Abstract
This chapter first presents an introduction to true stress and strain by establishing relationships between engineering/true stress and engineering/true strain while taking into consideration the stress-strain curves. In order to cover both elastic and plastic deformations, three moduli (Young’s modulus, plastic modulus, and tangent modulus) have been introduced; and a mathematical relationship between them have been derived with the aid of a comprehensive stress-strain diagram. Work hardening has also been explained by considering strength coefficient and strain-hardening exponent. Finally, various deformation models indicating yield criteria are presented along with the examples from industrial practice. This chapter contains 3 diagrams, 13 mathematical models, 8 worked examples (solved problems) and 5 MCQs, with their answers given at the end of the book.
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References
Bertram A, Glüge R (2015) Solid mechanics: theory, modeling, and problems. Springer International Publishing, Cham
Haddag B, Abed-Meraim F, Balan T (2009) Strain localization analysis using a large deformation anisotropic elastic–plastic model coupled with damage. Int J Plast 25(10):1970–1996
Huda Z (2020) Metallurgy for physicists and engineers. CRC Press, Boca Raton, FL
Huda Z, Bulpett R (2012) Materials science and design for engineers. Trans Tech Publication, Zurich-Durnten
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Questions and Problems
Questions and Problems
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6.1.
MCQs). Encircle the most appropriate answers for the following statements:
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(a)
Which modulus refers to the overall increment in strain?
(i) Young’s modulus, (ii) plastic modulus, (iii) tangent modulus, (iv) bulk modulus
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(b)
Which modulus refers to the increment in elastic strain?
(i) Young’s modulus, (ii) plastic modulus, (iii) tangent modulus, (iv) bulk modulus
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(c)
Which deformation behavior is exhibited in wire-drawing metal-forming operation?
(i) Linear elastic/plastic, (ii) elastic/perfectly plastic, (iii) rigid/linear hardening
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(d)
Which deformation behavior is exhibited by metals during hot working?
(i) Linear elastic/plastic, (ii) elastic/perfectly plastic, (iii) rigid/linear hardening
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(e)
Which deformation behavior is exhibited by during tensile testing of mild steel?
(i) Linear elastic/plastic, (ii) elastic/perfectly plastic, (iii) rigid/linear hardening
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(a)
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6.2.
Draw sketches showing plots of simple models for various elastic/plastic deformations.
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6.3.
A 170-mm-long metal rod with a diameter of 1.6 mm is subject to a tensile force of 1,800 N. The length increases to 200 mm at failure. Calculate the (a) true strain (b) true stress.
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6.4.
In a tensile test, the engineering strain is 0.12 and the engineering stress is 680 MPa. Calculate the true stress and the true strain.
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6.5.
Calculate the percent cold working that has to be inflicted to induce a true strain of 0.28 in a metallic part.
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6.6.
A sample of 4340 alloy steel is subjected to a true stress of 500 MPa. Calculate the true strain that will be produced in the material. (Hint: Refer to Table 6.1).
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6.7.
By using the data in Table 3.1 and Table 6.1, calculate the plastic modulus of mild steel.
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Huda, Z. (2022). Stress-Strain Relations and Deformation Models. In: Mechanical Behavior of Materials. Mechanical Engineering Series. Springer, Cham. https://doi.org/10.1007/978-3-030-84927-6_6
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DOI: https://doi.org/10.1007/978-3-030-84927-6_6
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Online ISBN: 978-3-030-84927-6
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