Mixed-mode cohesive fracture of adhesive joints: Experimental and numerical studies

doi:10.1016/j.engfracmech.2008.04.023

Engineering Fracture Mechanics

Volume 75, Issue 15, October 2008, Pages 4363-4382

https://doi.org/10.1016/j.engfracmech.2008.04.023 Get rights and content

Abstract

A broad experimental and analytical effort using fracture mechanics as the prime tool was conducted to investigate and improve the understanding of the mixed-mode cohesive fracture behavior of bonded joints. As a part of experimental efforts, mixed-mode fracture tests were performed using modified Arcan specimens consisting of several combinations of adhesive, composite and metallic adherends with a special loading fixture, in which by varying the loading angle, from 0° to 90°, mode-I, mixed-mode and mode-II fracture data were obtained. Finite element analyses were also carried out on specimens with different adherends. The main objective of this study was to determine the fracture toughness K_IC and K_IIC for a range of substrates under mixed-mode loading conditions. Another goal was to study the relationship between the stress intensity factors and the fracture toughness. Based on those analyses, mixed mode fracture criterion for the adhesively bonded systems under consideration determined. Fracture surfaces obtained at different mixed-mode loading conditions for various adherends were finally discussed.

Introduction

Adhesive joints offer significant advantages over traditional joining methods such as welding or mechanical fastening in structural applications. Adhesively bonded joints and bonded repairs for cracked metallic structures have been continuously receiving attention in the aerospace industry for the purpose of enhancing fatigue resistance and restoring the stiffness and strength of damaged/cracked structures. Although stress-based approaches, which focus on indicating both shear and normal (peel) stresses through standard lap shear tests, have been the subject of a vast amount of research, additional design considerations are required since adhesively bonded joints usually fail by initiation and propagation of flaws. Fracture mechanics deals with the effects of flaws and fatigue in the presence of cracks and has been proven to be a viable tool for adhesive joints analysis. The fracture aspects of adhesively bonded joints have been discussed by several researchers [1], [2], [3], [4], [5], [6].

A number of test methods have been proposed by many researchers to determine fracture toughness of adhesively bonded joints. The double cantilever beam (DCB) test is the most widely used method for measuring mode-I (opening) fracture toughness. The end-notched flexure (ENF) has emerged as one of the most convenient mode-II (shear) type fracture tests. Various attempts have been made to characterize fracture toughness under mixed-mode loading conditions in adhesively bonded joints, where mostly beam type specimens were used. The crack lap shear (CLS) and the mixed-mode bending (MMB) test specimens have been proposed by combining the schemes used for DCB and ENF tests to study the mixed-mode fracture of bonded joints [7], [8], [9], [10], [11], [12]. However, for these test methods there are problems to create a wide range of mixed-mode ratios which limits their usefulness. Also, different beam type specimens would be required in order to obtain reliable results for fracture toughness in pure mode-I, pure mode-II, and mixed-mode loading conditions.

Previous work in this area has centered on the double cantilever beam (DCB) and end-notched flexure (ENF) [13], [14], [15], [16], [17], [18], [19]. However, deeper understanding of the fracture behaviour of adhesively bonded joints, particularly under mixed-mode loading conditions, is needed in order to fully achieve the benefits of adhesive bonding. Several studies have been conducted on adhesively bonded joints under mode-I, mode-II and mixed mode loading conditions. Pang and Seetoch [3] using compact mixed mode (CMM) fracture specimen reported from his study with a two-part epoxy structural adhesive (Ciba Geigy AW106/HV953U) adhesive that the adhesive fracture toughness measured under different loading modes were ordered as mode-I < mixed-mode < mode-II. However, the similar study Pang [4] revealed that mode-II fracture toughness is lower than the mode-I. It is not clear whether the fracture surfaces were analysed to gain insight into the fracture mechanisms. Pirondi and Nicoletto [7] in their study using compact tension-shear (CTS) specimen with a commercial elastomer methacrylate adhesive (Loctite Multibond 330), reported that the K_IIc/K_Ic ratio is very close to unity and a fracture toughness in mode-II higher than in mode-I is not a unique possibility with considering the interaction of factors such as the roughness of the crack surfaces, the presence of residual stresses and the mismatch of elastic properties at the interface. In a study of mixed-mode fracture behavior of aluminum alloy specimens bonded with a tough one-part epoxy adhesive (Dow Automotive Betamate 46011^®), Liu et al. [12] adapted and modified MMB test used for mixed-mode, mode-I and mode-II delamination testing of composite laminates for fracture testing of adhesively bonded joints and reported that the mode-II strain energy release rate is higher than mode-I strain energy release rate. A study on mode-I, mode-II and mixed-mode (I and II) using double cantilever beam (DCB), end notch flexure (ENF), and mixed mode flexure (MMF) tests by Parvatareddy and Dillard [13] on a chromic acid anodized titanium (Ti-6A-4V)/polyimide (FM-5) adhesive system reported that the adhesive fracture toughness measured under different loading modes were ordered as mode-I > mixed-mode > mode-II and interfacial type failures were observed in the ENF and MMF specimens as a result of the mode-II loading inherent in these tests. They also reported that loading mode; changes in material properties along the length and thickness of the bond line, and environmental aging all play an important role in experimentally determining the fracture toughness of this bond system. Ducept et al. [11] studied the mode-I (DCB), mode-II (ENF) and mixed-mode I/II (MMB) fracture of adhesively bonded composite/composite joint by bonding together two 8 ply glass epoxy laminates (Cotech 250 g/m2 glass reinforcement, DGEBA based epoxy reference SR1500 with amine hardener SD2505 from Sicomin) with a two-part epoxy adhesive (Redux 420, from Ciba Geigy), reported from their study that the crack seems to propagate mainly in the first composite resin layer, very close to the composite/adhesive interface, but in some specimens cracks do appear in the adhesive layer and fracture toughness measured under different loading modes were ordered as mode-I < mixed-mode < mode-II. Except for the adhesive and adherends, the only obvious difference between the studies was different test methods used to obtain mixed mode loading conditions.

In this work, a modified version of the Arcan specimen is made for the mixed-mode fracture test of adhesively bonded joints, which allows mode-I, mode-II, and almost any combination of mode-I and mode-II loading to be tested with the same test specimen configuration. The Arcan test specimen was originally designed for use with fibre-composite materials [20], [21], [22], [23], but has been adapted by many researchers for use with adhesives [3], [4] and isotropic materials [24], [25], [26]. Therefore, the limitations presented in the previous mixed-mode toughness test methods can be avoided. Mixed-mode fracture experiments were conducted to determine the fracture toughness of adhesively bonded joints for various adherends. The stress intensity calibration was obtained by finite element analysis using the finite correction factors method. The mixed-mode fracture criteria were determined and fracture surfaces obtained at different loading angles for various substrates were discussed.

Section snippets

Mixed-mode cohesive fracture mechanics

The failures in adhesively bonded joints are mainly of two types; adhesive and cohesive (Fig. 1). Well-bonded joints should fail within the adhesive (cohesive) or within the adherends (interlaminar failure) when broken apart. Failure at the adherend–adhesive interface (interfacial failure) generally indicates that the bond was not performed properly. Since adhesive joints usually fail by the initiation and propagation of cracks, the application of fracture mechanics theories to adhesive joint

Materials and specimens

The modified Arcan test specimen and loading fixture (composed of a pair of grips) are shown in Fig. 4. The specimen is attached to the fixture by three pins at each end. The specimen is loaded by pulling apart grips of the fixture at a pair of grip holes on the opposite sides of a radial line. By varying the loading angle α (α = 0°, 15°, 30°, 45°, 60°, 75°, 90°), all mixed-mode conditions starting from pure mode-I to pure mode-II can be created and tested.

Experimental efforts focused on the

FE Analysis of mixed-mode cohesive fracture

Concepts of linear elastic fracture mechanics combining with finite element analysis provides a practical and convenient means to study the mixed-mode cohesive fracture characteristics of adhesively bonded joints. In the context of quasi-static analysis the J-integral in two dimensions is defined as [32] $J = \lim_{Γ \to 0} \int_{Γ} n \cdot (W I - σ \cdot \frac{\partial u}{\partial x}) \cdot q d Γ$ where Γ is an arbitrary contour, W is the elastic strain energy for elastic material, q is a unit vector in the virtual crack extension direction, n is the outward

Numerical results

In order to assess stress intensity factors at fracture $K_{I}$ and $K_{II}$ using Eq. (5), geometrical factors or non-dimensional stress intensity factors $f_{I} (a / w)$ and $f_{II} (a / w)$ for both pure mode-I and pure mode-II loadings were determined. The $a / w$ ratio was varied between 0.3 and 0.7 at 0.1 intervals and a fourth order polynomial was fitted through finite element analysis. From the finite element results, closed-form solutions using least square fitting for a modified Arcan specimen with aluminum

Conclusions and summary

In this study the mixed-mode fracture behaviour of adhesively bonded joints constructed from several combinations of adhesive, composite and metallic adherends was investigated based on experimental and numerical analyses. A modified version of an Arcan specimen was employed to conduct a mixed-mode test using a special test loading device. The full range of mixed-mode loading conditions including pure mode-I and pure mode-II loading can be created and tested. It is a simple test procedure,

Acknowledgments

The School of Aerospace, Mechanical and Mechatronic Engineering and the Electron Microscope Unit at the University of Sydney has kindly provided access to their facilities. I also would like to thank professor Lin Ye for his valuable time, advice, guidance, and support throughout my study.

References (37)

H.L.J. Pang et al.
A compact mixed mode (CMM) fracture specimen for adhesive bonded joints
Engng Fract Mech
(1997)
H.L.J. Pang
Mixed mode fracture analysis and toughness of adhesive joints
Engng Fract Mech
(1995)
I.A. Ashcroft et al.
Mode I fracture of epoxy bonded composite joints 2. Fatigue loading
Int J Adhes Adhes
(2002)
A. Baker
Bonded composite repair of fatigue-cracked primary aircraft structure
Compos Struct
(1999)
A. Pirondi et al.
Mixed mode I/II fracture toughness of bonded joints
Int J Adhes Adhes
(2002)
R. Rikards
Interlaminar fracture behaviour of laminated composites
Comput Struct
(2000)
G. Lawcock et al.
The effect of adhesive bonding between aluminum and composite prepreg on the mechanical properties of carbon-fiber-reinfored metal laminates
Compos Sci Technol
(1997)
F. Ducept et al.
An experimental study to validate tests used to determine mixed mode failure criteria of glass/epoxy composites
Compos Part A: Appl Sci Manuf
(1997)
F. Ducept et al.
Mixed mode failure criteria for a glass/epoxy composite and an adhesively bonded composite/composite joint
Int J Adhes Adhes
(2000)
C. Yan et al.
Effects of substrate materials on fracture toughness measurement in adhesive joints
Int J Mech Sci
(2001)

L. Banks-Sills et al.

A mixed mode fracture specimen for mode II dominant deformation

Engng Fract Mech

(1984)

M.A. Sutton et al.

A combined modeling-experimental study of the crack opening displacement fracture criterion for characterization of stable crack growth under mixed mode I/II loading in thin sheet materials

Engng Fract Mech

(2000)

M.A. Sutton et al.

Development and application of a crack tip opening displacement-based mixed mode fracture criterion

Int J Solids Struct

(2000)

K.-Y. Kim et al.

Interlaminar fracture toughness of CF/PEI composites at elevated temperatures: roles of matrix toughness and fibre/matrix adhesion

Compos Part A: Appl Sci Manuf

(2004)

X. Deng et al.

A study of some issues in stable tearing crack growth simulations

Engng Fract Mech

(1999)

E. Mahgoub et al.

Three-dimensional stress and deformation fields around flat and slant cracks under remote mode I loading conditions

Engng Fract Mech

(2003)

A.J. Kinloch

Adhesion and adhesives: science and technology

(1987)

G.P. Anderson et al.

Analysis and testing of adhesive bonds

(1977)

Cited by (64)

Extrinsic/intrinsic cohesive zone modelling and experiments on interface failure of multi-walled carbon nanotube reinforced adhesively bonded joints under mode II loading
2023, Theoretical and Applied Fracture Mechanics
The present work is primarily concerned with determining mode II cohesive zone parameters for eliminating the crack tip stress-field singularity for constant, linear, and parabolic extrinsic cohesive zone models (CZMs). A semi-analytical approach is used to estimate the stress intensity factor (SIF) associated with the cohesive zone ahead of the physical crack tip. Simultaneously, the obtained SIF is compared with the popular Interaction integral technique results considering the influence of crack face traction. The influence of the order of the traction-separation law (TSL) on the global load–displacement responses is numerically investigated using a crack propagation methodology based on the nullification of SIF. The effectiveness of the proposed approach has been demonstrated through a series of experiments involving the failure of epoxy-based adhesively bonded modified compact tension specimens (CTS) subjected to pure mode II loading. The adhesives are reinforced with different multi-walled carbon nanotubes (MWCNTs) reinforcement of 0.1 wt%, 0.2 wt%, and 0.3 wt%, and its effect on the global load vs displacement responses are recorded. Specific cohesive zone parameters are obtained for the experimental problem to model the failure behaviour for a broad spectrum of cases considered using extrinsic and intrinsic TSLs.
Experimental study and hybrid optimization of material extrusion process parameters for enhancement of fracture resistance of biodegradable nanocomposites
2023, Engineering Failure Analysis
Among the additive manufacturing processes, the material extrusion (ME) is the most popular and affordable technique in production of a wide range of products, from prototypes to the final products, for different industrial sectors. The most popular raw material in this process is the biodegradable polylactic acid (PLA) polymer that offers ease of production in relatively low price and wide applications in synthesis of medical proteases. However, the mechanical strength of fabricated samples and their resistance against the fracture loadings, which are critical for components synthesized for medical applications, are strongly dependent on the ME process parameters and the composition of the base material. Therefore, this study is aimed to address both the strengthening mechanisms of inorganic CaCO₃ nanoadditives in the PLA matrix and the influence of ME process parameters on the fracture resistance of fabricated samples. To this aim, the PLA/CaCO₃ nanocomposite filaments have been produced by mix-blending/extrusion technique and were employed to fabricate tensile and fracture test samples in ME process under different sets of parameters, including printing speed, layer thickness, filling ratio and printing pattern, determined by Taguchi L₂₇ orthogonal array. The fracture experiments were conducted on a uniaxial tensile test machine using a specially designed fixture that makes the application of mixed-mode loading on fracture samples possible. The results of fracture toughness of specimens were employed as input data to model the response of fabricated samples and to determine the ME parameter levels and nanoparticle concentrations for maximum fracture resistance of fabricated samples based on a hybrid algorithm of artificial neural network and ant colony optimization (ANN/ACO). Differential scanning calorimetry was used to characterize the thermal features (i.e. glass transition, crystallization and melting temperatures) as well as the degree of crystallization of ME samples. Scanning electron microscopy of fracture surfaces were employed to study the influence of ME parameters and CaCO₃ nanoadditives on the characteristics of fracture of 3D printed specimens under various modes of loading. Overall, the results showed that the effects of ME parameters on the fracture behavior of 3D printed samples are highly interconnected and, in the case of a semicrystalline polymer, are highly dependent on the physical characteristics of the fabrication process, including the heat transfer and crystallization rate of the matrix.
Hygrothermal aging of steel/FRP pipe repair systems: A literature review
2023, International Journal of Pressure Vessels and Piping
Fiber-reinforced polymers (FRP) have rapidly gained acceptance as a permanent repair material for damaged steel pipelines in oil and gas industry within the last few years, due to many advantages such as lower cost, possibility of repairing during operation and superior properties and corrosion resistance. However, several works have shown that these composites may undergo degradation with time mainly associated to water absorption, which is currently not addressed properly in design codes. This literature review intends to gather information and present the relevant aspects of hygrothermal aging of FRP and steel/FRP systems. Covered topics including: i) water ingress mechanisms; ii) damage formation/propagation in polymers and FRP; and iii) FRP's property retention and its interface with metallic substrates. Whenever possible, phenomenological Arrhenius models calibrated on available experimental results are presented as guidance. Gaps in the knowledge are identified throughout the work and some research needs and challenges are presented and discussed.
In situ optical observation of damage and failure process in adhesively bonded CFRP joints under mixed-mode loading
2023, Composite Structures
Citation Excerpt :
Fracture toughness slightly increased under pure mode I loading compared with that in the case of GII/GT = 0.25. Fracture toughness increased considerably with an increasing mode II component as already reported in previous studies [2–4,8,9]. The highest fracture toughness was obtained under pure mode II loading.
The effects of mode mixity on microscopic damage and failure process in adhesively bonded carbon fiber reinforced plastic (CFRP) joints were studied by in situ observation. Optical microscopy observation revealed that the damage and failure process were largely affected by the mixed-mode ratio of joints. The whitening of the adhesive resin due to cavitation was observed with an increasing mode I component, whereas the plastic zone length increased with an increasing mode II component. The damage and failure process observed by experiment were correlated with the stress state around the crack tip obtained by finite element analysis. The results indicated that the microscopic failure process well reflects the deformation and failure properties of epoxy resin depending on stress triaxiality.
Innovations in fracture testing of structural adhesive bonds
2023, Advances in Structural Adhesive Bonding, Second Edition
This chapter covers recent developments in the application of fracture mechanics methods to adhesive joints. The focus is on novel experimental methods and specimen types in single-mode and mixed-mode testing. Other aspects are experimental challenges that result from special fracture tests under fatigue, creep, impact, or aging conditions. In the area of test evaluation, nonlinear fracture mechanics with J-integral is becoming increasingly popular. The chapter closes with an assessment of future trends.
Durability study of adhesive joints used in high-speed crafts manufactured with composite materials subjected to impact fatigue
2020, Engineering Fracture Mechanics
Marine high-speed crafts manufactured with composite materials are exposed to constant impacts due to the cyclic contact of the vessel with the water surface. These low-energy impacts can affect the structural integrity of the hull and could be an example of impact fatigue. Certain fast boats manufactured with composite materials are designed in such a way that the hull and deck are assembled with adhesive joints. However, in most of these cases, the adhesive thickness is not measured or controlled. The purpose of this research is to evaluate the effects of the adhesive thickness on the durability and crack growth rate behaviour of adhesive joints used in certain types of high-speed crafts under constant amplitude fatigue and impact fatigue regimes. This study was performed by using experimental procedures with double cantilever beams and single lap joints specimens. The results showed that the durability at impact fatigue conditions is two orders of magnitude lower than constant amplitude fatigue at comparable force levels. In addition, the crack growth rate in impact fatigue conditions showed improvement of fatigue properties when a lower thickness of adhesive was used. On the other hand, the crack growth rate was lower in the constant amplitude fatigue regime in comparison to impact fatigue.

View all citing articles on Scopus

View full text

Mixed-mode cohesive fracture of adhesive joints: Experimental and numerical studies

Abstract

Introduction

Section snippets

Mixed-mode cohesive fracture mechanics

Materials and specimens

FE Analysis of mixed-mode cohesive fracture

Numerical results

Conclusions and summary

Acknowledgments

Engng Fract Mech

Engng Fract Mech

Int J Adhes Adhes

Compos Struct

Int J Adhes Adhes

Comput Struct

Compos Sci Technol

Compos Part A: Appl Sci Manuf

Int J Adhes Adhes

Int J Mech Sci

Engng Fract Mech

Engng Fract Mech

Int J Solids Struct

Compos Part A: Appl Sci Manuf

Engng Fract Mech

Engng Fract Mech

Adhesion and adhesives: science and technology

Analysis and testing of adhesive bonds