Viscoelasticity Introduction PDF

21. Introduction to viscoelasticity 21.1 Definitions Elastic deformation: temporary deformation under external force (recovering shape after removing the force or load.) Stress (symbol: σ) : the force applied to a material per unit area. (Unit: N/m2) Strain (symbol: e): relative deformation when...

21. Introduction to viscoelasticity 21.1 Definitions Elastic deformation: temporary deformation under external force (recovering shape after removing the force or load.) Stress (symbol: σ) : the force applied to a material per unit area. (Unit: N/m2) Strain (symbol: e): relative deformation when forces are applied to a material. For example, a thin rod of material of length l is extended a small amount δl by an externally applied stress. In this case, the strain e can be represented by e = δl/l. Hooke’s law: stress is proportional to strain. Hooke’s law enables us to define Young’s modulus E of a material that for simple uniaxial extension or compression is given by E=stress/strain. at low strains, polymer deformation obeys Hooke’s Law, i.e., linear elastic deformation. 𝑑𝜎 𝑑𝑒 𝜎 = 𝐸𝑒 𝑜𝑟 =𝐸 𝑑𝑡 𝑑𝑡 Newtonian fluid: viscous liquids obey Newton’s law whereby the stress is proportional to the strain-rate and independent of the strain. 𝑑𝑒 𝜎=𝜂 𝑑𝑡 Where η is the viscosity; de/dt is the strain rate. 21.2 Elastic deformation of polymers 1 The most striking feature of the elastic properties of polymer fibers is that they are very anisotropic. The moduli parallel to the chain direction are ∼1011 Pa, which is similar to the values of moduli found for metals (e.g., steel, E≈2.1 × 1011 Pa) 21.3. Viscoelasticity The behavior of most polymers can be thought of as being somewhere between that of elastic solids and viscous liquids. At low temperatures and high rates of strain they display elastic behavior, whereas at high temperatures and low rates of strain they behave in a viscous manner, flowing like a liquid. Polymers are, therefore, termed viscoelastic as they display aspects of both viscous and elastic types of behavior. 2 Figure a: During creep loading, a constant stress is applied to the specimen at t = 0 and the strain increases rapidly at first, slowing down over longer periods of time. (deform permanently under constant stress) Figure b: stress relaxation: the strain is held constant and the stress decays slowly with time/ Figure c: The effect of deforming a viscoelastic material at a constant stress rate Figure d: The effect of deforming a viscoelastic material at a constant strain rate. 3