Plane Strain Solutions for Highly Undermatched Specimens in Bending

  • Sergey AlexandrovEmail author
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


This chapter concerns with highly undermatched welded plates with no crack subject to pure bending. Two different kinematically admissible velocity fields are adopted. One of the fields results from an exact analytic solution for deformation of a plastic wedge between two rotating plates. The other kinematically admissible velocity field is obtained using simple assumptions and the known asymptotic singular behaviour of the real velocity field near velocity discontinuity surfaces given in Eq. (1.9). Since plane strain deformation is assumed, integration in the thickness direction is replaced with the multiplier 2B where 2B is the thickness of the plate. For the same reason, the term “velocity discontinuity surface” is replaced with the term “velocity discontinuity curve (or line)”. The latter refers to curves (lines) in the plane of flow. Base material is supposed to be rigid. The solutions given below have been proposed by Alexandrov and Kocak (2007) and Alexandrov (2008). Reviews of other solutions, including plates with cracks and three-point bending, have been presented in Kim and Schwalbe (2001a–c).


Plastic Zone Strain Rate Tensor Velocity Discontinuity Velocity Boundary Condition Velocity Jump 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. S. Alexandrov, Limit load in bending of welded samples with a soft welded joint. J. Appl. Mech. Tech. Phys. 49, 340–345 (2008)CrossRefGoogle Scholar
  2. S. Alexandrov, M. Kocak, Limit load analysis of strength undermatched welded T-joint under bending. Fatigue Fract. Eng. Mater. Struct. 30, 351–355 (2007)CrossRefGoogle Scholar
  3. R. Hill, The Mathematical Theory of Plasticity (Clarendon Press, Oxford, 1950)zbMATHGoogle Scholar
  4. Y.-J. Kim, K.-H. Schwalbe, Mismatch effect on plastic yield loads in idealised weldments I. Weld centre cracks. Eng. Fract. Mech. 68, 163–182 (2001a)CrossRefGoogle Scholar
  5. Y.-J. Kim, K.-H. Schwalbe, Mismatch effect on plastic yield loads in idealised weldments II. Heat affected zone cracks. Eng. Fract. Mech. 68, 183–199 (2001b)CrossRefGoogle Scholar
  6. Y.-J. Kim, K.-H. Schwalbe, Compendium of yield load solutions for strength mis-matched DE(T), SE(B) and C(T) specimens. Eng. Fract. Mech. 68, 1137–1151 (2001c)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.A.Yu. Ishlinskii Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia

Personalised recommendations