Joints AhnANDWaas 2011 H2

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Advanced computational analysis of adhesively bonded joints

Junghyun Ahn, Ph.D. Advanced Methods and Development Lead

General Atomics Aeronautical System, San Diego, CA 92128

Anthony M. Waas, Ph.D Professor of Aerospace Engineering,

Department of Aerospace Engineering University of Michigan, Ann Arbor, MI 48109

Keywords

Composite bonded, A4EI, shear stress distribution, cohesive zone, finite element analysis, joint analysis

Abstract Adhesively bonded structural components are increasingly being considered for

lightweight aerospace structures. In this article, the authors provide a state-of-the-art description of how contemporary advances in computational mechanics, based on the finite element method, can be used to obtain a basic understanding of the deformation response of adhesive joints in aerospace composite structures. In addition, engineering approaches that can be used to design bonded structural joints are also described. In particular, bonded joint analysis using cohesive zone modeling is described. As an example for a real-life design implementation of cohesive zone based bonded joint analysis, an integrated computational analysis approach is presented at the end of the article.

I. INTRODUCTION Structural joint design is one of the most challenging problems in aerospace

structures, regardless of whether joining metallic or composite parts. The traditional approach to efficient airframe structural design consists of breaking down the design cycle into various parts for specific load path (direction and magnitude), designing specific parts, taking particular loading components and using joints to transfer load among the structural members. The main load-bearing members in the wing are spar beams. These run span-wise to the wing and carry the force and moment due to lift generated from the wing. Wing skins and chord-wise airfoil shaped structural frames (ribs) transfer pressure and shear forces to the spars. Wing skins usually have stringers to add stiffness. Typical semi-monocoque fuselages have structural beams, frames, skins and stiffeners. Structural beams running longitudinally are called longerons, and a center beam, which is the major load carrying member, is called the keel. Frames can be either circumferential or fully enclosed disks (pressure bulkhead). Each component is joined either by mechanical fasteners and/or adhesives (Figure1).

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Figure1. Typical Airframe structure (Ref.1, Ref. 2)

Due to the nature of airframe structural systems (individual parts supporting particular loading components), the best overall, lightweight, design to maximize performance can be achieved by tight integration of different subsystem components; hence the most efficient design methods of joining components are crucial. Of course, the cost of parts and the total life cycle cost is always of concern in any structural design.

Joints in composite structures present an additional challenge, since the composite material, by itself, has complex failure mechanisms due to its synthetic microstructure which results in macroscopic anisotropy of properties and response. This adds complexity

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to issues associated with traditional joints including stress concentrations, eccentric load transfer through fasteners, joint interface, and out of plane failure modes at termination points. A stress concentration effect on mechanical composite joints is particularly severe because the nature of load transfer through contact interaction of fasteners is complex. Establishing allowables for various joint configurations is a very costly and time-consuming process (bearing, bypass, bearing failure allowables correlated by various fastener configurations, temperature effects and fastener geometry). Because of these issues, the preferred joining method for composite structures includes a bonded joint, whether in isolation or in conjunction with bolts (bonded-bolted joints). Modern UAV systems such as the Predator/Reaper family (Figure 2), and the Avenger Series (Figure 3) use adhesively bonded joints at most interfaces.

Figure 2 Predator-A and Reaper UAV

Figure 3 Avenger UAV

Adhesive joints are less intrusive (no need to punch holes for fasteners), and the relatively ductile response of adhesives results in less severe stress concentrations than mechanically fastened structures. The assembly process of a bonded structure can be simpler than a mechanically fastened structure (fewer parts count, no necessary treatment of holes, less inspection required during assembly process). On the other hand, bonded structures are difficult to dis-assemble and can add complexity to maintenance, repair,

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and access to other structures. Edge debonding, and delamination of thick bonded joints are a difficult issue to tackle. Impact resistance can be weak, and additional care needs to be taken in the quality control of bonding (by process control and environmental control) to ensure that consistent joint integrity is maintained throughout a production run. Predictable and docile degradation behavior without tendency to catastrophic degradation during operation use is highly sought, but difficult to achieve. This can be very hard to guarantee for certification and maintenance over a long period of time, especially for joining highly loaded, safety critical components. This is why deploying mechanically fastened composite structures is still the preferred approach in primarily loaded, safety critical composite structures.

II. BONDED JOINTS Adhesively bonded joints are more efficient than mechanical joints because they can

distribute load over a much broader area than mechanical joints. Bonded joints do not require intrusive processes such as drilling holes, putting fasteners in and tightening them. Therefore they do not create local stress concentrations which can cause bearing damage and/or delamination through the thickness of the adherend. Additionally, they are much lighter than mechanical joints. On the opposite side of the coin, bonded joints are difficult to disassemble without destroying the substrate. Particular caution needs to be taken in preparing bonding surfaces, treating bonding agents, and controlling the bonding process. Environmental degradation of bond integrity by means of galvanic corrosion of dissimilar joint materials, humidity, infrared, temperature fluctuations over a long period of time can also affect bonded joints. As a result, bonded joints require inspection techniques not traditionally adopted for mechanical joints, such as ultrasonic inspection. Typical bonded joint configurations are shown in Figure 4.

Figure 4. Typical Bonded Joints (Ref. 3)

The design approach to ensure that there is satisfactory joint reliability in the bonded joints is to avoid failure of the adhesive bond layer before adherend failure. Because of the weak nature of adhesives compared to adherends, the overall strength of the joint can be controlled by choosing different joining geometries that are suitable for an intended application.. For example, using a bond area and configuration that maximizes the bonding effect while minimizing stress concentrations, or, using an adhesive thickness that minimizes the bond shear stress and peel stress. Maximum shear stress and peel stress is achieved when the joint is designed such that the adherend fails before the

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adhesive. Joint configurations and corresponding failure effects are shown in Figure 5, from the work of Hart-Smith (Ref 4).

Figure 5. Joint configurations and strengths, as a function of adherend thickness (Ref.4)

The maximum integrity of adhesive joints is achieved by promoting adherend failure. This is achieved by controlling the joint configuration and the thicknesses of the adherends and adhesive. Good process control (surface treatment, bonding process) to ensure consistent integrity of bonding interface is crucial. Long term durability of adhesive joints, creep failure under cyclic loading with different environmental conditions (hot-wet particular) calls for detailed load spectrum analysis. Crack initiation and growth of within the adhesive layer, and also along the bond/adherend interface are major issues for the durability of bonded joints (life cycle prediction of bonded joints).

Certification of aircraft structures with bonded joints present in the primary structure is an additional challenge. The inspection limitations of bonded joints, especially for thick composite joints, have to be answered by full spectrum life analysis with a reasonable guarantee even if bond integrity is lost (fail-safe condition).

A simplified one dimensional approach by Hart-Smith along with the A4EI software codes (Ref. 3) and their derivative methods have been used in designing adhesive joints in various aerospace structures. Simple one-dimensional lap joint solutions are obtained by calculating the shear stress distribution in the adhesive for various adherend stiffness and loadings (Figure 5). For more complex adhesive joint configurations such as step joints, a one dimensional approach can be used to treat a joint as a serious of individual joints, each with uniform adherend thickness. Extensive test data is used to derive correction factors for confident failure predictions of adhesive joints.

Figure

Where

2

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11 ;dx

d

tE

T

dx

d == δδ

failure of the adhesive

The design approach using this method is from practical realization based on the feature of aerospace design that the adherends are thin relative to loading direction; hence the assumed to be linear. The adhesive joints are sized to accommodate dominant axial loading, and any complex behavior thick composite adherends, thick adhesive layers etc., empirical correction factors. are new methods that have emerged. One promising recent developmenStapleton and Waas (Ref. adhesive behavior in conjunction with standard finite element codes. extensive 3-dimensional finite element analysis accurate stress and strain distributions in the joint region and these approadescribed at the end of this section.

III. Cohesive Zone (CZTo analyze failure initiation (debonding) and crack propagation

traditional fracture mechanics based existing crack within the framework of calculate crack opening-calculated using the Virtual Crack Closure Technique (VCCT)Kanninen (Ref. 10). By comparing the SERR against critical values in pure modes or against a suitable mixed-assessment of a typical adhesive joint conveniently automated using commercially available software packages is the Zone Model (CZM), which, in addition to the SERRs also use cohesive strengths to assess crack growth predictions and accounts for finite size procescrack tip (Ref. 7). The CZM originated from the prediction of singular stresses at the crack tip (Ref. material ahead of the crack tip can be represented by a tracorigins can be micromechanical

Figure 5. Single lap joint geometry (Ref. 5)

22

2

tE

T, ADHADHADH Gand γτ

ηδδγ =−= 21

is assumed to occur when MAXADH γγ ≥ (Ref.

The design approach using this method is from practical realization based on the feature of aerospace design that the adherends are thin relative to other loading direction; hence the details of the stress distribution through the thickne

. The adhesive joints are sized to accommodate dominant axial loading, and any complex behavior induced by other factors such as, multithick composite adherends, thick adhesive layers etc., are incorporated empirical correction factors. For non-idealized, realistic behavior of adhesive jointsare new methods that have emerged. One promising recent developmen

Ref. 11), that uses a combination of analytical shape functioadhesive behavior in conjunction with standard finite element codes.

dimensional finite element analysis techniques can be used to obtain fairly accurate stress and strain distributions in the joint region and these approadescribed at the end of this section.

(CZM) based bonded joint analysis To analyze failure initiation (debonding) and crack propagation within a

traditional fracture mechanics based approaches can be used for propagation of within the framework of linear elastic fracture mechanics

-propagation, the strain energy release rateVirtual Crack Closure Technique (VCCT), as shown in

By comparing the SERR against critical values in pure modes or -mode criterion, the debonding initiation margin and growth

typical adhesive joint can be assessed. Another approach, conveniently automated using commercially available software packages is the

, which, in addition to the SERRs also use cohesive strengths to assess crack growth predictions and accounts for finite size process zones ahead of the

CZM originated from the need to re-examine the nonstresses at the crack tip (Ref. 12). It was argued that the failing

material ahead of the crack tip can be represented by a traction-separation law, whose origins can be micromechanical (Figure 6). CZM uses fracture energy as a parameter

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ADH , the shear

(Ref. 5).

The design approach using this method is from practical realization based on the other dimensions in the

stress distribution through the thickness is . The adhesive joints are sized to accommodate dominant axial

induced by other factors such as, multi-axial loads, incorporated using semi-

idealized, realistic behavior of adhesive joints, there are new methods that have emerged. One promising recent development is due to

, that uses a combination of analytical shape functions for adhesive behavior in conjunction with standard finite element codes. Alternatively,

techniques can be used to obtain fairly accurate stress and strain distributions in the joint region and these approaches are

within a bonded joint, used for propagation of a pre-

fracture mechanics (LEFM). To strain energy release rates (SERR) are

s shown in Rybicki and By comparing the SERR against critical values in pure modes or

debonding initiation margin and growth pproach, which can be

conveniently automated using commercially available software packages is the Cohesive , which, in addition to the SERRs also use cohesive strengths to

s zones ahead of the examine the non-physical

. It was argued that the failing separation law, whose

). CZM uses fracture energy as a parameter

(established from testing) to represent the effect of energy dissipation mechanisms (crack propagation) in the cohesive traction zone. strength are needed to formulate the tractionmust originate from a finite traction value since when failure occurs, the traction is finite at the crack tip (Ref. 13).

Figure 6

Implementation of CZM with (continuum cohesive zone model) or DCZM (discrete cohesive zone model). variant of the CCZM, an traction-separation law in the been proposed, and it is computed as a function of separation,

where,

The cohesive strength measure the cohesive strength and fracture energy

(established from testing) to represent the effect of energy dissipation mechanisms (crack propagation) in the cohesive traction zone. Typically a fracture energy and a cohesive strength are needed to formulate the traction-separation law. In reality, the traction law must originate from a finite traction value since when failure occurs, the traction is finite

Figure 6. Cohesive Zone Modeling (Ref. 6)

Implementation of CZM with the FEM framework can be either using CCZM (continuum cohesive zone model) or DCZM (discrete cohesive zone model).

an energy potential functionneeds to be established to define separation law in the cohesive zone. Various potential function

, and it is typical to have a polynomial form, with the tractions, computed as a function of separation, δ, using,

cohesive strength , and the maximum separation are deduced from tests that measure the cohesive strength and fracture energy.

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(established from testing) to represent the effect of energy dissipation mechanisms (crack fracture energy and a cohesive

separation law. In reality, the traction law must originate from a finite traction value since when failure occurs, the traction is finite

can be either using CCZM (continuum cohesive zone model) or DCZM (discrete cohesive zone model). In one

needs to be established to define the . Various potential functions, , have

, with the tractions, σ,

deduced from tests that

Figure 7. CCZM & DCZM

In DCZM, the cohesive behavior of discrete elements with prea robust alternative to CCZM, where applications, and suffer from convergence difficulties duringcohesive behavior. The DCZM, in contrast, treats the connections that are associated withseparation process. The method traction law with the size of an element, so that the fracture energy and cohesive strength are preserved, and is therefore

The result from a typical characterization is shown in Figure 8.

Load (P) & Displacement of Bonded Joint

Load (P) and Displacement Hybrid Joint

CCZM & DCZM and traction / separation behavior (Ref.

In DCZM, the cohesive behavior of the crack interface is embedded using nonlinear with pre-defined behavior as shown in Figure 7. The DCZM is seen as

alternative to CCZM, where the latter may become mesh sensitive in certapplications, and suffer from convergence difficulties during the unloading portion of the

DCZM, in contrast, treats the fracture behavior using discrete are associated with node pairs of the adjacent surfaces

. The method incorporates the characteristic length by scaling the traction law with the size of an element, so that the fracture energy and cohesive strength

is therefore mesh objective (Ref. 9).

typical CCZM based approach used in a characterization is shown in Figure 8.

Figure 8. Typical Hybrid - Bonded Joints

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(Ref. 7, Ref. 8)

crack interface is embedded using nonlinear The DCZM is seen as

latter may become mesh sensitive in certain unloading portion of the behavior using discrete

adjacent surfaces involved in the incorporates the characteristic length by scaling the

traction law with the size of an element, so that the fracture energy and cohesive strength

a basic hybrid joint

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For both joint interface models, the bonded surface behavior through contact definition is described along the bonded interface. The mechanical fasteners in the hybrid joints are modeled as beam elements, which may have a form of full 3D solid bolt model as well at the expense of computation cost. In the bonded joint pull off test, there is considerable crack arrest and further growth (non-smooth crack growth), prior to final failure, and the FE results are seen to capture the average trend observed in the test results. For the case of hybrid bonded joint simulation, the pull-off load is seen to increase with the displacement of the load point, followed by failure initiation through debonding (small load drop), then there is further increase in load with intermittent crack growth until final failure.

Hybrid joints consisting of adhesive and fasteners (bonded-bolted joints) are common in today's aircraft structures. The inherent redundancy of these joints solves some of the certification problems posed by purely bonded joints. The bond interface behavior between composite parts can be modeled using surface based contact behavior, which is an available function in modern nonlinear FE packages, such as LS-DYNA®, MARC®, and ABAQUS®. The advantages of this approach in real applications are;

1. No need to use expensive specialized elements, user subroutines or a user element

2. Using existing contact pair modeling, with prescribed traction-separation laws

3. Specifying the contact behavior in areas where debonding is most likely to occur (bond-lines)

The surface based cohesive behavior requires several parameters including bond line stiffness, damage initiation, damage evolution, and damage stabilization. These parameters come together to describe the behavior of the bond line. Coupon level test data are used to determine the values for describing the bond line response. These can be coupled with information from subcomponent level design studies and used for the system level model predictions. The latter is where testing becomes more complex and expensive and thus this is where a robust computational model can be made to be most useful. The flow chart in Figure 9 shows a typical procedure for evaluating joints up to the system level while minimizing cost.

Figure 9. Finite

IV. Design PerspectiveIn designing aerospace structures with

aspect of structural analysis is the tradeinformation usually takes more time) and efficiency of solution (quick turnaround, timely information necessary to advance design) per a given task scope and Understanding certification requirementoperational-environmental degradation and failsafe condition) of joint configurationdictates the airframe design as well. technologies in the field of finite pre/post-processing, together with a an entire system (airplane level)system) as part of an integrated product design processRepresenting a realistic joint interface in advantages in understanding joint behavior under more representative loading conditionidentifying critical design areabehavior for damage tolerance assessment. preceding work in validating component level before implementing in

An airplane level integrated analysis approach (full aircraft system with everything down to each joint simulated) for adhesive joint analysis, is

. Finite Element Model Procedure and Flow Chart

Perspective gning aerospace structures with bonded and hybrid structures, the most critical

aspect of structural analysis is the trade-off between analysis accuracy (the more accurate ally takes more time) and efficiency of solution (quick turnaround, timely

information necessary to advance design) per a given task scope and a set of Understanding certification requirements (impact resistance, damage tolerance,

environmental degradation and failsafe condition) of joint configurationthe airframe design as well. With appropriate deployment of

technologies in the field of finite element analysis methods, which includes essing, together with a system level-integrated analysis approach, analyzing

(airplane level) level structure (a full wing, fuselage and empennage integrated product design process has been quite successful

realistic joint interface in the airplane level analysis has distinct in understanding joint behavior under more representative loading condition

identifying critical design areas, and assessing the probability of debonding/degrbehavior for damage tolerance assessment. Airplane level design analysis requires preceding work in validating the joint modeling approach (Figure 9) from coupon to subcomponent level before implementing in an airplane level structure.

e level integrated analysis approach (full aircraft system with everything down to each joint simulated) for system level aircraft design, in addition to localized

is one of the sought after objectives in a modern integrated

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and Flow Chart

bonded and hybrid structures, the most critical between analysis accuracy (the more accurate

ally takes more time) and efficiency of solution (quick turnaround, timely a set of deliverables.

(impact resistance, damage tolerance, environmental degradation and failsafe condition) of joint configurations

With appropriate deployment of the latest which includes high speed

integrated analysis approach, analyzing level structure (a full wing, fuselage and empennage

has been quite successful. airplane level analysis has distinct

in understanding joint behavior under more representative loading conditions, debonding/degradation

Airplane level design analysis requires ) from coupon to sub-

e level integrated analysis approach (full aircraft system with everything in addition to localized

one of the sought after objectives in a modern integrated

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aerospace composite structure. Such analyses approaches are being considered for successful implementation in many ongoing airplane programs.

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