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Related Concept Videos

Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

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In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
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Shearing Stress01:18

Shearing Stress

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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.
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Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

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One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...
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Flexural Stress01:16

Flexural Stress

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When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
Hooke's Law states that within the material's elastic limits, stress is directly proportional to strain. In a member experiencing a bending moment, the strain at any point is relative to its distance...
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Shearing Strain01:20

Shearing Strain

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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...
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Plastic Deformation in Circular Shafts01:20

Plastic Deformation in Circular Shafts

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When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...
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Intertwined Multiple Spiral Fracture in Perforated Sheets.

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Cracks in thin sheets form radial patterns for four or more initial tears. Below four tears, fractures spiral, with a maximum of four spirals observed in this brittle sheet tearing study.

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Area of Science:

  • Materials Science
  • Fracture Mechanics
  • Physics of Soft Matter

Background:

  • Understanding fracture patterns in thin materials is crucial for predicting material failure.
  • The influence of initial crack geometry on macroscopic tearing behavior is not fully understood.

Purpose of the Study:

  • To investigate the mechanics of multiple tearing in thin, elastic, brittle sheets indented by a rigid cone.
  • To determine the relationship between the number of initial cracks and the resulting fracture patterns.
  • To develop a predictive model for spiral fracture formation.

Main Methods:

  • Experimental study of tearing thin elastic brittle sheets with a rigid cone indenter.
  • Analysis of crack propagation under varying numbers of initial symmetrical cracks (n).
  • Development and validation of a geometrical model for fracture mechanics.

Main Results:

  • Radial crack propagation observed for n≥4 initial cracks.
  • For n<4, fractures spontaneously form logarithmic spirals with n-fold rotational symmetry.
  • A geometrical model accurately predicts a maximum of 4 spirals, their growth rate, and perforation force for very thin sheets.
  • Similar spiral patterns were observed in a bending-dominated tearing experiment.

Conclusions:

  • The number of initial cracks dictates the transition from radial to spiral fracture patterns.
  • A simplified geometrical model effectively captures the complex fracture mechanics in the thin sheet limit.
  • The study reveals a universal limit of four spirals in this tearing configuration.