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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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Unsymmetric Loading of Thin-Walled Members: Problem Solving01:07

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The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
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Unsymmetric Loading of Thin-Walled Members01:23

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Thin-walled members with non-symmetrical cross-sections are vital to engineering structures, offering material efficiency and structural integrity. However, unsymmetrical loading on these members leads to complex stress distributions, resulting in simultaneous bending and twisting can cause deformation or structural failure. The interaction between bending and twisting requires detailed analysis to ensure structural resilience.
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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Elastic Strain Energy for Shearing Stresses01:20

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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...
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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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The tearing path in a thin anisotropic sheet from two pulling points: Wulff's view.

Alejandro Ibarra1, Benoît Roman2, Francisco Melo1

  • 1Departamento de Física Universidad de Santiago de Chile, Avenida Ecuador 3493, 9170124 Estación Central, Santiago, Chile. alejandro.ibarra@usach.cl francisco.melo@usach.cl.

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|June 11, 2016
PubMed
Summary

We developed a new method to predict crack propagation in polymers, accounting for material anisotropy. This approach accurately forecasts fracture paths and tearing forces, improving upon existing models.

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Area of Science:

  • Materials Science
  • Fracture Mechanics
  • Polymer Physics

Background:

  • Crack propagation in thin notched polymer sheets is influenced by material properties and applied forces.
  • Isotropic fracture energy models predict crack paths based on a tearing vector, but real materials exhibit anisotropy.
  • Anisotropy in thin sheets causes deviations from predicted crack paths, leading to cumulative errors in long fractures.

Purpose of the Study:

  • To develop a generalized criterion for predicting crack propagation in anisotropic thin polymer sheets.
  • To introduce a Wulff's type geometrical construction for determining crack trajectory and minimum tearing force.
  • To validate the proposed model through systematic experiments.

Main Methods:

  • Definition of an effective tearing vector for isotropic materials.
  • Generalization of the maximum energy released rate criterion to include anisotropy.
  • Application of Wulff's type geometrical construction for crack path and force prediction.

Main Results:

  • The generalized criterion accurately predicts crack trajectories in anisotropic polymer sheets.
  • The Wulff's type construction effectively determines the minimum force required for sustained tearing.
  • Experimental results show good agreement with the model's predictions for both fracture path and tearing force.

Conclusions:

  • Material anisotropy significantly affects crack propagation in thin polymer sheets.
  • The generalized maximum energy released rate criterion and Wulff's construction provide accurate predictions.
  • This work offers a more reliable method for analyzing and predicting fracture behavior in polymers.