Related Experiment Video
Updated: Jun 8, 2026
08:36
Fragility Assessment of Bovine Cortical Bone Using Scratch Tests
Published on: November 30, 2017
Fracture roughness in three-dimensional beam lattice systems.
Phani K V V Nukala1, Pallab Barai, Stefano Zapperi
1Oak Ridge National Laboratory, Oak Ridge, TN 37831-6164, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
This study on three-dimensional crack roughness in beam lattice systems reveals statistically isotropic crack surfaces. The findings suggest crack roughness is independent of system size, with a consistent roughness exponent.
Area of Science:
- Physics
- Materials Science
- Fracture Mechanics
Background:
- Understanding three-dimensional crack roughness is crucial for material science and fracture mechanics.
- Previous models suggested anisotropy in fracture surface roughness, but the underlying causes were debated.
Purpose of the Study:
- To investigate the scaling of three-dimensional crack roughness using large-scale beam lattice systems.
- To determine if crack surface roughness exhibits anisotropy and its dependence on system size.
Main Methods:
- Utilized large-scale beam lattice systems to simulate crack propagation.
- Analyzed crack surface statistics, including height differences and roughness exponents.
Main Results:
- Demonstrated that crack surfaces in beam lattice systems are statistically isotropic.
- Found no anomalous scaling or dependence of roughness on system size, unlike scalar fuse lattices.
- Estimated the three-dimensional crack roughness exponent (ζ) to be 0.48±0.03, matching external observations.
- Observed a Gaussian distribution for crack profile height differences.
Conclusions:
- The statistical isotropy of crack surfaces implies that experimental anisotropy findings are not due to the elasticity of the model.
- Beam lattice systems provide a more accurate representation of crack roughness scaling.
- The results align with experimental observations of crack profiles and roughness exponents.
Related Concept Videos
01:15Deformation of a Beam under Transverse Loading
Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
The insights from the bending moment diagram extend to...
The insights from the bending moment diagram extend to...
01:11Distribution of Stresses in a Narrow Rectangular Beam
In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these areas.
01:23Design of Prismatic Beams for Bending
The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and stress...
01:14Shearing Stresses in a Beam: Problem Solving
A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...
01:16Shear on the Horizontal Face of a Beam Element
To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's first...
01:15Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
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.