Advances in Modeling and Design of Adhesively Bonded Systems E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Adhesion and Adhesives - Fundamental and Applied Aspects
• Sprache: Englisch

Seitenzahl: 310

Veröffentlichungsjahr: 2013

Beschreibung

The book comprehensively charts a way for industry to employ adhesively bonded joints to make systems more efficient and cost-effective Adhesively bonded systems have found applications in a wide spectrum of industries (e.g., aerospace, electronics, construction, ship building, biomedical, etc.) for a variety of purposes. Emerging adhesive materials with improved mechanical properties have allowed adhesion strength approaching that of the bonded materials themselves. Due to advances in adhesive materials and the many potential merits that adhesive bonding offers, adhesive bonding has replaced other joining methods in many applications. Containing nine articles written by world-renowned experts, the book deals with the advances in theoretical and computational modeling as well as the design and experimental aspects of adhesively bonded structural systems. Stress analysis and strength prediction of adhesively bonded structural systems, considering a range of material models under a variety of loading conditions, are discussed. Finite element modeling using macro-elements is elaborated on. Recent developments in modeling and experimental aspects of bonded systems with graded adhesive layers and dual adhesives are described. Simulation of progressive damage in bonded joints is addressed. A novel vibration-based approach to detect disbonding and delamination in composite joints is also discussed. Readership The book is central to a range of engineers including mechanical, reliability, construction and surface engineers as well as materials scientists who are engaged in the mechanics of structural adhesive joints. Industries that will use this book include aerospace, electronics, biomedical, automotive, ship building, and construction.

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Preface

Acknowledgements

Chapter 1: Stress and Strain Analysis of Symmetric Composite Single Lap Joints Under Combined Tension and In-Plane Shear Loading

1.1 Introduction

1.2 Equations and Solution

1.3 Solution Verification

1.4 Yield Criterion

1.5 Case Studies

1.6 Summary

References

Chapter 2: Finite Element Modeling of Viscoelastic Behavior and Interface Damage in Adhesively Bonded Joints

2.1 Introduction

2.2 Finite Element Analysis of Viscoelastic Adhesively Bonded Joints

2.3 Damage Analysis of Viscoelastic Adhesively Bonded Joints

2.4 Summary and Conclusions

Acknowledgements

References

Chapter 3: Modeling of Cylindrical Joints with a Functionally Graded Adhesive Interlayer

3.1 Introduction

3.2 Axisymmetric Model

3.3 Constitutive Models of the Adherends and FMGB Adhesive

3.4 Variational Approach

3.5 Solution Procedure

3.6 Results and discussion

3.7 Summary

References

Chapter 4: A Simplified Stress Analysis of Bonded Joints Using Macro-Elements

4.1 Introduction

4.2 Linear Elastic 1D-Bar and 1D-Beam Models

4.3 Assuming a Non-linear Adhesive Material

4.4 Validation

4.5 Comparison with Finite Element Predictions

4.6 Conclusion

Acknowledgment

References

Chapter 5: Simulation of Bonded Joints Failure using Progressive Mixed-Mode Damage Models

5.1 Introduction

5.2 Cohesive Damage Model

5.3 Measurement of Cohesive Parameters

5.4 Continuum Damage Models

5.5 Conclusion

References

Chapter 6: Testing of Dual Adhesive Ceramic-Metal Joints for Aerospace Applications

6.1 Introduction

6.2 Experimental Details

6.3 Results

6.4 Conclusions

Acknowledgments

References

Chapter 7: Modelling of Composite Sandwich T-Joints Under Tension and Bending

7.1 Introduction

7.2 Description of the Experiment

7.3 Description of the Finite Element Model

7.4 Description of the Peel Stress Model: Strength of Materials Approach

7.5 Results and Discussion

7.6 Concluding Remarks

Acknowledgement

References

Chapter 8: Strength Prediction Methods for Adhesively Bonded Lap Joints between Composite–Composite/Metal Adherends

8.1 Introduction

8.2 Strength Prediction Using Characteristic Distances in Problems with Singular Stresses

8.3 Strength Prediction in Aluminium-Aluminium Joints

8.4 Strength Prediction in CFRP-Aluminium and CFRP-CFRP Joints

8.5 Results and Discussion

8.6 Conclusions

Acknowledgments

References

Chapter 9: Interface Failure Detection in Adhesively Bonded Composite Joints Using a Novel Vibration-Based Approach

9.1 Introduction

9.2 Conventionally Used Non-destructive Techniques (NDTs) for Damage Detection

9.3 Motivation and Methodology

9.4 Experimental Procedure

9.5 Experimental Results

9.6 Finite Element Modeling Investigation

9.7 Summary and Conclusions

Acknowledgments

References

Advances in Modeling and Design of Adhesively Bonded Systems

Scrivener Publishing100 Cummings Center, Suite 541JBeverly, MA 01915-6106

Adhesion and Adhesives: Fundamental and Applied Aspects

The topics to be covered include, but not limited to, basic and theoretical aspects of adhesion; modeling of adhesion phenomena; mechanisms of adhesion; surface and interfacial analysis and characterization; unraveling of events at interfaces; characterization of interphases; adhesion of thin films and coatings; adhesion aspects in reinforced composites; formation, characterization and durability of adhesive joints; surface preparation methods; polymer surface modification; biological adhesion; particle adhesion; adhesion of metallized plastics; adhesion of diamond-like films; adhesion promoters; contact angle, wettability and adhesion; superhydrophobicity and superhydrophilicity. With regards to adhesives, the Series will include, but not limited to, green adhesives; novel and high-performance adhesives; and medical adhesive applications.

Series Editor: Dr. K.L. Mittal1983 Route 52,P.O.1280, Hopewell Junction, NY 12533, USAEmail: [email protected]

Publishers at ScrivenerMartin Scrivener ([email protected])Phillip Carmical ([email protected])

Copyright © 2013 by Scrivener Publishing LLC. All rights reserved.

Co-published by John Wiley & Sons, Inc. Hoboken, New Jersey, and Scrivener Publishing LLC, Salem, Massachusetts.Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

ISBN 978-1-118-68637-9

Preface

Adhesively bonded systems find applications in a wide spectrum of industries (e.g., aerospace, electronics, construction, ship-building, biomedical, etc.) for various purposes. Emerging adhesive materials with improved mechanical properties has allowed adhesion strength approaching that of the bonded materials themselves. Owing to advances in adhesive materials and many potential merits adhesive bonding offers, adhesive bonding has replaced other joining methods in many applications. More recently there has been a high tempo of interest in bonding composite materials. The need for innovative joints and a variety of material combinations is inevitable to realize more efficient, cost-effective structural systems.

There are many aspects to proper fabrication and successful implementation of adhesive joints including adequate surface preparation, proper control of variables dictating the performance, durability and reliability. In this vein, the modeling and design of adhesively bonded joints is of cardinal importance in predicting the reliability and life of such joints.

This book containing 9 articles written by world-renowned experts deals with the advances in modeling (theoretical and computational), and the design and experimental aspects of adhesively bonded structural systems. Advances in stress analysis and strength prediction of adhesively bonded structural systems considering a range of material models under a variety of loading conditions are discussed. Finite element modeling using macro-elements is elaborated. Recent developments in modeling and experimental aspects of bonded systems with graded adhesive layer and dual adhesives are described. Simulation of progressive damage in bonded joints is addressed. A novel vibration-based approach to detect disbond and delamination in composite joints is also discussed.

In essence, this book represents a commentary on some of the advances which have been made in the arena of modeling and design of adhesively bonded systems. All signals indicate that the interest in this topic will continue unabated and innovative approaches to modeling and design of adhesively bonded systems will be taken in the future which will help in expanding the utilization of bonded systems in a host of applications with increased confidence.

It should be recorded that all manuscripts were rigorously peer-reviewed, properly edited and suitably revised before inclusion in this book. So this book is not a mere collection of papers but articles which have passed muster.

This book should be of interest to both academic researchers engaged in the mechanics of structural adhesive joints as well as to R&D personnel in various industries which rely on structural adhesive bonding for a variety of purposes.

Also we hope this book will serve as a fountainhead for new research ideas in modeling and design of adhesively bonded systems.

Acknowledgements

First of all, we are beholden to the authors for their contribution, interest, enthusiasm and cooperation without which this book would not have been possible. Second, we are very thankful to the reviewers for their time and effort in providing critical and constructive comments, as the comments from peers are sine qua non to maintain the highest standard of a publication. Also it is our pleasure to extend our appreciation to Martin Scrivener (Scrivener Publishing) for his steadfast interest in this book project and unwavering support in more ways than one.

S. KumarMasdar Institute of Science and TechnologyAbu Dhabi, UAEE-mail: [email protected]

K.L. MittalP.O. Box 1280Hopewell Junction, NY, USAE-mail: [email protected]

Chapter 1

Stress and Strain Analysis of Symmetric Composite Single Lap Joints Under Combined Tension and In-Plane Shear Loading

Jungmin Lee1 and Hyonny Kim2

1Samsung Mobile Display Inc., Yongin-City, Gyeonggi-Do, South Korea

2Department of Structural Engineering, University of California San Diego, La Jolla, California, USA

Abstract

An analysis is presented that predicts adhesive shear and peel stresses in adhesively bonded composite single lap joints. The single lap joint is under combined tension and in-plane shear loading, and accounts for moments induced by geometric eccentricity. These eccentricity moments primarily contribute to the peel stress. When shear, tension, and eccentricity moments are simultaneously applied to a joint, a combined multi-axial stress state (two shear stress components and peel) in the adhesive can be calculated. Example calculations presented in this paper show that the predicted stress profiles are well matched with finite element analysis (FEA) predictions. The von Mises yield criterion is applied to predict the elastic limit of the adhesive for a lap joint under combined loading. This approach allows the calculation of an envelope of combined loading conditions under which the joint is expected to behave elastically.

Keywords: Adhesive bonding, combined load, multiaxial stress, peel, elastic limit

1.1 Introduction

A closed-form model is derived that predicts shear and peel stress profiles in adhesively bonded symmetric single lap joints under multiaxial loading: in-plane shear load Nxy and in-plane tension load Nx. Edge moments induced from the geometric eccentricity have been accounted for when formulating shear and peel governing equations corresponding to in-plane tension load Nx. Shear stress components are computed based on shear-lag assumptions and peel stress is obtained from a beam on elastic foundation (BOEF) approach.

Classical analyses, based on shear-lag, have been previously developed to predict only the adhesive shear stress in bonded joints of uniform bondline thickness for a symmetric joint subjected to tension loading only [1, 2]. Improvements to the classical model include predicting peel stress and edge moments in single lap joints [3–6], accounting for plasticity in the adhesive prior to failure [7, 8], and allowing for transverse shear deformation of the symmetric adherends [9]. Delale et al. [10] extended Goland and Reissner’s approach for symmetric joints by formulating the adhesive shear stress equation to account for asymmetric adherends. Similar approaches for the asymmetric joints are presented by Yang and Pang [11], Bigwood and Crocombe [12], and Wu et al. [13].

Adhesively bonded lap geometries loaded by in-plane shear have been discussed by Hart-Smith [2], van Rijn [14], and the Engineering Sciences Data Unit [15]. The authors of these works indicate that shear loading can be analytically accounted for by simply replacing the adherend Young’s modulus in the tensile loaded lap joint solution with the respective adherend shear modulus. This assumption is valid only for simple cases with one-dimensional loading, whereas in-plane shear loaded joints are generally two- or three-dimensional. A closed-form solution for combined multiaxial loading is presented by Mortensen and Thomson [16], although the boundary conditions are treated as input parameters and the solution is not validated by FEA or experiment. To the authors’ best knowledge, there are no closed-form analytical works that are applicable to symmetric joints under combined shear loading and tension loading with self-induced eccentricity moments. Previous work by Lee and Kim [17] predicts adhesive shear and peel stress profiles for a generally asymmetric joint and includes the effects of eccentricity moments. Kim and Kedward [18] have computed failure envelopes for combined tension and shear but did not account for adherend bending and peel stress. Mathias et al. [19] and Adams and Peppiatt [20] have also developed stress analyses predicting the multi-axial stress state from bi-directional loading and Poisson’s ratio effects. Like the work of Kim and Kedward [18], however, these did not account for the bending moments due to load path eccentricity.

This work is the combination of recent tension/bending calculations [17] with the prediction of stresses due to in-plane shear [21]. The presented analysis accounts for uncoupled bending rigidity, Young’s modulus and shear modulus of the composite adherends depending on the laminate lay-up sequence and different lamina types (e.g., glass/epoxy versus carbon/epoxy). For an example analysis, the three adhesive stress component profiles (two shear stress components, one normal stress) for joints having [0/45]s and [45/0]s woven glass/epoxy adherends are compared with FEA predictions. Yield criterion based on von Mises effective stress is applied using the analytically predicted adhesive stress solutions to establish elastic limit loading envelopes. Carbon/epoxy composite adherends and glass/epoxy composite adherends with four different lay-ups are used to compare the effects of bending rigidity and modulus on the yield envelope.

1.2 Equations and Solution

1.2.1 Model Description

A general single lap joint with in-plane tension load (per unit width) Nx and the in-plane shear (per unit width) Nxy is shown in Figure 1.1. The following assumptions are made for the single lap joint:

Figure 1.1 Lap joint transferring in-plane shear Nxy and in-plane tension Nx.

adherends and adhesive have uniform thickness

adhesive carries shear and peel stresses only

uniform shear and peel stress profiles through the adhesive thickness (z-direction)

adherends do not deform due to transverse shear

linear elastic material behavior

The multi-axially loaded joint can be considered as a combination of two independent problems since the material behavior is assumed elastic and the in-plane tension load Nx and the in-plane shear load Nxy are independent of each other. For the tension loading (which includes edge moments), two adhesive strain components γxza and εzza are developed and, therefore, needed to be considered [17]. For the shear loading, only one adhesive strain component γyza exists [21] and is independent of the strains produced from tension loading. The governing equations, written in terms of these three independent adhesive strain components, are based on the in-plane x-direction (u1, u2), in-plane y-direction (v1, v2) and transverse z-direction (w1, w2) displacements at the upper and lower adherend-adhesive interfaces, where the index 1 refers to (upper) Adherend 1, and the index 2 refers to (lower) Adherend 2, as shown in Figure 1.1.

1.2.2 Governing Equations for Tension Loading Nx

Figure 1.2 Differential segment of single lap joint under tension loading.

(1.1)

Differentiating Eq. 1.1 with respect to x yields

(1.2)

εxx1 and εxx2 are the x-directional normal strains in the adherends at the adhesive interface. These can be determined from the in-plane normal stress resultants (N1 and N2) and the internal moment resultants (M1 and M2) based on simple beam theory [17].

(1.3)

(1.4)

(1.5)

where τaxz is the adhesive shear stress which can be shown to relate Ni, Mi and the transverse shear resultants Qi via force and moment equilibrium applied to the differential slices shown in Figure 1.2 [17].

The adhesive peel strain εazz is defined in terms of the interface-adjacent z-direction displacements w1 and w2 and thickness ta of the adhesive.

(1.6)

The adhesive peel stress σazz is determined from a beam on elastic foundation model by considering the two adherends as beams connected by a deformable interface. The relative transverse displacements of the adherends are related as [17]

(1.7)

where σazz is the adhesive peel stress. Eq. 1.7 can be written as a function of adhesive peel strain εazz via the relationship in Eq. 1.6.

(1.8)

1.2.3 Governing Equation for In-Plane Shear Loading Nxy

The in-plane shear loading Nxy produces an adhesive shear strain γayz which is defined in terms of the interface-adjacent y-direction displacements v1 and v2 in adherends 1 and 2, respectively, and thickness ta of the adhesive.

(1.9)

Differentiating Eq. 1.9 with respect to x and assuming very small (negligible) variation of the displacements with respect to y yields

(1.10)

where γxy1, γxy2 and τxy1, τxy2 are the in-plane (x-y plane) shear strain and average shear stress components in adherends 1 and 2, respectively. G1 and G2 are the in-plane (x-y) effective shear moduli of adherends 1 and 2.

In Figures 1.1 and 1.3, the applied in-plane shear load Nxy is shown to be continuous through the overlap region and at any point it must be equal to the sum of the product of each adherend’s in-plane shear stress with its respective thickness t1 and t2.

Figure 1.3 Differential element of single lap joint under in-plane shear loading.

(1.11)

From Eq. 1.11, the shear stress in the adherend 2 can be written as,

(1.12)

Substituting Eq. 1.12 into Eq. 1.10 yields

(1.13)

Force equilibrium performed on a differential element of the adherend 1, shown in Figure 1.4, results in relationship between the adhesive shear stress components τayz and the adherend 1 in-plane shear stress τxy1.

Figure 1.4 Adhesive and adherend stresses acting on element of adherend 1.

(1.14)

Differentiating Eq. 1.13 with respect to x one more time yields

(1.15)

Substituting Eq. 1.14 into Eq. 1.15 yields the relationship

(1.16)

where Ga is the adhesive shear modulus.

Eqs. 1.5, 1.8 and 1.16 are the adhesive strain governing equations for a generally asymmetric joint, i.e., one with different adherends. The case of a symmetric joint is now considered for design purposes since symmetric joints are generally more used in practice. Due to the geometry and material properties of adherends 1 and 2 being the same for a symmetric joint, Eqs. 1.5, 1.8 and 1.16 can be further simplified to Eqs. 1.17 to 1.19, respectively.

(1.17)

(1.18)

(1.19)

where

(1.20)

(1.21)

(1.22)

1.2.4 Solutions

(1.23)

The transverse shear stress resultant boundary condition, Q1, within the adherends can be written in terms of third derivative of adhesive peel strain component εazz (Eq. 1.6) resulting in:

(1.24)

(1.25)

(1.26)

Substituting Eq. 1.26 into Eq. 1.25 gives the boundary condition for Eq. 1.17.

(1.27)

The adhesive shear strain γayz is produced by the applied in-plane shear loading and is governed by Eq. 1.19. The boundary condition is defined based on the applied in-plane shear loading Nxy.

(1.28)

Substituting Eq. 1.28 into Eq. 1.13 and using the symmetric condition gives the boundary condition needed to solve Eq. 1.19.

(1.29)

1.2.4.1 Adhesive Peel Stress σzza Due to Nx

Eq. 1.18 is solved for the vertical adhesive strain component, εazz, using the general solution

(1.30)

Since εazz is symmetric with respect to and two constants are eliminated allowing Eq. 1.30 to be written as

(1.31)

The substitution of Eq. 1.31 into Eqs. 1.23 and 1.24 yields a system of linear equations from which c1 and c2 can be determined.

(1.32)

where

(1.33)

The adhesive peel stress σazz can then be obtained from the assumed linear constitutive relationship, , where Ea is the adhesive Young’s modulus.

(1.34)

1.2.4.2 Adhesive Shear Stress τxza Due to Nx

In addition to peel stress, the axial loading Nx also produces the shear strain component γaxz. Eq. 1.17 is solved using the general solution

(1.35)

(1.36)

1.2.4.3 Adhesive Shear Stress τayz Due to Nxy

The in-plane shear loading Nxy produces the shear strain component γayz. Eq. 1.19 is solved using the general solution

(1.37)

(1.38)

1.3 Solution Verification

Finite Element Analysis (FEA) was used to evaluate the accuracy of the analytically predicted adhesive stress profiles in a single lap joint. In order to analyze a state of pure in-plane shear and in-plane tension, two-dimensional axisymmetric quadratic 8-node elements CGAX8R in the commercial FEA software ABAQUS were used to model two thin-walled cylinders of very large radius (radius/thickness ratio > 1500) bonded to each other, as shown in Figure 1.6. The wall cross section of this joined cylinder represents the single lap joint described in Figure 1.1. A rotation about the cylinder’s symmetry axis and an axial displacement were applied at the upper end of the cylinder (see Figure 1.6), and the other end had all degrees of freedom (D.O.F.) fixed. This modeling approach allows a two-dimensional axisymmetric model (with non-axisymmetric loading) to be used to develop a state of in-plane shear instead of a fully three-dimensional model with complicated boundary conditions.

The smallest element size is 0.055 mm in the adhesive zone which was represented by six layers of the 8-node quadratic elements. A biased mesh was used to focus the mesh in high stress gradient zones, and to match the element size across the transition between the adhesive and the adherends. Ten elements were used through the adherends thickness with bias ratio of 3. A mesh sensitivity study had been conducted with even more refined mesh defined at the corners of the adhesive-adherend junctions (see expanded-view inset in Figure 1.6). It should be noted that these corners are singular points and thus for the elastic material properties used in the modeling, ever-increasing stresses resulted as one further reduced the mesh size. This stress singularity is not realistic, however, as adhesives exhibit some degree of nonlinearity (plasticity) and also since the perfectly sharp corner geometry is not typically created in practice as there will always exist some amount of spew forming a smooth fillet geometry. Thus, with the exception of the last element adjacent to those singular points, smaller mesh sizes were not found to affect the results, and the 0.055 mm size was chosen based on moderate computing time for a high level of refinement (recall elements are 8-node with quadratic interpolation).

Table 1.1 Joint parameters and loads for single lap joint.

Joint Parameters

Value

Adherend Thickness

t

1

,

t

2

(mm)

1.02

Adhesive Thickness

t

a

(mm)

0.33

Overlap Length 2

c

(mm)

25.4

Adherend Effective Young’s Moduli

E

1

,

E

2

(GPa)

17.6

Adherend Effective Shear Moduli

G

12

(GPa)

6.51

Adherend Bending Rigidity

D

1

,

D

2

for [45/0]

s

(kN·mm

2

)

38.2

Adherend Bending Rigidity

D

1

,

D

2

for [0/45]

s

(kN·mm

2

)

50.8

Adhesive Young’s Modulus

E

a

(GPa)

2.59

Adhesive Shear Modulus

G

a

(GPa)

0.93

Adhesive Yield Stress σ

Y

(MPa)

43.5

In-plane Tension Load

N

x

(N/mm)

17.5

In-plane Shear Load

N

xy

(N/mm)

17.5

FEA results were harvested along the adhesive centerline and are compared in Figures 1.7–1.9 with stress predictions computed by the analytical model. The three adhesive stress components and τayz are normalized by the corresponding average shear stress (Nx/ 2c) for σazz and or (Nxy/2c) for τayz. As shown in Figures 1.7–1.9, the analytical predictions are found to closely match the FEA results in all cases. A summary of the peak stresses in Figures 1.7–1.9 is given in Table 1.2, together with a percent error calculated relative to the FEA results. The stress components (τaxz, σazz) produced by the tension loading Nx tended to be under-predicted by the analytical model, while the shear stress τayz produced by shear loading Nxy tended to be overpredicted by the model, relative to the FEA results. The maximum error of 8.4% was found for the τaxz (due to Nx) stress component for the [45/0]s laminate.

Figure 1.7 Adhesive shear stress τaxz profiles due to Nx loading.

Figure 1.8 Adhesive peel stress σazz profiles due to Nx loading.

Figure 1.9 Adhesive shear stress τayz profiles due to Nxy loading.

Table 1.2 Summary of peak stress values and % error relative to FEA.

1.4 Yield Criterion

(1.39)

(1.40)

(1.41)

While other criteria can be used instead, here the von Mises yield criterion is used to predict the elastic limit of the adhesive.

(1.42)

where

(1.43)

(1.44)

(1.45)

Eq. 1.42 can be rearranged to express Nxy as a function of Nx and the yield stress σY.

(1.46)

where

(1.47)

1.5 Case Studies

Table 1.3 Adherend parameters for case studies.

For these eight laminates, Eq. 1.46 is used to plot the elastic limit load envelopes for a joint loaded simultaneously by tension and in-plane shear. Figures 1.10 and 1.11 plot normalized Nxy in terms of Nx defining the elastic limit envelopes. These envelopes are particularly useful for the design of joints subject to varying ratios of Nx and Nxy loading. For example, consider the glass/epoxy adherends case (Figure 1.10). The [45]2s lay-up will make the strongest joint if loaded by in-plane shear Nxy only. Meanwhile, the [0]2s lay-up will be the strongest joint when loaded by in-plane tension load Nx. If the joint is loaded by the combined loading, [45/0]s or [0/45]s can be a better choice than [0]2s and [45]2s. [0/45]s shows lower shear and peel stresses than [45/0]s for the in-plane tension loading due to its higher bending rigidity. Similar observations can be made for the carbon/epoxy adherends (Figure 1.11).

Figure 1.10 Yield envelopes for glass/epoxy adherends.

Figure 1.11 Yield envelopes for carbon/epoxy adherends.

1.6 Summary

A closed-form model to predict the adhesive shear and peel stress profiles for a multiaxially loaded symmetric composite single lap joint has been derived based on a coupled shear-lag and beam on elastic foundation model. The analytical model predictions of adhesive peel and shear stress profiles account for composite adherend bending rigidity variation (due to differences in lay-up sequence) and are shown to closely match with FEA predictions (within ~8%) for the example cases analyzed. The von Mises yield criterion was used to define Nx vs Nxy elastic limit envelopes within which elastic behavior can be expected. These envelopes have obvious utility in the design of composite bonded joints and show a significant difference in behavior between laminated adherends having identical in-plane stiffness but varying bending stiffness due to ply lay-up sequence. Specifically, joints with higher bending rigidity can carry higher loads under tension loading Nx, due to the lower shear and peel stresses produced by that loading mode. Thus it is recommended that the main load bearing 0° fibers be placed towards the outer surface of the composite lay-up. Under in-plane shear loading Nxy, bending rigidity was found to have no influence. However, adherends with higher shear stiffness will produce a reduction in the corresponding shear stress component.

The application of these models should be restricted to joints loaded within the linear-elastic material range and having relatively thin (up to 0.33 mm) adhesive bondline thickness, since thick bondlines tend to exhibit significant through-thickness gradients which are not captured by the uniform stress profile assumption of these models. While the models can be used to estimate failure of brittle adhesives, they can also be applied to ductile adhesives for determining what loads are associated with the joint’s elastic limit to avoid accumulation of plastic strain. Finally, while the solution presented here is for the case of identical adherends (i.e., a symmetric joint), the general governing equations have been provided by which joints with non-identical adherends can also be analyzed.

References

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