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Research Papers

# Development of Component-Level Damage Evolution Models for Mechanical Prognosis

[+] Author and Article Information
Muhammad Haroon1

Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University, 140 South Intramural Drive, West Lafayette, IN 47907-2031mharoon@purdue.edu

Douglas E. Adams

Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University, 140 South Intramural Drive, West Lafayette, IN 47907-2031deadams@purdue.edu

1

Corresponding author.

J. Appl. Mech 75(2), 021017 (Feb 26, 2008) (15 pages) doi:10.1115/1.2793137 History: Received December 25, 2006; Revised August 17, 2007; Published February 26, 2008

## Abstract

This paper presents component-level empirical damage evolution regression models based on loads and damage information that do for mechanical damage prediction what the Paris law does for predicting crack growth under fatigue loading. Namely, these regression models combine information about the current damage state and internal system loads to predict the progress of damage to failure. One of the drawbacks of Paris-like crack evolution laws is that localized information about the loading (stress) and damage (crack length) is required. In structural health monitoring applications, it is not feasible to instrument every potential crack initiation region to collect this localized information. The component-level damage evolution regression models developed here only require global measurements that quantify the damage and loading at the level of the component rather than at the site of damage. This paper develops damage evolution regression models for an automotive sway bar link undergoing axial fatigue loading with two different damage mechanisms at a weldment and at an electrical discharge machining notch. Restoring force diagrams are used to calculate the load indicators as damage progresses and transmissibility functions are used to calculate the damage indicator during tests to failure. A component-level load intensity factor $(ΔK)$ is calculated during these tests so that the rate of damage accumulation can be used to predict the growth of damage and ultimate failure.

###### FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
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## Figures

Figure 1

Two DOF quarter car model

Figure 2

SDOF linear system

Figure 3

Change in area of acceleration-velocity ellipse with system parameters: (a) stiffness, (b) damping, and (c) mass

Figure 4

Fatigue test setup

Figure 5

Fixture for placing link under test in fatigue machine grips

Figure 6

Accelerometers attached to the ends of sway bar link

Figure 7

Weld location on sway bar link

Figure 8

Initial circumferential crack in sway bar link under cyclic loading

Figure 9

Change in restoring force with the appearance of the initial circumferential crack in link: undamaged (—) and initial crack (---)

Figure 10

Change in transmissibility with the appearance of the initial circumferential crack in link: undamaged (—) and initial crack (---)

Figure 11

Appearance and progressive growth of circumferential crack to failure in sway bar link under tension-tension fatigue loading: (a)–(e)

Figure 12

Fatigue failure of sway bar link under constant amplitude cyclic loading

Figure 13

Change in velocity restoring force with appearance and progressive growth of circumferential crack to failure in sway bar link under tension-tension fatigue loading: undamaged (—), initial crack (---), progression 1 (∙ ∙ ∙ ∙), progression 2 (-.-.-), just before failure (-+-+-+), and after failure (-°-°-)

Figure 14

Change in transmissibility with appearance and progressive growth of circumferential crack to failure in sway bar link under tension-tension fatigue loading: undamaged (—), initial crack (---), progression 1 (∙ ∙ ∙ ∙), progression 2 (-.-.-), just before failure (-+-+-+), and after failure (-°-°-)

Figure 15

Increase in the frequency content of the link response as the fatigue crack grows toward failure: undamaged link (—), partially grown crack (---), and just before failure (∙ ∙ ∙ ∙)

Figure 16

Empirical regression model relating estimated change in transmissibility to change in restoring force area for experimental circumferential crack damage in sway bar link: damage indicator (—) and damage model (---)

Figure 17

Correlation of damage growth rate (change in transmissibility) with applied load intensity factor demonstrating analogy of developed damage growth model to Paris crack law; experimental circumferential fatigue crack damage in sway bar link

Figure 18

EDM crack in front sway bar link

Figure 19

Progressive growth of EDM crack to failure in sway bar link under tension-tension fatigue loading: (a)–(e)

Figure 20

Change in velocity restoring force with progressive growth of EDM crack to failure in sway bar link under tension-tension fatigue loading: initial EDM crack (—), progression 1 (---), progression 2 (∙ ∙ ∙ ∙), and just before failure (-.-.-)

Figure 21

Change in transmissibility with progressive growth of EDM crack to failure in sway bar link under tension-tension fatigue loading: initial EDM crack (—), progression 1 (---), progression 2 (∙ ∙ ∙ ∙), and just before failure (-.-.-)

Figure 22

Empirical regression model relating estimated change in transmissibility to change in restoring force area for experimental EDM crack damage in sway bar link: damage indicator (—) and damage model (---)

Figure 23

Fatigue testing of opposite weld of failed sway bar link

Figure 24

Empirical regression model relating estimated change in transmissibility to change in restoring force area for experimental fatigue crack damage in sway bar link with one failed end: damage indicator (—) and damage model (---)

Figure 25

Correlation of damage growth rate (change in transmissibility) with applied load intensity factor demonstrating analogy of developed damage growth model to Paris crack law; experimental circumferential crack damage in sway bar link with one failed end

Figure 26

Empirical regression model in Eq. 22 predicting growth of experimental fatigue crack damage in second sway bar link with one failed end: damage indicator (—) and damage model (---)

Figure 27

Empirical regression model in Eq. 22 predicting growth of experimental fatigue crack damage in third sway bar link with one failed end: damage indicator (—) and damage model (---)

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