ThermalStrainsandElementoftheTheoryofPlasticity.ppt

Thermal Strains and Element of the Theory of Plasticity Thermal Strains Thermal strain is a special class of Elastic strain that results from expansion with increasing temperature, or contraction with decreasing temperature Increased temperature causes the atoms to vibrate by large amount. In isotropic materials, the effect is the same in all directions. Over a limited range of temperatures, the thermal strains at a given temperature T, can be assumed to be proportional to the change, ?T. where T0 is the reference temperature (? = 0 at T0). The coefficient of thermal expansion, ?, is seen to be in units of 1/oC, thus making strain dimensionless. Since uniform thermal strains occur in all directions in isotropic material, Hooke’s law for 3-D can be generalized to include thermal effects. The theory of plasticity is concerned with a number of different types of problems. It deals with the behavior of metals at strains where Hooke’s law is no longer valid. From the viewpoint of design, plasticity is concerned with predicting the safe limits for use of a material under combined stresses. i.e., the maximum load which can be applied to a body without causing: Excessive Yielding Flow Fracture Plasticity is also concerned with understanding the mechanism of plastic deformation of metals. Plastic deformation is not a reversible process, and depends on the loading path by which the final state is achieved. In plastic deformation, there is no easily measured constant relating stress to strain as with Young’s modulus for elastic deformation. The phenomena of strain hardening, plastic anisotropy, elastic hysteresis, and Bauschinger effect can not be treated easily without introducing considerable mathematical complexity. A true stress-strain curve is frequently called a flow curve, because it gives the stress required to cause the metal to flow plastically to any given strain. The mathematical equation used to describe the stress-strain relationship is a power expressi