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Influence of material ductility and crack surface roughness on fracture instability

Khezrzadeh, H ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1088/0022-3727/44/39/395302
  3. Abstract:
  4. This paper presents a stability analysis for fractal cracks. First, the Westergaard stress functions are proposed for semi-infinite and finite smooth cracks embedded in the stress fields associated with the corresponding self-affine fractal cracks. These new stress functions satisfy all the required boundary conditions and according to Wnuk and Yavari's (2003 Eng. Fract. Mech. 70 1659-74) embedded crack model they are used to derive the stress and displacement fields generated around a fractal crack. These results are then used in conjunction with the final stretch criterion to study the quasi-static stable crack extension, which in ductile materials precedes the global failure. The material resistance curves are determined by solving certain nonlinear differential equations and then employed in predicting the stress levels at the onset of stable crack growth and at the critical point, where a transition to the catastrophic failure occurs. It is shown that the incorporation of the fractal geometry into the crack model, i.e. accounting for the roughness of the crack surfaces, results in (1) higher threshold levels of the material resistance to crack propagation and (2) higher levels of the critical stresses associated with the onset of catastrophic fracture. While the process of quasi-static stable crack growth (SCG) is viewed as a sequence of local instability states, the terminal instability attained at the end of this process is identified with the global instability. The phenomenon of SCG can be used as an early warning sign in fracture detection and prevention
  5. Keywords:
  6. A-stability ; Catastrophic failures ; Catastrophic fracture ; Crack extension ; Crack model ; Crack surfaces ; Critical points ; Critical stress ; Ductile materials ; Early warning signs ; Fractal cracks ; Fractal geometry ; Fracture detection ; Fracture instability ; Global failure ; Global instability ; Local instability ; Material resistance ; Nonlinear differential equation ; Quasi-static ; Self-affine fractals ; Stable crack growth ; Stress and displacements ; Stress field ; Stress functions ; Stress levels ; Threshold levels ; Boundary conditions ; Crack propagation ; Ductility ; Fractals ; Fracture ; Nonlinear equations ; Stability ; Surface roughness ; Cracks
  7. Source: Journal of Physics D: Applied Physics ; Volume 44, Issue 39 , 2011 ; 00223727 (ISSN)
  8. URL: http://iopscience.iop.org/article/10.1088/0022-3727/44/39/395302/pdf