Damage dynamics, rate laws, and failure statistics via Hamilton’s principle

Joseph P. Cusumano, Arjun Roy, Qiang Li

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We present a new model for studying the coupled-field nonlinear dynamics of systems with evolving distributed damage, focusing on the case of high-cycle fatigue. A 1D continuum model is developed using Hamilton’s principle together with Griffith energy arguments. It captures the interaction between a damage field variable, representing the density of microcracks, and macroscopic vibrational displacements. We use the perturbation method of averaging to show that the nonautonomous coupled-field model yields an autonomous Paris-Erdogan rate law as a limiting case. Finite element simulations reveal a brittle limit for which the life cycle dynamics is dominated by leading-order power-law behavior. Space-time failure statistics are explored using large ensembles of simulations starting from random initial conditions. We display typical probability distributions for failure locations and times, as well as “(Formula presented.)” curves relating load to the number of cycles to failure. A universal time scale is identified for which the failure time statistics are independent of the applied load and the damage rate constant. We show that the evolution of the macro-displacement frequency response function, as well as the statistical variability of failure times, can vary substantially with changes in system parameters, both of which have significant implications for the design of failure diagnostic and prognostic systems.

Original languageEnglish (US)
Pages (from-to)77-98
Number of pages22
JournalMeccanica
Volume50
Issue number1
DOIs
StatePublished - Jan 1 2015

Fingerprint

Statistics
statistics
damage
Microcracks
Probability distributions
cycles
Frequency response
Macros
Life cycle
Rate constants
Fatigue of materials
universal time
microcracks
frequency response
simulation
continuums
perturbation
curves
interactions
energy

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Cusumano, Joseph P. ; Roy, Arjun ; Li, Qiang. / Damage dynamics, rate laws, and failure statistics via Hamilton’s principle. In: Meccanica. 2015 ; Vol. 50, No. 1. pp. 77-98.
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Damage dynamics, rate laws, and failure statistics via Hamilton’s principle. / Cusumano, Joseph P.; Roy, Arjun; Li, Qiang.

In: Meccanica, Vol. 50, No. 1, 01.01.2015, p. 77-98.

Research output: Contribution to journalArticle

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