understanding_stress_and_strain - Part of MATERIALS SCIENCE...

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Understanding Stress & Strain Understanding Stress & Strain In these brief set of slides we try to get a grasp of tensile, compressive and shear stresses MATERIALS SCIENCE MATERIALS SCIENCE & ENGINEERING ENGINEERING Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email: [email protected], URL: home.iitk.ac.in/~anandh AN INTRODUCTORY E-BOOK Part of http://home.iitk.ac.in/~anandh/E-book.htm http://home.iitk.ac.in/~anandh/E-book.htm A Learner’s Guide A Learner’s Guide A Learner’s Guide Sorry, this will not help with worldly stresses!!!
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How do forces lead to stresses and strains? Can stress exist without strain and can strain exist without stress? How to ‘physically’ understand stress? Understanding stress and strain tensors in terms of their components. Hydrostatic and deviatoric components of stress and strain. Planes of maximum shear stress (role in plasticity). Understanding surface stress. Residual stress. Microstructural origins of residual stress. What will you learn in this chapter?
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In normal life we are accustomed to loads/forces and displacements . These are most appropriate variables when one talks about ‘point masses’, ‘rigid bodies’ or is sitting outside a body. Inside a body (typically a deformable body with mass and extent) , one can locate other (appropriate) ‘field variables’ to describe the state of the system. E.g. inside a gas kept in a cylinder, instead of tracking the velocities of the molecules, we come up with a field variable called pressure, which describes the momentum transferred by these molecules per unit area per unit time (pressure is a ‘time averaged’ macroscopic quantity). To understand the above point let us consider the ‘pulling’ of a body in tension (figure to right). Assume there is a weak plane (AA’), the two sides of which can slip past one another. We note as in the graphic that the inclined plane ‘shears’ even though we applied tensile forces . That is the plane feels shear stresses ( ). Hence, when we apply only tensile forces to the body (in the simple example considered) , ‘certain field’ develops within the body, which depending on the orientation of the plane in the body (or a unit volume being considered) can* undergo shear and/or dilatation. This field is the stress field and is a second order tensor with 9 components in general in 3D (4 in 2D). Stress and Strain A A’ * It may so happen that some planes do not feel any shear stresses (like the horizontal and vertical planes in in figures)
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Stress in 1D is defined as: Stress = Force/Area . This implies that in 1D stress is a scalar. Clearly, this is valid in 1D only, where a even a tensor looks like a scalar!!
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