipe Finite Element under Internal Pressure

ISSN : 48-96, Vol. 6, Issue 8, ( Part -4 August 06, pp.3-38 RESEARCH ARTICLE Stresses Analysis of Petroleum Pipe Finite Element under Internal Pressure Dr.Ragbe.M.Abdusslam Eng. Khaled.S.Bagar ABSTRACT

### Failure analysis of serial pinned joints in composite materials

Indian Journal of Engineering & Materials Sciences Vol. 18, April 2011, pp. 102-110 Failure analysis of serial pinned joints in composite materials Alaattin Aktaş* Department of Mechanical Engineering,

### MECHANICS OF MATERIALS

2009 The McGraw-Hill Companies, Inc. All rights reserved. Fifth SI Edition CHAPTER 3 MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Torsion Lecture Notes:

### ANSYS Mechanical Basic Structural Nonlinearities

Lecture 4 Rate Independent Plasticity ANSYS Mechanical Basic Structural Nonlinearities 1 Chapter Overview The following will be covered in this Chapter: A. Background Elasticity/Plasticity B. Yield Criteria

### ME 243. Mechanics of Solids

ME 243 Mechanics of Solids Lecture 2: Stress and Strain Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil6791@gmail.com Website: teacher.buet.ac.bd/sshakil

### EMA 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

### A PAPER ON DESIGN AND ANALYSIS OF PRESSURE VESSEL

A PAPER ON DESIGN AND ANALYSIS OF PRESSURE VESSEL P.Palanivelu 1, R.Siva Prasad 2, 1 PG Scholar, Department of Mechanical Engineering, Gojan School of Business and Technology, Redhills, Chennai, India.

### ME 354, MECHANICS OF MATERIALS LABORATORY COMPRESSION AND BUCKLING

ME 354, MECHANICS OF MATERIALS LABATY COMPRESSION AND BUCKLING PURPOSE 01 January 2000 / mgj The purpose of this exercise is to study the effects of end conditions, column length, and material properties

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

### INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011

Interlaminar failure analysis of FRP cross ply laminate with elliptical cutout Venkateswara Rao.S 1, Sd. Abdul Kalam 1, Srilakshmi.S 1, Bala Krishna Murthy.V 2 1 Mechanical Engineering Department, P. V.

### Standard Practice for Heat Aging of Plastics Without Load 1

Designation: D 3045 92 (Reapproved 2003) Standard Practice for Heat Aging of Plastics Without Load 1 This standard is issued under the fixed designation D 3045; the number immediately following the designation

### Plasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur

Plasticity R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 9 Table of Contents 1. Plasticity:... 3 1.1 Plastic Deformation,

### University 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

### Plane Strain Test for Metal Sheet Characterization

Plane Strain Test for Metal Sheet Characterization Paulo Flores 1, Felix Bonnet 2 and Anne-Marie Habraken 3 1 DIM, University of Concepción, Edmundo Larenas 270, Concepción, Chile 2 ENS - Cachan, Avenue

### Standard Test Methods for Glass-Bonded Mica Used as Electrical Insulation 1

Designation: D 1039 94 (Reapproved 1999) e1 An American National Standard Standard Test Methods for Glass-Bonded Mica Used as Electrical Insulation 1 This standard is issued under the fixed designation

### Modelling 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

### Finite element simulations of fretting contact systems

Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 45 Finite element simulations of fretting contact systems G. Shi, D. Backman & N. Bellinger Structures and Materials

### 9 MECHANICAL PROPERTIES OF SOLIDS

9 MECHANICAL PROPERTIES OF SOLIDS Deforming force Deforming force is the force which changes the shape or size of a body. Restoring force Restoring force is the internal force developed inside the body

### Modelling 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

### Enhancing 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

### Solid Mechanics Chapter 1: Tension, Compression and Shear

Solid Mechanics Chapter 1: Tension, Compression and Shear Dr. Imran Latif Department of Civil and Environmental Engineering College of Engineering University of Nizwa (UoN) 1 Why do we study Mechanics

### FE Modeling of H-SECTION Connecting Rod

FE Modeling of H-SECTION Connecting Rod Virendra Kumar Verma,Shailendra Kumar, Ashish Gupta P.G Student, Department of Mechanical Engineering, Babu Banarasi Das University, Lucknow, India P.G Student,

### 7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment

7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment à It is more difficult to obtain an exact solution to this problem since the presence of the shear force means that

### A Finite Element Study of Elastic-Plastic Hemispherical Contact Behavior against a Rigid Flat under Varying Modulus of Elasticity and Sphere Radius

Engineering, 2010, 2, 205-211 doi:10.4236/eng.2010.24030 Published Online April 2010 (http://www. SciRP.org/journal/eng) 205 A Finite Element Study of Elastic-Plastic Hemispherical Contact Behavior against

### Chapter 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.

### Tensile stress strain curves for different materials. Shows in figure below

Tensile stress strain curves for different materials. Shows in figure below Furthermore, the modulus of elasticity of several materials effected by increasing temperature, as is shown in Figure Asst. Lecturer

### Life Prediction Under Multiaxial Fatigue

Lie Prediction Under Multiaxial Fatigue D. Ramesh and M.M. Mayuram Department o Mechanical Engineering Indian Institute o Technology, Madras Chennai-600 036 (India) e-mail: mayuram@iitm.ac.in ABSTRACT

### Effect Of The In-Situ Stress Field On Casing Failure *

Effect Of The In-Situ Stress Field On Casing Failure * Tang Bo Southwest Petroleum Institute, People's Republic of China Lian Zhanghua Southwest Petroleum Institute, People's Republic of China Abstract

### Volume 2 Fatigue Theory Reference Manual

Volume Fatigue Theory Reference Manual Contents 1 Introduction to fatigue 1.1 Introduction... 1-1 1. Description of the applied loading... 1-1.3 Endurance curves... 1-3 1.4 Generalising fatigue data...

### REPORT TO D-FLEX LTD APRIL 2009 REPORT. (to D-Flex Ltd, NWDA Innovation Vouchers Award, 28 April 2009)

REPORT (to D-Flex Ltd, NWDA Innovation Vouchers Award, 28 April 2009) Finite Element Modelling of Rigidity of Fishing Rods with Various Cross-sections Report to D-Flex Ltd by Z Guan Department of Engineering,

### SIMPLIFIED CONCRETE MODELING WITH *MAT_CONCRET_DAMAGE_REL3

SIMPLIFIED CONCRETE MODELING WITH *MAT_CONCRET_DAMAGE_REL3 Leonard E Schwer Schwer Engineering & Consulting Services, Windsor CA, USA and L. Javier Malvar Karagozian & Case Structural Engineers, Burbank

### DAMAGE MECHANICS MODEL FOR OFF-AXIS FATIGUE BEHAVIOR OF UNIDIRECTIONAL CARBON FIBER-REINFORCED COMPOSITES AT ROOM AND HIGH TEMPERATURES

DAMAGE MECHANICS MODEL FOR OFF-AXIS FATIGUE BEHAVIOR OF UNIDIRECTIONAL CARBON FIBER-REINFORCED COMPOSITES AT ROOM AND HIGH TEMPERATURES M. Kawai Institute of Engineering Mechanics University of Tsukuba,

### Module-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

### Brittle Deformation. Earth Structure (2 nd Edition), 2004 W.W. Norton & Co, New York Slide show by Ben van der Pluijm

Lecture 6 Brittle Deformation Earth Structure (2 nd Edition), 2004 W.W. Norton & Co, New York Slide show by Ben van der Pluijm WW Norton, unless noted otherwise Brittle deformation EarthStructure (2 nd

### Task 1 - Material Testing of Bionax Pipe and Joints

Task 1 - Material Testing of Bionax Pipe and Joints Submitted to: Jeff Phillips Western Regional Engineer IPEX Management, Inc. 20460 Duncan Way Langley, BC, Canada V3A 7A3 Ph: 604-534-8631 Fax: 604-534-7616

### Lecture #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

### Computational 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

### The Frictional Regime

The Frictional Regime Processes in Structural Geology & Tectonics Ben van der Pluijm WW Norton+Authors, unless noted otherwise 1/25/2016 10:08 AM We Discuss The Frictional Regime Processes of Brittle Deformation

### Mechanical 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

### Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test

Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test M. Praveen Kumar 1 and V. Balakrishna Murthy 2* 1 Mechanical Engineering Department, P.V.P. Siddhartha Institute of Technology,

### VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS

The 4 th World Conference on Earthquake Engineering October -7, 008, Beijing, China VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS K.

### Influence of fibre proportion and position on the machinability of GFRP composites- An FEA model

Indian Journal of Engineering & Materials Sciences Vol. 12, October 2005, pp. 443-450 Influence of fibre proportion and position on the machinability of GFRP composites- An FEA model D Abdul Budan* Department

### MAE 322 Machine Design Lecture 2. Dr. Hodge Jenkins Mercer University

MAE 322 Machine Design Lecture 2 Dr. Hodge Jenkins Mercer University Statics Load Failure Theories to Understand Maximum Normal Stress (MNS) Maximum Shear Stress (MSS) Distortion Energy (DE) Coulomb-Mohr

### Open-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

### STANDARD SAMPLE. Reduced section " Diameter. Diameter. 2" Gauge length. Radius

MATERIAL PROPERTIES TENSILE MEASUREMENT F l l 0 A 0 F STANDARD SAMPLE Reduced section 2 " 1 4 0.505" Diameter 3 4 " Diameter 2" Gauge length 3 8 " Radius TYPICAL APPARATUS Load cell Extensometer Specimen

### Bone Tissue Mechanics

Bone Tissue Mechanics João Folgado Paulo R. Fernandes Instituto Superior Técnico, 2016 PART 1 and 2 Introduction The objective of this course is to study basic concepts on hard tissue mechanics. Hard tissue

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

### Don Robbins, Andrew Morrison, Rick Dalgarno Autodesk, Inc., Laramie, Wyoming. Abstract

PROGRESSIVE FAILURE SIMULATION OF AS-MANUFACTURED SHORT FIBER FILLED INJECTION MOLDED PARTS: VALIDATION FOR COMPLEX GEOMETRIES AND COMBINED LOAD CONDITIONS Don Robbins, Andrew Morrison, Rick Dalgarno Autodesk,

### When you are standing on a flat surface, what is the normal stress you exert on the ground? What is the shear stress?

When you are standing on a flat surface, what is the normal stress you exert on the ground? What is the shear stress? How could you exert a non-zero shear stress on the ground? Hydrostatic Pressure (fluids)

### Study of Circular and Elliptical Holes as a Stress Relieving Feature in Spur Gear

Study of Circular and Elliptical Holes as a Stress Relieving Feature in Spur Gear Prof. S.B.Naik 1, Mr. Sujit R. Gavhane 2 Asst. Prof. Department of Mechanical Engineering, Walchand Institute of Technology,

MICROMECHANICAL ANALYSIS OF FRP COMPOSITES SUBJECTED TO LONGITUDINAL LOADING N. Krishna Vihari 1, P. Phani Prasanthi 1, V. Bala Krishna Murthy 2* and A. Srihari Prasad 3 1 Mech. Engg. Dept., P. V. P. Siddhartha

### EFFECT OF STRAIN HARDENING ON ELASTIC-PLASTIC CONTACT BEHAVIOUR OF A SPHERE AGAINST A RIGID FLAT A FINITE ELEMENT STUDY

Proceedings of the International Conference on Mechanical Engineering 2009 (ICME2009) 26-28 December 2009, Dhaka, Bangladesh ICME09- EFFECT OF STRAIN HARDENING ON ELASTIC-PLASTIC CONTACT BEHAVIOUR OF A

### [5] Stress and Strain

[5] Stress and Strain Page 1 of 34 [5] Stress and Strain [5.1] Internal Stress of Solids [5.2] Design of Simple Connections (will not be covered in class) [5.3] Deformation and Strain [5.4] Hooke s Law

### DEVELOPMENT 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

### A FINITE ELEMENT STUDY OF ELASTIC-PLASTIC HEMISPHERICAL CONTACT BEHAVIOR AGAINST A RIGID FLAT UNDER VARYING MODULUS OF ELASTICITY AND SPHERE RADIUS

Proceedings of the International Conference on Mechanical Engineering 2009 (ICME2009) 26-28 December 2009, Dhaka, Bangladesh ICME09- A FINITE ELEMENT STUDY OF ELASTIC-PLASTIC HEMISPHERICAL CONTACT BEHAVIOR

### Mechanical behaviour of wood in the orthotropic directions

Mechanical behaviour of wood in the orthotropic directions J.. Morais 1, J. C. Xavier 1, N. M. Dourado 1, J.. ousada 2 1 Departamento de Engenharias, ICETA/UTAD, Portugal 2 Departamento de Florestal, ICETA/UTAD,

### Effective stress assessment at rectangular rounded lateral notches

Focussed on characterization of crack tip fields Effective stress assessment at rectangular rounded lateral notches Enrico Maggiolini, Roberto Tovo, Paolo Livieri University of Ferrara Enrico.maggiolini@unife.it,

### LINEAR AND NONLINEAR BUCKLING ANALYSIS OF STIFFENED CYLINDRICAL SUBMARINE HULL

LINEAR AND NONLINEAR BUCKLING ANALYSIS OF STIFFENED CYLINDRICAL SUBMARINE HULL SREELATHA P.R * M.Tech. Student, Computer Aided Structural Engineering, M A College of Engineering, Kothamangalam 686 666,

### 3D 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

### Example-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

### Finite Element Analysis of Bicycle Crank

IJSTE - International Journal of Science Technology & Engineering Volume 3 Issue 10 April 2017 ISSN (online): 2349-784X Finite Element Analysis of Bicycle Crank Mohammed Asif Kattimani Assistant Professor

### The plastic behaviour of silicon subjected to micro-indentation

JOURNAL OF MATERIALS SCIENCE 31 (1996) 5671-5676 The plastic behaviour of silicon subjected to micro-indentation L. ZHANG, M. MAHDI Centre for Advanced Materials Technology, Department of Mechanical and

### Multi 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

### Influence of the filament winding process variables on the mechanical behavior of a composite pressure vessel

Influence of the filament winding process variables on the mechanical behavior of a composite pressure vessel G. Vargas 1 & A. Miravete 2 1 Universidad Pontificia Bolivariana, Facultad de Ingeniería Mecánica,

### Chapter 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

### Finite Element Analysis of Compression of Thin, High Modulus, Cylindrical Shells with Low-Modulus Core

Finite Element Analysis of Compression of Thin, High Modulus, Cylindrical Shells with Low-Modulus Core Robert S. Joseph Design Engineering Analysis Corporation, McMurray, PA ABSTRACT Long, cylindrical

### Tolerance Ring Improvement for Reducing Metal Scratch

International Journal of Scientific and Research Publications, Volume 2, Issue 11, November 2012 1 Tolerance Ring Improvement for Reducing Metal Scratch Pattaraweerin Woraratsoontorn*, Pitikhate Sooraksa**

### MECE 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.

### UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich

UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST

### Final Design Project: Biodiesel Settling Tank Analysis

MESSIAH COLLEGE ENGR 495 Finite Element Methods Tuesday, December 16, 2003 : Biodiesel Settling Tank Analysis Brandon Apple Jon Bitterman Becky Gast Kyle McNamara ENGR 495 Finite Element Methods 1 Abstract

### Lecture #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

### PRELIMINARY 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

### Influence of residual stresses in the structural behavior of. tubular columns and arches. Nuno Rocha Cima Gomes

October 2014 Influence of residual stresses in the structural behavior of Abstract tubular columns and arches Nuno Rocha Cima Gomes Instituto Superior Técnico, Universidade de Lisboa, Portugal Contact:

### Strength of Materials (15CV 32)

Strength of Materials (15CV 32) Module 1 : Simple Stresses and Strains Dr. H. Ananthan, Professor, VVIET,MYSURU 8/21/2017 Introduction, Definition and concept and of stress and strain. Hooke s law, Stress-Strain

### MECHANICS OF MATERIALS

Third CHTR Stress MCHNICS OF MTRIS Ferdinand. Beer. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech University and Strain xial oading Contents Stress & Strain: xial oading Normal

### Excerpt from the Proceedings of the COMSOL Conference 2010 Boston

Excerpt from the Proceedings of the COMSOL Conference 21 Boston Uncertainty Analysis, Verification and Validation of a Stress Concentration in a Cantilever Beam S. Kargar *, D.M. Bardot. University of

### Materials and Structures. Indian Institute of Technology Kanpur

Introduction to Composite Materials and Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 16 Behavior of Unidirectional Composites Lecture Overview Mt Material ilaxes in unidirectional

### Fatigue Algorithm Input

Methods Fatigue Algorithm Input By default, fe-safe analyses stress datasets that contain elastic stresses The calculation of elastic-plastic stress-strains, where necessary, is performed in fe-safe using

### Lecture #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

### INFLUENCE 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,