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Ultrasonic and Optical Evaluation of Deformation Stages from the Beginning to Fracture: A Case Study of Low-Carbon Steels

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Abstract

This paper reports the results of acoustic parameter measurements in a deformed material with simultaneous recording of autowave patterns of localized plastic deformation for steels of various compositions. It discusses the possibility of using an autowave model for the derivation of structural strength criteria of materials. It was shown that the time and place of future fracture in steel specimens can be predicted from the kinetic dependences of localized deformation sites at the prefracture stage long before visible necking. It was found that the ultrasonic velocity vs. strain curve has a kink in the elastic–plastic transition in low-carbon steels. This kink may serve as an acoustic criterion for the onset of irreversible deformation in metal forming and non-destructive testing of components and structures.

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Acknowledgments

The work was performed according to the Government research assignment for ISPMS SB RAS.

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Correspondence to Dina V. Orlova.

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Appendix

Appendix

1.1 Graphical Representation of Determining the Plastic Deformation Stages

The stress–strain curve of a polycrystal is described by the Ludwick equation \(s\left( e \right) = s_{0} + Ke^{n}\), where K is the strain hardening coefficient and n is the hardening exponent, s0 ≈ σ0.2 – is the point of plastic flow onset defined in the se0.5 coordinates. The true stress is defined as the ratio of the current load to the current cross-sectional area, which continuously decreases during stretching s = σ(1 + ε). The true strain takes into account the continuously changing length of the tensile specimen e = ln(1 + ε). Then the flow curve stages can be characterized by the parabolicity factor n. Figure 

Fig. 12
figure 12

True stress–strain curves for the experimental steels (a). True stress–strain curves in logarithmic coordinates for: 1008 (b), 1010 (c), 1020 (d)

12a shows the s(e) curves from the beginning of plastic flow. The processing of the s(e) curves revealed that the quantity \(n = \frac{{\ln \left[ {\left( {s - s_{0} } \right)/K} \right]}}{\ln e}\) varies discretely along the s(e) curve (Fig. 12b-d). The linear portion with n = 0.5 corresponds to the Taylor parabolic stage. The next portion that continues until the neck is formed (\(\frac{ds}{{de}} < 0\)) corresponds to the prefracture stage with 0 ≤ n ≤ 0.5. In the case of a long prefracture stage, there may be several portions with n ≤ 0.5.

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Lunev, A.G., Orlova, D.V., Danilova, L.V. et al. Ultrasonic and Optical Evaluation of Deformation Stages from the Beginning to Fracture: A Case Study of Low-Carbon Steels. J Nondestruct Eval 40, 31 (2021). https://doi.org/10.1007/s10921-021-00763-z

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