ch9a-CZM class notes

# ch9a-CZM class notes - Modeling Fracture in Elastic-plastic...

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Modeling Fracture in Elastic-plastic Solids Using Cohesive Zone CHANDRAKANTH SHET Department of Mechanical Engineering FAMU-FSU College of Engineering Florida State University Tallahassee, Fl-32310 Sponsored by US ARO, US Air Force

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Fracture Mechanics - Linear solutions leads to singular fields- difficult to evaluate Fracture criteria based on Non-linear domain- solutions are not unique Additional criteria are required for crack initiation and propagation Basic breakdown of the principles of mechanics of continuous media Damage mechanics- can effectively reduce the strength and stiffness of the material in an average sense, but cannot create new surface σ Fracture/Damage theories to model failure IC IC IC K ,G ,J ,CTOD,. .. E D 1 , Effective stress = E 1 D σ = - σ = - %
CZM can create new surfaces. Maintains continuity conditions mathematically, despite the physical separation. CZM represent physics of fracture process at 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. Ideal framework to model strength, stiffness and failure in an integrated manner. Applications: geomaterials, biomaterials, concrete, metallics, composites… CZM is an Alternative method to Model Separation

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Conceptual Framework of Cohesive Zone Models for interfaces S is an in terface su rface separatin g two dom ain s 1 , 2 (iden tical/ separate con stitu tive beh avior). After fractu re th e su rface S com prise of u n separated su rface an d com pletely separated su rface (e.g. ); all m odeled with in th e con- cept of CZM. Su ch an approach is n ot possible in con ven tion al m ech an ics of con- tin u ou s m edia. * 2 u * 1 t * 1 u 1 2 1 s s P N 1 1 X , x 2 2 X , x 3 3 X , x (a) 2 s * 2 t * 1 t * 1 u 1 P ˆ n * 2 u 2 P ′′ * (b) 1 S 2 S 1 ˆn 2 P P ,T δ n δ t δ 1 2 (d) sep δ max δ max σ n T (c) x (X,t) = χ
Interface in the undeformed configuration 1 2 1 1 2 2 1 1 2 2 and are separated by a common boundary S, such that and and normals and Hence in the initial configuration S S N N S S = 1 2 1 2 1 2 1 2 defines the interface between any two domains is metal, is ceramic, S = metal ceramic interface , represent grains S N N N S = = = 1 2 1 2 in different orientation, S = grain boundary , represent same domain ( = ), S = internal surface yet to separate * 2 u * 1 t * 1 u 1 2 1 s s P N 1 1 X , x 2 2 X , x 3 3

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## This note was uploaded on 12/11/2011 for the course EML 3004c taught by Professor Staff during the Fall '11 term at FSU.

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ch9a-CZM class notes - Modeling Fracture in Elastic-plastic...

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