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Published on: April 10, 2017
ON POWER EQUATIONS RELATING STRESS TO SHEAR RATE IN RHEOLOGY
1Grist Cottage, Iffley, Oxford, England.
Journal of Texture Studies
|April 4, 2017
Summary
Power equations are widely used in rheology despite dimensional challenges. This study reviews their history and potential applications in texture analysis.
Area of Science:
- Rheology
- Material Science
- Physics
Background:
- The historical application of power equations in rheology is reviewed.
- Dimensional inconsistencies associated with power-law models are discussed.
Purpose of the Study:
- To provide an overview of the historical usage of power equations in rheology.
- To explore potential applications of these equations in texture studies.
Main Methods:
- Literature review of power equation applications in rheology.
- Analysis of dimensional challenges in rheological models.
Main Results:
- The widespread use of power equations in rheology is noted, though a complete theoretical explanation remains elusive.
- Specific examples illustrating the application of power equations are presented.
Conclusions:
- The utility of power equations in rheology is acknowledged, particularly in specific contexts.
- Further investigation into the application of power equations for texture studies is suggested.
Related Concept Videos
01:18Shearing Stress
Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
01:15Stress: General Loading Conditions
To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes.
01:20Shearing Strain
The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
01:18Stresses in a Shaft
The shaft PQ is subjected to a twisting force when equal and opposite torques are applied on either side. A section that cuts perpendicular to the shaft's axis at any arbitrary point R is examined to understand this. When the free-body diagram of the QR segment is analyzed, it reveals the shearing forces exerted by the PR portion onto the QR segment as the shaft experiences twisting.
Applying equilibrium conditions to the QR segment establishes that the internal shearing forces within the...
Applying equilibrium conditions to the QR segment establishes that the internal shearing forces within the...
01:13Circular Shaft - Stresses in Linear Range
Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.
01:20Elastic Strain Energy for Shearing Stresses
As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...