Читать книгу The Rheology Handbook - Thomas Mezger - Страница 193

As soon as the force is removed, the spring recoils elastically, and this means immediately, step-like and completely, returning to the initial state. No deformation remains finally at all.

Comparison: This is in contrast to a Newtonian liquid whose behavior can be illustrated using the dashpot model (see Chapter 2.3.1b).

Summary: Behavior of the spring model

Under a constant load, the spring deforms immediately and remains deformed as long as the load is applied. After removing the load, the previously occurring deformation disappears immediately and completely. In other words: After a load-and-removal cycle, an ideal-elastic material completely returns to the initial state.

Comparison: Metal spring and elasticity law

For tension and compression springs, the force/deflection law or elasticity law according to Hooke holds:

Equation 4.12

F = CH · s

with the spring force F [N], the spring constant CH [N/m] which is the rigidity of the spring and the index H is due to Hooke; and the deflection s [m] of the spring.

Here: F corresponds to the shear stress τ, CH corresponds to the shear modulus G, and s corresponds to the shear deformation γ.

Note: Elastic behavior , and stored deformation energy

Deformation energy acting on an ideal-elastic body during a shear process will be completely stored within the deformed material. When the load is removed, the stored energy can be recovered without any loss, enabling the complete reformation of the material. Therefore here, after deformation and reformation, a completely reversible process has taken place since the shape of the sample is unchanged after the experiment is finished.

For all materials showing ideal-elastic deformation behavior, there are interactive forces between their atoms or molecules. As examples for those very dense, stiff and rigid materials can be imagined stone and steel with crystalline structures at room temperature. If the linear-elastic range is exceeded, they show brittle fracture without any sign of time-dependent creep or creep recovery, e. g. in the form of very slow time-dependent deformation, partial reformation or stress relaxation, respectively. These kinds of materials do not show any visco-elastic behavior, since there is absolutely no viscous component available.

End of the Cleverly section