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Measurement of third-order elastic constants and applications to loaded structural materials.

Takahashi S, Motegi R - Springerplus (2015)

Bottom Line: The theory is applied to the measurement of the third-order elastic constants of common steels containing carbon of 0.22 and 0.32 wt%.As a result, the stress at various sites in the structural materials could be estimated by measuring the elastic wave propagation times.The results obtained are graphed for illustration.

View Article: PubMed Central - PubMed

Affiliation: National Research Institute for Metals, 6-13-12 Kanamori, Machida, Tokyo, 194-0012 Japan.

ABSTRACT
The objective of this study is to obtain the propagation velocity of an elastic wave in a loaded isotropic solid and to show the usefulness of the third-order elastic constant in determining properties of practical materials. As is well known, the infinitesimal elastic theory is unable to express the influence of stress on elastic wave propagating in loaded materials. To solve this problem, the authors derive an equation of motion for elastic wave in a finitely deformed state and use the Lagrangian description where the state before deformation is used as a reference, and Murnaghans finite deformation theory for the unidirectional deformed isotropic solid. Ordinary derivatives were used for the mathematical treatment and although the formulas are long the content is simple. The theory is applied to the measurement of the third-order elastic constants of common steels containing carbon of 0.22 and 0.32 wt%. Care is taken in preparing specimens to precise dimensions, in properly adhering of transducer to the surface of the specimen, and in having good temperature control during the measurements to obtain precise data. As a result, the stress at various sites in the structural materials could be estimated by measuring the elastic wave propagation times. The results obtained are graphed for illustration.

No MeSH data available.


Specimen.
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Fig1: Specimen.

Mentions: Figure 1 gives a diagram of the axial cross-section through a specimen for tensile testing. In its fabrication, we had to take special care in mixing the raw materials, melting, casting, annealing, and precision working to fix the final form. As stress in the gripping regions is complicated, and should be eliminated, two specimens with identical grip sizes but different gauge lengths were prepared (Takahashi and Motegi 1987).


Measurement of third-order elastic constants and applications to loaded structural materials.

Takahashi S, Motegi R - Springerplus (2015)

Specimen.
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4493263&req=5

Fig1: Specimen.
Mentions: Figure 1 gives a diagram of the axial cross-section through a specimen for tensile testing. In its fabrication, we had to take special care in mixing the raw materials, melting, casting, annealing, and precision working to fix the final form. As stress in the gripping regions is complicated, and should be eliminated, two specimens with identical grip sizes but different gauge lengths were prepared (Takahashi and Motegi 1987).

Bottom Line: The theory is applied to the measurement of the third-order elastic constants of common steels containing carbon of 0.22 and 0.32 wt%.As a result, the stress at various sites in the structural materials could be estimated by measuring the elastic wave propagation times.The results obtained are graphed for illustration.

View Article: PubMed Central - PubMed

Affiliation: National Research Institute for Metals, 6-13-12 Kanamori, Machida, Tokyo, 194-0012 Japan.

ABSTRACT
The objective of this study is to obtain the propagation velocity of an elastic wave in a loaded isotropic solid and to show the usefulness of the third-order elastic constant in determining properties of practical materials. As is well known, the infinitesimal elastic theory is unable to express the influence of stress on elastic wave propagating in loaded materials. To solve this problem, the authors derive an equation of motion for elastic wave in a finitely deformed state and use the Lagrangian description where the state before deformation is used as a reference, and Murnaghans finite deformation theory for the unidirectional deformed isotropic solid. Ordinary derivatives were used for the mathematical treatment and although the formulas are long the content is simple. The theory is applied to the measurement of the third-order elastic constants of common steels containing carbon of 0.22 and 0.32 wt%. Care is taken in preparing specimens to precise dimensions, in properly adhering of transducer to the surface of the specimen, and in having good temperature control during the measurements to obtain precise data. As a result, the stress at various sites in the structural materials could be estimated by measuring the elastic wave propagation times. The results obtained are graphed for illustration.

No MeSH data available.