Introduction to Elasticity Part 12 docx

... Analogously to the way an inchworm moves, only those atoms lying in a plane above a single line might be displaced one atomic spacing. This would force the plane of atoms previously there into a midway ... free volume and more hindrance to molecular motion. The effect of this modification is to slide the von Mises ellipse to extend less into the I quadrant and more into the III quadrant...

Ngày tải lên: 11/08/2014, 09:21

... used today. Eventually, we’ll likely be ordering steel rod using inches rather than meters, so we’ll convert the MPa to psi rather than convert the pounds to Newtons. Also using A = πd 2 /4 to ... the loads to be applied to the structure are known at the outset, and we wish to compute how much material will be needed to support them. As a very simple case, let’s say we wish to...

Ngày tải lên: 11/08/2014, 09:20

... stretches to λ d , after which the engineering stress there would have to rise to stretch it further. But this stress is greater than that needed to stretch material at the edge of the neck from λ Y to ... material, but it is also possible to arrange for them to be oriented preferentially in the direction expected to have the highest stresses. Such a material is said to be a...

Ngày tải lên: 11/08/2014, 09:20

... force vector F: T = r × F (6) This vector is in a direction given by the right hand rule, and is normal to the plane containing the point O and the force vector. The torque tending to loosen ... cross-sectional dimension b × h, are to be glued together using a tongue-and-groove joint as shown in Fig. 3, and we wish to estimate the depth d of the glue joint so as to make the joint ap...

Ngày tải lên: 11/08/2014, 09:20

... pseudovector form. This relation serves to define the stress concept as an entity that relates the traction (a vector) acting on an arbitrary surface to the orientation of the surface (another vector). ... planes to appear at ±45 ◦ to the chalk’s long axis. The crack will appear transverse to the principal tensile stress, producing a spiral-like failure surface. (As the crack progres...

Ngày tải lên: 11/08/2014, 09:21

... materials:       1  2 γ 12      =    1/E 1 −ν 21 /E 2 0 −ν 12 /E 1 1/E 2 0 001/G 12         σ 1 σ 2 τ 12      (11) The parameter ν 12 is the principal Poisson’s ratio; ... said to be orthotropic. 6 Constitutive Equations David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 October 4, 20...

Ngày tải lên: 11/08/2014, 09:21

... radius r 1 to r 2 over the length L. We wish to determine the deflection caused by a force F applied to the free end of the beam, at an angle θ from the horizontal. Turning to Maple to avoid the ... moments of inertia of the individual parts of the compound area with respect to their own centroids are just ab 3 /12 and cd 3 /12. These moments can be referenced to the horizonta...

Ngày tải lên: 11/08/2014, 09:21

... Axes It is important to be able to transform the axes to and from the “laboratory” x − y frame to a natural material frame in which the axes might be labeled 1 − 2 corresponding to the fiber and transverse ... the adaptation to viscoelastic response consists of adding the following steps. 3. The current ply stress σ k 12 in the 1-2 directions is: σ k 12 = D [ p e 12 +( p lc...

Ngày tải lên: 11/08/2014, 09:21

... the stress intensity factor, with units of Nm −3/2 or psi √ in. (The factor π seems redundant here since it appears to the same power in both the numerator and denominator, but it is usually included ... be extremely difficult to fit solutions of the governing equations to them. One approach to this impasse is the experimental one, in which we seek to construct a physical laboratory mo...

Ngày tải lên: 11/08/2014, 09:21

... characteristic time for relaxation τ , by a factor equal to the ratio of the glassy to the rubbery modulus. This is a general result, not restricted to the particular model used. A less awkward form ... initially to the “glassy” compliance C g ; this is the elastic deformation corresponding to bond distortion. In time, the compliance rises to an equilibrium or “rubbery” value C r...

Ngày tải lên: 11/08/2014, 09:21