Laws of Plastic Flow and Film Theories of Plasticity

After reading this article you will learn about the laws of plastic flow and film theories of plasticity.

Laws of Plastic Flow:

The essential difference between viscous and plastic flow is that a certain amount of stress must be added to plastic soils before flow is produced (Fig. 8.1).

The following equation shows that the volume flow is a function of the force applied.

V = Kµ (F – f)

where, V = volume of flow

µ = co-efficient of mobility

F = applied force

F = force necessary to overcome the cohesive forces of the system and just enough to start the flow (this force is termed “Yield value”)

K = constant.

The flow of viscous nature when the value of f is 0 (Fig. 8.1) and then the volume of flow is proportional to the applied force and the co-efficient of viscosity of the liquid. Curve AB shows the viscous flow and it increases directly with the applied pressure.

Curve APQR shows a plastic flow and here a certain force is applied to start the flow and then flow is proportional to the applied force (as shown in segment QR). The yield value is obtained by extrapolating the segment QR to the point S on the abscissa. The magnitude of yield value is correlated with the extent of the cohesive forces of the water films between the particles.

Film Theories of Plasticity:

The colloidal clay particles in the soil act as a lubricant between coarser particles and diminish their friction. It is highly probable that the plate shaped particles are oriented in such a way that their flat surfaces are in contact. This orientation increases the amount of contact between the colloidal particles.

The increased contact together with the raising of the ratio of water-film surface to the particle mass maybe considered as producing the plastic effects.

Within a certain moisture range, the tension effects of the water films between the oriented plate-like colloidal particles, which impart to the soil its cohesion phenomenon, enable the soil to be molded into any deformed shape. This moisture range corresponds to the range of plasticity of a soil.

Orientation of particles and their subsequent sliding over each other takes place when sufficient water has been added to provide a film around each particle. The amount of water required to produce these films corresponds to the moisture content at which the soil ceases to be friable.

With an excess of water, the water films become so thick that the cohesion between particles decreases and the soil mass becomes viscous and flows.

When the amount of adsorbed water in the soil system reaches a moisture content corresponding to that of the lower limit of plastic consistency, the particles become oriented when pressure is applied. The tension of the absorbed water films holds the adjacent oriented particles together.

As the pressure is increased above that of the tension of the films, the particles slide over each other. After the pressure is removed, the particles do not return to their original positions because they are held in place in their new positions by the tension of the moisture films.

Cohesion is a function of the number of films and it can be applied to plate shaped particles.

The cohesive force of a water film between two particles is given by the following formula:

F = K 4πr T cos α/d

where, K = constant

r = radius of the particles

T = surface tension,

α = angle of contact between the liquid and the particle (generally assumed to be zero)

d = distance between particles

F = cohesive force.

The cohesive force should vary inversely with the moisture content for a given size and number of particles. Cohesion increases up to a maximum and then decreases rapidly as the moisture content of the soil is raised which results thickening of water films. Maximum contact between particles results high cohesion due to inter particle attractions. Maximum cohesion increases with the clay content of the soil.

So for the development of plasticity in the soil system, the two conditions must be satisfied:

(i) Enough water must be added to provide for the formation of rigid layers of water on the adjacent colloidal surfaces, and

(ii) There must be enough extra water to serve as a lubricant between the rigid water layers when the system is subjected to a small deforming stress.

The thickness of the films is a function of the nature of the clay mineral, which determines the amount of water that is adsorbed before a distinct film around each point of contact is formed and the quantity of water added to the system.