Why direct tension test specimens break flexing to the side

Zdeněk P. Bažant, Luigi Cedolin

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20 Scopus citations


Contrary to the traditional view, unnotched direct tension test specimens of quasi-brittle materials that exhibit post-peak strain softening do not deform symmetrically. After passing the peak load, the equilibrium path bifurcates and the secondary postbifurcation branch represents flexing to the side. The bifurcation is shown to be analogous to Shanley's bifurcation in elastoplastic columns. According to the thermodynamic criterion of stable path, the flexing to one side must occur even if the geometry is perfect and if the straightening effect of the moment of the axial force about the centroid of the deflected cross section is taken into account. The lateral flexing favors failure of the specimen at midlength. The phenomenon (which is similar to the recently discovered behavior of notched tensile fracture specimens) is first illustrated using a simple model in which the specimen consists of two rigid bars of unequal lengths, joined by a strain-softening link. It is shown that flexing to the side is retarded if the attachments to the loading machine exert a sufficient restraint against rotation. The analysis is then extended to a specimen consisting of two unloading elastic beams joined by a short strain-softening segment, and similar conclusions are reached. The maximum load in the unnotched direct-tension test gives the material strength limit, but the postpeak load-deflection response cannot yield the strain-softening material properties and energy-absorption capability except when sophisticated stability analysis is made and the size of the strain-softening zone is known a priori.

Original languageEnglish (US)
Pages (from-to)1101-1113
Number of pages13
JournalJournal of Structural Engineering (United States)
Issue number4
StatePublished - Apr 1993

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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