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Self-similar crack propagation along a viscoelastic interface in a double-cantilever beam test

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Abstract

Double-Cantilever Beam (DCB) testing is a common protocol to evaluate bonded interface toughness. The data-analysis procedures are initially based on the classical Linear Elastic Fracture Mechanics (LEFM) and have been extended to deal with plastic behavior. Nevertheless, those analyses are not suitable when time-dependent behavior is involved in the crack propagation process. In this paper, an analysis of crack propagation along a viscoelastic interface during a DCB test is conducted, assuming a Standard Linear Solid (SLS) model for the adhesive. During the self-similar crack propagation regime, a steady-state stress–strain distribution is achieved ahead of the crack tip and a Eulerian description is used. A finite-difference scheme is implemented to solve the set of differential equations from which stress–strain evolutions along the bondline are determined as the specimen deforms. The crack propagation response under stationary loading conditions is then simulated and the energy-based failure criteria are evaluated comparing both local and global estimations of the Strain-Energy Release Rate (SERR).

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Data Availability

All data generated or analyzed during this study are included in this published article.

Abbreviations

DCB:

Double-Cantilever Beam

LEFM:

Linear Elastic Fracture Mechanics

SLS:

Standard Linear Solid

SERR, \(G\) :

Strain-Energy Release Rate

CZM:

Cohesive-Zone Modeling

DIC:

Digital Image Correlation

ENF:

End-Notched Flexure

FD:

Finite Difference

\(w\) :

adherend width

\(t\) :

adherend thickness

\(C\) :

compliance

\(\Delta \) :

opening displacement

\(P\) :

applied force

\(a\) :

crack length

\(E\) :

adherend Young’s modulus

\(I\) :

quadratic moment

\(G_{c}\) :

critical strain-energy release rate

CBBM:

Compliance-Based Beam Method

\(M\) :

bending moment

\(T\) :

shear force

\(\sigma \) :

peel stress

\(X\) :

position along the specimen

\(\varphi \) :

beam cross-sectional rotation

\(v\) :

deflection

\(G\) :

adherend shear modulus

\(S\) :

adherend cross section

\(\kappa \) :

shear correction factor

\(K\) :

interface stiffness

\(E^{*}\) :

apparent elastic modulus

\(E_{a}\) :

bonded interface modulus

DOE:

Differential Ordinary Equation

\(N\) :

number of discrete points

\(\Delta X\) :

spatial step

\(L\) :

specimen length

\(t_{a}\) :

bonded interface thickness

\(\lambda _{\sigma}\) :

characteristic wavenumber for flexible adherend

\(\lambda _{\gamma}\) :

characteristic wavenumber for shear deformable adherend

SLS:

Standard Linear Solid

\(\Delta v_{tot}\) :

relative normal displacement across the interface

\(\Delta v_{e}\) :

elastic contribution to \(\Delta v\)

\(\Delta v_{ve}\) :

viscoelastic contribution to \(\Delta v\)

\(K_{e}\) :

elastic stiffness

\(K_{ve}\) :

elastic stiffness

\(\eta_{ve}\) :

dynamic viscosity

\(\tau_{r}\) :

characteristic relaxation time

\(\tau _{c}\) :

characteristic creep time

\(K_{0}\) :

charged interface stiffness

\(K_{\infty}\) :

relaxed interface stiffness

\(da/dt\) :

crack propagation rate

\(x(t)\) :

distance to the instant crack-tip position

\(v_{max}\) :

ultimate deflection criteria

\(l^{PZ}\) :

process-zone length

\(\varepsilon \) :

strain

\(\dot{\varepsilon} \) :

strain rate

ℛ:

relaxation function

\(d\Delta/dt\) :

opening displacement rate

\(F^{*}\) :

critical applied force

\(\Delta^{*}\) :

critical opening deflection

\(G_{LEFM}\) :

critical strain energy based on LEFM

\(G_{VE}\) :

critical strain energy based on stress versus strain curve

\(SERR^{*}\) :

Reference SERR related to the relaxed interface stiffness

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Authors and Affiliations

  1. Institut de Recherche Dupuy de Lôme (UMR CNRS 6027), Brest, France

    J. P. Márquez Costa, J. Jumel, C. Badulescu & G. Stamoulis

  2. ENSTA Bretagne (UMR CNRS 6027), Brest, France

    J. P. Márquez Costa, J. Jumel & C. Badulescu

  3. Université Bretagne Occidentale, Brest, France

    G. Stamoulis

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  1. J. P. Márquez Costa
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  2. J. Jumel
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Correspondence to J. Jumel.

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Márquez Costa, J.P., Jumel, J., Badulescu, C. et al. Self-similar crack propagation along a viscoelastic interface in a double-cantilever beam test. Mech Time-Depend Mater (2022). https://doi.org/10.1007/s11043-022-09559-8

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