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Stress-Strain Diagram - Brittle Materials01:24

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Brittle materials, including glass, cast iron, and stone, exhibit unique characteristics. They fracture without considerable change in their elongation rate, indicating that their breaking and ultimate strength are equivalent. Such materials also show lower strain levels at the point of rupture. The failure in brittle materials predominantly results from normal stresses, as evidenced by the rupture created along a surface perpendicular to the applied load. These materials do not display...
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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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A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation
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Elastic Instability behind Brittle Fracture.

D Riccobelli1, P Ciarletta1, G Vitale2

  • 1MOX-Dipartimento di Matematica, <a href="https://ror.org/01nffqt88">Politecnico di Milano</a>, 20133 Milano, Italy.

Physical Review Letters
|July 1, 2024
PubMed
Summary
This summary is machine-generated.

Brittle crack nucleation in soft solids initiates from a nonlinear elastic instability, requiring precise finite deformation analysis. This instability involves large rotations and geometric sensitivity, preceding crack formation.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Fracture Mechanics

Background:

  • Understanding brittle fracture in soft elastic solids is crucial for material design and failure analysis.
  • Traditional models often fail to capture the complex phenomena preceding crack nucleation.
  • Finite elastic deformation and nonlinear instabilities play a significant role in material failure.

Purpose of the Study:

  • To investigate the role of nonlinear elastic instability in the nucleation of brittle cracks in soft solids.
  • To demonstrate that crack nucleation is preceded by a symmetry-breaking elastic instability.
  • To explore the post-bifurcational behavior and scale-dependent strain localization.

Main Methods:

  • Analysis of a homogeneous elastic body under tension with a free surface.
  • Incorporation of geometrically precise finite elastic deformation.
  • Utilizing a phase-field approach to model subcontinuum phenomena.

Main Results:

  • Brittle fracture emerges from a symmetry-breaking elastic instability involving large elastic rotations.
  • The instability exhibits strong sensitivity to geometry, unlike typical nonlinear elasticity.
  • Scale-dependent strain localization, signaling crack formation, is captured beyond continuum limits.

Conclusions:

  • Nonlinear elastic instability is a prerequisite for brittle crack nucleation in soft solids.
  • Finite deformation theory and geometric precision are essential for accurate fracture modeling.
  • The phase-field approach effectively captures subcontinuum effects leading to crack formation.