Influence of Mesoscale and Macroscale Heterogeneities in Metals on Higher Harmonics Under Plastic Deformation

  • Negar Kamali
  • Niloofar Tehrani
  • Amir Mostavi
  • Sheng-Wei ChiEmail author
  • Didem Ozevin
  • J. Ernesto Indacochea


In nonlinear ultrasonic techniques, the material nonlinearity is observable in the ultrasonic signal through the generation of higher harmonics (HH). The HH generation, however, can be triggered by many sources. Any variation in the micro-, meso-, and macroscopic scales of the structure may collectively lead to HH generation. This paper presents a finite element approach with mesoscale heterogeneities explicitly modeled for the nonlinear wave propagation. The aim of this paper is to understand HH generation due to the non-mesoscale variation and non-uniform deformations introduced by the uniaxial tensile test. The study is divided into two parts: first, the effect of non-uniform plastic deformation resulted by geometrical variation of structures on HH is studied. The effect of non-uniformity due to mesoscale variations on HH is then analyzed. The numerical studies and predictions are crossly validated with nonlinear ultrasonic experiments and microscale imaging, including X-ray diffraction scanning. Numerical and experimental studies both indicate that non-uniform variations in different length scales affect the generation of both second- and third-harmonics and that both second- and third-harmonics acoustic nonlinearity parameters grow with the increase of plastic strain level. However, the third-harmonics acoustic nonlinearity coefficient is more sensitive when micro-, meso- and macrostructural variations exist.


Non-linear ultrasonic testing Higher harmonics Acoustic nonlinearity parameter Multiscale modeling X-ray diffraction Non-uniform stress distribution 



This research is based upon work supported by the National Science Foundation (NSF) under Award Number CMMI 1463501 entitled “Assessing Microstructural Damage Using Nonlinear Ultrasonics and Multiscale Numerical Modeling”. Any opinions, findings and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the NSF.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Negar Kamali
    • 1
  • Niloofar Tehrani
    • 1
  • Amir Mostavi
    • 1
  • Sheng-Wei Chi
    • 1
    Email author
  • Didem Ozevin
    • 1
  • J. Ernesto Indacochea
    • 1
  1. 1.Department of Civil and Material EngineeringUniversity of Illinois at Chicago ChicagoUSA

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