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Estimation of 3D field quantities and energy flux associated with elastic waves in a bar
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Materials Science.
2003 (English)In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 259, no 4, 893-915 p.Article in journal (Refereed) Published
Abstract [en]

A method to estimate dispersion relations and warping associated with elastic wave propagation in a bar is presented. The method is based on Hamilton's principle. It is shown how the theoretical model together with strain measurements can be used to evaluate three dimensional (3D) field quantities like displacements and stresses at an arbitrary position in the bar, as well as energy flux through an arbitrary cross-section of the bar. It is also shown how redundant measurements can be used to increase the accuracy. The method is general and can be applied to any mode of wave propagation, isotropic or anisotropic linearly elastic material, and any cross-sectional geometry. Here, it is applied to longitudinal waves in a split Hopkinson pressure bar with linear elastic isotropic material behaviour and square cross-section. In particular, axial displacement, axial stress and energy flux are evaluated at a free end of the bar in order to test the method. The method is also used to estimate the Poisson ratio of the bar material, by measuring axial and transverse strains at the same axial position.

Place, publisher, year, edition, pages
2003. Vol. 259, no 4, 893-915 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:uu:diva-90058DOI: 10.1006/jsvi.2002.5128OAI: oai:DiVA.org:uu-90058DiVA: diva2:162131
Available from: 2002-11-15 Created: 2002-11-15 Last updated: 2013-05-17Bibliographically approved
In thesis
1. A Method for Dispersive Split Hopkinson Pressure Bar Analysis Applied to High Strain Rate Testing of Spruce Wood
Open this publication in new window or tab >>A Method for Dispersive Split Hopkinson Pressure Bar Analysis Applied to High Strain Rate Testing of Spruce Wood
2002 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [sv]

En metod för dispersiv analys av försök med delad hopkinsonstång tillämpad på provning av granved vid hög töjningshastighet

Syftet var att etablera en metod för att studera sambandet mellan spänning och töjning för granved vid hög töjningshastighet. Detta åstadkoms genom att anpassa och något vidareutveckla tekniken med delad hopkinsonstång ("Split Hopkinson Pressure Bar", SHPB).

Vanligtvis har hopkinsonstavar cirkulärt tvärsnitt och en diameter som är mycket mindre än de verksamma våglängderna. Under sådana förhållanden är vågutbredningen i stängerna approximativt ickedispersiv, och en endimensionell (1D) vågutbredningsmodell kan användas. När det, som är fallet i denna studie, däremot inte kan säkerställas att stängernas tvärdimensioner är små i förhållande till våglängderna, är en helt igenom 1D vågutbredningsmodell otillräcklig, och tvärsnittets geometri, vilken var kvadratisk i denna studie, måste beaktas. Därför utvecklades med hjälp av Hamiltons princip en approximativ 3D vågutbredningsmodell för stänger med godtyckligt tvärsnitt. Modellen ger ett dispersionssamband (vågtal som funktion av vinkelfrekvens) samt medelvärden för förskjutningar och spänningar över gränsytorna mellan stänger och provstav. En kalibreringsprocedur utvecklades också.

Provning av granved genomfördes vid hög töjningshastighet (omkring 103 s-1) med den anpassade SHPB-tekniken, samt för jämförelse vid låg (8×10-3 s-1) och måttlig (17 s-1) töjningshastighet med en servohydraulisk provningsmaskin. Fukthalterna i veden motsvarade ugnstorr, fibermättnad och fullständig mättnad, och proven utfördes i radiell, tangentiell och axiell riktning i förhållande till trädets stam. För vart fall utfördes fem försök vid rumstemperatur. Resultaten visar töjningshastighetsberoendet för sambandet mellan spänning och töjning för granved under alla studerade förhållanden.

Abstract [en]

The aim was to establish a method for studying the relation between stress and strain in spruce wood at high strain rate. This was achieved by adapting and somewhat further developing the split Hopkinson pressure bar (SHPB) technique.

Hopkinson bars usually have a circular cross-section and a diameter much smaller than the operative wavelengths. The wave propagation in the bar is then approximately non-dispersive and a one-dimensional (1D) wave propagation model can be used. When, as in this study, it is not certain that the transverse dimensions of the bars are small in relation to the wavelengths, a solely 1D wave propagation model is insufficient and the geometry of the cross-section, which was square in this study, must be taken into account. Therefore, an approximate 3D wave propagation model for bars with arbitrary cross-section was developed using Hamilton's principle. The model provides a dispersion relation (wavenumber vs. angular frequency) and average values for displacements and stresses over the bar/specimen interfaces. A calibration procedure was also developed.

Tests on spruce wood specimens were carried out at a high strain rate (about 103 s-1) using the adapted SHPB technique, and for comparison at low (8×10-3 s-1) and medium (17 s-1) strain rates using a servohydraulic testing machine. The moisture contents of the wood specimens corresponded to oven dry, fibre saturated and fully saturated, and the testing was performed in the radial, tangential and axial directions relative to the stem of the tree. In each case, five tests were run at room temperature. The results show the strain rate dependence of the relation between stress and strain for spruce wood under all conditions studied.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2002. 41 p.
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 772
Keyword
Materials science, split Hopkinson, wave propagation, dispersion, Hamilton's principle, strain rate, calibration, spruce, wood, Materialvetenskap
National Category
Materials Engineering
Research subject
Technical Physics
Identifiers
urn:nbn:se:uu:diva-2872 (URN)91-554-5461-5 (ISBN)
Public defence
2002-12-09, sal O111, Mitthögskolan - Sundsvall, Uppsala, 14:00
Opponent
Available from: 2002-11-15 Created: 2002-11-15Bibliographically approved

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