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Abstract:
The purpose of this work is to model the ductile fracture of porous metals from a micromechanical point of view. To do this, the Rousselier model is implemented in the finite element code ABAQUS using a VUMat (Vectorized User MATerial) subroutine. The integration algorithm selected for the implementation is the Aravas algorithm, which is based on the 'backward-Euler' method; it follows the principle of the elastic prediction - plastic correction. To check the validity of the implemented model, simulations of academic examples and fracture mechanics problems (i.e. CT test and Charpy test) are performed, and a good description of the fracture process is obtained.
Key words: Damage, ductile fracture, porous media, implementation, micromechanics.
(ProQuest: ... denotes formulae omitted.)
1. Introduction
The mechanisms behind the ductile fracture of metals are associated with the development of the cavities within the material. We distinguish generally three phases which are the germination, growth and coalescence of cavities. The Rousselier model is based on microstructural assumptions which introduce a microstructure consisting of cavities and a matrix whose elastic deformations are negligible compared to plastic deformations [1].
Formulated by G. Rousselier [2-4], and considered as a variant of the A. L. Gurson model [5], it remains little used compared to this latter. However, modifications and extensions were made to him [6-8]. It has also been applied by many authors for the study of ductile fracture of steels and alloys through academic examples and industrial issues [9-13].
In this work, we list the steps required for the implementation of the Rousselier model in a finite element code, in order to simulate the ductile fracture in Abaqus explicit, application of this model to academic and fracture mechanics examples is performed in order to verify its validity.
2. Formulation of the Rousselier model
Introduced by Rousselier [2], it's considered as a thermodynamically consistent ductile damage theory. The plastic potential in this model has the form
... (1)
Where: ... (2)
... (3)
... (4)
β is a scalar damage variable. Its evolution is determined by equation (2)
B is the damage function, ρ is a dimensionless density which depends on β . D and σ1 are material constants, f0 is the initial void volume fraction.
H(...) is a term describing the hardening...