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Theory of the tensile test

Theory of the tensile test,10.1016/0001-6160(67)90211-8,Acta Metallurgica,E HART

Theory of the tensile test   (Citations: 138)
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Journal: Acta Metallurgica , vol. 15, no. 2, pp. 351-355, 1967
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    • ...The lifetime model developed by Hart (1967 )i s based on necking, which was first studied by Considère (1885) and more recently by Dumoulin et al. (2003)...
    • ...At any given time, a small portion of the gauge length is assumed to have a cross-section differing by a small amount, δS, from the rest of the gauge part, which is supposed to have a homogeneous cross-section, S. According to the definition of Hart (1967), deformation is unstable if this difference in cross-section increases with time...
    • ...After time integration, if we consider that deformation develops in a ductile way and slowly, the cross-section difference between the homogeneous parts and necking part is thus small (δS � S). Using the Taylor first order approximation, we deduce the relationship given by Hart (1967): δS = δSnecking Snecking/S N −1 (18)...

    Rattanak Limet al. Modelling and experimental study of the tertiary creep stage of Grade ...

    • ...Using the Lagrangian approach to motion description, Hart considered unstable regimes of homogeneous deformation and derived a criterion, which implies that the capability of materials to long tensions is retained even if there are inhomogeneities in the sample geometry [4]...
    • ...As a stress–strain state arises in the course of deformation of the inhomogeneity, the assumption 2 is not completely correct: Hart noted that this assumption induced an error of the same order of smallness as δS [4]...
    • ...It should be noted that this statement is not completely correct either: Hart [4] did not say anything about the perturbation geometry, which is an important characteristic of the sample and which determines the inhomogeneity of the stress distribution...
    • ...In contrast to [4], Il’yushin [5] described the problem formulation in more detail and presented a universal method for solving this problem...
    • ...Hart’s paper [4] gave an impetus to the development of this research direction, but it had some drawbacks (one-dimensional analysis of neck development was performed, and rather rigorous restrictions were imposed on the process considered)...
    • ...i.e., stability is observed for λ< 0, which is equivalent to the inequalities m< 0a nd m> 1. Thus, in the limiting case with a → 0, the result obtained agrees with Hart’s analysis [4]...
    • ...Hart’s paper [4] gave an impetus to this research direction, but its drawback was a one-dimensional analysis of development of the “neck.” A universal method of solving stability problems was proposed in the papers of Il’yushin [5] and Ishlinskii [6], though they seem to have nothing to do with SP at first glance...

    P. V. Trusovet al. Comparative analysis of some formulations of the stability problem

    • ...In mechanical engineering, elasticity parameters are commonly measured using the socalled tensile test where uniaxial loading is applied to a te st object (see e. g. [Har67])...

    Markus Beckeret al. Robust and Efficient Estimation of Elasticity Parameters using the lin...

    • ...Hart [2] proposed an instability criterion based on the growth of an...

    R. C. Batraet al. Instability strain and shear band spacing in simple tensile/compressiv...

    • ...Incorporating the modified constitutive equation (1) along with the evolution equations (2) and (3) into the framework of Hart’s stability analysis [13], a stability criterion accounting for geometrical instabilities, microstructure aspects, and stress state was developed by Thuramalla and Khraisheh [8]; which has the following form at the onset of instability:...

    M. A. Nazzalet al. The effect of strain rate sensitivity evolution on deformation stabili...

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