Equation of State for Solids For use in Manufacturing Usable form of EOS….. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi.

Slides:

Advertisements

Similar presentations

Modes of Work Transfer P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Development of Power for Different Needs!!!

Advertisements

III. Strain and Stress Strain Stress Rheology Reading Suppe, Chapter 3 Twiss&Moores, chapter 15.

General Concepts for Development of Thermal Instruments P M V Subbarao Professor Mechanical Engineering Department Scientific Methods for Construction.

1cs533d-term Notes  No lecture Thursday (apologies)

Stokes Law of Cause & Effect in VFF… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Deformation Law for Navier-Stokes Equations.

Basic Terminology • Constitutive Relation: Stress-strain relation

Behavior of Substance During A Process P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Selection of Substance for A Happening…..

Basic Concepts in Thermodynamics P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Thorough Familiarization of Simple Premises…..

Continuum Mechanics, part 4 Stress_1 Engineering and Cauchy First and second Piola-Kirchhoff Example for 1D strain and stress Green-Naghdi stress rate.

Constitutive Relations in Solids Elasticity

APPLIED MECHANICS Lecture 10 Slovak University of Technology

Department of Mechanical Engineering ME 322 – Mechanical Engineering Thermodynamics Lecture 6 Thermodynamic Diagrams Phase Change Determination of Properties.

Deformation of Solids Stress is proportional to Strain stress = elastic modulus * strain The SI unit for stress is the Newton per meter squared (N/m 2.

Electromagnetism 2004 Fall Reference: 《 Electromagnetism, principles and application 》 by P.Lorrain & D.Corson.

Thermodynamic Property Relations

Know Your Thermodynamic Systems P M V Subbarao Professor Mechanical Engineering Department I I T Delhi A Thorough Understanding of Your System will Make.

The Heat Conduction Equation P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi An Easy Solution to Industrial Heat Transfer.

Method to Use Conservations Laws in Fluid Flows…… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Mathematics of Reynolds Transport.

Microscopic Energy P M V Subbarao Professor Mechanical Engineering Department A Thermodynamic Property of Substances…..

Primary Elements of Engineering Thermodynamics P M V Subbarao Professor Mechanical Engineering Department I I T Delhi The First step to Develop Engineering.

Deduction of Fundamental Laws for Heat Exchangers P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Modification of Basic Laws for.

Basic Concepts in Thermodynamics Construction of Simple Premises ….. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi.

ME 520 Fundamentals of Finite Element Analysis

Department of Mechanical Engineering ME 322 – Mechanical Engineering Thermodynamics Lecture 3 Thermodynamic Concepts.

Rheology I. Rheology Part of mechanics that deals with the flow of rocks, or matter in general Deals with the relationship of the following: (in terms.

Analysis of Disturbance P M V Subbarao Associate Professor Mechanical Engineering Department I I T Delhi Modeling of A Quasi-static Process in A Medium.

Properties of Materials & Equation of State Mathematical Description of Material Behaviour….. P M V Subbarao Professor Mechanical Engineering Department.

Thermodynamics of Phase Change from Liquid to Vapor Description of most bountiful State of Matter ….. P M V Subbarao Professor Mechanical Engineering.

Stress and Strain Unit 8, Presentation 1. States of Matter  Solid  Liquid  Gas  Plasma.

Examples of Rigid Objects in Static Equilibrium.

Thermodynamic Work consumed during Manufacturing Processes P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Estimation of manufacturing.

ME 254. Chapter I Integral Relations for a Control Volume An engineering science like fluid dynamics rests on foundations comprising both theory and experiment.

Equation of sate for Liquids & vapours Essential Information for development of casting systems….. P M V Subbarao Professor Mechanical Engineering Department.

III. Strain and Stress Strain Stress Rheology Reading Suppe, Chapter 3

Chapter 12 Static Equilibrium and Elasticity. Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular.

Fluid Flows due to Pure Mechanical Forces… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Construction of Navier-Stokes Equations.

Department of Mechanical Engineering ME 322 – Mechanical Engineering Thermodynamics Lecture 5 Thermodynamic Properties.

Chapter 12 Static Equilibrium and Elasticity. Introduction Equilibrium- a condition where an object is at rest OR its center of mass moves with a constant.

Historically the First Fluid Flow Solution …. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Second Class of Simple Flows.

Dr. Wang Xingbo Fall ， 2005 Mathematical & Mechanical Method in Mechanical Engineering.

Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

PHYSICAL PROPERTIES OF MATTER Phases of Matter.

Thermodynamic Work P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Civilized methods for manufacturing works!!!

FLUID PROPERTIES Independent variables SCALARS VECTORS TENSORS.

Definitions ! Forces and Motion. Acceleration ! Acceleration is the rate of change of velocity, with respect to time. Velocity ! Velocity is the rate.

Powerful tool For Effective study and to Understand Flow Devices…… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Tensor Notation.

ME Manufacturing Systems Introduction To Manufacturing Systems by Ed Red Introduction To Manufacturing Systems by Ed Red.

Scalar-Vector Interaction for better Life …… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Vector Calculus for Fluid Mechanics.

To understand this cartoon, you have to be a physicist, but you must also understand a little about baseball! Elastic Properties of Solids Topics Discussed.

Unit 61: Engineering Thermodynamics Lesson 4: Properties of Pure Substances.

Micro & Macro Descriptions of Internal Energy P M V Subbarao Professor Mechanical Engineering Department Important Form of Energy for Engineering Systems.

Plots of Fluid Flow Data Profile plots- A profile plot indicates how the value of a scalar (or vector can be plotted but only the magnitude) property varies.

Thermodynamics of Ideal Processes P M V Subbarao Professor Mechanical Engineering Department Entropy View of Theoretical Processes …..

Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Summary of Energy Topics Chapter 1: Thermodynamics / Energy Introduction Chapter 2: Systems.

Continuum Mechanics (MTH487)

Solution of Thermodynamics: Theory and applications

Lecture 6: Elastic Deformation of laminates

Review for Final Exam Basic knowledge of vector & index notation, matrix-tensor theory, coordinate transformation, principal value problems, vector calculus.

Enthalpy & First Law for CVs

Equipartition of Energy

Thermodynamic Analysis of Ramjet Engines

Chapter 4 Revision.

Continuum Mechanics for Hillslopes: Part III

Review for Mid-Term Exam

Thermodynamic Description of A Manufacturing Process

Thermodynamics of Phase Change from Solid to Liquid

The Minimum Work/Energy for Manufacturing

Variation of Fluid Temperature in Heat Exchangers

Performance Analysis of Heat Exchangers

P M V Subbarao Professor Mechanical Engineering Department

Presentation transcript:

Equation of State for Solids For use in Manufacturing Usable form of EOS….. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi

The Need Knowledge of the equation of state {P V T - relation}, is of primary importance in Manufacturing. It provides insight into the nature of metal working/cutting theories, and determines the values of fundamental thermodynamic parameters.

Universal Equation of State for Solids where and V 0 is the volume of solid and B 0 is bulk modulus at reference pressure.

Constants of EoS ParameterGoldNaclXenon B 0 (10 10 Pa)  0 (10 -5 K -1 ) (  B/  p) – T R, K

A common equation of state for Solid V m = molar volume T = temperature p = pressure C 1, C 2, C 3, C 4, C 5 = empirical constants The empirical constants are all positive and specific to each substance. For constant pressure processes, this equation is often shortened to V mo = molar volume at 0 0 C A, B = empirical constants

p-V-T Diagram of crystalline solid Phase Volume Pressure Temperature

Thermodynamic Property Models for Manufacturing : Solids Manufacturing systems deal with three fundamental properties, namely: Stress Strain Temperature Unlike general thermodynamic Scalar EoS, manufacturing systems demands Tensor EoS. Basic definition of stress is:

Tensor Nature of Stress In 1823, the French mathematician, Augustin Baron Cauchy (1789– 1857) introduced the concept of stress by eliminating the difficulty that.σ is a function of two vectors, at the price that stress became a second- order tensor.

Stress Tensor

Definition of strain The strain can be specified by the displacement of each point in the solid from its position in some reference configuration. We treat the solid as a continuum, and consider only strains which are effectively uniform over distances of several atomic spacings. One Dimensional Strain:

Deformation of Solid

Three Dimensional Strain

Pure Translation of A Solid Projection

Translation & Rotation of A Solid Projection

Translation & Deformation of A Solid Projection

Translation, Rotation & Deformation of a Solid Projection

The strain Vs Rotation