Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures

TLDR: The obtained results shed light on the behavior of crack paths, which are drastically affected by the elastic modulus mismatch between two layers and interface types, and reveal the important role of the proposed interfacial transition zone in phase field modeling of crack-interface interactions.

About: This article is published in Journal of Computational Physics.The article was published on 2019-06-01 and is currently open access. It has received 51 citations till now. The article focuses on the topics: Cohesive zone model & Phase field models.

Figures

Fig. 2. Problem definition: phase field description of smeared cracks in a heterogeneous bi-material.

Fig. 4. Schematic of bi-material layered structures containing cracks and their geometry and boundary conditions for (a) 2-D model and (b) 3-D model. The material information used for these two layered structures and other relevant parameters are detailed in the numerical results section.

Fig. 21. Comparison of crack paths and stress-displacement curves among (C1), (C2), and (C3), with `Trans/` = 2, zoom in the interested region (x = [12 28]; y = [2 10])

Fig. 22. Schematic of geometry and boundary conditions for a multi-layered structure according to the experimental set-up in [61] (unit in mm)

Table 4. Material parameters used for the multi-layered structure depicted in Fig. 23.

Fig. 8. Displacement in y− direction on the line of investigation. Sharp transition stands for the (C1) while Cohesive transition for (C2).

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures" ?

In the past decades, the failure in such layered media has been studied by many researchers due to their critical role in the mechanics and physics of solids. This study aims at investigating crackinterface interaction in two-dimensional ( 2-D ) and three-dimensional ( 3-D ) layered media by a phase field model. Their objectives are fourfold: ( a ) to better understand fracture behavior in layered heterogeneous systems under quasi-static load ; ( b ) to introduce a new methodology for better describing interfaces by a regularized interfacial transition zone in the context of variational phase field approach, exploring its important role ; ( c ) to show the accuracy, performance and applicability of the present model in modeling material failure at the interfaces in both 2-D and 3-D bodies ; and ( d ) to quantitatively validate computed crack path with respect to experimental data. 

Q2. What are the future works mentioned in the paper "Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures" ?

This interesting work is out of the scope of the current study but has already been scheduled for their future studies. 

Q3. What is the popular technique for studying the fracture phenomena in layered media?

Linear Elastic Fracture Mechanics (LEFM) is the popular technique, where the fracture phenomena are often investigated through stress intensity factors (SIFs), toughness or asymptotic solutions. 

Q4. What are the factors that must be analyzed thoroughly?

In fact, the change of elastic properties and fracture characteristics from layer to layer, type of loading experienced, crack orientation, etc. are certainly important factors that must be analyzed thoroughly. 

Q5. What is the advantage of the phase field model?

The most advantage of the phase field model is its ability in modeling crack initiation and propagation without any prescriptions of crack geometries. 

Q6. What is the evolution of phase field that could guarantee the irreversibility of the process?

The evolution of phase field that could guarantee the irreversibility of the process is derived from the thermodynamically consistent framework. 

Q7. What is the phase field method at small strains?

In the phase field method at small strains, the regularized form of the energy describing the cracked structure is expressed asE(u, d) = ∫Ωψu(ε(u), d) dΩ + ∫Ωgcγ(d,∇d) dΩ, (4)where ε is the linearized strain tensor, while ψu is the elastic strain energy density, which depends on both the displacements u(x) and the phase field d(x) describing the damage of solid. 

Q8. What is the effect of the material mismatch ratio on the fracture behavior at the interface?

The material mismatch ratio has a strong influence on the fracture behavior at the interface in layered structures, showing a substantial dependence of crack penetration and branching on the material mismatch.• 

Q9. What is the effect of the sudden gap between the material parameters?

In the case of sharp transition (see Fig. 12(a)) the sudden gapwithin the material parameters leads to a large change of the displacement between two layers (see Fig. 8), inducing also a sudden gap of the strain energy. 

Q10. What does it mean that the crack is propagated in the second layer?

It means that, while keeping the critical fracture energy, it is expected the propagation of the crack in the second layer when increasing the strain energy ψ+(x) at the interface region. 

Q11. What is the main reason why layered systems have great potential in applications?

Although layered systems have great potential in applications, their mechanical behavior however heavily depends on the mechanical properties and performance of the interfaces. 

Q12. How is the strain energy controlled by the phase field method?

Noted that the crack creation by means of the phase field method is controlled by the ratio between the positive part of strain energy ψ+(x) and fracture energy gc. 

Q13. What is the effect of the smooth transition zone on the thickness of the interface?

the smooth transition zone creates the thickness interface, where the strain energy transmits smoothly from layer to layer (see Fig. 12(b)). 

Q14. What is the importance of the knowledge of failure behavior at the interfaces in layered media?

The knowledge of failure behavior at the interfaces in layered media thus is of great importance to the design of engineering applications, and it holds one major research subject to the scientific community. 

Q15. What is the cost of the cohesively bonded interface model?

this model seems to be more computationally expensive (i.e., significant increase of the computational time for direct/indirect solving FEM equations of phase field problem, requiring more iterations for Newton-Raphson method in the coupling with cohesive zone model).