Journal of Failure Analysis and Prevention

, Volume 18, Issue 4, pp 782–790 | Cite as

Failure Analysis of Composite Mono Leaf Spring Using Modal Flexibility and Curvature Method

  • N. I. Jamadar
  • S. B. Kivade
  • Rakesh Raushan
Technical Article---Peer-Reviewed


Post-failure analysis of composite structures by damage identification at pre-stage has gained considerable interest in recent years. In the paper, modal flexibility and modal curvature methods have been used for premature failure analysis of composite mono leaf spring through analytical and finite element approaches. Initially, finite element model of healthy and cracked spring is used to evaluate the eigenvalue and eigenvectors. Subsequently, change in flexibility and absolute curvature difference among both springs are evaluated after mass normalization. The presence, location and severity of crack in a spring are identified through differences in local flexibilities and change in absolute modal curvatures. The modal curvature method predicts location and severity of crack more precisely than the modal flexibility method.


Failure analysis Modal flexibility Modal curvature Composite mono leaf spring Analytical Healthy and cracked spring 

List of symbols


Elemental mass of healthy beam


Elemental mass of cracked beam


Elemental stiffness of healthy beam


Elemental stiffness of cracked beam


Elemental length of beam


Assembled stiffness matrix of healthy beam


Assembled stiffness matrix of cracked beam


Assembled mass matrix of healthy beam


Assembled mass matrix of cracked beam




Flexibility matrix of healthy beam at distance x


Flexibility matrix of cracked beam at distance x


Mass normalized modal vector at distance x


Change in flexibility


Bending moment of healthy beam at distance x


Bending moment of cracked beam at distance x


Curvature of healthy beam at distance x


Curvature of cracked beam at distance x


Absolute modal curvature difference

Uh1, Uh2, Uh3 and Uh4

Are the normalized eigenvectors of healthy beam for 1st, 2nd, 3rd and 4th modes, respectively

Ud1, Ud2, Ud3 and Ud4

Are the normalized eigenvectors of cracked beam for 1st, 2nd, 3rd and 4th modes, respectively

Kh1, Kh2, Kh3 and Kh4

Are the modal curvatures of healthy beam for 1st, 2nd, 3rd and 4th modes, respectively

Kd1, Kd2, Kd3 and Kd4

Are the modal curvatures of cracked beam for 1st, 2nd, 3rd and 4th modes, respectively


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Copyright information

© ASM International 2018

Authors and Affiliations

  1. 1.Research Resource CenterVTUKalaburagi RegionIndia
  2. 2.Basavakalyan Engineering CollegeBasavakalyanIndia
  3. 3.Dr. D. Y. Patil Institute of TechnologyPimpri, PuneIndia

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