Abstract
This paper presents a new 1-D non-local damage-plasticity deformation model for ductile materials. It uses the thermodynamic framework described in Houlsby and Puzrin (2000) and holds, nevertheless, some similarities with Lemaitre’s (1971) approach. A 1D finite element (FE) model of a bar fixed at one end and loaded in tension at the other end is introduced. This simple model demonstrates how the approach can be implemented within the finite element framework, and that it is capable of capturing both the pre-peak hardening and post-peak softening (generally responsible for models instability) due to damage-induced stiffness and strength reduction characteristic of ductile materials. It is also shown that the approach has further advantages of achieving some degree of mesh independence, and of being able to capture deformation size effects. Finally, it is illustrated how the model permits the calculation of essential work of rupture (EWR), i.e. the specific energy per unit cross-sectional area that is needed to cause tensile failure of a specimen.
Similar content being viewed by others
References
Cotterell B., Redell J.K. (1977), The essential work of plane stress ductile fracture. Int. J. Fracture 13, 267–277
Criesfield M.A., Willis J. (1988), Solution strategies and softening materials. Comput. Methods Appl. Engrg. 66, 267–289
Fleck N.A., Muller G.M., Ashby M.F., Hutchinson J.W. (1994), Strain Gradient Plasticity: Theory and Experiment. Acta Metallurgica et Materialia 42, 475–487
Houlsby G.T., Puzrin A.M. (2000), A thermodynamical framework for constitutive models for rate independent dissipative materials. Int. J. Plasticity 16, 1017–1047
Korsunsky A.M., Kim K. (2005), Determination of essential work of necking and tearing from a single tensile test. Int. J. Fracture 132, 37–34
Korsunsky A.M., Nguyen G.D., Houlsby G.T. (2005), Analysis of essential work of rupture using non-local damage-plasticity modelling. Int. J. Fracture 135, 19–26
Lemaitre, J., 1971, Evaluation of dissipation and damage in metals, Proc. I.C.M. Kyoto, Japan, Vol. 1
Lemaitre, J., 1992, A course on damage mechanics, Springer Verlag
Lemaitre, J., Chaboche J.-L., 1990, Mechanics of Solid Materials, Cambridge University Press
Ma Q., Clarke D.R. (1995), Size-dependent hardness in silver single crystals. J. Mater. Res, 10, 853–863
Nguyen, G.D., Houlsby, G.T., 2007, Nonlocal damage modelling of concrete: a procedure for the determination of parameters, Int. J. Numer. Anal. Meth. in Geomech., in press
Nguyen, G.D., Korsunsky, A.M., 2007, A nonlocal coupled damage-plasticity model for concrete, FramCos6 conference, to appear.
Nguyen, G.D., Korsunsky, A.M., Belnoue, J.P., 2007, A nonlocal coupled damage-plasticity model for fracture analysis of metallic materials, in preparation
Poole W.J., Ashby M.F., Fleck N.A. (1996), Micro-Hardness of Annealed and Work-Hardened Copper Polycrystals. Scripta Materialia 34, 559–564
Stolken J.S., Evans A.G. (1998), A Microbend Test Method for Measuring the Plasticity Length-Scale. Acta Mater 46, 5109–5115
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Belnoue, J.P., Nguyen, G.D. & Korsunsky, A.M. A One-Dimensional Nonlocal Damage-Plasticity Model for Ductile Materials. Int J Fract 144, 53–60 (2007). https://doi.org/10.1007/s10704-007-9075-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-007-9075-4