scholarly journals The J-integral for mixed-mode loaded cracks with cohesive zones

2020 ◽  
Vol 227 (1) ◽  
pp. 79-94
Author(s):  
Johannes Scheel ◽  
Alexander Schlosser ◽  
Andreas Ricoeur
Keyword(s):  
Cohesive Zone ◽  
Mixed Mode ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Constitutive Law ◽  
Zone Model ◽  
J Integral ◽  
Cohesive Law ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement

AbstractThe J-integral quantifies the loading of a crack tip, just as the crack tip opening displacement (CTOD) emanating from the cohesive zone model. Both quantities, being based on fundamentally different interpretations of cracks in fracture mechanics of brittle or ductile materials, have been proven to be equivalent in the late 60s of the previous century, however, just for the simple mode-I loading case. The relation of J and CTOD turned out to be uniquely determined by the constitutive law of the cohesive zone in front of the physical crack tip. In this paper, a J-integral vector is derived for a mixed-mode loaded crack based on the cohesive zone approach, accounting for the most general case of a mode-coupled cohesive law. While the $$J_1$$ J 1 -coordinate, as energy release rate of a straight crack extension, is uniquely related to the cohesive potential at the physical crack tip and thus to the CTOD, the $$J_2$$ J 2 -coordinate depends on the solution of the specific boundary value problem in terms of stresses and displacement gradients at the cohesive zone faces. The generalized relation is verified for the Griffith crack, employing solutions of the Dugdale crack based on improved holomorphic functions.

Development of a cohesive zone model for three-dimensional simulation of joint de-bonding/delamination under mixed-mode I/II fatigue loading

2014 ◽  
Vol 5 (3) ◽  
pp. 171-186 ◽  
Author(s):  
A. Pirondi ◽  
G. Giuliese ◽  
F. Moroni
Keyword(s):  
Cohesive Zone ◽  
Mixed Mode ◽  
Cohesive Zone Model ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Constitutive Law ◽  
Mode I ◽  
Zone Model ◽  
Pure Mode ◽  
Content Type

Purpose – In this work, the cohesive zone model (CZM) developed by some of the authors to simulate the propagation of fatigue defects in two dimensions is extended in order to simulate the propagation of defects in 3D. The paper aims to discuss this issue. Design/methodology/approach – The procedure has been implemented in the finite element (FE) solver (Abaqus) by programming the appropriate software-embedded subroutines. Part of the procedure is devoted to the calculation of the rate of energy release per unit, G, necessary to know the growth of the defect. Findings – The model was tested on different joint geometries, with different load conditions (pure mode I, mode II pure, mixed mode I/II) and the results of the analysis were compared with analytical solutions or virtual crack closure technique (VCCT). Originality/value – The possibility to simulate the growth of a crack without any re-meshing requirements and the relatively easy possibility to manipulate the constitutive law of the cohesive elements makes the CZM attractive also for the fatigue crack growth simulation. However, differently from VCCT, three-dimensional fatigue de-bonding/delamination with CZM is not yet state-of-art in FE softwares.

scholarly journals An Improved Cohesive Zone Model for Interface Mixed-Mode Fractures of Railway Slab Tracks

2021 ◽  
Vol 11 (1) ◽  
pp. 456
Author(s):  
Yanglong Zhong ◽  
Liang Gao ◽  
Xiaopei Cai ◽  
Bolun An ◽  
Zhihan Zhang ◽  
...  
Keyword(s):  
Interface Crack ◽  
Cohesive Zone ◽  
Mixed Mode ◽  
Cohesive Zone Model ◽  
Complex Loading ◽  
Bending Test ◽  
Mixed Mode Fracture ◽  
Zone Model ◽  
Slab Track ◽  
Interfacial Cracks

The interface crack of a slab track is a fracture of mixed-mode that experiences a complex loading–unloading–reloading process. A reasonable simulation of the interaction between the layers of slab tracks is the key to studying the interface crack. However, the existing models of interface disease of slab track have problems, such as the stress oscillation of the crack tip and self-repairing, which do not simulate the mixed mode of interface cracks accurately. Aiming at these shortcomings, we propose an improved cohesive zone model combined with an unloading/reloading relationship based on the original Park–Paulino–Roesler (PPR) model in this paper. It is shown that the improved model guaranteed the consistency of the cohesive constitutive model and described the mixed-mode fracture better. This conclusion is based on the assessment of work-of-separation and the simulation of the mixed-mode bending test. Through the test of loading, unloading, and reloading, we observed that the improved unloading/reloading relationship effectively eliminated the issue of self-repairing and preserved all essential features. The proposed model provides a tool for the study of interface cracking mechanism of ballastless tracks and theoretical guidance for the monitoring, maintenance, and repair of layer defects, such as interfacial cracks and slab arches.

Investigation of Fracture Criterion for HTPB Propellant

2012 ◽  
Vol 591-593 ◽  
pp. 745-749
Author(s):  
Bo Han ◽  
Yu Tao Ju ◽  
Chang Sheng Zhou
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Cohesive Zone ◽  
Fracture Criterion ◽  
Cohesive Zone Model ◽  
Rate Effect ◽  
Zone Model ◽  
J Integral ◽  
Loading Rates ◽  
Htpb Propellant

The fracture toughness of HTPB propellant has a significant rate effect. In order to establish a fracture criterion considering rate effect for HTPB propellant, experiments were conducted at different loading rates. Two kinds of specimens were used to get the fracture properties. Stress intensity factor and J-integral were obtained by the single edge notched tension specimen test. A power law cohesive zone model was obtained by the experiment based inverse method. Through comparing we found that the stress intensity factor and J-integral cannot model the rate effect in fracture process. The cohesive zone model (CZM) has a constant critical separation distance at different loading rates and has a capability to model the rate effect during the crack initiation and propagation process. A finite element simulation in ABAQUS was given to demonstrate its capability to model the crack propagation.

scholarly journals Critical value of the generalized stress intensity factor for a crack perpendicular to an interface

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150571 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Critical Value ◽  
Zone Model ◽  
Cohesive Stress ◽  
Generalized Stress Intensity Factor

When a crack tip impinges upon a bi-material interface, the order of the stress singularity will be equal to, less than or greater than one-half. The generalized stress intensity factors have already been determined for some such configurations, including when a finite-length crack is perpendicular to the interface. However, for these non-square-root singular stresses, the determination of the conditions for crack growth are not well established. In this investigation, the critical value of the generalized stress intensity factor for tensile loading is related to the work of adhesion by using a cohesive zone model in an asymptotic analysis of the separation near the crack tip. It is found that the critical value of the generalized stress intensity factor depends upon the maximum stress of the cohesive zone model, as well as on the Dundurs parameters ( α and β ). As expected this dependence on the cohesive stress vanishes as the material contrast is reduced, in which case the order of the singularity approaches one-half.

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.

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