Crack initiation and propagation phases detection in fatigue life of adhesively bonded joints

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Università di Pisa

Scuola di Ingegneria

Corso di Laurea Magistrale in Ingegneria Meccanica

Crack initiation and propagation phases

detection in fatigue life of adhesively bonded

joints

Tesi di

Giuseppe Andrea Monaco

Candidato:

Giuseppe Andrea Monaco

Relatore:

Prof. Francesco Frendo

Dr.-Ing. Jörg Baumgartner

Sessione di Laurea 10 Luglio 2019 Anno Accademico 2018/2019

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Chapter 1 Introduction

Nowadays, screws, nuts, washer and all other classical mechanical fasten-ing represent a reliable way to join various components, furthermore many design approaches are available in literature. However, the use of adhesive bonding has spread during the last few decades, especially in automotive and aerospace industries. The major advantages of adhesives are their high fatigue resistance, long fatigue life and the opportunity to join thin and dissimilar components. Furthermore, automotive and aerospace industries widely use adhesively bonded joints due to the requirement of lightweight materials allowing vehicles to achieve less power consumption.

Fatigue is one of the most important and critical load for structural compo-nents. Therefore, fatigue analysis and fatigue strength evaluation are highly required in industrial machine design. Analytical and experimental fatigue analysis are generally carried out together. The latter still plays the major role in research activities.

Based on that, an analytical approach followed by experimental tests is ex-plored in this work in order to gather informations about multi-material bonded joints. The present work and all the fatigue tests have been carried out at Fraunhofer Institute for Structural Durability and System Reliability LBF in Darmstadt, Hessen.

1.1 Summary

Previous to work presentation and results illustration, a brief introduction to adhesives is given focusing on their properties and composition. Subse-quently, some information about fluctuating load application on mechanical structures and analytical models for fatigue life evaluation are illustrated, concluding the introduction with a overview on experimental methods

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avail-CHAPTER 1. INTRODUCTION able for crack initiation and propagation detection.

To gather information about a bonding method is common approach to man-ufacture a simple geometry specimen analysing strength and resistance. Re-sults can be subsequently used to design various kind of component. As a matter of fact, in the present work two kind of specimen are taken into ac-count: single lap shear specimen and T-peel specimen. This two geometries are selected for two main reasons:

• to simulate the bonding performances under two basic types of load: shear and peel;

• the simple geometry leads to easier and faster manufacturing process. Instead the overlap length is chosen as a widely used value in literature. Previous to experimental analysis, preliminary investigation through Finite Element Analysis is carried out. Crack initiation surface for single lap shear specimen is evaluated while some geometry parameters are set in FEA for T-peel specimen. As explained in detail in Chapter 3, FEA play an important role also in defining strain gauges position for crack initiation and propaga-tion detecpropaga-tion using backface strain method.

Chapter 4 presents the experimental analysis carried out, illustrating results obtained from the various method of crack initiation and propagation detec-tion selected. L-N curves are evaluated from fatigue tests. However, S-N curves are more important in engineering design and for this reason in Chap-ter 5 FE models are modified in order to evaluate stresses in the adhesive layer deriving Wöhler curves.

Bearing in mind that one of the method for crack initiation detection take advantage of optical inspection through photos taken during fatigue tests, in Chapter 6 a procedure for automatic crack initiation detection is devel-oped. After a brief introduction and overview about image analysis methods available, two approaches are presented and compared. A camera set-up is defined.

Finally, a brief conclusion and future developments are outlined in Chapter 7.

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Chapter 2 State of Art

2.1 Adhesive

The first use of adhesives dates back to thousands of years ago. The major part of them was extracted from natural products such as bones, fish skin, milk proteins and plants. During the last hundred of years, adhesive use has increased due to improved mechanical properties because of a change in composition. Nowadays, adhesives are made of synthetic polymers and are employed in many industrial applications.

The joining weight is not the only reason for the growing adhesive usage. Comparing adhesive to traditional mechanical fasteners, the first ensures a wider contact area providing a much more constant stress distribution (Fig-ure 2.1a) and enough strength for structural application even though adhesive has mechanical properties well below that of metals. Instead considering a bolted joint (Figure 2.1b), stress distribution shows discontinuities in the connection area. Beyond these advantages, adhesive allows to connect dis-similar materials minimizing and preventing electrochemical corrosion and due to polymeric nature ensures to the joint good damping properties. Besides these convenient aspects, adhesively bonded joint shows big disad-vantages. Following a joint from its design to commissioning: no classical or simple rules can be used to design this type of joint, such as the one used for typical mechanical joints. Production also requires specific operations and tools e.g. holding fixtures and oven to apply and then perform the adhe-sive heat curing. The latter process is carried out to harden polymer and it needs high temperature for a long period representing a big economical disadvantage. The quality control of the joint is more difficult too. It is not possible to dismantle an adhesive bond but a series of non-destructive technique are available. Lastly, external conditions play an important role

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CHAPTER 2. STATE OF ART

(a) (b)

Figure 2.1: Stress in: (a) adhesive joint; (b) bolted joint.

in reducing adhesive mechanical properties. Humidity and temperature has a big influence on the strength of the "polymeric fastener". As a matter of fact, joint exposure to environmental conditions (e.g. automotive applica-tions) over a significant period of time shows a marked decrease in strength mainly due to the water absorption of the adhesively bonded joints [1]. Even though the disadvantages are numerous, the use of adhesive is becoming popular in automotive and aeronautical industry, as research finds solutions to some of these problems. Before continuing in the presentation of adhe-sives, materials and theories developed to explain adhesion, is useful to define some elements of the joint showed in Figure 2.2:

Adherend is a generally used term to indicate metal sheets connected to-gether by adhesive;

Adhesive material which transmit loads from an adherends to the other. Adhesives can be divided into two groups: non-structural which do not need to support substantial loads but merely hold lightweight materials; structural adhesive defined as having a shear strength > 7 MP a and responsible for the strength and stiffness of the structure;

Interphase is the region between adherend and adhesive. Chemical and physical characteristics differ from raw adhesive or adherends and are a critical factor to identify mechanical properties of the joint.

Interface represents the plane that divide two material region. It should be noted that it differs from the Interphase;

Primer a substance often used to increase bonding performance or to pro-tect surfaces until the application of adhesives.

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Adhesive Adherend

Adherend

Primer Interphases

Figure 2.2: Adhesive joint and its regions.

2.1.1 Theories and Mechanisms of Adhesion

The phenomenon of adhesion has been of interest for many decades. One of the main problem in analysing and understanding adhesion lies in the fact that this subject is at the boundary of several scientific field. As a matter of fact, the term adhesion is ambiguous, it means both the mechanical load required to break an adhesively bonded joint and the establishment of interfacial bonds [2]. As a consequence, various theories were formulated to explain adhesion:

1. Mechanical theory; 2. Electrostatic theory; 3. Diffusion theory; 4. Adsorption theory;

5. Weak Boundary Layers theory.

However, these mechanisms are not self-excluding and can also occur simul-taneously depending on specific bonding parameters.

Mechanical theory

The mechanical model was proposed by McBain and Hopkins in 1925 [3]. They focused their studies on the asperities and cavities of a solid surface, considering mechanical keying as the main factor in determining adhesive strength. However, this idea is widely criticized. For example Tabor et al. [4] studied the adhesion in perfectly smooth surfaces clearly showing that adhesive strength is not connected only to surfaces roughness.

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Electrostatic theory

The electrostatic theory was put forward by Deryagin in 1948 [5]. This is based on electrons migration between adherend and adhesive. This transfer mechanisms creates a double electrical layer at the interface leading to the assumption of the joint as capacitor. Therefore, the adhesive strength result-ing from the attractive electrostatic forces and the energy of separation can be related to the discharge potential of a capacitor.

Diffusion theory

Voyutskii proposed diffusion theory in 1963 [6]. The basic principles of this work is the polymer adhesion by which molecules at the interfaces spread across adherends and adhesive making interfaces disappear. This theory is accepted as mechanism of adhesion for identical polymer but it is not accepted for adhesion of different material even of polymer-polymer.

Weak Boundary Layers theory

Weak Boundary Layers theory states that the cohesive strength of an adhesively bonded joint is determined by the weaker interfacial layer. This theory is based on the probabilistic idea that a purely adhesive-substrate interface failure should not happen instead the failure through the weaker layer is a more favourable event. However, this assumption is not supported by experimental evidence.

Adsorption theory

Nowadays, Adsorption or Thermodynamic theory is widely used in ad-hesion science. According to this principle, the adad-hesion of adherends and adhesive is caused by interatomic and intermolecular forces established at the interface, Van der Waals forces and Lewis acid-base interactions are the most common examples.

2.1.2 Composition of Adhesives

Examining adhesive nature, two main classes can be defined: natural and synthetic. As mentioned above, the natural adhesive is the earliest exam-ple of adhesive. Nowadays, its applications are limited to paper and light wood bonding. However, it can be used in structural application especially in bonding wooden structures due to the capability of adherends to absorb and take away solvent (e.g. water [7]) from bondline [2], although synthetic

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CHAPTER 2. STATE OF ART component are necessary to increase bonding strength [8]. This natural ad-hesive is made up of proteins, carbohydrates and other compounds. Because of this chemical structure, adhesion properties are not clear. This connection complexity and the weakness of joint in wet condition make natural adhesive less common in industrial application, in favour of synthetic adhesive. The latter are instead made of polymers and the main advantages of this chemical structure are:

1. the possibility to obtain the mechanical properties needed;

2. repeatability, i.e. getting the same mechanical properties at each pro-duction batch.

The way by which mechanical properties are manipulated is checking care-fully adhesive composition and adding the right substance in the right quan-tity. Multiple are the components of an adhesive. The primary resin is the main one. This name "resin" derives from a hydrocarbon secretion of many plants, but in synthetic adhesives primary resin stands for the main chain in adhesive molecular structure which gives all the main properties to the final product. Adhesives can be classified according to the primary resin in: ther-mosetting, thermoplastics and elastomeric resins. Examples of each group are written in Table 2.1

Thermoset polymers are in viscous or soft solid state before application of heat and they do not flow upon reheating. 3-D and crosslinked network of bonds gives thermosets resin a lower temperature sensitivity and better me-chanical properties compared to thermoplastics.

Thermoplastic polymer can turn to a melting liquid when it is heated and turning back to solid when cooled down. This characteristics are inherited from linear and branched molecular structure.

Finally, Elastomers are special polymers that are stretchable due to their particular molecular structure which can be visualized as made of a one long molecule of macroscopic size. This structure combined with the weakness of intermolecular forces between polymer chains gives elastomer resin a low Young’s modulus, i.e. small forces lead to large deformation.

In addition to primary resin, hardener, solvents, fillers, plasticizers, reinforce-ments and other additives are added to the final adhesive.

Hardener is a component added to the adhesive to promote the curing pro-cess through catalysis or cross-linking. For two component adhesives, the hardener is supplied in a distinct container in order to separate the reactive components. During the manufacturing process of the bonded joint, the curing process can take place at room temperature mixing

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CHAPTER 2. STATE OF ART Themoset Thermoplastic Elastomeric

Epoxy Acrylate Polyisoprene

Polyurethanes Polyamide Polybutadiene Phenolics Polyolefins Polychloroprene Cyanoacrylates Polysulfone Polysiloxanes

Table 2.1: Examples of primary resin of each group.

together the constituent of the two component adhesive, conversely to single component adhesive. Final strength is reached in minutes to weeks after bonding depending on the formulation.

Solvents are liquids comprising one or more components that are volatile under specified drying conditions. The purpose in adding those sub-stances is to reduce viscosity and make adhesive easier to apply. Dilu-ents are used in conjunction with solvent to increase the bulk of another substance without causing precipitation.

Fillers are non-adhesive materials added to modify mechanical properties of the adhesive or to make adhesive conductive by adding conducting particles. Generally, these elements enhance strength allowing to re-duce the quantity of resin needed, in this way production price is lower, however too much fillers can change adhesive properties.

Plasticizers are substances useful for workability, flexibility or extensibility improvement of a polymer. However this advantage come in conjunc-tion with a decrease in strength, stiffness, hardness and a lower cohesive strength.

Reinforcements are generally used to enhance mechanical properties. Some reinforcement are designed for a particular primary resin.

2.2 Fatigue

Fatigue concept has not been introduced until the end of the nineteenth century. Before, engineers designed structures considering fluctuating loading equal to static loading. As a result, larger safety factors were used avoiding in this way a large number of failures even tough the cost of these fracture was enormous. For this reason, fatigue has been deeply studied and nowadays its mechanism has been clarified.

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2.2.1 Fatigue fracture

Applying a fluctuating load can lead to the fracture of the component after many cycles even if loading maximum value is far from material ultimate strength. A fatigue crack basically initiates on the surface of a component in a high local stresses area, generally areas in which a geometric stress raiser is present such as sharp corners or surface defects. Close to these points, failure starts and each cycle a crack propagates through the part as long as applied stress does not exceed the ultimate strength. At this point, brittle fracture takes place in accordance with the fracture mechanics concepts. Inspecting the fracture surface, the crack initiation and propagation and the final fracture can often be identified. As a matter of fact, crack gradually enlarges leaving a mark on fracture area called "Beach marks". The curvature of these marks is useful to identify where crack originates. When the section is sufficiently weakened and final fracture takes place, a relatively rough surface is revealed. All these areas on a fracture surface are shown in Figure 2.3.

Final fracture

"Beach marks"

Crack initiation

Figure 2.3: Fatigue failure originating in the fillet of an aircraft crank-shaft (SAE 4340 steel) [9].

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CHAPTER 2. STATE OF ART Adherend Adherend Adhesive (a) Adherend Adherend Adhesive (b) Adherend Adherend Adhesive Interfacial failure (c)

Figure 2.4: Failures modes in adhesively bonded joints: (a) Cohesive failure in adhesive layer, (b) Cohesive failure in adherends, (c) Adhesive failure.

2.2.2 Failure modes for adhesively bonded joints

In adhesively bonded joints however, the fatigue failure is not exactly sim-ilar to the metallic fracture surface explained in Chapter 2.2.1. Furthermore, failure modes are multiple. As pointed out in Chapter 2.1.1, adhesion is the phenomenon of attraction between two substances. Cohesion is instead de-fined as a mechanism established between molecules of one substance. Thus, two bonding failure can occur, depending on the phenomena involved.

• Since the fact that cohesion involves forces between the same element of the joint, cohesive failure takes place in adhesive or adherends. Figure 2.4a illustrates an example of cohesive failure of the adhesive. After rupture, both adherend surfaces remain covered with adhesive. Figure 2.4b shows an example of cohesive failure in adherend.

• Adhesive failure defines instead a rupture mode that takes place at the interfaces between adhesive and adherends.

In general applications, both phenomena are involved and the failure mode is described as a percentage of cohesive and adhesive failure (calculated based on the fraction of area).

2.2.3 Crack initiation and propagation

Crack initiation and propagation are the two main phases of a compo-nent fatigue life. In flaw-free materials, the stage of crack initiation takes the major part of the whole fatigue life-time, for this reason a significant number of cycles are needed before a detectable micro-crack appears. At low stress amplitude, the initiation can occupy the majority of the fatigue life, whereas at high amplitudes it usually occupies a small fraction of the life-time [10]. Cyclic plastic deformation often controls the fatigue process and crack initiation. Micro-cracks originates at free surfaces because of higher

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CHAPTER 2. STATE OF ART stresses and lower degree of constraint. In fact, grains are under constraints imposed by neighbouring grains. As a matter of fact, while grains inside the component are connected to neighbouring grains in each direction, external grains have an exposed surface [10]. Macroscopically instead, notches, fillets or other geometries are the source of stress concentration. Additionally, the micro-geometry of the surfaces, micro-grooves or other surface imperfections are stress concentrators.

Crack propagation follows the initiation phase, physically representing the lifetime fraction in which small cracks develop in the component reaching the size of macro-cracks. For many material, the differentiation between crack propagation and crack initiation is not clear. Similarly, there is no clear aspect that defines crack initiation, however its definition is linked to the presence of flaws or stress concentration on the surface of the adhesive while usually the detection of a first crack defines the transition to the crack propagation phase.

2.2.4 Fatigue analysis parameters

In order to develop analytical models to estimate fatigue life during struc-ture design, various parameters are necessary to completely define the loading conditions. Usually, a fluctuating load of constant amplitude is defined as a sinusoidal trend over time. Figure 2.5 illustrates two examples of fluctuating stress and all the parameters used in fatigue analysis:

• stress amplitude:

σa =

σmax− σmin

2

where σmax and σmin are respectively the maximum stress and the

minimum stress during load application; • stress ratio: R = σmin σmax • mean stress: σm = σmax+ σmin 2

Figure 2.5a shows a fluctuating applied stress with σm = 0 and a stress ratio

R = −1. This loading condition is also known as fully reversed. However, in common applications, the applied stress is a combination of a static plus a completely reversed stress, as illustrated in Figure 2.5b. As a matter of fact, mean stress and stress ratio has been defined in addition to the alternating stress to completely characterize fatigue load.

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CHAPTER 2. STATE OF ART Time Stress σa σM ax σmin R = −1 (a) Time Stress σa σM ax σmin σm (b)

Figure 2.5: Examples of fluctuating stress: (a) Fully reversed: R = −1; (b) Generic loading cycle.

In common high cycle fatigue situations, S-N curves, also known as Wöh-ler curves, are used to characterize material strength. These curves are plot-ted either on log-log or on semilog coordinates, as illustraplot-ted in Figure 2.6. This figure also shows the presence of three different areas:

1. Low cycle fatigue: a maximum stress level in a cycle exceeding the yield strength and a low number of cycles to failure, N < ·104 _[11],

are the two main characteristics of this area. In low cycle fatigue, a strain-life curve is usually used to describe fatigue behaviour instead of the classical S-N curve;

2. High cycle fatigue: includes the part of the graph in which the material behaviour is fully elastic. Here can be identified another area which characterize the infinite life. An endurance limit (usual symbol Sn) can

be identified as the maximum alternating stress that the component can withstand indefinitely without failure. Generally, the knee appears at 106 for ferrous material (Figure 2.6), instead for aluminium component the knee is set to 108_{. However, in common application fatigue strength}

decreases with the number of cycles;

3. Very high cycle fatigue: comprehend applications in which fatigue life reaches 109 _{cycles. Even if an endurance limit has been set, [11]}

indi-cated the absence of fatigue limit in case of high temperature and/or corrosive environment, jointed components or welded joints. Further-more, the fatigue life of current engines for automotive ranges around 108_{cycles or big diesel engines for ships or high speed trains have ranges}

to 109 _{cycles. As a matter of fact, further investigation has shown that}

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Sn

103 104 105 106 107

Life cycles, N (log)

Stress

amplitude

σa

,(log)

Figure 2.6: Example of S-N curve for ferrous materials.

Should be noted that due to the absence of a relationship between average shear stress and the maximum stress in the adhesive layer, L-N curves are common for adhesively bonded joints. For this reason, all the parameter defined above are evaluated using the applied load:

• load amplitude:

La =

Lmax− Lmin

2

where Lmaxand Lminare respectively the maximum and minimum load

applied; • load ratio: R = Lmin Lmax • mean load: Lm = Lmax+ Lmin 2

Figure 2.7 illustrates an example of a L-N curve of an adhesively bonded joint.

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Figure 2.7: Load-life curve for CFRP-epoxy double lap joints [13].

2.2.5 Analytical models

Models to estimate the fatigue life of a component are useful during design and in-service monitoring of structures. Various analytical models [14] have been developed for fatigue analysis, depending on the final purpose which could be the estimation of fatigue life or the number of cycles for a crack to propagate in the component. In this section, these models are presented marking their main advantages.

Total-Life

Infinite life or "High cycle fatigue" is commonly the main goal in design-ing metallic structures. For this reason, the Total-Life approach is mostly used. The S-N curves are employed to estimate the number of cycles that leads to failure applying a specific alternating load. The biggest disadvan-tage of the Wöhler curves (and of this method) is that they do not give any information about progression of damage. Furthermore, it is not possible to distinguish between crack initiation and crack propagation.

The mean stress affects fatigue life reducing lice cycles. Comparing a com-ponent withstanding two different loading cycles, a fully reversed Figure 2.5a and a generic load Figure 2.5b, to gain the same lifetime for both cases, a lower σashould be applied in the second condition than in the first. However,

a negative σmcould increase fatigue life (for example as in surface treatment).

Many methods have been developed to estimate the effect of mean stress on fatigue life by examining experimental data. Three main models are avail-able in literature: Gerber, Soderberg and Goodman (Figure 2.8). The latter is commonly used in component design because it gives reliable results and it is easy to apply due to its linearity.

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CHAPTER 2. STATE OF ART Sy Su Gerber Goodman Soderberg Stress amplitude, σa

Value from S-N curve

Mean stress, σm

Figure 2.8: Mean stress effect on fatigue life, three models.

Phenomenological

Generally, a reasonable approach to characterize fatigue damage is achiev-able using measurachiev-able parameters. The Phenomenological model follow this guideline searching a relation between fatigue damage and strength or stiff-ness reduction. The first one has been deeply studied and has been linked to the degradation of residual strength. Two numerical model represent ac-curately the damage accumulation in adhesively bonded joints:

• the strength wearout method;

• the normalized nonlinear strength wearout model.

Various modified form of these model can be found in literature to take also into account a variable fatigue load. However, destructive tests are required to acquire information on the residual strength. This represent the main disadvantage of this method.

Otherwise, reduction in stiffness could lead to similar model as the strength reduction giving in addition the advantage of a non destructive measuring. Tough, the correlation has not been found yet.

Fracture mechanics

The fracture mechanics approach estimates the number of cycles to failure assuming that a crack initiate in the early stages of fatigue cycles or studying the propagation of a pre-existing crack.

This model uses the basic concepts of fracture mechanics. While in common applications stress is considered as the main parameter, in this field of study an appropriate parameter has to be defined. The stress intensity factor K

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CHAPTER 2. STATE OF ART is applied for metallic structures. Otherwise, the strain energy release rate G is taken into account to characterize the rate of fatigue crack growth in adhesives if Linear Elastic Fracture Mechanics is applicable otherwise J-integral is used. G expresses the energy dissipated during fracture divided by the newly created surface. In static loading, a value of G = Gccorresponds

to a crack length for example of a = ac which will lead to fracture, instead

below this value (G < Gc) the crack will not propagate. In dynamic loading,

the crack may still propagate even if G < Gc.

Experimental data clarifies the correlation between crack propagation and strain energy release rate. As shown in Figure 2.9, three main areas can be identified:

• Region I: clearly show the presence of threshold value of G below which fatigue cracks will not propagate. This value is named as Gth;

• Region II: the crack growth rate is governed by an expression similar to the Paris’ law adapted to adhesives. Two main models were proposed to characterize the relationship between log(da/dN) and G:

da dN = CG m max da dN = C∆G m _{= C(G} max− Gmin)m

where a is the crack length, N is the number of cycles, m and C are curve fitting parameters.

• Region III: a strain energy release rate, higher than GC, lead to an

accelerating crack growth rate followed by the final fracture.

2.2.6 Creep in fatigue

Due to the polymeric nature of adhesives, creep is another important element in estimation of fatigue life. Mean stress has effects on fatigue life not only in the way explained in Chapter 2.2.5, but it leads to a viscoplastic behaviour. Neglecting this aspect and using the model presented above could conduce to an overestimation of the fatigue life of a component. The basic principle of LEFM and EPFM are valid, however time-dependent fracture mechanics gives reliable results due to the time dependence of creep. As mentioned in [15], three main approaches are available:

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I II

Strain energy release rate, log(GM ax)

Crac k gro wth rate, log (da/dN ) Gth GC III

Figure 2.9: Plot of the relationship between crack growth rate and strain energy release rate.

1. Experimental approach: this method is based on fatigue tests and the analysis of data acquired fitting a crack growth rate law to experimental data.

2. Dominant damage approach assumes that creep does not influence fa-tigue and vice versa. As a matter of fact, crack growth is powered by the dominant of the two mechanisms.

3. Crack growth partitioning approach takes into account the influence of both mechanism on crack growth:

da dN = da dN f atigue + 1 t da dt creep

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2.3 Crack initiation and propagation detection

Crack initiation detection and crack propagation observation are of great importance in the evaluation of fatigue behaviour of mechanical components. In fact, crack initiation phase represents an important stage of a component fatigue life, since after initiation lifetime of a component could be dramat-ically reduced. Experimental validation and analysis of fatigue mechanical properties represent a field of great importance in development and design of mechanical components and structures.

Experimental observation of crack initiation and propagation can be per-formed through an on-line or an off-line detection. Among the latter cate-gory, two example are the Electronic Speckle Pattern Interferometry (ESPI) and the 3DGrey Scale Correlation.

On-line damage detection and monitoring is generally a better approach. In fact, damage identification during entire fatigue life can be achieved. For ex-ample, an optical observation of the component could give direct information about crack initiation and propagation. However, an optical detection could not be performed if crack initiates in non accessible areas.

Optical detection is not the only on-line method available. In literature, many methods have been presented and used to analyse the crack initiation and propagation. A first selection in the range of measuring methods can be performed according to the geometry of specimen. In [16], [17] and [18], vari-ous methods are presented to detect on-line crack initiation and propagation in thin sheet plate structures:

• Photo detection;

• Continuous monitoring of dynamic stiffness or test frequency; • Backface strain method;

• Thermo-elastic stress analysis.

2.3.1 Photo detection

Due to the simple geometry and to the possibility of optically inspec-tion of crack initiainspec-tion surface, photo detecinspec-tion is one of the method taken into account for crack initiation detection. Capturing photos during fatigue tests and consequently analysing the images could give important informa-tion and help in crack initiainforma-tion and propagainforma-tion detecinforma-tion. However, the position where crack could initiate should be known a priori and this aspect represents a great disadvantage of this method, but not the only one. In

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CHAPTER 2. STATE OF ART fact, this method is a non-continuous monitoring of component fatigue life, furthermore to increase chances to detect a crack a big amount of photo is captured which are difficult to asses.

2.3.2 Continuous monitoring of dynamic stiffness

At the beginning of fatigue tests specimen are intact but after many cycles the stiffness of components changes due to the crack formation and growth. Thus, the stiffness of the entire specimen changes. This has consequences on testing machine behaviour:

• in case of servo-hydraulic and resonance testing machine, dynamic stiff-ness changes and elongation of the specimen during loading increases, • in case of resonance testing machine, testing frequency decreases. The analysis of these parameters lead to an identification of the crack growth during fatigue life.

In addition to testing machine stiffness evaluation, more precise informations can be acquired directly analysing area of interest using an extensometer. This device records changes of length in objects. Through this data and applied force, stiffness can easily be evaluated.

There are two types of extensometer: contact and non-contact. As the name suggests, contact extensometer are directly applied to component surface and are mainly used in applications that require a high precision measurement. Non-contact extensometer instead are able to measure length variation or strain without a direct contact with the component. For example, distance can be evaluated over time using a laser measuring system.

2.3.3 Backface strain method

Tracing crack initiation and propagation in adhesively bonded joints is also possible using strain gauges. These are placed on the free adherend sur-faces in the overlap area. The strain measured will rise to a peak value, when the damage is adjacent to the strain gauge, and then decrease gradually as the crack grows and progressively passes the gauge. This method is called Backface strain in literature and has been widely used to identify crack ini-tiation and propagation in adhesively bonded joints [18].

In this context, the Optical Backscatter Reflectometry technique leads to the same results as the Backface strain method. As a matter of fact, strain gauges are replaced by optical fibre in this method permitting to measure strain on a wider surface and not only in some points. In this way, it could

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SG1 SG2

Figure 2.10: Scheme of backface strain gauge method.

be applied on larger parts or on complex geometries. However, the higher costs of the system and the higher standard deviation of measurements [17] are the main disadvantages of this method.

2.3.4 Thermo-elastic Stress Analysis

Any substance in nature, whether solid, liquid or a gas, becomes slightly warmer or slightly cooler when its volume is changed. This phenomenon is known as thermoelastic effect and lead to an increase in temperature applying a compressive load instead a decrease in temperature applying a tensile load, Figure 2.11.

(a) (b)

Figure 2.11: (a) A component under tensile load decreases its temperature; (b) A component compressed load increases its temperature.

Thermo-elastic effect is a reversible conversion between mechanical and thermal forms of energy. As a matter of fact, cyclic deformations, during fatigue tests, will lead to a cyclic temperature change in the specimen. How-ever, this change is proportional to stress amplitudes only if:

• strain is macroscopic elastic; • strain rate is not too high;

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CHAPTER 2. STATE OF ART A different behaviour could indicate the beginning of plasticity. In fact, dur-ing plastic deformation, conversion between thermal and mechanical forms of energy is not reversible.

To measure thermoelastic effect, a high-precision thermographic system, which has a high thermal resolution (in the range of mK), acquires temperature data over time and using a reference signal, evaluates thermal differences during load application. An image map of the field is the output of thermo-camera. These images show the different amounts of thermal change and, hence, the varying intensities of stresses.

Even if component testing is usually performed in a standard environment, sometimes conditions could be considered adiabatic. In fact, high frequency loading leads to a fast enough temperature variation that transport of heat (e.g. by conduction) can be neglected.

The great advantage of this method is the optical localization of crack initi-ation even in non-accessible areas.

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Chapter 3 FE analysis

Previous to experimental tests, Finite Element simulations have been performed using the software Abaqus® _{to estimate experimental test results}

and to analyse and compare various geometries.

In this chapter, all the FE models analysed are illustrated explaining all the aspects taken into account and the reasons that lead to the selection of geometries for experimental investigations. Initially, the common aspects of FE models for both specimen are explained then each specimen is deeply analysed. Finally, an approach to define strain gauges position for backface strain method is explained.

All the FE models are two dimensional under plane strain condition in order to reduce the computational resources needed. The specimen available and used during tests are:

• Single lap shear specimen shown in Figure 3.1; • T-peel specimen visible in Figure 3.2;

3.1 Materials and mesh

The adhesively bonded joints analysed are multi-material. The adherends are made one of steel and the other of series 6000 aluminium, bonded together using the epoxide adhesive Terokal 5089 (Henkel®_{). Their mechanical}

prop-erties are listed in Table 3.1. The thickness of the steel plate is tSt= 0.9 mm

and the thickness of the aluminium plate is tAl = 1.5 mm.

Three different part have been modelled in Abaqus® _{assigning to each one a}

linear-elastic isotropic material model and the material properties of Table 3.1. Adherends are connected to adhesive using "Tie constraint" to simu-late the adhesive bonding. A tie constraint connects two separate surfaces

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CHAPTER 3. FE ANALYSIS 86 0 .9 1.5 12.5 159.5

Figure 3.1: Geometry of the single lap shear specimen.

12

.5

R = 1

Figure 3.2: Geometry of the T-peel specimen.

together linking displacement and rotation.

Due to the simple geometry a mapped mesh is created applying on each edge a specified seed to gain a better control of element size. A bias is applied over the thickness of adherends and over the overlap due to the higher stress gradient in the area of connection between metal and adhesive. The element type used is CPE4R: a 4-node bilinear plane strain quadrilateral.

3.2 Model constraint

The asymmetry of the analysed specimens lies in the usage of two mate-rials, with different stiffness, and also in the geometry for the single lap shear

Part Young’s Modulus Poisson’s ratio

Steel adherend 210 GP a 0.3

Aluminium adherend 69.5 GP a 0.34

Cured adhesive 1.59 GP a 0.4

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CHAPTER 3. FE ANALYSIS

Figure 3.3: Clamping device to perform fatigue tests.

Figure 3.4: Complete model of the clamping device.

specimen. Therefore, the adopted steel plate is thinner than aluminium plate in order to reduce the asymmetry of peel specimens.

The special clamping device outlined in Figure 3.3 is used to perform tests in order to guarantee a free deformation of specimen during load application avoiding bending moments in the machine connections. This device allows free rotation of the clamped surface and free displacement in the plane of the applied force.

The fixing device is modelled using two approaches, subsequently compared: • complete model of the mechanism: on one side a rigid beam connects the testing machine to the middle hinge (MPC constraint) connected to the specimen using a coupling constraint, while on the other side the coupling constraint links specimen and testing machine, Figure 3.4; • free rotation of edges on one side and displacement fixed in both

di-rections on the other side. Coupling constraints connect specimen to testing machine, Figure 3.5.

Figure 3.6 and Figure 3.7 show the Max principal stresses in both specimen along the middle plane of adhesive (Figure 3.6a for single lap shear specimen and Figure 3.7a for T-peel specimen) applying a unit load. The equivalence of both method is clear (as could have been presumed in advance), therefore the second constraining model is applied in the following analysis in order to reduce the computational resources required.

3.3 Single lap shear specimen: crack initiation

The basic geometry, the simplicity of the manufacturing process and the low costs make single lap shear specimen a widely used method to acquire

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Figure 3.5: Free rotation and displacement of edges.

Path

(a) (b)

Figure 3.6: Comparison of Max Principal stresses in both modelling approaches along path (a) for single lap shear specimen (b).

Path

(a) (b)

Figure 3.7: Comparison of Max Principal stresses in both modelling approaches along path (a) for T-peel specimen (b).

Constraint

Coupling constraint Constrains the motion of a surface to the mo-tion of one or more point.

MPC constraint Constrains the motion of slave nodes of a re-gion to the motion of a point

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Crack initiation site

Figure 3.8: Areas in which crack could initiate in single lap shear specimen.

Steel adherend Aluminium adherend Max p rincipal ∆ σ

Figure 3.9: Max principal stress along adhesive.

information about adhesive properties. As a matter of fact, this test has been standardized by international organization outlining methods load ap-plication and surface treatments. To cite an instance, ASTM D1002 defines a standard method for determining the shear strength of a single lap joint. However, the results cannot be considered design-allowable stress values. The present work does not follow any standardized method.

The main purpose of fatigue tests is determining crack initiation phase. As a matter of fact, the FE model is useful to gain information about crack initiation site.

The likelihood of crack initiation for standard specimen with equal thick-ness and material is equivalent on both free surfaces underlined in Figure 3.8 due to a symmetric distribution of stress in the adhesive layer. However, the analysed adhesive bonds two metal sheets, one of aluminium and one of steel, each with a different thickness. For this reason, an FE model of this sample is carried out to get information about the surface where the crack could begin growing in adhesive.

Figure 3.9 shows the Maximum principal stress along adhesive. As explained above, the stress increases on the boundary surfaces of adhesive, although a disparity on the two sides is identified. The higher stress in the connection with aluminium adherend denotes a higher probability of crack initiation on this side.

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(a) Superior surface on the same level.

(b) Inferior surface on the same level.

Figure 3.10: Geometries analysed and compared.

3.4 T-peel specimen: geometry definition

T-peel tests are performed to measure the strength of adhesively joints, particularly in automotive industry application, with thin sheet of metal which could largely deform during standard adhesion tests. The parameter determined in T-peel tests is the peel force per unit length of the specimen [N/mm]. These investigations are generally carried out to select a suitable adhesive for given adherends or to investigate the effect of a parameter on adhesion strength.

Figure 3.2 shows the standard shape of a T-peel specimen with equal thickness adherends, hence a symmetric specimen.

As mentioned above, the present work analyses multi-material joints with dissimilar thickness of metal sheets. Therefore, the specimen geometry is not unique. Mathematically the possible configurations are infinite, however only two conformation are taken into account and compared due to manufacturing issues. Each differs from the other for the aligned edges between steel and aluminium adherend:

• the first one places the superior surface of both adherends, in connection with the fixing device, on the same level, as illustrated in Figure 3.10a; • the second instead places on the same level the inferior surface as visible

in Figure 3.10b.

Applying a symmetric load to a symmetric geometry lead to symmetrical deformation of structure. Bearing this in mind, the two geometries are com-pared exerting loads symmetrically and examining the resultant deformed shape. In Abaqus®_{, this condition is achieved applying a concentrated force}

on each reference point of the coupling which represents the machine connec-tion. The force vectors have equivalent magnitude although have opposite direction as illustrated in Figure 3.11.

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F F

Figure 3.11: Symmetrical loading condition.

X Y Z

(a) Superior surface on the same level: deformed shape.

X Y Z

(b) Inferior surface on the same level: deformed shape.

Figure 3.12: FE result of geometry comparison.

Analysing the FE model results, the geometry with the superior edges on the same level (Figure 3.10a) is selected for experimental tests due to the more symmetrical deformed shape illustrated in Figure 3.12a compared to the second configuration shown in Figure 3.12b.

3.5 Crack propagation

Chapter 2.3.2 presents the backface strain method used in experimental analysis to detect crack propagation and initiation. The strain recorded rise to a peak as the crack propagates and approaches the strain gauges. Hence, the damage identified clearly depends on the position of the strain gauge. In Abaqus®_{, the FE model is set up to determine the suitable position of}

strain gauges. The crack propagation is modelled in adhesive removing from the analysis a set of elements in each step. The number of elements removed per step, hence the length of adhesive removed, defines the crack growth rate. However, the significant aspect to define strain gauges position is the strain change compared to undamaged model. For this reason, the model without crack is defined as the reference condition and the difference between strain components is evaluated for each step. This procedure is applied for both specimen analysis extracting strain on the external surface of aherends that

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Figure 3.13: Strain difference between undamaged joint and specimen with a crack. Strain evaluated in T-peel specimens analysis along path in Figure 3.17.

matches the adhesive.

3.5.1 Single lap shear specimen

In Abaqus®_{, paths on the bonded surfaces of aluminium and steel}

ad-herends are created. Figure 3.14 illustrates the position of these paths. Bearing in mind that the strain gauges record strain on the surface to which their are connected, strain along single lap shear specimen is analysed. Figure 3.15 shows ∆εxx along the path for various crack length along the adhesive.

The area of crack initiation is estimated in Chapter 3.3.

As explained above, the aim of this analysis is define the position of strain gauges on the specimen during fatigue tests to identify crack initiation and propagation. The areas of high strain difference define a suitable position. Therefore, the first crest determines the location for the first strain gauge, at 1 mm from the edge, leading to a possible determination of 0.3 mm crack. Aluminium adherend represents a suitable surface for strain gauges due to the higher strain difference peaks.

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Path

Figure 3.14: Path defined in Abaqus® in Single lap shear specimen to identify strain gauges position on adherends.

Figure 3.15: Strain difference between undamaged joint and specimen with a crack of various crack length.

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3.5.2 T-peel specimen

Bearing in mind the method explained in Chapter 3.5.1, an identical procedure is adopted for T-peel specimen. Figure 3.16 illustrates the paths defined on adherends surface to gain informations about the strain, plotted in Figure 3.17. The first strain gauge is positioned at 0.5 mm from the edge on the steel adherend, as visible in the drawing in Appendix A.

Path Path

Figure 3.16: Path defined in Abaqus® in T-peel specimen to identify strain gauges position on adherends.

Figure 3.17: Strain difference between undamaged joint and specimen with a crack of various crack length.

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Chapter 4 Experimental Analysis

The following section explains the procedure adopted for specimen pro-duction and analysis. In the first part, steps of the manufacturing process are explained in detail, while in the second part, results of crack initiation and propagation detection are illustrated.

4.1 Specimen production

Before focusing the attention on testing methods, some information about production and challenges encountered during manufacturing process are given. Specimen production can be divided in various phases starting from the adherends cutting to the bonding process.

4.1.1 Adherends cutting

Material for adherends is provided as metal sheets. As a matter of fact, the first step in the manufacturing process is cutting of the sheets. The dimensions of the final adherends are illustrated in Figure 4.1 for single lap shear joints and in Figure 4.2 for T-peel specimen. Two are the procedure taken into account to cut metal sheets:

1. Manual cutting process using a metal shearing machine; 2. Water-jet cutting.

The production of specimen for preliminary tests (Chapter 4.2) is performed using the first method. This first trials show the low repeatability achievable using this method. Length and width of the adherends are inconstant leading to a misalignment of adherends in the final specimen. As a matter of fact, water jet cutting is taken into account to cut metal plates for multi-material

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CHAPTER 4. EXPERIMENTAL ANALYSIS

86

20

Figure 4.1: Dimensions of single lap shear specimen adherends.

92

20

Figure 4.2: Dimensions of T-peel specimen adherends, before bending.

specimen production. This method leads to more precise metal sheets cut-ting, hence with tighter tolerance.

Previous to surface preparation, aluminium and steel plates are manually bended for T-peel specimen production.

4.1.2 Surface preparation

In industrial environment, the manufacturing process aims at increasing the production rate. However, this generally leads to a decreased monitor-ing of production parameters, e.g. surface conditions which has a significant effect on the final joint.

Nowadays, some polymer resins are capable to produce a durable metal-metal bonding even if the surfaces have not been previously cleaned by oil and grease contaminants. This aspect represents a remarkable advance in adhesives technology that leads to a rapidly increase in usage of oil-accommodating adhesives in automotive industry.

To reproduce accurately working conditions during experimental campaign, aluminium and steel adherend surfaces are covered respectively with grease and oil before the application of the adhesive. The quantity used for both is defined in Table 4.1.

The exact application of such small quantities of grease and oil is a chal-lenging process. Furthermore, an equal distribution on surface is not easily achievable. However, high precision systems could be employed to achieve good results. The oil application demonstrate to be an easier task compared to grease application. As a matter of fact, a high precision syringe ideal

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CHAPTER 4. EXPERIMENTAL ANALYSIS Steel, oil Aluminium, grease

Quantity per m2 _{1.5 g/m}2 _{1.5 g/m}2

Area 250 mm2 _{1720 mm}2

Quantity applied 0.41 µl 0.0026 g

Table 4.1: Values of contaminant used during specimen production.

for dispensing volumes from 0.05 µl to 2 µl is used. Thus, the oil could be applied only on the bonding surface and then is distributed on the area with a finger.

A different approach instead should be used for grease application. In fact, syringe is not useful due to the solid form of grease, therefore the use of a high precision scale is taken into account. The narrow bonding surface requires a small amount of grease that could not be easily weighted and applied. For this reason, the entire aluminium surface is covered with grease and then manually distributed.

4.1.3 Adhesive application, bonding and curing

After the application of the contaminant on adherend surfaces, the adhe-sive is applied using a standard cartridge gun. Adheadhe-sive is pre-heated before use to facilitate flow of the adhesive due to a decreased viscosity. Glass beads of 0.2 mm are distributed on the adhesive to achieve exactly the desired ad-hesive layer thickness. The presence of these glass beads has shown to have no influence on the final joint characteristics.

Even if the thickness is defined through the use of glass beads, during the curing process the exothermic reaction could lead to a volume increase of adhesive consequently modifying the layer thickness. Therefore, a device should be used to fix the metal sheet positions helping also in edges align-ment. In [19] a bonding fixture is used, which allows to bond six specimen at a time ensuring correct overlap length and adherends alignment. However, the number of specimen for each batch is limited to this value.

Appendix B shows the technical drawings of the device designed and man-ufactured for single lap shear specimen production. During production pro-cess, the bonding fixture ensures the correct relative position of adherends, however does not guarantee control on the adhesive thickness. As a matter of fact, spring clamp are applied on the overlap. After, specimens are removed from the fixing device leaving free space for the manufacturing of two more specimen. In this way, the production batch can be extended to a higher number of specimen.

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CHAPTER 4. EXPERIMENTAL ANALYSIS The same device is helpful also for T-peel specimen production. Removing gauge blocks, the device helps in aligning edges (Chapter 3.4). Spring clamp are subsequently applied on the overlap to ensure a correct relative position-ing of adherends.

Finally, the last step in the production is the curing process. Clamped single lap shear and T-peel specimens are placed in the oven pre-heated at 180°C. The temperature in the overlap is evaluated over time, using a temperature recorder, leaving specimen in the oven for 20 min as soon as the desired temperature is reached.

4.2 Preliminary tests

One of the methods taken into account for crack initiation is photo detec-tion. During fatigue tests, photos of the specimen are captured and subse-quently analysed to identify the number of cycles at which a crack initiates. However, the sinusoidal load application should be stopped to capture im-ages during the constant load application. As a matter of fact, the strategy pursued is to stop the sinus application, apply a constant load equal to the maximum force, to have a clear view of the crack in the adhesive layer, cap-ture the photo and then continuing with the sinusoidal test, as illustrated in Figure 4.3. Though, the effect of the holding time on fatigue life should be evaluated. For this reason, fatigue tests on steel-steel (1.4 mm thick metal sheets) specimen have been performed previous to multi-material specimen. Furthermore, steel-steel single lap shear joint tests have been performed also to get information on the production process.

The first batches are manufactured mainly to test the production procedure verifying if grease application using the scale gives reliable results. Therefore, the results of tests are not shown.

To evaluate the effect of the holding time, three batches have been man-ufactured following the production process explained above. The testing procedures compared are: the method shown in Figure 4.3 and the applica-tion of a sinusoidal load for the entire fatigue life. The L-N curves in Figure 4.4 are evaluated based on the data collected. The fatigue life appears to be not strongly affected by the holding time at the maximum load during tests, as shown by sixth batch results. As a matter of fact, this procedure is applied during fatigue tests of multi-material joints.

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Figure 4.3: Test method for photo detection. Data extracted during fatigue tests.

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18

49

(a) Old geometry.

12

.5

20

(b) New geometry.

Figure 4.5: T-peel specimen geometry.

4.2.1 T-peel geometry

In previous analysis on other type of adhesive carried out at Fraunhofer Institute LBF, T-peel specimen geometry used is outlined in Figure 4.5a. However, the position of clamping devices is too close to adhesive and to metal plates bended edges possibly leading to some effect during fatigue testing. As a matter of fact, a different geometry is taken into account with longer and narrower adherends.

The reduced bonded area and consequently the low loads that should be ap-plied to specimens during tests represent the main problem of this geometry. In fact, maximum loads that should be applied vary between 200 N and 400 N. The maximum load of the testing machine is 5 kN, hence should be investigated if there are any deviation in load application. As a matter of fact, preliminary tests on steel-steel (0.9 mm thick metal sheets) T-peel specimen are carried out.

Figure 4.6 illustrates an example of force applied during fatigue tests over time. The sinusoidal load is correctly applied on the specimen and for this reason multi-material T-peel specimen are manufactured with this geometry.

4.3 Multi-material specimen tests

Bearing in mind the manufacturing process outlined in Chapter 4.1 and the testing procedure defined in Chapter 4.2, production and fatigue tests of multi-material specimen are performed. All the load controlled tests have been carried out using a stress ratio R = 0.1 and with a frequency f = 10 Hz. The latter is selected as a best compromise between testing time reduction and no effect on adhesive fatigue life due to a self-warming of the adhesive.

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CHAPTER 4. EXPERIMENTAL ANALYSIS 50 100 150 200 250 300 50 100 150 200 250 300 350 400

Figure 4.6: Applied force on the new geometry of T-peel specimen.

For single lap shear specimen, load is applied in the middle of the adhesive layer.

Results of tests are shown separated by the two specimen types.

4.3.1 Single lap shear specimen

The first problem encountered during fatigue testing, is the cohesive fail-ure of aluminium adherend. Water-jet cutting edges of aluminium base mate-rial are highly rough and plenty of critical defects that increase local stresses possibly leading to initiation of a crack. As a matter of fact, edges are smoothed using sand paper before testing to avoid aluminium failure. An example of this type of failure is visible in Figure 4.7.

Figure 4.8 illustrates L-N curves derived from fatigue tests on single lap shear specimen. Fracture surface on steel adherend shows constantly an ad-hesive failure. This behaviour has already been shown during some tests carried out by project partners and has been explained as caused by the surface conditions of the steel adherend. In fact, failure mode was mainly co-hesive also in preliminary tests carried out with another type of steel plates, so with different surface conditions, even if no changes were made in the manufacturing process.

Furthermore, project partners have also pointed out a correlation between lower load levels and wider adhesive failure area. This correlation can also be seen in the results of tests performed at Fraunhofer Institute LBF. Figure 4.9 shows a wider area of adhesive failure as load amplitude decreases.

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Figure 4.7: Example of cohesive failure in aluminium adherend.

First of all, oil and grease application is avoided to verify that there is no influence on adhesive failure. Consequently, three methods are tested to avoid this problem, bearing in mind that the adhesive failure on steel ad-herend could be caused by surface conditions. A first trial is to get a rougher surface using sand paper however this method does not lead to good results. The second method tested is to completely remove the zink on the surface through glass beads blasting. However, also this approach does not solve the problem of adhesive failure on steel surface.

The last method consist in increasing bonding performances through the use of a special surface treatment called silicate coating. The DELO-SACO PLUS technique is similar to classical sand blasting however a thin layer of silicate is added on the component surface. This method is used to increase bonding performances on various kind of materials: metal, ceramic, plastic and glass. Similarly to sand blasting, DELO-SACO PLUS technique removes the upper layer of the surface cleaning and creating a roughened surface. In addition to this advantage, the corundum grains with siliceous layer, accel-erated towards the surface and heated up due to the higher temperatures reached during the collision with the component surface, lose part of their siliceous coating which is firmly inserted on the target surface.

Figure 4.10 shows a specimen with a silicate coated steel adherend. Both metal surfaces are covered with adhesive showing cohesive failure of adhesive layer. In this way a much more reliable identification of adhesive properties can be achieved.

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Figure 4.8: L-N curve multi-material specimen with adhesive layer of 0.2 mm.

Figure 4.9: Area of adhesive failure on steel adherends of multi-material speci-men. Higher loads starting from left.

Figure 4.10: Specimen M SJ 45 produced with increased bonding performances using silicate coating. Cohesive failure of the adhesive layer.

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Figure 4.11: T-peel specimen 1, adhesive failure on steel.

(a) T P 4. (b) T P 5.

Figure 4.12: Failure surface of two T-peel specimens tested under the same load amplitude L_a= 180 N . Cycles to failure: Nf ' 47 · 103 for T P 4,

Nf ' 84 · 104 for T P 5.

4.3.2 T-peel specimen

As explained above for single lap shear specimen, adhesive failure has also been the main issue performing fatigue tests of T-peel specimens. Figure 4.11 illustrates the surface of failure of specimen T P 1. Adhesive layer is completely missing on the bended surface of the steel adherend.

This failure mode affects fatigue life. In Figure 4.12 two specimens tested applying the same load level are compared. Specimen T P 4 has a fatigue life of Nf ' 47 · 103 while T P 5 has a fatigue life of Nf ' 84 · 104. The difference

of factor 20 between specimens fatigue life could be explained looking into fracture surface. On steel adherend of specimen T P 4 Figure 4.12a, no adhesive layer is visible, instead a thin layer of adhesive still covers metal surface of specimen T P 5 in Figure 4.12b. As a matter of fact, crack initiates in the middle of adhesive layer for T P 5 then propagating in the interface between adhesive and steel adherend, finally taking place in the middle of the adhesive layer.

Bearing in mind results of single lap shear specimen and methods tested to avoid adhesive failure, DELO-SACO PLUS technique should be taken into account to change surface conditions of steel plates and increasing bonding performances also in T-peel specimen production.

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4.4 Crack initiation detection

4.4.1 Photo detection

As mentioned above, photos of the specimen are captured during fatigue tests. This approach leads to an optical detection of crack in the specimen and to an automatic detection as illustrated in Chapter 6.

During fatigue life, a white line usually appears on the adhesive surface, gradually growing and finally showing clearly a crack as it opens. The first change in colour is chosen as a crack initiation criteria. The analysis of the photo captured during tests for single lap shear specimens tested at different load levels shows a correlation in crack initiation in all the specimen. Figure 4.13 illustrates L-N curve of multi-material specimen tests with information about crack initiation phase. The diamond shaped points show the number of cycles after which crack initiates in the adhesive layer. Excluding the low life cycle fatigue, hence below 104 _{cycles, an L-N curve could be evaluated}

for crack initiation stage.

The crack initiation L-N curve gives important information. Through this correlation in fact, crack initiation in specimen tested without photo detec-tion could also be evaluated cross checking this data with the data of other methods used for crack initiation detection.

For T-peel specimen, the same approach has been followed, however due to the problems encountered during fatigue testing and explained in Chapter 4.3.2 a L-N curve for crack initiation could not be evaluated. Though, photo detection have been used to define a stiffness decrease criteria for crack ini-tiation.

4.4.2 Dynamic stiffness

As crack initiates and subsequently propagates in the specimen, displace-ment amplitude increases applying the same load value. This is directly connected to stiffness reduction of the specimen.

Testing machine used has no stiffness as a direct output however it can be easily evaluated through the data recorded. Stiffness is defined as force di-vided by displacement. Thus, dynamic stiffness is evaluated as:

k = La ∆sa N mm

where La is load amplitude and ∆s is displacement amplitude. Stiffness

could also be evaluated for each data recorded dividing force applied by dis-placement. However, force and displacement amplitude are selected due to

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Figure 4.13: L-N curve of multi-material specimen. L-N curve for crack initiation through photo detection.

the elevated mean stress (R = 0.1), that can lead to creep, affecting stiffness evaluation.

Thus, data analysis for each tested specimen is carried out in Matlab®

eval-uating stiffness and how the stiffness decreases during tests.

For single lap shear specimens, the first noticeable aspect is an initial set-tling phase during which stiffness increases reaching a plateau. Consequently, stiffness decreases until crack initiates leading to an accelerated decrease, as visible in Figure 4.14.

Figure 4.14 shows also a comparison between four specimens: MSJ 16, MSJ 34, MSJ 39 and MSJ 40. Normalized stiffness curves are decreasing, after an initial settling phase, showing crack initiation around the same percentage of decrease in stiffness. Crack initiation is identified through data collected in photo detection analysis.

All specimens tested show a similar behaviour. As a matter of fact, a decrease in stiffness of 0.2% is chosen as crack initiation criteria.

For T-peel specimens, stiffness during tests show a trend similar to single lap shear specimen. A first settling phase followed by a slow decrease until a crack initiates leading to a fast decrease in stiffness. Due to the problems encountered during fatigue tests and explained in Chapter 4.3.2, a decrease in stiffness of 2% could be chosen as crack initiation criteria, however more fatigue tests should be carried out to validate this parameter.

Crack initiation and propagation phases detection in fatigue life of adhesively bonded joints

Università di Pisa

Scuola di Ingegneria

Crack initiation and propagation phases

detection in fatigue life of adhesively bonded

joints

Giuseppe Andrea Monaco

Giuseppe Andrea Monaco

Prof. Francesco Frendo

Dr.-Ing. Jörg Baumgartner

Contents

Chapter 1

Introduction

1.1

Summary

Chapter 2

State of Art

2.1

Adhesive

2.1.1

Theories and Mechanisms of Adhesion

2.1.2

Composition of Adhesives

2.2

Fatigue

2.2.1

Fatigue fracture

2.2.2

Failure modes for adhesively bonded joints

2.2.3

Crack initiation and propagation

2.2.4

Fatigue analysis parameters

2.2.5

Analytical models

2.2.6

Creep in fatigue

2.3

Crack initiation and propagation detection

2.3.1

Photo detection

2.3.2

Continuous monitoring of dynamic stiffness

2.3.3

Backface strain method

2.3.4

Thermo-elastic Stress Analysis

Chapter 3

FE analysis

3.1

Materials and mesh

3.2

Model constraint

3.3

Single lap shear specimen: crack initiation

3.4

T-peel specimen: geometry definition

3.5

Crack propagation

3.5.1

Single lap shear specimen

3.5.2

T-peel specimen

Chapter 4

Experimental Analysis

4.1

Specimen production

4.1.1

Adherends cutting

4.1.2

Surface preparation

4.1.3

Adhesive application, bonding and curing

4.2

Preliminary tests

4.2.1

T-peel geometry

4.3

Multi-material specimen tests

4.3.1