Mechanics of solids simple stress and strain part 1. The firm line denotes engineering stress strain plot where as the dotted line is the true stress strain plot. Mar 23, 2020 stress is defined as a force that can cause a change in an object or a physical body while a strain is a change in the form or shape of the object or physical body on which stress is applied. Civl 78117 chapter 6 plane stressplane strain stiffness equations part 1. Engineering stress true stress engineering strain true strain. Modulus of elasticity, poisons ratio, shear modulus etc. Unit 1 stress and straintopics covered lecture 1 introduction, state of plane stress lecture 2 principle stresses and strains lecture 3 mohrs stress circle and theory of failure lecture 4 3d stress and strain, equilibrium equations and impact loading lecture 5 generalized hooks law and. Stress strain relation considering thermal effects. Stressstrain relationship, hookes law, poissons ratio, shear stress, shear strain, modulus of rigidity. A number of forces are acting on this body in different directions but the net force the vector sum of the forces on the body is 0. Mechanics of solids simple stress and strain simple stress and strain part 1. Stress and strain study notes for mechanical engineering.
Strain energy elastic strain energy, u energy spent by the external forces in deforming an elastic body du0. Nptel syllabus experimental stress analysis video course course outline the course covers the basic aspects of experimental stress analysis that includes exhaustive treatment of the most versatile techniques like photoelasticity and strain gauges and also a brief introduction to the emerging techniques like digital image correlation. Relationship between material properties of isotropic materials. Mechanical engineering advanced strength of materials nptel. For any state of stress, we can find a set of planes on which only normal stresses act and the shearing stresses are zero. The stress can be measured and has a unit of measure while strain. Stressstrain curve for this material is plotted by elongating the sample and recording the stress variation with strain until the sample fractures. Strain approximationin terms of straindisplacement matrix stress approximation summary. Stressstrain curves david roylance department of materials science and engineering massachusetts institute of technology cambridge, ma 029 august 23, 2001. E106 stress and strain tensor summary page 7 for yielding to occur.
The three invariants are given by the roots of the following equation. No matter what stresses are imposed on an elastic body, provided the material does not. This number is a function of many variables, including stress level, stress state, cy. Ghosh, dept of metallurgical and materials engineering be divided into elastic and plastic parts. Introduction free body diagram revisited normal, shear and bearing stress stress on inclined planes under axial loading strain mechanical properties of materials true. Nptel video lectures, iit video lectures online, nptel youtube lectures, free video lectures, nptel online courses. Here, the fully three dimensional stress state is examined. Unit 1 stress and straintopics covered lecture 1 introduction, state of plane stress lecture 2 principle stresses and strains lecture 3 mohrs stress circle and theory of failure lecture 4 3d stress and strain, equilibrium equations and impact loading lecture 5 generalized hooks law and castiglionos. Stress strain curves david roylance department of materials science and engineering massachusetts institute of technology cambridge, ma 029 august 23, 2001. Stress strain curve of mild steel bar in tension created by aman.
For the most part, the discussion was confined to twodimensional states of stress. By convention, the strain is set to the horizontal axis and stress is set to vertical axis. Stress is a directed force distributed over an area. Strain,% stress,mpa toughness,mjm 3kgm jkg ancientiron 0. The stress can occur without strain, but strain cannot occur with the absence of stress. Nptel video lectures, iit video lectures online, nptel youtube lectures. Stress and straindefinition, curve or diagram, formula, pdf. Modulus of elasticity e elastic materials always spring back into shape when released. Shear strain is the complement of the angle between two initially perpendicular line segments. This notes are best for strength of material subject. Stresses in terms of the original xy reference frame used to form the element equations and the n and b matrices. Ppt stress and strain powerpoint presentation free to.
Stress is defined as a force that can cause a change in an object or a physical body while a strain is a change in the form or shape of the object or physical body on which stress is applied. The relationship of stress and strain for steel can be observed in the following movie. Strain effects on flow stress and hence on extrusion pressure are predominant for hot extrusion. We are satisfied with engineering stress strain diagrams since this is good enough to estimate these.
The stressstrain curve depends on two types of material. Module 3 constitutive equations learning objectives understand basic stressstrain response of engineering materials. Both mathematical and engineering mi stakes are easily made if this crucial difference is not recognized and understood. If the material is subjected to torsion, it results in torsional strain. Ductile materials are materials that can be plastically twisted with no crack. This expression is identical in form with the equation defining the direct stress on any inclined plane q with ix and iy replacing sx and sy and. Second invariant, i2, is the sum of principal minors third invariant, i3, is the determinant of the matrix. Lecture 2 principal stress and strain linkedin slideshare. Bhattacharyya, department of civil engineering, iit kharagpur. Stresses, however, cannot be directly measured, but stain is measurable and can be directly related to stress. Constant strain triangle cst recommendations for use.
The true stress is defined as the ratio of the load to the crosssection area at any instant. Quantify the linear elastic stressstrain response in terms of tensorial quantities and in particular the fourthorder elasticity or sti ness tensor describing hookes law. To determine the shear stain in the direction om consider the displacement of point p at the foot of the. There will be some repetition of the earlier analyses. As the engineering design of different components, structures etc. Straindisplacement, stressstraintemperature, and stressequilibrium. A free powerpoint ppt presentation displayed as a flash slide show on id. For each element element stiffness matrix element nodal load vector u n d. In most crystals, slip occurs with equal ease forward or backward, so a characteristic shear stress is required for slip. Strength of material som notes free pdf download strength of material notes by prof. Nptel mechanical engineering forming joint initiative of iits and iisc funded by mhrd page 4 of. Above this point, stress is no longer linearly proportional to strain. Lecture 6 numerical problems on shear strain, modulus of rigidity lecture 7 stressstrain diagram for uniaxial loading of ductile and brittle materials. But strength models are often intimately related to stress.
Definitionof prameters related to material properties. Stress required for forming, yield or flow stress therefore depends on several factors, such as strain, strain rate, temperature etc. Mechanical engineering strength of materials nptel. This lecture includes following topics what is stress. Imagine an arbitrary solid body oriented in a cartesian coordinate system.
Concepts of stress and strain one of our principal concerns in this course is material behavior strength. Definition of stress, stress tensor, normal and shear stresses in axially loaded members. Aug 08, 2011 lecture 2 principal stress and strain 1. Stressstrain curves david roylance department of materials science and engineering massachusetts institute of technology cambridge, ma 029. Basic concepts of stress and strain since compliant mechanisms are used for mems devices, there is a significant need to understand the mechanics of materials.
The truestresstruestrain curves are obtained by converting the tensile stress and its corresponding strain into true values and extending the curve. Lecture notes mechanics and materials ii mechanical. Lecture 1 stresses and strains linkedin slideshare. They have the tendency to hold the deformation that occurs in the plastic region. The above geometrical data the strains will be multiplied by material properties to define a new physical. Stressstrain testing tension tests engineering stress engineering strain compression tests a0. Aug 08, 2011 unit 1 stress and straintopics covered lecture 1 introduction, state of plane stress lecture 2 principle stresses and strains lecture 3 mohrs stress circle and theory of failure lecture 4 3d stress and strain, equilibrium equations and impact loading lecture 5 generalized hooks law and castiglionos.
The fe solution was based on the approximate linear displacement. Hookes law, poissons ratio, shear stress lecture 5 shear strain, modulus of rigidity, bulk modulus. The stress tensor the secondorder tensor which we will be examining has. Civl 78117 chapter 6 plane stress plane strain stiffness equations part 1 1181. An assessment of the true stresstrue strain curve provides a realistic characteristic of the material. Note that for engineering purposes we often assume the crosssection area of the material does not change. Materials are subjected to complex states of stresses during forming. It is defined as the ratio of change in dimensionmight be length,dia etc. Consider a crystal with acrosssectionalareaa 0 being deformed in tension by an applied force f along the axis of the cylindrical crystal. Normal stresses cause linear strains, while the shear stresses cause shear strains.
This curve is a behavior of the material when it is subjected to load. However for metal working we need to know the true stress versus true strain plots. Examples on calculation of strains and tractions, principal stresses and. Basic concepts of stress and strain mechanics of materials describes how solid materials will deform change shape and how they will fail break when subjected to applied forces. Prediction of fatigue life the fatigue life of any specimen or structure is the number of stress strain cycles required to cause failure.
Normal strain is the change in length in a given direction divided by the initial length in that direction. The mechanical properties that we look for the selection of metals and alloys for a given application are the yield strength or the tensile strength. Apr 08, 2018 engineering stress true stress engineering strain true strain. Nptel mechanical engineering forming joint initiative of iits and iisc funded by mhrd page 3 of 9 further analysis and extrusion defects 1. Strain life continued the apparent poor fit of the coffinmanson relationship in figure 1 is due to the narrow strain range of the gathered data, demonstrating a caveat of the strainlife method. We can recover any stressstrain information using the given the node displacements, including. Nptel mechanical engineering forming joint initiative of iits and iisc funded by mhrd page 4. On stress strain curve, proportional limit is shown by p. There is no relationship exists in between stress and strain of the. Strength of materials is a fundamental subject needed primarily for the students of mechanical sciences.