Lab7-Mohr_s_Circle - Lab 7 - Mohrs Circle Mechanics of...

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Lab 7 - Mohr’s Circle Mechanics of Deformable Solids Laboratory Spring 2011 Introduction This experiment will investigate the two-dimensional strain state using a geometric tool known as Mohr’s Circle. Mohr’s Circle can help us visualize the strain state in a planar object. Two-dimensional stress/strain state On a two-dimensional plane, a strain state consists of two normal strains and one shear strain. In the x-y coordinate system, this would be ε x, ε y, and γ xy as shown in Figure 1. = y yx xy x εγ γε ε Figure 1. Plane strain and corresponding strain tensor representing the state of strain Experimentally we can measure these strains using a strain gage rosette. A gage rosette is simply three strain gages arranged along three different directions. In Figure 2, the most common rosette configuration of 0 ° , 45 ° and 90 ° is aligned in such a way that the 0 ° gage lies on the x-axis while the 90 ° gage lies on the y-axis. Figure 2. Strain gage rosette and a rosette applied to a dog-bone shaped specimen Within the above configuration, the transverse and axial strain will be measured by the gages in the 0 ° and 90 ° directions, respectively. It is important to note that shear strain 1
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cannot be directly measured. Instead, it is calculated using three strain measurements from all gages as follows 90 0 45 2 ε γ = xy ( 1) Once the three strain components, ε x, ε y, and γ xy are determined, a set of relationships known as the Transformation Equations are used to calculate the state of strain at any arbitrary orientation. This is important for the purpose of failure analysis in ductile materials, because it is often required to determine the planar orientation in which maximum shear strains occur. Strain Transformation Equations
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Lab7-Mohr_s_Circle - Lab 7 - Mohrs Circle Mechanics of...

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