A Superposition Framework for Discrete Dislocation Plasticity

2004 ◽  
Vol 71 (6) ◽  
pp. 805-815 ◽  
Author(s):  
M. P. O’Day ◽  
W. A. Curtin
Keyword(s):  
Boundary Conditions ◽  
Crack Growth ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Bimaterial Interface ◽  
Homogeneous Material ◽  
Plastic Behavior ◽  
Zone Model ◽  
Discrete Dislocation ◽  
Wide Range

A superposition technique is introduced that allows for the application of discrete dislocation (DD) plasticity to a wide range of thermomechanical problems with reduced computational effort. Problems involving regions of differing elastic and/or plastic behavior are solved by superposing the solutions to i) DD models only for those regions of the structure where dislocation phenomena are permitted subject to either zero traction or displacement at every point on the boundary and ii) an elastic (EL) (or elastic/cohesive-zone) model of the entire structure subject to all desired loading and boundary conditions. The DD subproblem is solved with standard DD machinery for an elastically homogeneous material. The EL subproblem requires only a standard elastic or elastic/cohesive-zone finite element (FE) calculation. The subproblems are coupled: the negative of the tractions developed at the boundaries of the DD subproblem are applied as body forces in the EL subproblem, while the stress field of the EL subproblem contributes a driving force to the dislocations in the DD subproblem structure. This decomposition and the generic boundary conditions of the DD subproblem permit the DD machinery to be easily applied as a “black-box” constitutive material description in an otherwise elastic FE formulation and to be used in a broader scope of applications due to the overall enhanced computational efficiency. The method is validated against prior results for crack growth along a plastic/rigid bimaterial interface. Preliminary results for crack growth along a metal/ceramic bimaterial interface are presented.

scholarly journals On the influence of delamination on laminated paperboard creasing and folding

2012 ◽  
Vol 370 (1965) ◽  
pp. 1912-1924 ◽  
Author(s):  
Lars A. A. Beex ◽  
Ron H. J. Peerlings
Keyword(s):  
Cohesive Zone ◽  
Mechanical Model ◽  
Cohesive Zone Model ◽  
Packaging Material ◽  
Friction Model ◽  
Zone Model ◽  
General Mechanics ◽  
Single Fold ◽  
Wide Range

Laminated paperboard is used as a packaging material for a wide range of products. During production of the packaging, the fold lines are first defined in a so-called creasing (or scoring) operation in order to obtain uncracked folds. During creasing as well as folding, cracking of the board is to be avoided. A mechanical model for a single fold line has been proposed in a previous study (Beex & Peerlings 2009 Int. J. Solids Struct. 46 , 4192–4207) to investigate the general mechanics of creasing and folding, as well as which precise mechanisms trigger the breaking of the top layer. In the present study, we employ this modelling to study the influence of delamination on creasing and folding. The results reveal the separate role of the cohesive zone model and the friction model in the description of delamination. They also show how the amount of delamination behaviour should be controlled to obtain the desired high folding stiffness without breaking of the top layer.

A Crack Close to and Perpendicular to an Interface: Resolution of Anomalous Behavior With a Cohesive Zone

2019 ◽  
Vol 86 (3) ◽  
Author(s):  
George G. Adams
Keyword(s):  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Applied Pressure ◽  
Stress Singularity ◽  
Crack Tip ◽  
Anomalous Behavior ◽  
Work Of Adhesion ◽  
Bimaterial Interface ◽  
Zone Model ◽  
Finite Distance

In this investigation, we consider a crack close to and perpendicular to a bimaterial interface. If the crack tip is at the interface then, depending on material properties, the order of the stress singularity will be equal to, less than, or greater than one-half. However, if the crack tip is located any finite distance away from the interface the stress field is square-root singular. Thus, as the crack tip approaches the interface, the stress intensity factor approaches zero (for cases corresponding to a singularity of order less than one-half) or infinity (for a singularity of order greater than one-half). The implication of this behavior is that for a finite applied pressure the crack will either never reach the interface or will reach the interface with vanishing small applied pressure. In this investigation, a cohesive zone model is used in order to model the crack behavior. It is found that the aforementioned anomalous behavior for the crack without a cohesive zone disappears and that the critical value of the applied pressure for the crack to reach the interface is finite and depends on the maximum stress of the cohesive zone model, as well as on the work of adhesion and the Dundurs' parameters.

Irreversible cyclic cohesive zone model for prediction of mode I fatigue crack growth in CFRP-strengthened steel plates

2020 ◽  
Vol 110 ◽  
pp. 102804
Author(s):  
M. Mohajer ◽  
M. Bocciarelli ◽  
P. Colombi ◽  
A. Hosseini ◽  
A. Nussbaumer ◽  
...  
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Steel Plates ◽  
Mode I ◽  
Zone Model

Existence and Convergence Questions in Computational Modelling of Crack Growth in Brittle and Quasi-Brittle Materials

2016 ◽  
Vol 258 ◽  
pp. 157-160 ◽  
Author(s):  
Jiří Vala
Keyword(s):  
Crack Growth ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Computational Modelling ◽  
Brittle Materials ◽  
Zone Model ◽  
Static Tests ◽  
Materials Used ◽  
Proper Analysis

Computational modelling of the crack growth in brittle and quasi-brittle materials used in mechanical, civil, etc. engineering applies the cohesive zone model with various traction separation laws; determination of micro-mechanical parameters comes then from static tests, microscopic observation and numerical calibration. Although most authors refer to ill-possedness and need of artificial regularization in inverse problems (identification of material parameters), some difficulties originate even in nonlinear formulations of direct and sensitivity problems. This paper demonstrates the possibility of proper analysis of the existence of a weak solution and of the convergence of a corresponding numerical algorithm for such model problem, avoiding non-physical assumptions.

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