Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Experimental Mechanics
Erschienen in: Experimental Mechanics 7/2014

01.09.2014

Residual Stress Analysis of Orthotropic Materials Using Integrated Digital Image Correlation

verfasst von: A. Baldi

Erschienen in: Experimental Mechanics | Ausgabe 7/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Measuring residual stress in an orthotropic material is a difficult task due to the complex behavior of the material. Recently, two different approaches based on Smith’s simplified real value formulation and the general solution developed by Lekhnitskii have been proposed. Both solutions assume the measurement of the displacement field via interferometric optical methods and estimate stress values through solving an inverse problem. However, the high sensitivity to vibrations of interferometric techniques makes their use difficult outside optical laboratories; standard Digital Image Correlation could be used, but its low sensitivity and relatively high standard deviation of displacements severely affect the reliability of estimates. In this work we propose to integrate the residual stress displacement functions related to orthotropic materials into the shape functions of Digital Image Correlation. This makes it possible overcome most of the problems related to low sensitivity and large standard deviation because a single large patch can be used for the measurement, thus providing an accurate and reliable algoritm for the measurement of residual stress.
Vorheriger Artikel Repeatability of the Contour Method for Residual Stress Measurement
Nächster Artikel Friction Between Steel and a Confined Inert Material Representative of Explosives Under Severe Loadings

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Fußnoten
1
Note that the stated assumption implies that intensity variation at a point is due only to motion (and that no intensity variation means no motion). This is not always true: a simple counterexample is a spinning sphere with a specular surface: if no texture is present, there will be no correlation between the motion of the surface and the image (which does not change in time). To solve this problem, a random texture must be applied on the surface of the specimen; moreover, the illumination must be isotropic and uniform.
 
2
The most commonly used functionals are the Normalized Correlation
$$ \chi^{2}_{CC}(i_{0},j_{0},u,v) \,=\, 1\,-\,\frac{\sum_{k} \sum_{l} I(k,l)\, J(k+u_{x},l+u_{y})}{\sqrt{\sum_{k}\sum_{l} I^{2}(k,l)}\,\sqrt{\sum_{k}\sum_{l} J^{2}(k+u_{x},l+u_{y})}} $$
and the Least Square Difference
$$ \chi^{2}_{LSD}(i_{0},j_{0},u_{x},u_{y}) = \sum\limits_{k}\sum\limits_{l} \left[I(k,l) - J(k+u_{x},l+u_{y})\right]^{2} $$
where u x and u y are the X and Y displacement components to be measured, k and l range over the rows (columns) of the block and finally I and J are the intensities of the reference and target images (i.e. the images of the specimen before and after motion).
 
3
Assuming subsets do not overlap.
 
4
It is quite easy to design a material whose behavior cannot be described using Smith’s formulation: if you consider a graphite-epoxy lamina (E 1 = 206840 MPa, E 2 = 5170 MPa, ν 12 = 0.25, G 12 = 2186 MPa) a simple computation shows that κ = 6.283; however, if you take into account the (+45,−45) s graphite-epoxy laminate, the classical lamination theory estimates a completely different set of parameters (E 1 = E 2 = 8402 MPa, ν 12 = 0.922, G 12 = 52438 MPa) and κ = − 0.8417.
 
5
Lekhnitskii [33] shows that to have real roots a material must be isotropic. Note that \(\mu _{3} = \overline {\mu _{1}}\) (the complex conjugate of μ 1) and \(\mu _{4} = \overline {\mu _{2}}\).
 
6
The general expression for the Γ i functions also includes a linear term (respectively A L z 1 and B L z 2); however, A L and B L depend on the displacement value at infinity, which is null in the residual stress case, thus both coefficients are zero and have been omitted for simplicity.
 
7
Note that equation (13) can easily be rewritten in terms of σ x , σ y and τ xy to obtain a final result which is formally identical to Kirsh’s solution for isotropic materials. However, in this case φ plays a different role: in Lekhnitskii’s solution, φ is the (unknown) orientation of principal stress, whereas in the isotropic case it is simply one of the coordinates of the inspected point in the cylindrical reference system.
 
8
Due to the orthotropy and loading configurations, the mesh cannot make use of symmetries, thus a complete circular disk has to be analyzed.
 
9
It is to be noted that the FEM and Lekhnitskii solutions are not completely equivalent even in the through-hole case: indeed, the theoretical formulas include only the first term of the solution series (equation 12), thus small numerical deviations (a few percentage points) can be observed when comparing them.
 
10
Each speckle is described by a bell-shaped polynomial function. The entire field results from the superposition of several thousand bells whose parameters (radius, location and value of maximum) are sampled from user-specified random distributions.
 
Literatur
1.
ASTM E1426 98(2009)e1 (1998) Standard test method for determining the effective elastic parameter for x-ray diffractionmeasurements of residual stress. Technical report, American Society for Testing and Materials, West Conshohocken, PA, doi:10.​1520/​E1426-98R09E01
2.
ASTM E837-08e1 (2008) Standard test method for determining residual stresses by the hole-drilling strain-gage method. American Society for Testing and Materials, West Conshohocken, PA. doi:10.​1520/​E0837-08E01
3.
Lin ST, Hsieh CT, Lee CK (1995) Full field phase-shifting holographic blind-hole techniques for in-plane residual stress detection. In: Honda T (ed) International conference on applications of optical holography, vol 2577. Proceedings of SPIE, Bellingham, pp 226–237CrossRef
4.
Nelson DV, McCrickerd JT (1986) Residual-stress determination through combined use of holographic interferometry and blind hole drilling. Exp Mech 26:371–378CrossRef
5.
Nelson DV, Makino A, Fuchs EA (1997) The holographic-hole drilling method for residual stress determination. Opt Lasers Eng 27:3–23CrossRef
6.
Steinzig M, Hayman G, Rangaswamy P (2001) Data reduction methods for digital holographic residual stress measurement. In: Proceedings of the 2001 SEM annual conference and exposition on experimental and applied mechanics. Portland
7.
Bulhak J, Lu J, Montay G, Surrel Y, Vautrin A (2000) Grating shearography and its application to residual stress evaluation. In: Jacquot P, Fournier J M (eds) Interferometry in speckle light: theory and applications. Springer, Berlin, pp 607–614CrossRef
8.
Schwarz RC, Kutt LM, Papazian JM (2000) Measurement of residual stress using interferometric moiré: a new insight. Exp Mech 40(3):271–281CrossRef
9.
Wu Z, Lu J (2000) Study of surface residual stress by three-dimensional displacement data at a single point in hole drilling method. J Eng Mater Tech 122(2):215–220CrossRef
10.
Wu Z, Lu J, Han B (1998) Study of residual stress distribution by a combined method of moiré interferometry and incremental hole drilling, part I: theory. J Appl Mech 65(4):837–843CrossRef
11.
Albertazzi AJ, Kanda C, Borges MR, Hrebabetzky F (2000) A radial in-plane interferometer for espi measurement. In: Kujawinska M, Pryputniewicz RJ, Takeda M (eds) Laser interferometry X, techniques and analysis, vol 4101. Proceedings of SPIE, Bellingham, pp 77–88
12.
Baldi A (2005) A new analytical approach for hole drilling residual stress analysis by full field method. J Eng Mater Tech 127(2):165–169CrossRef
13.
Baldi A, Jacquot P (2003). In: Gastinger K, kberg O J L, Winther S (eds) Speckle Metrology 2003, Bellingham, Washington, Proceedings of SPIE, vol 4933, pp 141–148
14.
Diaz FV, Kaufmann GH, Galizzi GE (2000) Determination of residual stresses using hole drilling and digital speckle pattern interferometry with automated data analysis. Opt Lasers Eng 33(1):39–48CrossRef
15.
Focht G, Schiffner K (2002) Numerical processing of measured full-field displacement data around holes for residual stress determination. In: Mang HA, Rammerstorfer F G, Eberhrdsteiner J (eds) 5th World congress on computational mechanics, Vienna
16.
Ponslet E, Steinzig M (2003) Residual stress measurement using the hole drilling method and laser speckle interferometry part II: analysis technique. Exper Tech 27(4):17–21CrossRef
17.
Schajer G (2010) Advances in hole-drilling residual stress measurements. Exp Mech 50(2):159–168CrossRef
18.
Schajer GS, Steinzig M (2005) Full-field calculation of hole drilling residual stresses from electronic speckle pattern interferometry data. Exper Mech 45(6):526–532CrossRef
19.
Steinzig M, Ponslet E (2003) Residual stress measurement using the hole drilling method and laser speckle interferometry: part I. Exp Tech 27(3):43–46CrossRef
20.
Vikram CS, Pechersky MJ, Feng C, Engelhaupt D (1996) Residual-stress analysis by local laser heating and speckle-correlation interferometry. Exp Tech 20(6):27–30CrossRef
21.
Zhang J, Chong TC (1998) Fiber electronic speckle pattern interferometry and its applications in residual stress measurements. Appl Opt 37(27):6707–6715CrossRef
22.
Lord JD, Penn D, Whitehead P (2008) The application of digital image correlation for measuring residual stress by incremental hole drilling. Appl Mech Mater 13:65–73CrossRef
23.
Schajer G, Winiarski B, Withers PJ (2013) Hole-drilling residual stress measurement with artifact correction using full-field dic. Exp Mech 53(2):255–265CrossRef
24.
25.
Cárdenas-García JF, Ekwaro-Osire S, Berg JM, Wilson WH (2005) Non-linear least-square solution to the moiré hole method problem in orthotropic materials. part I: residual stresses. Exp Mech 45(4):301–313
26.
Schajer GS, Yang L (1994) Residual-stress measurement on orthotropic materials using the hole-drilling method. Exp Mech 34(4):324–333CrossRef
27.
28.
Pagliaro P, Zuccarello B (2007) Residual stress analysis of orthotropic materials by the through-hole drilling method. Exp Mech 47(2):217–236CrossRef
29.
Baldi A (2013) Residual stress measurement using hole drilling and integrated digital image correlation techniques. Exp Mech Under Rev
30.
Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, NY. doi:10.​1007/​978-0-387-78747-3
31.
Schajer GS (1988) Measurement of non-uniform residual stresses using the hole-drilling method. part II—practical application of the integral method. J Eng Mater Tech 110(4):344–349CrossRef
32.
Smith CB (1944) Effect of elliptic or circular holes on the stress distribution in plates of wood or plywood considered as orthotropic materials. Technical Report Mimeo 1510, USDA Forest Products Laboratory, Madison
33.
Lekhnitskii SG (1963) Theory of elasticity of an anistotropic elastic body. Holden-day, translation of 1950 Russian ed
34.
Lekhnitskii SG (1968) Anistropic plates. Gordon and Breach Science Publisher, translation of 1957 Russian ed
35.
Schimke J, Thomas K, Garrison J (1968) Approximate solution of plane orthotropic elasticity problems. Management Information services, Detroit
36.
Tan SC (1988) Finite-width correction factors for anisotropic plate containing a central opening. J Compos Mater 22(11):1082–1105CrossRef
37.
Baldi A, Bertolino F (2013) A posteriori compensation of the systematic error due to polynomial interpolation in digital image correlation. Opt Eng 52(10). accepted for publication
Metadaten
Titel
Residual Stress Analysis of Orthotropic Materials Using Integrated Digital Image Correlation
verfasst von
A. Baldi
Publikationsdatum
01.09.2014
Verlag
Springer US
Erschienen in
Experimental Mechanics / Ausgabe 7/2014
Print ISSN: 0014-4851
Elektronische ISSN: 1741-2765
DOI
https://doi.org/10.1007/s11340-014-9859-1

Weitere Artikel der Ausgabe 7/2014

Experimental Mechanics 7/2014 Zur Ausgabe

Brief Technical Note

Discussion on “Interfacial Residual Stress Analysis of Thermal Spray Coatings by Miniature Ring-Core Cutting Combined with DIC Method” by J.G. Zhu et al., Experimental Mechanics DOI:10.1007/s11340-012-9640-2

Brief Technical Note

Authors’ Closure to the Discussion on “Interfacial Residual Stress Analysis of Thermal Spray Coatings by Miniature Ring-Core Cutting Combined with DIC Method”

OriginalPaper

Mechanical Testing of Thin Sheet Magnesium Alloys in Biaxial Tension and Uniaxial Compression

OriginalPaper

Measurement and Prediction of Residual Stresses in Quenched Stainless Steel Components

OriginalPaper

Determination of Anisotropic Plastic Constitutive Parameters Using the Virtual Fields Method

OriginalPaper

Is There An Optimal Gauge Length for Dynamic Tensile Specimens?

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise