Quasi-Fragile And Fragile Fracture Behavior With The Cohesive Surface Methodology.
Abstract
The cohesive surface methodology is probably the most used in recent Fracture Mechanics researches
(see Needleman, A., A continuum model for void nucleation by inclusion debonding, J. Appl. Mech., 54:525-
531, 1987). This methodology is characterized by two parameters, the energy fracture and a characteristic length
(or maximum stress at crack tip), and has been used to model fragile and ductile material satisfactorily. On the
other side, quasi-fragile materials (as concrete) also need two fracture parameters to be characterized, depending
on the used methodology. Then concrete seems to be a material that can be model by the above mentioned
methodology. However, concrete is a strong heterogeneous material and its behavior depends on mortar
properties and aggregate size and shape. Also, a factor that complicates the analysis of this material is the fact
that the fracture process is accompanied by intense micro-cracking and bridging of main cracks. Recent
numerical applications to concrete show that not only these two parameters are sufficient to correctly model its
fracture process, but also other parameters as the shape of crack tip stress - crack opening function.
In this paper a discussion about the relations among all the above mentioned parameters is introduced and
suggestions are raised on how to capture the quasi-fragile behavior with the cohesive surface methodology. The
effect of micro-cracking is addressed as well as the effect of the shape of the stress-opening interface curve. A
three-point bending beam is used as a numerical experimentation and compared to experimental results. The
results show that micro-cracking and unloading shape of the stress-opening interface curve are variables as
important as maximum stress at crack tip. Also it is shown that the original shape proposed by Needleman can
not be used in quasi-fragile material when micro-cracking is considered. However, the methodology works quite
well when only one main crack is considered, at least for the material and boundary conditions tested here.
(see Needleman, A., A continuum model for void nucleation by inclusion debonding, J. Appl. Mech., 54:525-
531, 1987). This methodology is characterized by two parameters, the energy fracture and a characteristic length
(or maximum stress at crack tip), and has been used to model fragile and ductile material satisfactorily. On the
other side, quasi-fragile materials (as concrete) also need two fracture parameters to be characterized, depending
on the used methodology. Then concrete seems to be a material that can be model by the above mentioned
methodology. However, concrete is a strong heterogeneous material and its behavior depends on mortar
properties and aggregate size and shape. Also, a factor that complicates the analysis of this material is the fact
that the fracture process is accompanied by intense micro-cracking and bridging of main cracks. Recent
numerical applications to concrete show that not only these two parameters are sufficient to correctly model its
fracture process, but also other parameters as the shape of crack tip stress - crack opening function.
In this paper a discussion about the relations among all the above mentioned parameters is introduced and
suggestions are raised on how to capture the quasi-fragile behavior with the cohesive surface methodology. The
effect of micro-cracking is addressed as well as the effect of the shape of the stress-opening interface curve. A
three-point bending beam is used as a numerical experimentation and compared to experimental results. The
results show that micro-cracking and unloading shape of the stress-opening interface curve are variables as
important as maximum stress at crack tip. Also it is shown that the original shape proposed by Needleman can
not be used in quasi-fragile material when micro-cracking is considered. However, the methodology works quite
well when only one main crack is considered, at least for the material and boundary conditions tested here.
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