Question

1. According to the deformation of materials under uniaxial tension and pure shear, please tell what kind of materials it is. (Undeformed plate is shown by broken line) Uniaxial Tension Pure Shear T. T. 2. What are the four independent engineering constants? 3. What is the difference between the specially orthotropic lamina and generally orthotropic lamina?

Answer 1

Ans. (1). (a) The Material shown in example (a) is Isotropic Material, as Isotropic MAterial Behaviour is independent of of Direction. As we can see in (a), Due to Normal stress normal strains are getting produced while Shear Strains are getting Produced by Shear Stress Only, which means deformation is independent of Direction. Hence this type of behaviour is of Isotropic Material.

(b) In example (b) the material is of Anisotropic Type as shown in figure b, uniaxial tension is showing tensional and shear deformations are getting generated, similarly Pure Shear Stress is also generating Tensional and Shear deformation, which means deformation is dependent of direction. Hence it is Anisotropic Material.

(c) In example (c) the material is of Orthotropic Material as we can see when the load is applied on material coordinates in the plane of Lamina, longitudinal coordinate gets aligned with the fiber reinforcement and transverse cordinate gets aligned normal to the fiber reinforcement. Also when load is applied to these coordinates, the material behaves like an Isotropic Material. Hence in example c, the material is Orthotropic One.

Ans. (2). The basic four engineering constants are:

Young's Modulus E, Moldulus of Rigidity G, Bulk Modulus K and Poisson 's Ratio v.

Ans. (3). As we know that in Orthotropic Material, 3 mutual Orthogonal planes of material property symmetry are there. The intersections of these 3 planes (of symmetry) give Principal Material directions.

An Orthotropic Material will be Specially Orthotropic if normal stresses are applied in the Principal Material directions. Whereas it would be Generally Orthotropic Material if it behaves like an Anisotropic Material i.e. which means deformations are dependent upon directions.