Dr.R.Narayanasamy - Plastic instability in uniaxial tension
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This document discusses plastic instability in uniaxial tension testing of materials. It defines true stress and strain, which account for changes in cross-sectional area during tension, and explains how they relate to engineering stress and strain. The condition for plastic instability is derived as the maximum in the true stress-strain curve where the rate of true stress increase with respect to true strain is equal to the true stress. This occurs at a uniform true strain value called the instability strain. Examples of true stress-strain curves and determinations of the strain hardening exponent are also provided.
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The stress-strain curve is a graphical representation of the mechanical properties of a material under the influence of an applied force. It illustrates how a material deforms and responds to stress (force per unit area) as it undergoes strain (deformation).
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Plastic Deformation:
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311ch9
This document summarizes key concepts in stresses and strains from strength of materials including:
1) Definitions of stress as force per unit area and strain as deformation per original length. Common types of stress include axial/tensile, compressive, shear, and bearing stresses.
2) The proportional relationship between stress and strain for a material below its proportional limit, defined by modulus of elasticity E. Stress and strain can then be calculated from each other.
3) Examples calculating stresses, strains, and deformations in axially loaded members and bolts, finding required member sizes, and checking stresses are below limits.
stress strain sm
Mohamad Redhwan Abd Aziz is a lecturer at the DEAN CENTER OF HND STUDIES who teaches the subject of Solid Mechanics (BME 2023). The 3 credit hour course involves 2 hours of lectures and 2 hours of labs/tutorials each week. Student assessment includes quizzes, assignments, tests, lab reports, and a final exam. The course objectives are to understand stress, strain, and forces in solid bodies through various principles and experiments. Topic areas covered include stress and strain, elasticity, shear, torsion, bending, deflection, and more. References for the course are provided.
Strength of Materials _Simple Strees and Stains _Unit-1.pptx
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Young's modulus by single cantilever method
Young's modulus is a method to find the elasticity of a given solid material. The present article gives the explanation how to perform the experiment to determine the young's modulus by the use of material in the form of cantilever. The single cantilever method is used here.
Mechanical properties
This document discusses various mechanical properties that are important for selecting materials for structural components. It describes different types of mechanical tests like tension, compression, torsion, bending, impact and fatigue tests that are conducted on metal specimens to determine properties like strength, ductility and toughness. Specifically, it outlines the process for a uniaxial tension test including the equipment used, steps to conduct the test, and how to analyze the stress-strain diagram produced. It also discusses factors that influence mechanical properties like temperature, notches, grain size and hardness tests.
Unit 1 part 1 mechanics for AKTU 2021 first year ( KME 101T)
strictly as per AKTU syllabus for BTech first yr 2021
subject- fundamentals of mechanical and mechatronics
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Som complete unit 01 notes
This document provides an overview of strength of materials and introduces key concepts. It discusses stress and strain, ductile and brittle materials, and stress-strain diagrams. Stress is defined as the internal resisting force per unit area acting on a material. Strain is the ratio of change in dimension to the original dimension when a body is subjected to external force. Ductile materials show deformation under stress, while brittle materials do not. The stress-strain diagram shows the relationship between stress and strain for ductile and brittle materials.
Stress-strain.pptx
The document discusses stress and strain in engineering materials. It defines stress as the resistance force generated per unit area, and strain as the ratio of change in length under force to the original length. It describes different types of stress including tensile, compressive, and shear stress. It also defines important aspects of a stress-strain curve including elastic limit, yield points, ultimate tensile stress, and breaking stress. Hooke's law and Poisson's ratio are explained. Stress-strain curves for different materials are shown to illustrate how materials respond differently to stresses.
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The document discusses the mechanical properties of materials when subjected to different types of loading like axial, lateral, and torsional loads. It defines concepts like stress, strain, elastic and plastic deformation. It explains stress-strain diagrams and how they are used to determine properties like modulus of elasticity, yield strength, tensile strength, ductility, toughness, and resilience. Typical stress-strain behaviors of ductile and brittle materials are compared. Examples of determining properties from stress-strain curves are also provided.
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More from Dr.Ramaswamy Narayanasamy
Dr. R. Narayanasamy, Retired Professor (HAG) - Bio data with list of publicat...
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Dr. Ramaswamy Narayanasamy is a retired professor from the National Institute of Technology in Tiruchirappalli, India. He has over 40 years of experience in teaching and research related to metal forming, powder metallurgy, and mechanical behavior of materials. Some of his key accomplishments include authoring over 240 publications, guiding over 30 PhD students, and leading numerous research projects funded by government and industry. He is recognized as a top 2% scientist in India by Stanford University for his significant contributions to the field.Dr. R. Narayanasamy - Presentation on Formability of Deep Drawing Grade Steels
Dr. R. Narayanasamy - Presentation on Formability of Deep Drawing Grade SteelsDr.Ramaswamy Narayanasamy
Step 1: The document summarizes a presentation given by Dr. Ramaswamy Narayanasamy on the formability of deep drawing grade steels.
Step 2: It provides details of the speaker's achievements and scientific contributions related to sheet metal forming and formability studies on various steel grades.
Step 3: The presentation describes the methodology used to construct forming limit diagrams (FLDs), including the different strain conditions tested, grid circle marking on sheet specimens, measurement of strain after deformation, and plotting of the FLD curves.Dr. R. Narayanasamy - Forming and fracture behavior of stainless steel 430 gr...
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Presentation on Forming and fracture behavior of stainless steel 430 grade sheet metal by Dr. R. Narayanasamy, Retired Professor (HAG), Department of Production Engineering, NIT - TrichyDr.R.N. updated bio data with list of publications(28-08-2018)
1. The document is a resume for Dr. Ramaswamy Narayanasamy, a professor of production engineering at the National Institute of Technology in Tiruchirappalli, India.
2. It details his administrative and teaching experience, awards, research projects, publications, guided PhD candidates and areas of research expertise including sheet metal forming, forging, and mechanical behavior of materials.
3. He has over 240 publications, supervised 7 PhD candidates, led over 20 research projects, and has over 36 years of experience in industrial and academic fields.
Proof of ss 430 paper revised
The document analyzes the formability, fracture behavior, void coalescence, and texture of batch annealed (BA), continuous annealed (CA), and cold rolled (CR) 430 grade stainless steel sheets through tensile testing, forming limit diagrams, fractography, and texture analysis. Microstructural observations found elongated grains in the rolling direction, with average grain size decreasing in the order of CA, BA, and CR sheets. CA and BA sheets exhibited better formability than CR sheets based on forming limit diagrams and texture analysis, though CR sheets still showed satisfactory performance for certain applications.
Dr.R.N updated Bio-Data with list of publications(01-07-2016)
This document provides a summary of the qualifications and experience of Dr. Ramaswamy Narayanasamy, including his administrative and teaching experience, research projects completed, publications, courses attended, and PhD candidates advised. Specifically:
- He has over 36 years of experience in teaching and industry and currently works as a professor. Some of his past roles include department head and research positions.
- He has completed over 20 research projects in areas like sheet metal forming, forging, and composites. Many were government or industry funded.
- He has over 342 publications in international and national journals and conferences. He is also the author of 4 books.
- He has advised over 20 PhD candidates whose research
Dr.R.Narayanasamy - Effect of Microstructure on formability of steels - Modif...
Dr.R.Narayanasamy - Effect of Microstructure on formability of steels - Modif...Dr.Ramaswamy Narayanasamy
The document discusses the effect of microstructure on the formability of steels. It states that the amount of pearlite and ferrite phases affect formability, with pearlite decreasing ductility and ferrite increasing it. Finer pearlite and ferrite grain sizes increase strength but decrease formability. Spheroidizing pearlite increases ductility. The presence of inclusions like oxides and sulfides reduces ductility depending on their shape, size, and distribution. Globular inclusions perform better than elongated ones. The document also discusses how these microstructural factors affect the formability of different steel types like austenitic stainless steels.Dr.R.Narayanasamy - Bio data/resume.
1. Dr. Ramaswamy Narayanasamy is a professor at the National Institute of Technology in Tiruchirappalli, India with over 36 years of experience in teaching and industry.
2. He has extensive administrative and research experience, including serving as the head of the Production Engineering department and chairing committees. He has also completed numerous research projects for government and industry.
3. Dr. Narayanasamy has published over 242 papers in international journals and conferences. He has also authored 4 books. He has supervised over 30 PhD students to completion and currently has a student undergoing research.
Dr.R.Narayanasamy - Metal forming part - I.
The document discusses various aspects of metal forming processes including strain hardening, work hardening, annealing, cold working, hot working, and the effects of temperature and strain rate on formability.
Some key points include: Strain hardening occurs during metal forming at lower temperatures and increases flow stress. Work hardening is caused by an increase in dislocation density during plastic deformation. Annealing heat treats cold worked metals to restore ductility by reducing dislocation density. Cold working is done below the recrystallization temperature and causes strain hardening, while hot working allows recrystallization during forming. Temperature and strain rate impact formability, with higher temperatures and lower strain rates generally improving formability.
Dr.R.Narayanasamy - FLD on HSLA, IF steels and Al alloys.
This document discusses forming limit diagrams (FLDs) for different types of steel sheets, including interstitial free (IF) steels, HSLA steels, and aluminum alloys. It analyzes the FLDs for different thicknesses of IF steel sheets and examines the effects of thickness, coating, microstructure, and other properties on formability. The document also compares the formability of HSLA, microalloyed, and carbon-manganese steels based on their FLDs and considers the effects of properties like strain hardening exponent and anisotropy. Factors influencing void growth and fracture behavior under various stress conditions are also evaluated.
Dr.R.Narayanasamy - Mohr's circle and Formability
This document discusses Mohr's circle and its representation of different states of stress, including uniaxial tension and compression, biaxial tension and compression, triaxial tension and compression, and combined tension and compression. It also covers engineering stress-strain curves and how they are obtained from tensile testing. Key parameters like yield strength, tensile strength, ductility measures, and how the curve is influenced by material properties and prior processing are summarized. Videos are embedded to demonstrate some of the stress states and a wire drawing process.
Dr.R.Narayanasamy, Dr.S.Sivasankaran and Dr.K.Siva Prasad on Mechanical Alloying
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The document outlines a study on the synthesis, characterization, and workability behavior of nanocrystalline AA6061 alloy reinforced with TiO2 composite prepared by mechanical alloying. It describes the experimental procedures used to produce microcomposite and nanocomposite powders, and characterize their properties including morphology, particle size, flow characteristics, compressibility, and mechanical strength. The objectives are to investigate the effect of TiO2 reinforcement content and particle size on the composite properties and deformation behavior.Dr.R.Narayanasamy - Bending of sheet metals
This document discusses bending of sheet metals. It covers the following key points:
1) When a sheet metal is bent, a neutral axis forms along the center where there is no strain. The thickness of the metal decreases after bending.
2) As the bend radius decreases or the bend angle increases, the thinning of the metal increases. The minimum bend radius is dependent on factors like sheet thickness, metal properties, and bend angle.
3) Above the neutral axis the stress is tensile while below it is compressive. The circumferential strain is highest and non-uniform below a bend angle of 90 degrees.
4) When the bend is released, springback occurs where the bend radius increases as
Dr.R.Narayanasamy - Wrinkling Behaviour of Sheet Metals
This document summarizes research on the wrinkling behavior of pure aluminum, copper, and steel sheets during deep drawing processes. Tests were conducted using conical and tractrix dies on commercially pure aluminum grades annealed at different temperatures. Results show the aluminum grade ISS 19660 exhibited the best wrinkling resistance, while ISS 19000 showed the lowest. Higher annealing temperatures improved wrinkling resistance for all grades. The tractrix die also demonstrated better wrinkling suppression compared to the conical die. Charts and diagrams are presented comparing strain and stress ratios at wrinkling onset between die types and aluminum grades.
Dr.R.Narayanasamy - Formability of Automobile grade steels
The document discusses a research project analyzing the formability and wrinkling limits of various high strength steel sheets supplied by TATA Steel. Dr. R. Narayanasamy is the principal investigator, studying properties like tensile strength, forming limit diagrams, strain distribution, fractography, and texture. Tests were conducted on interstitial free steel, dual phase steel, and other varieties in thicknesses from 0.6mm to 2.0mm. Charts of chemical composition, microstructure, tensile properties, and forming limit diagrams are presented for each steel type.
Dr.R.Narayanasamy - Power Point on Formability of Stainless Steels
This document summarizes a study on the formability of various Indian stainless steel sheets formed under different stress conditions. Experimental work was conducted to determine the forming limit diagrams, microstructures, tensile properties, crystallographic textures and void characteristics of SS301, SS304, SS409M, SS430 and SSLN1 steel grades. Micrographs showed SS304 has a mixed grain structure while SS301 has coarse grains with carbides. Forming limit diagrams were plotted from strain measurements. Texture analysis was performed using X-ray diffraction. Void size, shape and spacing were analyzed from SEM images. Properties including yield strength, elongation and strain hardening exponent were calculated and correlated with formability.
Dr.R.Narayanasamy - Power Point on Powder Compaction
Triaxial compaction provides improved green density and strength over other compaction methods like unidirectional pressing and isostatic pressing. Applying both axial pressure and confining pressure during triaxial compaction allows independent control of stresses and improves density uniformity. Higher confining pressures and shear stresses lead to higher green densities and strengths for powder compacts.
Dr.R.Narayanasamy - Power Point on Deep Drawing
This document discusses deep drawing, a sheet metal forming process where a punch is used to push a flat sheet into a die cavity. It describes the typical tool setup, components made via deep drawing like cups and conical shapes, and calculations for blank diameter. Stress patterns in different regions during drawing are explained. Factors affecting drawability and defects in formed components like wrinkling and bottom fracture are also summarized. Formulas for total punch force and drawability ratio are provided. Methods to improve drawability like redrawing and controlling texture are outlined.
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Dr. R. Narayanasamy - Presentation on Formability of Deep Drawing Grade Steels
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Dr.R.Narayanasamy - Formability of Automobile grade steels
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Dr.R.Narayanasamy - Plastic instability in uniaxial tension
- 1. Plastic Instability in Uniaxial Tension By Dr. R. Narayanasamy, B.E.,M.Tech.,M.Engg.,Ph.D.,(D.Sc.), Professor, Department of Production Engineering, National Institute of Technology, Tiruchirappalli- 620 015 , Tamil Nadu, India.
- 2. True Stress vs Engineering Stress • Engineering Stress(s)=Load(P)/A0 A0 is the initial area of cross section of tensile sample. • True Stress(σ) =Load(P)/Ai Ai is the instantaneous area of cross section • In the Load-Extension graph, volume constancy principle can be applied upto the maximum load point.
- 3. Engineering Strain vs True Strain • Engineering Strain(e)= Change in length(Δl)/𝑙0 l0 is the initial gauge length of tensile sample. lf is the final or intermediate length of sample during tensile test. • Natural (or) True Strain(ϵ) = 𝑙0 𝑙 𝑓 𝑑𝑙 𝑙 • True Strain(ϵ) =ln(lf/l0) = ln((l0 + Δl)/l0) = ln(1+e)
- 4. Plastic Instability in Uniaxial Tension • Load(P) = σ A where σ is True Stress and A is instantaneous area of cross section. • Differentiating on the both sides, we get dP=dσ A + σdA • At maximum load, the value of dP = 0 . • The equation becomes: (dσ/σ) = -(dA/A).
- 5. Plastic Instability in Uniaxial Tension cont.. • For Constant Volume : A l = Constant . • Differentiating on both sides, we get dA l +A dl =0 This can be written as: -(dA/A) = (dl/l) = dϵ • Therefore, the above equation becomes: (dσ/σ) = dϵ This can be written as: (dσ/dϵ) = σ This is the condition for plastic instability.
- 6. True Stress vs True Strain Plot
- 7. Plastic Instability in Uniaxial Tension
- 8. True Stress vs True Strain • True Stress(σ) and True Strain(ϵ) can be related using Power Law equation according to Ludwik as follows: where σ is True Stress, ϵ is True Strain, n is strain hardening exponent and K is the strength coefficient. • Unit for True Stress and Strength coefficient is MPa (metric unit). • K and n are to be determined by curve fitting. σ = 𝐾ϵ 𝑛
- 9. Determination of K and n- values
- 10. Determination of K and n- values Strain hardening exponent (n) is the ratio of the physical distance (mm) of “a” by the physical distance (mm) of “b”. n – value has no unit. n – value represents the strain hardening ability of the material. n – value varies from 0.1 to 0.5 for conventional metals.
- 11. The effect of Strain hardening exponent on True stress -True strain
- 12. Typical K and n values for various metals
- 13. Plastic Instability in uniaxial tension We know that: Differentiating on both sides, we get: (Or) This can be written as: (Or)
- 14. Plastic Instability in uniaxial tension cont… At maximum load, (Or) Hence, the above expression becomes: Therefore, n = ε Where ε is the true uniform strain, which is denoted by the symbol έ.
- 15. Plastic Instability in uniaxial tension cont… It is important to note that rate of strain hardening is not identical with strain hardening exponent (n)value.
- 16. Plastic Instability in uniaxial tension The rate of strain hardening can be written as follows:
- 17. Plastic Instability in uniaxial tension Considere’s construction for the determination of the point of maximum load
- 18. Necking in uniaxial tension test illustration of diffuse necking and localized necking in case of sheet metal tensile specimen
- 19. Diffused necking & Localized necking • Necking in cylindrical specimen is symmetrical around tensile axis in case of isotropic • For sheet tensile specimen width is greater than thickness and two type of tensile instability occurs • Diffused necking: Its extension is greater than thickness. It will end in fracture and also it is followed by second instability (localized necking) • Localized necking: Neck is narrow width is approximately equal to thickness inclined at an angle to the specimen axis. • Localized necking corresponds to plane-strain deformation
- 20. Diffused necking & Localized necking cont…
- 21. Diffused necking & Localized necking cont…
- 22. Reference • Mechanical Metallurgy by George E.Dieter, McGraw – Hill Publication, London,1988.
- 23. Thank you