Structure, Stiffness, and Strength

Séminaire Île-de-France
Jeudi 14 novembre 2013 à 14 heures
Amphithéâtre L108
Ecole des Mines de Paris
60, Boulevard Saint-Michel, Paris 6ème
Métro : Luxembourg
Fan Song (chinese Academy of Sciences,
Beijing)
Corrado Maurini (UPMC, Paris)
Jia Li (LSPM, Université Paris Nord)
[email protected]
[email protected]
Study on the crack patterns of the ceramic materials subjected to thermal shock
Fan Song
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences,
Beijing, China
The suddenly catastrophic reduction of the strength of the ceramic materials subjected to thermal
shock is a long-standing problem in thermostructural engineering, in which the crack patterns sprouted
in the ceramics during thermal shock plays a key role in understanding the mechanisms of the strength
reduction. In this talk, we mainly summarize our recently experimental findings on the crack patterns,
including: (1) the size and boundary effects on the crack patterns; (2) the numerical simulations of the
crack patterns and the residual strength; (3) The effects of porosity on the crack pattern and the residual
strength; and (4) the thermal shock critical size of the ceramic materials.
Complex crack patterns under thermal shock loadings: application of the variational approach
to fracture and damage
Corrado Maurini
UPMC and CNRS Univ Paris 6, UMR 7190, Institut Jean Le Rond d’Alembert,
4 Place Jussieu, F-75005, Paris, France.
Predicting the nucleation and the propagation of complex crack patterns is one of the major issue of
theoretical and numerical fracture mechanics. In our work we tackle this problem using gradient
damage models with an internal length and a variational approach. First, I will illustrate how the
creation of a crack in a homogeneous structure without stress singularities can be understood as a
stability problem of gradient damage models. Hence, I will report on the theoretical and numerical
results obtained for the thermal shock problem, where we study the quasi-static evolution driven by the
inelastic shrinkage strains induced by the evolving temperature field. In close qualitative and
quantitative agreement with the experimental results, we obtain the creation of periodic crack patterns
and their selective propagation with a period doubling phenomenon. I will show that the genesis of the
periodic cracks may be theoretically explained as a bifurcation of a fundamental solution with
homogeneous damage toward a solution with damage periodically localized in thin bands. Large scale
numerical simulations obtained through a finite element method show good agreement with analytical
and experimental results. In a three-dimensional setting the numerical results predict the creation and
the propagation of hexagonal crack patterns, according to what is observed in many real settings,
spanning from the microscopic to the geological scales.
Direct numerical simulations on crack formation in ceramic materials under thermal shock by
using a non-local fracture model
Jia Li
LSPM, CNRS UPR 3407, Université Paris XIII, Villetaneuse, France
In this work, a non-local failure model was proposed and implemented into a finite element code. It
was then used to simulate the crack evolution in ceramic materials subjected to thermal shock. By
using this numerical model, the initiation and propagation of cracks in water quenched ceramic
specimens were simulated within quasi-static and dynamic frameworks. The numerical simulations
reproduced faithfully the crack patterns in ceramic specimens underwent quenching tests. The
periodical and hierarchical characteristics of the crack patterns were accurately predicted. The
numerical simulations allow a direct observation on whole the process of crack initiation and growth,
which is quite a difficult task in experimental studies. Without introducing any fitting parameter, the
numerical model is simple, robust, accurate and efficient in simulating crack evolution in real structures
under thermal shock.