czm内聚力模型
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difficult to evaluate
2. Fracture criteria based on K IC ,G IC ,JIC ,C T O D ,... 3. Non-linear domain- solutions are not
unique
4. Additional criteria are required for crack initiation and propagation
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….
CZM offers an alternative way to view and failure in materials.
Fracture/Damage theories to model failure
1. Fracture Mechanics -
1. Linear solutions leads to singular fields-
2. Basic breakdown of the principles of mechanics of continuous media
3. Damage mechanics-
1. can effectively reduce the strength and stiffness of the material in an average sense, but cannot create new surface
D 1 E ,E ffe c tiv estre ss=
E
1 D
CZM is an Alternative method to Model Separation
➢ CZM can create new surfaces. ➢ Maintains continuity conditions mathematically,
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.
What happens beyond that condition is the realm of ‘fracture’, ‘damage’, and ‘failure’ mechanics.
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.
Wake of crack tip
Forward of crack tip
Fibril (MMC bridging Grain bridging
Microvoid coalescence
Plastic zone
Metallic
Cleavage fracture
Oxide bridging
Fibril(polymers) bridging
MATHEMATICAL CRACK TIP
INACTIVE PLASTIC ZONE (Plastic wake)
d sep
dD
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
Dissipative Micromechanisims Acting in the wake and forward region of the process zone at the Interfaces of Monolithic and Heterogeneous Material
ˆ
max
despite the physical separation. ➢ CZM represents physics of the fracture process at
the atomic scale. ➢ It can also be perceived at the meso- scale as the
Fra Baidu bibliotek
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
2. Fracture criteria based on K IC ,G IC ,JIC ,C T O D ,... 3. Non-linear domain- solutions are not
unique
4. Additional criteria are required for crack initiation and propagation
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….
CZM offers an alternative way to view and failure in materials.
Fracture/Damage theories to model failure
1. Fracture Mechanics -
1. Linear solutions leads to singular fields-
2. Basic breakdown of the principles of mechanics of continuous media
3. Damage mechanics-
1. can effectively reduce the strength and stiffness of the material in an average sense, but cannot create new surface
D 1 E ,E ffe c tiv estre ss=
E
1 D
CZM is an Alternative method to Model Separation
➢ CZM can create new surfaces. ➢ Maintains continuity conditions mathematically,
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.
What happens beyond that condition is the realm of ‘fracture’, ‘damage’, and ‘failure’ mechanics.
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.
Wake of crack tip
Forward of crack tip
Fibril (MMC bridging Grain bridging
Microvoid coalescence
Plastic zone
Metallic
Cleavage fracture
Oxide bridging
Fibril(polymers) bridging
MATHEMATICAL CRACK TIP
INACTIVE PLASTIC ZONE (Plastic wake)
d sep
dD
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
Dissipative Micromechanisims Acting in the wake and forward region of the process zone at the Interfaces of Monolithic and Heterogeneous Material
ˆ
max
despite the physical separation. ➢ CZM represents physics of the fracture process at
the atomic scale. ➢ It can also be perceived at the meso- scale as the
Fra Baidu bibliotek
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