What happens beyond that condition is the realm of ‘fracture’, ‘damage’, and ‘failure’ mechanics.
CZM offers an alternative way to view and failure in materials.
can effectively reduce the strength and stiffness of the material in an average sense, but cannot create new surface
D 1 E , Effective stress =
MATHEMATICAL CRACK TIP
d d d INACTIVE PLASTIC ZONE (Plastic wake)
sep
D max
A
E
D
C
WAKE
FORWARD
y ACTIVE PLASTIC ZONE
x
ELASTIC SINGULARITY ZONE
Concept of wake and forward region in the cohesive process zone
the atomic scale. It can also be perceived at the meso- scale as the
effect of energy dissipation mechanisms, energy dissipated both in the forward and the wake regions of the crack tip. Uses fracture energy(obtained from fracture tests) as a parameter and is devoid of any ad-hoc criteria for fracture initiation and propagation. Eliminates singularity of stress and limits it to the cohesive strength of the the material. It is an ideal framework to model strength, stiffness and failure in an integrated manner. Applications: geomaterials, biomaterials, concrete, metallics, composites….
Theoretical and Computational Aspects of Cohesive Zone Modeling
NAMAS CHANDRA
Department of Mechanical Engineering FAMU-FSU College of Engineering Florida State University
Tallahassee, Fl-32310
AMML
What is CZM and why is it important
In the study of solids and design of nano/micro/macro structures,
thermomechanical behavior is modeled through constitutive equations.
Fracture/Damage theories to model failure
Fracture Mechanics -
Linear solutions leads to singular fields-
difficult to evaluate
Fracture criteria based on KIC,GIC,JIC,CTOD,... Non-linear domain- solutions are not
Typically is a continuous function of , , f(, , ) and their history. Design is limited by a maximum value of a given parameter () at any local point.
Байду номын сангаас
E
1 D
CZM is an Alternative method to Model Separation
CZM can create new surfaces. Maintains continuity conditions mathematically,
despite the physical separation. CZM represents physics of the fracture process at
C
y B
NO MATERIAL SEPARATION
A
l1
d max
FORWARD
D
LOCATION OF COHESIVE CRACK TIP
d D
l2
WAKE
COMPLETE MATERIAL SEPARATION
E d, X
d sep
MATERIAL CRACK TIP
COHESIVE CRACK TIP
unique Additional criteria are required for crack
initiation and propagation
Basic breakdown of the principles of mechanics of continuous media
Damage mechanics-
Dissipative Micromechanisims Acting in the wake and forward region of the process zone at the Interfaces of Monolithic and Heterogeneous Material
ˆ
max