The residual stress state due to a spherical hard-body impact


*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

136 Citations (Scopus)


The current study assesses the residual stresses and remnant damage caused by a spherical projectile impacting upon a flat surface. The immediate application of this information is to the problem of foreign object damage (FOD) associated with the ingestion of debris into an aircraft turbine engine and the subsequent reduction in component lifetime. The work is focused on two primary features: (i) the development of numerical models for the evaluation of the deformation and stresses associated with the impact process and (ii) the use of spatially resolved residual stress measurements to verify experimentally the numerical analysis. As a first approximation, a quasi-static numerical model was developed by ignoring time-dependent effects (i.e., strain-rate sensitivity, wave and inertia effects, etc.), where the effects of velocity were approximated by adjusting the depth and diameter of the resulting impact crater to match that of actual impact craters at the corresponding velocity. The computed residual stresses and associated elastic strain gradients were compared to experimentally measured values, obtained using synchrotron X-ray diffraction (XRD) methods. This comparison indicated that the quasi-static numerical analysis was adequate for moderate impact conditions (velocity = 200 m/s, energy = 2.7 J); however, under more aggressive conditions (velocity = 300 m/s, energy = 6.1 J), there was significant discrepancy between the numerical predictions and experimental measurements. Such discrepancy may be attributed to several factors that can occur at higher impact velocities, including strain-rate sensitivity, microcrack formation, and shear-band formation. A dynamic simulation, where the time-dependent effects of strain-rate sensitivity and elastic-wave interactions were approximated, provided results in closer agreement with the experimental diffraction observations. © 2001 Published by Elsevier Science Ltd.
Original languageEnglish
Pages (from-to)441-454
Number of pages14
JournalMechanics of Materials
Issue number8
Publication statusPublished - Aug 2001
Externally publishedYes

Bibliographical note

This work was supported by the US Air Force Office of Scientific Research under Grant No. F49620-96-1-0478 under the auspices of the Multidisciplinary University Research Initiative on High Cycle Fatigue to the University of California (for numerical modeling and fatigue analysis), the Office of Science, US Department of Energy under contract #DE-AC03-76SF00098 (for experimental diffraction results), and the Stanford Synchrotron Radiation Laboratory, operated by the Department of Energy, Office of Basic Energy Sciences (for X-ray beamtime). BLB acknowledges the financial support of the Hertz Foundation in the form of a fellowship. Thanks are due to Dr. J.O. Peters for performing the ballistic impacts, to Dr. J.M. McNaney for assisting with the in situ straining experiments, and to R.K. Nalla for helpful discussions.


  • Fatigue
  • Foreign object damage
  • Impact
  • Residual stress
  • Ti-6Al-4V
  • Titanium
  • X-ray diffraction


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