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Gradual degradation of a thin-walled aluminum adhesive joint with omega cross section under bending
International Journal of Adhesion and Adhesives 89 (2019) 72–81
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Gradual degradation of a thin-walled aluminum adhesive joint with omega cross section under bending
T
⁎
T. Sadowski , M. Nowicki, D. Pietras, P. Golewski Faculty of Civil Engineering and Architecture, Lublin University of Technology, Nadbystrzycka 38, 20-618 Lublin, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Thin-walled profile 3 - point bending test Adhesively bonded aluminum omega cross section FEA numerical model of bending failure DIC analysis
The aim of the study was to examine deformation and degradation of a longeron fragment or a crossbeam in aircraft fuselage. The study included: (1) performing new laboratory investigations and (2) developing a corresponding numerical model of the structural element's behavior. Laboratory tests, i.e. controlled deformation by 3 PB (3-point bending) until bending collapse, were performed on specimens with a thin-walled omega cross section consisting of 2 aluminum parts: a roll-formed omega shape and a flat strip. Both parts were continuously bonded with 4 different types of structural adhesives, Fig. 1. Results of the laboratory tests and numerical analysis provided comprehensive knowledge of the structural element's behavior over the full range of loading conditions, starting from the elastic response, through the initialization of bending collapse and degradation processes, local folding and cracking, up to the final phase of bending collapse. A Finite Element Analysis (FEA) model of the structural element's deformation including adhesive layer damage and ductile damage in the aluminum parts of the test specimen was elaborated. The model allowed for the description of the longeron's gradual degradation until the final failure including: (1) plastic collapse mechanisms with cracking inside the aluminum parts and (2) delamination of the adhesive layers under 3 PB deformation. The agreement between the experimental and FEA results confirms that the numerical model of the investigated structural element was designed based on correct assumptions.
1. Introduction Structural elements can be joined using different methods:
• purely mechanical joining techniques (welding, fastening, riveting, clinching, etc.), • purely adhesive joining techniques, e.g. [1,2], • the use of hybrid joints with the application of riveting [3,4], clinching [3,5] or spot welding, [6].
The effectiveness of purely adhesive joints depends on the geometry of joined structural elements as well as the applied material and technology, e.g. [7,8]. The above include: (a) (b) (c) (d)
⁎
shape and dimensions of the lap areas, surface preparation, thickness of the adhesive layer and adherends, geometric complexity of the joined elements.
Most research papers only report various experiments and provide descriptions of modelling simple connections such as single- or doublelap joints. In real structures, however, one usually has to deal with more complex 3-D shapes of joined adherends consisting of thin-walled elements. Typical examples of such structures are girders, i.e. beams, pillars and thin-walled profiles made of one or several thin-walled elements joined together along the common edge, e.g. [9]. In the engineering practice, one can find different profiles with circular, rectangular, polygonal, solid filled with foam or hollow cross sections. The simplest applications are ribs having C or I cross sections which stiffen thin panes made of different kinds of metallic alloys or carbon/epoxy composites, [10]. Examples of thin-walled composite structures critical in aerospace engineering include plates braced with omega cross section stringers, [11]. This shape of stringers is frequently used in new generation aircraft fuselage designs, [12]. What poses a significant problem in aerospace design is the numerical modelling of omega stringer debonding from the panel and its experimental verification. A new concept in the aerospace design philosophy for composite structures is the application of omega stringers
Corresponding author. E-mail addresses: [email protected] (T. Sadowski), [email protected] (M. Nowicki).
https://doi.org/10.1016/j.ijadhadh.2018.11.011 Accepted 19 November 2018 Available online 30 November 2018 0143-7496/ © 2018 Elsevier Ltd. All rights reserved.
International Journal of Adhesion and Adhesives 89 (2019) 72–81
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2. Preparation of specimens for 3 PB testing
with a varying closed cross-section, [13]. However, the use of varying cross sections leads to higher manufacturing efforts and costs. Current lightweight automotive and aerospace design concepts ([14]) can be implemented by the use of:
2.1. Materials used for specimens preparation All analyzed specimens (Fig. 1) consisted of 3 parts:
• high-strength deep-drawing steel (e.g. [15,16]), • metallic alloys (e.g. aluminum, magnesium or titanium), • fiber reinforced plastics instead of metal, e.g. [17], • hybrid materials e.g. made of metal and carbon fiber reinforced
• an omega profile made of 7075 aluminum (T6), • a flat sheet made of 7075 aluminum (T6), • an adhesive layer placed between the two above profiles made of 4
plastics, e.g. [16,18].
types of adhesive: Hysol 9514, Hysol 9466, Hysol 9483 and Hysol 3423.
However, in many classical applications, metallic thin-walled profiles are often employed to fabricate support frames and stiffeners for many structures used in different branches of modern engineering. These can be formed as single profiles by extrusion or can be joined by welding, riveting or adhesive bonding. The last of the above-mentioned joining techniques is becoming increasingly popular, and adhesively bonded joints are more and more widely used in technology. In the aerospace industry, different types of aluminum alloys are used to design different parts of classic and modern aircrafts. In particular, deep-drawn thin-walled aluminum profiles with an omega cross section are frequently used in the design of longerons or crossbeams. These structural elements can be subjected to high in-plane loads (e.g. buckling, [9,11,15]) or out-of-plane loads (e.g. bending – [16,18]). In this study we present new results of laboratory tests and a corresponding FEA model of a deep-drawn thin-walled aluminum profile with omega cross section consisting of 2 parts (a roll-formed omega shape and a flat strip). The two parts were bonded with 4 different types of adhesives to estimate the effectiveness of each joint, Fig. 1. The specimens were subjected to controlled deformation by 3 PB testing up to their final failure to obtain comprehensive knowledge of the structural element's behavior over the full range of loading conditions, from the elastic response, through the initialization of bending collapse and degradation processes, local folding and cracking, up to the final phase of bending collapse. In addition, the paper proposes a FEA model that fills a gap in the research literature with respect to 3 PB deformation of this type of profiles, e.g. [16]. The analytical model, like in [15], describes the postfailure behavior of a structure based on the rigid-plastic theory. However, it does not fully describe the actual post-failure behavior of box section beams. In contrast, the proposed numerical model accurately describes the behavior of the bonding layer, including the damage process and plastic collapse mechanisms associated with ductile damage of the specimen's aluminum parts. The FEA model describes the longeron's gradual degradation until failure, including: (1) crack occurrence in the aluminum parts and (2) delamination of the adhesive layers with the evolution of deformation. The agreement between the experimental and FEA results confirms that the numerical model was designed based on correct assumptions.
The above structural element components were used in the construction of the PZL M28 aircraft manufactured in Poland. Material properties of the aluminum components were determined experimentally using an MTS system (100 kN) and the ARAMIS digital image correlation (DIC) system. Table 1 lists the material properties of aluminum 7075. Fig. 2 shows the stress-strain curve obtained for the tested material 7075 and the specimen. Basic data of the applied adhesives provided by the manufacturer are collected in Table 2. 2.2. Specimen preparation 4 types of specimens (Fig. 3) with different bonding layers were prepared, as shown in Table 2, using:
• 1-part structural bonding epoxy adhesive Loctite 9514, • 2-part structural bonding epoxy adhesives Loctite 9466, 3423 and
9483, supplied by Henkel. The surface area of the adhesive was equal to 2 × 60 cm2.
Before bonding, metal surfaces were cleaned and degreased with the Loctite 7063 cleaner (Henkel). The bonding process of the adhesive layer was controlled by pressure in order to ensure a uniform, almost zero-thickness interface layer. A specially designed fixture was used to maintain specimen alignment. The specimens were cured in conditions ensuring the maximum strength of the adhesive layer. The following curing parameters were used for the Loctite adhesives:
• Hysol 9514 – cured at 150 °C for 60 minutes, • Hysol 9466 – cured at 80 °C for 30 minutes, • Hysol 9483 – cured at 80 °C for 30 minutes, • Hysol 3423 – cured at 80 °C for 30 minutes. 3. Numerical models used in the FEA analysis to describe the response of a thin-walled omega section joint Numerical models of a thin-walled omega profile should include the
Fig. 1. Specimen, a) omega cross section of the specimen, b) view of the adhesively bonded specimen. 73
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Table 1 Material properties of aluminum 7075(T6) – obtained from the authors’ own tests. Material
Density [kg/m3]
Young's modulus [GPa]
Poisson ratio
Yield strength σy [MPa]
Ultimate strength σmax [MPa]
Aluminum 7075
2700
69.18
0.327
470
652
Fig. 2. Determination of material properties of aluminum 7075: a) specimen during the test; b) stress-strain curve for the tested aluminum.
Table 2 Material data of the adhesives used in numerical analysis [19–22]. Adhesive parameters
Density [kg/m3]
Young's modulus E [GPa]
Tensile strength tnmax [MPa]
Lap shear strength tsmax [MPa]
Hysol Hysol Hysol Hysol
1440 1000 1450 1120
1.460 1.718 1.498 2.100
44.0 43.2 24.0 47.0
45.0 26.0 10.5 10.0
9514 9466 3423 9483
Fig. 4. Ductile Damage Model (DDM) of an elastic-plastic material.
with damage, see Fig. 4. At first, the material is linearly elastic and the Young's modulus is maintained constant at E = E0 = tg (α) = 69.18 GPa. The yield stress of the analyzed aluminum is equal to σy = 470 MPa, whereas the maximum stress is reached when σmax = 652 MPa. At the maximum stress, a damage process begins in the material and is manifested as void initiation and coalescence (e.g. [6,23]), Fig. 4. After that, the damage parameter D starts to gradually increase, from the initial value of 0 for the equivalent fracture strain ε¯0pl to the end value of 1 for the equivalent fracture strain ε¯fpl at complete damage. The S4R shell finite element was used to create the geometric model, which greatly simplified the entire computational process. The model assumes that the equivalent plastic strain ε¯0pl at the onset of damage is a function of stress triaxiality η and equivalent plastic pl strain rate ε¯0̇ . The stress triaxiality η = -p / q, where p is the pressure stress and q is the equivalent von Mises stress. The damage initiation criterion is met when:
Fig. 3. Continuously bonded joint used in the omega profile.
description of two materials used for specimen preparation. The first one is aluminum used to construct 2 joined parts of the omega profile and the other one is a bonding layer connecting the two metal parts, Fig. 3. The material of the joined aluminum parts was described with a shell finite element (S4R) with plastic damage, while the bonding layers were described with surface-based cohesive contact.
pl
ωD =
∫ ε¯ pl (d¯ηε, ε¯ ̇pl) = 1, 0
0
(1)
where ωD is a state variable that increases monotonically with plastic deformation. Damage develops when the ε¯0pl point is exceeded. The state of stress σ is a function of damage parameter D (e.g. [23–29]) and stress of the virgin material σ̅:
3.1. Ductile damage model (DDM) of elastic-plastic materials created in ABAQUS software
σ = (1 − D) σ¯ .
Aluminum profiles were described using an elastic-plastic model
The current value of Young's modulus E is equal to: 74
(2)
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Table 3 Fracture energy parameters of the adhesives used in analysis. Adhesive
Fracture energy Gc [J/m2]
Tensile strength tnmax [MPa]
Lap shear strength tsmax [MPa]
9514 9466 3423 9483
900 490 400 200
44.0 43.2 24.0 47.0
45.0 26.0 10.5 10.0
2
2
2
⎛ GI ⎞ + ⎛ GII ⎞ + ⎛ GIII ⎞ = 1, ⎝ GIc ⎠ ⎝ GIIc ⎠ ⎝ GIIIc ⎠ ⎜
Fig. 5. Energy-based damage evolution – linear softening.
E = (1 − D) E0.
(3)
(4)
To describe the mechanical response of 2 adhesive layers (Fig. 3), surface-based cohesive contact was applied. A zero-thickness interface was introduced between the two parts of the aluminum profiles and modelled using the traction-separation constitutive relation (Fig. 6), e.g. [4,24,26,33]. The adhesive layer's behavior was modelled as linear elastic traction-separation with damage. Fig. 6 shows this model, where δ is the contact separation, t is the contact stress (traction), and Gc is the fracture energy of the adhesive. Traction is a function of contact force F and current area A at each contact point.
⎟
(7)
4. Experimental test and numerical model for mode I deformation The specimens were subjected to controlled deformation by 3 PB on the MTS 810 testing machine. The displacement speed of the MTS head was set to U̇ = 0.036mm/s . In order to ensure precise monitoring of the entire deformation process, the ARAMIS DIC system was used. 4.1. Laboratory tests
(5)
The lower indices denote a direction, where n – normal, s – shear 1, t – shear 2. Damage initiation occurs when the maximum stress criterion is satisfied, [30]:
〈tn 〉 ts tt ⎫ , max , max MAX ⎧ max = 1. ⎨ ⎬ t t t s t ⎩ n ⎭
⎜
The FEA was performed using the Abaqus/Explicit simulation software since the specimens were subjected to large deformation and strains while the deformation process was related to time. The joined metallic parts were modelled using 17,550 S4R finite elements having 17,969 nodes. Calculations were made using data from the experiments (Table 1) and Fig. 2. Fracture energy of the considered material was calculated as an area under the tensile stress-strain curve (Fig. 2) and was found to equal Gf = 22.1 mJ. The adhesive layer was modelled as surface-based cohesive contact with damage. The adhesive material properties were taken from the manufacturer's specification data sheet (Table 2). The fracture energy parameters Gc used to create numerical models of the adhesive layers were determined by DCB tests in [31,32], Table 3.
3.2. Adhesive layer – cohesive zone model (CZM)
F . A
⎟
3.3. Description of the numerical model of thin-walled specimens
where u¯ fpl is the equivalent plastic displacement.
t=
⎜
where GIc , GIIc , GIIIc are the critical values of fracture energies corresponding to Gc . Due to a lack of experimental data, it was assumed that GIIc = GIIIc = GIc , i.e., the failure of the adhesive layer is isotropic.
When the D parameter reaches the final value D = 1, the material is pl completely damaged. The equivalent plastic deformation ε¯eq = ε¯fpl . To address the strain softening issue, a fracture energy parameter Gf with linear softening was applied (Fig. 5). Fracture energy is the energy needed to open a unit area of crack and is equal to:
Gf = 0.5(σmax u¯ fpl ),
⎟
In mode I deformation, the specimens undergo concentrated bending in the central cross section of the box beam under 3 PB loading, Fig. 7a. Past the yield strength of the aluminum parts, one can observe plastic collapse of the side walls of the omega cross section after the initiation of a local plastic damage and further crack propagation in the top fragment of the specimen, Fig. 8. The deformation shape of the damaged profile is characteristic of bent thin-walled box beams, see [16] and [18], whereas the sheet plate in the specimen bottom is elongated and partially bent. Specimen delamination depends on the type of adhesive used for fabricating the bonding layer. When the state of stress of the adhesive layer in the deformation process reaches the critical value of the maximum stress criterion, Eq. (6), the bonding layer begins to collapse. Finally, there occurs delamination between 2 parts of the omega cross section. Results of the experimental tests are presented in Fig. 8. It has been found that Hysol 9483 is the weakest out of the tested adhesives, whereas Hysol 9514 is the strongest adhesive that was used for joining specimen parts. The adhesive layer was completely debonded in the case of Hysol 9483, Fig. 8c. The delamination process of this adhesive layer starts when deflection of the central point is about U = 22 mm. Hysol 3423 exhibits a higher resistance to delamination, as the first symptoms of adhesive layer damage are not noticed until the displacement U reaches 35 mm. The two other types of adhesives have a much higher resistance to damage initiation, i.e., failure of the bonding
(6)
The failure criterion for the most general case is formulated as a power law and depends on the fracture energy in three considered loading modes: normal n = I and two tangential: t = II, s = III:
Fig. 6. Triangular traction-separation model of the adhesive layer. 75
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Fig. 7. Geometry of 3 PB tests (dimensions in [mm]) for: a) mode I deformation, b) mode II deformation.
layers does not take place until the maximum deflection is Umax = 36 mm. One can notice from Fig. 9 that the deflection of the reference point does not depend on the applied type of adhesive. This is due to the fact that the specimen rigidity primarily depends on its geometry and material of the metal profiles.
loading
unloading
4.2. Numerical simulation Results of the numerical analysis are given in Fig. 10. It can be observed that the simulated shape of the specimen is very similar to that obtained in the experimental tests, Fig. 8a. Moreover, Fig. 10 shows the distribution of the reduced Huber – von Mises stress. As expected, the maximum reduced stresses (red color) are concentrated just under the loading point. Locally, they are equal to σmax, and one can notice the onset of damage initiation in the aluminum parts. In addition to that, one can observe full degradation (plastic collapse) of the aluminum alloy (blue color), i.e., the presence of visible discontinuities in the form of open spaces or cracks. This perfectly agrees with the experimental findings – Fig. 8a. The adhesive layer does not undergo delamination, except for the specimen bonded with the
Fig. 8. Laboratory test. Photographs of the specimens after deflection U 3423, d) Hysol 9483.
max
Fig. 9. Displacement of the central (U) and reference points versus time of deformation (measured by ARAMIS DIC system).
weakest adhesive, HYSOL 9483, Fig. 8d. Summarizing, it can be claimed that the developed FEA model reflects the nature of damage growth in both the metal parts of the joined elements and the adhesive layer with very good accuracy. In Fig. 11 experimental and numerical results obtained for the four tested types of adhesives are plotted as force-deflection curves. In mode I deformation all analyzed specimens generally behave in a similar way.
= 36 mm with adhesive layers fabricated with: a) Hysol 9514, b) Hysol 9466, c) Hysol
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Fig. 10. Huber – von Mises residual stress distribution in mode I deformation by 3 PB testing in a specimen bonded with Hysol 9514: a) after deflection U = 5 mm; b) after deflection U = 10 mm, c) after deflection Umax = 36 mm.
5. Mode II deformation – experimental tests and numerical model
It can be observed that the adhesives have little impact on the maximum carrying force Pmax. The force is significantly affected by the specimen geometry and the type of material used in the metal parts. Only the numerical results show small differences between the forcedisplacement plots for all considered cases. These small differences between the numerical Pmax values are caused by:
In mode II deformation the omega profile is placed in the bottom position (Figs. 7b, 12, 13). The specimens were subjected to 3 PB testing on the MTS 810 testing machine (100 kN). The deflection velocity U̇ was set equal to 0.036 mm/s. To ensure on-line monitoring of the entire gradual degradation process during 3-D deformation, the ARAMIS DIC system was employed.
• Different types of local damage growth, • Local decohesion of the adhesive layer (Figs. 8c and 8d). The shapes of the curves in Fig. 11 are typical of bending processes for thin-walled box beams [9,16]. At the beginning of the deformation process, the force changes linearly up to the limit of proportionality. When the maximum reduced stress is reached locally (σmax = 652 MPa), the omega profile walls undergo plastic collapse, and the structural element's load capacity begins to gradually decrease. With further deformation of the specimen, one can observe both: (1) plastic absorption of energy and (2) dissipation due to continuous damage and cracking.
5.1. Laboratory tests In mode II deformation, the joined elements also undergo concentrated bending yet this occurs in a direction from the sheet plate part, Fig. 12. Initially, the specimen response is elastic; once the maximum loading force is exceeded however, the plastic collapse mechanism occurs and the side walls undergo intensive damage, including local plastic buckling and cracking. In contrast to the previous case, this bending collapse develops towards the inner part of the omega profile. 77
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Fig. 11. Force-deflection plots in mode I deformation for 4 types of adhesive layers fabricated with Hysol: a) 9514, b) 9466, c) 3423, d) 9483.
Fig. 12. Mode II deformation in 3 PB testing (Hysol 9514): a) start of the experiment (U = 5 mm), b) end of the experiment (Umax = 36 mm).
5.2. Numerical simulation
Simultaneously with the collapse mechanism, there occurs the initiation and propagation of bonding layer degradation. The damage and further delamination of the adhesive layer begin just under the central loading point and propagate towards the end of the specimen. As for mode II deformation, in advanced stages of loading one can observe damage in the form of concentrated cracks in the aluminum parts, i.e., the side walls undergo buckling and cracking only in the case of specimens bonded with Hysol 9514. As regards other adhesives, there are no visible cracks in the aluminum omega profile. In all cases, the bonding layer is completely delaminated. Fig. 12 shows two stages of mode II deformation testing for the specimen bonded with Hysol 9514, whereas Fig. 13 shows the omega profile geometries after the maximum deflection and complete unloading of all tested specimens. Figs. 14 and 15 show the displacement of the central and reference points in relation to time of the deformation process. The maximum displacement Umax of the central point is equal to 36 mm like in mode I deformation. In mode II deformation, the applied adhesive type visibly affects the whole rigidity of the joined system. The specimen bonded with Hysol 9514 is the most prone to deformation, i.e. the highest deflection in the reference point. In contrast, the specimens bonded with Hysol 9466 and Hysol 9483 exhibit the smallest deflection.
Numerical calculations were performed based on a previously elaborated model. A comparison of permanent strains after total unloading of the specimens obtained in the experiments (Fig. 12) and in FEA simulations (Fig. 16) reveals that the numerical model is also effective for the full range of loading conditions, from the elastic response, through the initialization of bending collapse and degradation processes, local folding and cracking, up to the final phase of bending collapse in mode II deformation. However, in all analyzed cases the bonding layer undergoes complete delamination. In addition, the damage and geometry of the omega profile after total unloading are similar to those obtained in the laboratory experiments. Fig. 16 shows the stress distribution in the test specimen for U = 5 mm, 10 mm and 36 mm. The stress is concentrated in the central cross section of the specimen. After the failure of the adhesive layer and the separation of the flat sheet from the omega profile, the load capacity of the specimen decreases. After that, the stiffness of the adhesively bonded structural element decreases and the element behaves as in [33].
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Fig. 13. Geometries of the omega profiles adhesively bonded with Hysol: a) 9514, b) 9466, c) 3423, d) 9483 after the end of deformation and total unloading.
Fig. 17 compares all experimental and numerical force-deflection diagrams for mode II deformation. The curves in these plots are similar to those obtained for mode I deformation, Fig. 11, but the load capacity of the specimens is almost twice higher. The first part of the plots is linear elastic and becomes slightly nonlinear up to the maximum force Pmax. Past this value, bending collapse occurs in the omega profile, and degradation of the adhesive layer is initiated. After that, a sudden drop in the load capacity P can be observed, and further deformation of the joined structural element is associated with the progression of: (1) cracking in the omega profile and (2) deterioration of the bonding layer. At the maximum deflection Umax = 36 mm, all specimens exhibits complete delamination of the adhesive layers. The impact of the adhesive type on the stress distribution is more significant here than in mode I deformation. The discrepancy between the experimental and numerical findings results from the imperfect geometry of the manufactured specimens. The lack of perfect specimen geometry can cause local damage of the metal profile or degradation of the bonding layer. Numerical force-displacement results obtained for the continuous thin-walled omega cross sections without adhesive layers are plotted in Fig. 18 for both modes of deformation. It can be observed that in mode I deformation the distribution of the carrying force P does not significantly differ from that obtained for the adhesively bonded structural element. However, in mode II deformation, the maximum load Pmax is greater by about 20% when compared to the adhesive-bonded specimens, Fig. 11. After the sudden drop in the carrying force P, the forcedisplacement curves become similar.
Fig. 14. Deflection field measured by the ARAMIS DIC system in the specimen adhesively bonded with Hysol 9514 for t = 415 s.
6. Conclusions The paper described a gradual degradation process of thin-walled aluminum adhesive joints with an omega cross section subjected to two modes of deformation by 3 PB testing. The study included performing experimental tests and developing a new FEA model with two damage mechanisms taken into account: (1) plastic collapse with cracking of the aluminum profiles and (2) gradual degradation of the adhesive layers.
Fig. 15. Displacement of the central (U) and reference points (Fig. 7) versus time of deformation (measured by ARAMIS DIC system).
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Fig. 16. Huber – von Mises stress distribution in mode II deformation by 3 PB testing in a specimen bonded with Hysol 9514: a) after deflection U = 5 mm; b) after deflection U = 10 mm, c) after deflection Umax = 36 mm.
Fig. 17. Force-deflection plots for 4 different types of adhesive layers and mode II deformation. A comparison of experimental and numerical results for Hysol: a) 9514 b) 9466 c) 3423 d) 9483.
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Manufacturing and investigation of steel-CFRP hybrid pillar structures for automotive applications by intrinsic resin transfer moulding technology. International. J Automot Compos 2016;2:229–43. [19] Technical Data Sheet Hysol 9514, November 2012. [20] Technical Data Sheet Hysol 9466, February 2006. [21] Technical Data Sheet Hysol 3423, June 2012. [22] Technical Data Sheet Hysol 9483, March 2008. [23] Postek E, Sadowski T. Assessing the influence of porosity in the deformation of metal-ceramic composites. Compos Interfaces 2011;18:57–76. [24] Gajewski J, Sadowski T. Sensitivity analysis of crack propagation in pavement bituminous layered structures using a hybrid system integrating artificial neural networks and finite element method. Comput Mater Sci 2014;82:114–7. [25] Sadowski T, Marsavina L. Multiscale modelling of two-phase ceramic matrix composites. Comput Mater Sci 2011;50:1336–46. [26] Dębski H, Sadowski T. Modelling of microcracks initiation and evolution along interfaces of the WC/Co composite by the finite element method. Comput Mater Sci 2014;83:403–11. [27] Golewski G, Sadowski T. An analysis of shear fracture toughness KIIc and mictrostructure in concrete containing fly-ash. Constr Build Mater 2014;51:207–14. [28] Sadowski T, Ataya S, Nakonieczny K. Thermal analysis of layered FGM cylindrical plates subjected to sudden cooling process at one side – comparison of two applied methods for problem solution. Comput Mater Sci 2009;45:624–32. [29] Sadowski T, Marsavina L, Peride N, Craciun EM. Cracks propagation and interaction in an orthotropic elastic material: analytical and numerical methods. Comput Mater Sci 2009;46:687–93. [30] Abaqus 6.13. User’s Manual. 〈http://dsk.ippt.pan.pl/docs/abaqus/v6.13/index. html〉. [31] Pirondi A, Fersini D, Perotti E, Moroni F. Applicabilita del modello di zona coesiva in simulazioni della frattura per diverse geometrie di giunti incollati. Atti Del Congr IGF 2007;19:85–93. [32] Pirondi A, Fersini D, Perotti E, Moroni F. Applicabilita del modello di zona coesiva in simulazioni della frattura per diverse geometrie di giunti incollati. Atti Del Congr IGF 2007;19:85–93. [33] Pastor MM, Roure F. Open cross-section beams under pure bending. I. Experimental investigations. Thin-Walled Struct 2008;46:476–83.
Fig. 18. Force-displacement curves for continuous and uniform structural elements without adhesion layers – numerical simulations in ABAQUS.
The 3 PB experimental results were plotted as force-displacement curves and the following structural parameters were assessed: the maximum force Pmax and the residual force after the plastic collapse of degraded structural elements. The post buckling behavior of the structural element was examined taking into account cracking of the metal parts and degradation of the adhesive layer. A general conclusion that can be drawn from the above investigation is that the new developed numerical model shows high agreement with the experimental results obtained for the 2 modes of 3 PB deformation. The specimen geometry after deformation and the size of discontinuities after the maximum displacement Umax are very similar, in the experiments and numerical simulations alike. Particular conclusions can be formulated as follows:
• higher maximum forces P are obtained for the second mode of deformation (omega profile in the bottom position), Fig. 17, • for both modes of deformation, the displacement distribution in max
• • • •
different points of the thin-walled aluminum adhesive joints with an omega cross section are not uniform due to the concentration of deformation in the central part of the specimens and the formation of a plastic hinge with macroscopically visible local cracks, when the maximum force Pmax is exceeded, one can observe plastic collapse with cracking in the aluminum parts while the load carrying capacity of the joints sharply drops to the residual value, in mode I deformation the bonded layers do not undergo delamination, except for the specimens bonded with the weakest adhesive, HYSOL 9483. In mode II deformation all specimens exhibit complete delamination of the adhesive layers at the maximum deflection Umax = 36 mm, i.e., degradation growth is faster in this case. damage initiation in the adhesive layers occurs when the aluminum omega profile walls undergo local buckling, the numerical model of 3 PB deformation of the analyzed structural element is efficient and shows good accuracy with the experimental findings, and thus provides detailed knowledge of its mechanical response over the full range of loading conditions, starting from the elastic response, through the initialization of bending collapse and degradation, local folding and cracking, and up to the final phase of bending collapse.
Acknowledgment This work was financially supported by the Ministry of Science and Higher Education, Poland under statutory research project No S/20/ 2018.
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International Journal of Adhesion and Adhesives journal homepage: www.elsevier.com/locate/ijadhadh
Gradual degradation of a thin-walled aluminum adhesive joint with omega cross section under bending
T
⁎
T. Sadowski , M. Nowicki, D. Pietras, P. Golewski Faculty of Civil Engineering and Architecture, Lublin University of Technology, Nadbystrzycka 38, 20-618 Lublin, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Thin-walled profile 3 - point bending test Adhesively bonded aluminum omega cross section FEA numerical model of bending failure DIC analysis
The aim of the study was to examine deformation and degradation of a longeron fragment or a crossbeam in aircraft fuselage. The study included: (1) performing new laboratory investigations and (2) developing a corresponding numerical model of the structural element's behavior. Laboratory tests, i.e. controlled deformation by 3 PB (3-point bending) until bending collapse, were performed on specimens with a thin-walled omega cross section consisting of 2 aluminum parts: a roll-formed omega shape and a flat strip. Both parts were continuously bonded with 4 different types of structural adhesives, Fig. 1. Results of the laboratory tests and numerical analysis provided comprehensive knowledge of the structural element's behavior over the full range of loading conditions, starting from the elastic response, through the initialization of bending collapse and degradation processes, local folding and cracking, up to the final phase of bending collapse. A Finite Element Analysis (FEA) model of the structural element's deformation including adhesive layer damage and ductile damage in the aluminum parts of the test specimen was elaborated. The model allowed for the description of the longeron's gradual degradation until the final failure including: (1) plastic collapse mechanisms with cracking inside the aluminum parts and (2) delamination of the adhesive layers under 3 PB deformation. The agreement between the experimental and FEA results confirms that the numerical model of the investigated structural element was designed based on correct assumptions.
1. Introduction Structural elements can be joined using different methods:
• purely mechanical joining techniques (welding, fastening, riveting, clinching, etc.), • purely adhesive joining techniques, e.g. [1,2], • the use of hybrid joints with the application of riveting [3,4], clinching [3,5] or spot welding, [6].
The effectiveness of purely adhesive joints depends on the geometry of joined structural elements as well as the applied material and technology, e.g. [7,8]. The above include: (a) (b) (c) (d)
⁎
shape and dimensions of the lap areas, surface preparation, thickness of the adhesive layer and adherends, geometric complexity of the joined elements.
Most research papers only report various experiments and provide descriptions of modelling simple connections such as single- or doublelap joints. In real structures, however, one usually has to deal with more complex 3-D shapes of joined adherends consisting of thin-walled elements. Typical examples of such structures are girders, i.e. beams, pillars and thin-walled profiles made of one or several thin-walled elements joined together along the common edge, e.g. [9]. In the engineering practice, one can find different profiles with circular, rectangular, polygonal, solid filled with foam or hollow cross sections. The simplest applications are ribs having C or I cross sections which stiffen thin panes made of different kinds of metallic alloys or carbon/epoxy composites, [10]. Examples of thin-walled composite structures critical in aerospace engineering include plates braced with omega cross section stringers, [11]. This shape of stringers is frequently used in new generation aircraft fuselage designs, [12]. What poses a significant problem in aerospace design is the numerical modelling of omega stringer debonding from the panel and its experimental verification. A new concept in the aerospace design philosophy for composite structures is the application of omega stringers
Corresponding author. E-mail addresses: [email protected] (T. Sadowski), [email protected] (M. Nowicki).
https://doi.org/10.1016/j.ijadhadh.2018.11.011 Accepted 19 November 2018 Available online 30 November 2018 0143-7496/ © 2018 Elsevier Ltd. All rights reserved.
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2. Preparation of specimens for 3 PB testing
with a varying closed cross-section, [13]. However, the use of varying cross sections leads to higher manufacturing efforts and costs. Current lightweight automotive and aerospace design concepts ([14]) can be implemented by the use of:
2.1. Materials used for specimens preparation All analyzed specimens (Fig. 1) consisted of 3 parts:
• high-strength deep-drawing steel (e.g. [15,16]), • metallic alloys (e.g. aluminum, magnesium or titanium), • fiber reinforced plastics instead of metal, e.g. [17], • hybrid materials e.g. made of metal and carbon fiber reinforced
• an omega profile made of 7075 aluminum (T6), • a flat sheet made of 7075 aluminum (T6), • an adhesive layer placed between the two above profiles made of 4
plastics, e.g. [16,18].
types of adhesive: Hysol 9514, Hysol 9466, Hysol 9483 and Hysol 3423.
However, in many classical applications, metallic thin-walled profiles are often employed to fabricate support frames and stiffeners for many structures used in different branches of modern engineering. These can be formed as single profiles by extrusion or can be joined by welding, riveting or adhesive bonding. The last of the above-mentioned joining techniques is becoming increasingly popular, and adhesively bonded joints are more and more widely used in technology. In the aerospace industry, different types of aluminum alloys are used to design different parts of classic and modern aircrafts. In particular, deep-drawn thin-walled aluminum profiles with an omega cross section are frequently used in the design of longerons or crossbeams. These structural elements can be subjected to high in-plane loads (e.g. buckling, [9,11,15]) or out-of-plane loads (e.g. bending – [16,18]). In this study we present new results of laboratory tests and a corresponding FEA model of a deep-drawn thin-walled aluminum profile with omega cross section consisting of 2 parts (a roll-formed omega shape and a flat strip). The two parts were bonded with 4 different types of adhesives to estimate the effectiveness of each joint, Fig. 1. The specimens were subjected to controlled deformation by 3 PB testing up to their final failure to obtain comprehensive knowledge of the structural element's behavior over the full range of loading conditions, from the elastic response, through the initialization of bending collapse and degradation processes, local folding and cracking, up to the final phase of bending collapse. In addition, the paper proposes a FEA model that fills a gap in the research literature with respect to 3 PB deformation of this type of profiles, e.g. [16]. The analytical model, like in [15], describes the postfailure behavior of a structure based on the rigid-plastic theory. However, it does not fully describe the actual post-failure behavior of box section beams. In contrast, the proposed numerical model accurately describes the behavior of the bonding layer, including the damage process and plastic collapse mechanisms associated with ductile damage of the specimen's aluminum parts. The FEA model describes the longeron's gradual degradation until failure, including: (1) crack occurrence in the aluminum parts and (2) delamination of the adhesive layers with the evolution of deformation. The agreement between the experimental and FEA results confirms that the numerical model was designed based on correct assumptions.
The above structural element components were used in the construction of the PZL M28 aircraft manufactured in Poland. Material properties of the aluminum components were determined experimentally using an MTS system (100 kN) and the ARAMIS digital image correlation (DIC) system. Table 1 lists the material properties of aluminum 7075. Fig. 2 shows the stress-strain curve obtained for the tested material 7075 and the specimen. Basic data of the applied adhesives provided by the manufacturer are collected in Table 2. 2.2. Specimen preparation 4 types of specimens (Fig. 3) with different bonding layers were prepared, as shown in Table 2, using:
• 1-part structural bonding epoxy adhesive Loctite 9514, • 2-part structural bonding epoxy adhesives Loctite 9466, 3423 and
9483, supplied by Henkel. The surface area of the adhesive was equal to 2 × 60 cm2.
Before bonding, metal surfaces were cleaned and degreased with the Loctite 7063 cleaner (Henkel). The bonding process of the adhesive layer was controlled by pressure in order to ensure a uniform, almost zero-thickness interface layer. A specially designed fixture was used to maintain specimen alignment. The specimens were cured in conditions ensuring the maximum strength of the adhesive layer. The following curing parameters were used for the Loctite adhesives:
• Hysol 9514 – cured at 150 °C for 60 minutes, • Hysol 9466 – cured at 80 °C for 30 minutes, • Hysol 9483 – cured at 80 °C for 30 minutes, • Hysol 3423 – cured at 80 °C for 30 minutes. 3. Numerical models used in the FEA analysis to describe the response of a thin-walled omega section joint Numerical models of a thin-walled omega profile should include the
Fig. 1. Specimen, a) omega cross section of the specimen, b) view of the adhesively bonded specimen. 73
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Table 1 Material properties of aluminum 7075(T6) – obtained from the authors’ own tests. Material
Density [kg/m3]
Young's modulus [GPa]
Poisson ratio
Yield strength σy [MPa]
Ultimate strength σmax [MPa]
Aluminum 7075
2700
69.18
0.327
470
652
Fig. 2. Determination of material properties of aluminum 7075: a) specimen during the test; b) stress-strain curve for the tested aluminum.
Table 2 Material data of the adhesives used in numerical analysis [19–22]. Adhesive parameters
Density [kg/m3]
Young's modulus E [GPa]
Tensile strength tnmax [MPa]
Lap shear strength tsmax [MPa]
Hysol Hysol Hysol Hysol
1440 1000 1450 1120
1.460 1.718 1.498 2.100
44.0 43.2 24.0 47.0
45.0 26.0 10.5 10.0
9514 9466 3423 9483
Fig. 4. Ductile Damage Model (DDM) of an elastic-plastic material.
with damage, see Fig. 4. At first, the material is linearly elastic and the Young's modulus is maintained constant at E = E0 = tg (α) = 69.18 GPa. The yield stress of the analyzed aluminum is equal to σy = 470 MPa, whereas the maximum stress is reached when σmax = 652 MPa. At the maximum stress, a damage process begins in the material and is manifested as void initiation and coalescence (e.g. [6,23]), Fig. 4. After that, the damage parameter D starts to gradually increase, from the initial value of 0 for the equivalent fracture strain ε¯0pl to the end value of 1 for the equivalent fracture strain ε¯fpl at complete damage. The S4R shell finite element was used to create the geometric model, which greatly simplified the entire computational process. The model assumes that the equivalent plastic strain ε¯0pl at the onset of damage is a function of stress triaxiality η and equivalent plastic pl strain rate ε¯0̇ . The stress triaxiality η = -p / q, where p is the pressure stress and q is the equivalent von Mises stress. The damage initiation criterion is met when:
Fig. 3. Continuously bonded joint used in the omega profile.
description of two materials used for specimen preparation. The first one is aluminum used to construct 2 joined parts of the omega profile and the other one is a bonding layer connecting the two metal parts, Fig. 3. The material of the joined aluminum parts was described with a shell finite element (S4R) with plastic damage, while the bonding layers were described with surface-based cohesive contact.
pl
ωD =
∫ ε¯ pl (d¯ηε, ε¯ ̇pl) = 1, 0
0
(1)
where ωD is a state variable that increases monotonically with plastic deformation. Damage develops when the ε¯0pl point is exceeded. The state of stress σ is a function of damage parameter D (e.g. [23–29]) and stress of the virgin material σ̅:
3.1. Ductile damage model (DDM) of elastic-plastic materials created in ABAQUS software
σ = (1 − D) σ¯ .
Aluminum profiles were described using an elastic-plastic model
The current value of Young's modulus E is equal to: 74
(2)
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Table 3 Fracture energy parameters of the adhesives used in analysis. Adhesive
Fracture energy Gc [J/m2]
Tensile strength tnmax [MPa]
Lap shear strength tsmax [MPa]
9514 9466 3423 9483
900 490 400 200
44.0 43.2 24.0 47.0
45.0 26.0 10.5 10.0
2
2
2
⎛ GI ⎞ + ⎛ GII ⎞ + ⎛ GIII ⎞ = 1, ⎝ GIc ⎠ ⎝ GIIc ⎠ ⎝ GIIIc ⎠ ⎜
Fig. 5. Energy-based damage evolution – linear softening.
E = (1 − D) E0.
(3)
(4)
To describe the mechanical response of 2 adhesive layers (Fig. 3), surface-based cohesive contact was applied. A zero-thickness interface was introduced between the two parts of the aluminum profiles and modelled using the traction-separation constitutive relation (Fig. 6), e.g. [4,24,26,33]. The adhesive layer's behavior was modelled as linear elastic traction-separation with damage. Fig. 6 shows this model, where δ is the contact separation, t is the contact stress (traction), and Gc is the fracture energy of the adhesive. Traction is a function of contact force F and current area A at each contact point.
⎟
(7)
4. Experimental test and numerical model for mode I deformation The specimens were subjected to controlled deformation by 3 PB on the MTS 810 testing machine. The displacement speed of the MTS head was set to U̇ = 0.036mm/s . In order to ensure precise monitoring of the entire deformation process, the ARAMIS DIC system was used. 4.1. Laboratory tests
(5)
The lower indices denote a direction, where n – normal, s – shear 1, t – shear 2. Damage initiation occurs when the maximum stress criterion is satisfied, [30]:
〈tn 〉 ts tt ⎫ , max , max MAX ⎧ max = 1. ⎨ ⎬ t t t s t ⎩ n ⎭
⎜
The FEA was performed using the Abaqus/Explicit simulation software since the specimens were subjected to large deformation and strains while the deformation process was related to time. The joined metallic parts were modelled using 17,550 S4R finite elements having 17,969 nodes. Calculations were made using data from the experiments (Table 1) and Fig. 2. Fracture energy of the considered material was calculated as an area under the tensile stress-strain curve (Fig. 2) and was found to equal Gf = 22.1 mJ. The adhesive layer was modelled as surface-based cohesive contact with damage. The adhesive material properties were taken from the manufacturer's specification data sheet (Table 2). The fracture energy parameters Gc used to create numerical models of the adhesive layers were determined by DCB tests in [31,32], Table 3.
3.2. Adhesive layer – cohesive zone model (CZM)
F . A
⎟
3.3. Description of the numerical model of thin-walled specimens
where u¯ fpl is the equivalent plastic displacement.
t=
⎜
where GIc , GIIc , GIIIc are the critical values of fracture energies corresponding to Gc . Due to a lack of experimental data, it was assumed that GIIc = GIIIc = GIc , i.e., the failure of the adhesive layer is isotropic.
When the D parameter reaches the final value D = 1, the material is pl completely damaged. The equivalent plastic deformation ε¯eq = ε¯fpl . To address the strain softening issue, a fracture energy parameter Gf with linear softening was applied (Fig. 5). Fracture energy is the energy needed to open a unit area of crack and is equal to:
Gf = 0.5(σmax u¯ fpl ),
⎟
In mode I deformation, the specimens undergo concentrated bending in the central cross section of the box beam under 3 PB loading, Fig. 7a. Past the yield strength of the aluminum parts, one can observe plastic collapse of the side walls of the omega cross section after the initiation of a local plastic damage and further crack propagation in the top fragment of the specimen, Fig. 8. The deformation shape of the damaged profile is characteristic of bent thin-walled box beams, see [16] and [18], whereas the sheet plate in the specimen bottom is elongated and partially bent. Specimen delamination depends on the type of adhesive used for fabricating the bonding layer. When the state of stress of the adhesive layer in the deformation process reaches the critical value of the maximum stress criterion, Eq. (6), the bonding layer begins to collapse. Finally, there occurs delamination between 2 parts of the omega cross section. Results of the experimental tests are presented in Fig. 8. It has been found that Hysol 9483 is the weakest out of the tested adhesives, whereas Hysol 9514 is the strongest adhesive that was used for joining specimen parts. The adhesive layer was completely debonded in the case of Hysol 9483, Fig. 8c. The delamination process of this adhesive layer starts when deflection of the central point is about U = 22 mm. Hysol 3423 exhibits a higher resistance to delamination, as the first symptoms of adhesive layer damage are not noticed until the displacement U reaches 35 mm. The two other types of adhesives have a much higher resistance to damage initiation, i.e., failure of the bonding
(6)
The failure criterion for the most general case is formulated as a power law and depends on the fracture energy in three considered loading modes: normal n = I and two tangential: t = II, s = III:
Fig. 6. Triangular traction-separation model of the adhesive layer. 75
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Fig. 7. Geometry of 3 PB tests (dimensions in [mm]) for: a) mode I deformation, b) mode II deformation.
layers does not take place until the maximum deflection is Umax = 36 mm. One can notice from Fig. 9 that the deflection of the reference point does not depend on the applied type of adhesive. This is due to the fact that the specimen rigidity primarily depends on its geometry and material of the metal profiles.
loading
unloading
4.2. Numerical simulation Results of the numerical analysis are given in Fig. 10. It can be observed that the simulated shape of the specimen is very similar to that obtained in the experimental tests, Fig. 8a. Moreover, Fig. 10 shows the distribution of the reduced Huber – von Mises stress. As expected, the maximum reduced stresses (red color) are concentrated just under the loading point. Locally, they are equal to σmax, and one can notice the onset of damage initiation in the aluminum parts. In addition to that, one can observe full degradation (plastic collapse) of the aluminum alloy (blue color), i.e., the presence of visible discontinuities in the form of open spaces or cracks. This perfectly agrees with the experimental findings – Fig. 8a. The adhesive layer does not undergo delamination, except for the specimen bonded with the
Fig. 8. Laboratory test. Photographs of the specimens after deflection U 3423, d) Hysol 9483.
max
Fig. 9. Displacement of the central (U) and reference points versus time of deformation (measured by ARAMIS DIC system).
weakest adhesive, HYSOL 9483, Fig. 8d. Summarizing, it can be claimed that the developed FEA model reflects the nature of damage growth in both the metal parts of the joined elements and the adhesive layer with very good accuracy. In Fig. 11 experimental and numerical results obtained for the four tested types of adhesives are plotted as force-deflection curves. In mode I deformation all analyzed specimens generally behave in a similar way.
= 36 mm with adhesive layers fabricated with: a) Hysol 9514, b) Hysol 9466, c) Hysol
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Fig. 10. Huber – von Mises residual stress distribution in mode I deformation by 3 PB testing in a specimen bonded with Hysol 9514: a) after deflection U = 5 mm; b) after deflection U = 10 mm, c) after deflection Umax = 36 mm.
5. Mode II deformation – experimental tests and numerical model
It can be observed that the adhesives have little impact on the maximum carrying force Pmax. The force is significantly affected by the specimen geometry and the type of material used in the metal parts. Only the numerical results show small differences between the forcedisplacement plots for all considered cases. These small differences between the numerical Pmax values are caused by:
In mode II deformation the omega profile is placed in the bottom position (Figs. 7b, 12, 13). The specimens were subjected to 3 PB testing on the MTS 810 testing machine (100 kN). The deflection velocity U̇ was set equal to 0.036 mm/s. To ensure on-line monitoring of the entire gradual degradation process during 3-D deformation, the ARAMIS DIC system was employed.
• Different types of local damage growth, • Local decohesion of the adhesive layer (Figs. 8c and 8d). The shapes of the curves in Fig. 11 are typical of bending processes for thin-walled box beams [9,16]. At the beginning of the deformation process, the force changes linearly up to the limit of proportionality. When the maximum reduced stress is reached locally (σmax = 652 MPa), the omega profile walls undergo plastic collapse, and the structural element's load capacity begins to gradually decrease. With further deformation of the specimen, one can observe both: (1) plastic absorption of energy and (2) dissipation due to continuous damage and cracking.
5.1. Laboratory tests In mode II deformation, the joined elements also undergo concentrated bending yet this occurs in a direction from the sheet plate part, Fig. 12. Initially, the specimen response is elastic; once the maximum loading force is exceeded however, the plastic collapse mechanism occurs and the side walls undergo intensive damage, including local plastic buckling and cracking. In contrast to the previous case, this bending collapse develops towards the inner part of the omega profile. 77
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Fig. 11. Force-deflection plots in mode I deformation for 4 types of adhesive layers fabricated with Hysol: a) 9514, b) 9466, c) 3423, d) 9483.
Fig. 12. Mode II deformation in 3 PB testing (Hysol 9514): a) start of the experiment (U = 5 mm), b) end of the experiment (Umax = 36 mm).
5.2. Numerical simulation
Simultaneously with the collapse mechanism, there occurs the initiation and propagation of bonding layer degradation. The damage and further delamination of the adhesive layer begin just under the central loading point and propagate towards the end of the specimen. As for mode II deformation, in advanced stages of loading one can observe damage in the form of concentrated cracks in the aluminum parts, i.e., the side walls undergo buckling and cracking only in the case of specimens bonded with Hysol 9514. As regards other adhesives, there are no visible cracks in the aluminum omega profile. In all cases, the bonding layer is completely delaminated. Fig. 12 shows two stages of mode II deformation testing for the specimen bonded with Hysol 9514, whereas Fig. 13 shows the omega profile geometries after the maximum deflection and complete unloading of all tested specimens. Figs. 14 and 15 show the displacement of the central and reference points in relation to time of the deformation process. The maximum displacement Umax of the central point is equal to 36 mm like in mode I deformation. In mode II deformation, the applied adhesive type visibly affects the whole rigidity of the joined system. The specimen bonded with Hysol 9514 is the most prone to deformation, i.e. the highest deflection in the reference point. In contrast, the specimens bonded with Hysol 9466 and Hysol 9483 exhibit the smallest deflection.
Numerical calculations were performed based on a previously elaborated model. A comparison of permanent strains after total unloading of the specimens obtained in the experiments (Fig. 12) and in FEA simulations (Fig. 16) reveals that the numerical model is also effective for the full range of loading conditions, from the elastic response, through the initialization of bending collapse and degradation processes, local folding and cracking, up to the final phase of bending collapse in mode II deformation. However, in all analyzed cases the bonding layer undergoes complete delamination. In addition, the damage and geometry of the omega profile after total unloading are similar to those obtained in the laboratory experiments. Fig. 16 shows the stress distribution in the test specimen for U = 5 mm, 10 mm and 36 mm. The stress is concentrated in the central cross section of the specimen. After the failure of the adhesive layer and the separation of the flat sheet from the omega profile, the load capacity of the specimen decreases. After that, the stiffness of the adhesively bonded structural element decreases and the element behaves as in [33].
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Fig. 13. Geometries of the omega profiles adhesively bonded with Hysol: a) 9514, b) 9466, c) 3423, d) 9483 after the end of deformation and total unloading.
Fig. 17 compares all experimental and numerical force-deflection diagrams for mode II deformation. The curves in these plots are similar to those obtained for mode I deformation, Fig. 11, but the load capacity of the specimens is almost twice higher. The first part of the plots is linear elastic and becomes slightly nonlinear up to the maximum force Pmax. Past this value, bending collapse occurs in the omega profile, and degradation of the adhesive layer is initiated. After that, a sudden drop in the load capacity P can be observed, and further deformation of the joined structural element is associated with the progression of: (1) cracking in the omega profile and (2) deterioration of the bonding layer. At the maximum deflection Umax = 36 mm, all specimens exhibits complete delamination of the adhesive layers. The impact of the adhesive type on the stress distribution is more significant here than in mode I deformation. The discrepancy between the experimental and numerical findings results from the imperfect geometry of the manufactured specimens. The lack of perfect specimen geometry can cause local damage of the metal profile or degradation of the bonding layer. Numerical force-displacement results obtained for the continuous thin-walled omega cross sections without adhesive layers are plotted in Fig. 18 for both modes of deformation. It can be observed that in mode I deformation the distribution of the carrying force P does not significantly differ from that obtained for the adhesively bonded structural element. However, in mode II deformation, the maximum load Pmax is greater by about 20% when compared to the adhesive-bonded specimens, Fig. 11. After the sudden drop in the carrying force P, the forcedisplacement curves become similar.
Fig. 14. Deflection field measured by the ARAMIS DIC system in the specimen adhesively bonded with Hysol 9514 for t = 415 s.
6. Conclusions The paper described a gradual degradation process of thin-walled aluminum adhesive joints with an omega cross section subjected to two modes of deformation by 3 PB testing. The study included performing experimental tests and developing a new FEA model with two damage mechanisms taken into account: (1) plastic collapse with cracking of the aluminum profiles and (2) gradual degradation of the adhesive layers.
Fig. 15. Displacement of the central (U) and reference points (Fig. 7) versus time of deformation (measured by ARAMIS DIC system).
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Fig. 16. Huber – von Mises stress distribution in mode II deformation by 3 PB testing in a specimen bonded with Hysol 9514: a) after deflection U = 5 mm; b) after deflection U = 10 mm, c) after deflection Umax = 36 mm.
Fig. 17. Force-deflection plots for 4 different types of adhesive layers and mode II deformation. A comparison of experimental and numerical results for Hysol: a) 9514 b) 9466 c) 3423 d) 9483.
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Fig. 18. Force-displacement curves for continuous and uniform structural elements without adhesion layers – numerical simulations in ABAQUS.
The 3 PB experimental results were plotted as force-displacement curves and the following structural parameters were assessed: the maximum force Pmax and the residual force after the plastic collapse of degraded structural elements. The post buckling behavior of the structural element was examined taking into account cracking of the metal parts and degradation of the adhesive layer. A general conclusion that can be drawn from the above investigation is that the new developed numerical model shows high agreement with the experimental results obtained for the 2 modes of 3 PB deformation. The specimen geometry after deformation and the size of discontinuities after the maximum displacement Umax are very similar, in the experiments and numerical simulations alike. Particular conclusions can be formulated as follows:
• higher maximum forces P are obtained for the second mode of deformation (omega profile in the bottom position), Fig. 17, • for both modes of deformation, the displacement distribution in max
• • • •
different points of the thin-walled aluminum adhesive joints with an omega cross section are not uniform due to the concentration of deformation in the central part of the specimens and the formation of a plastic hinge with macroscopically visible local cracks, when the maximum force Pmax is exceeded, one can observe plastic collapse with cracking in the aluminum parts while the load carrying capacity of the joints sharply drops to the residual value, in mode I deformation the bonded layers do not undergo delamination, except for the specimens bonded with the weakest adhesive, HYSOL 9483. In mode II deformation all specimens exhibit complete delamination of the adhesive layers at the maximum deflection Umax = 36 mm, i.e., degradation growth is faster in this case. damage initiation in the adhesive layers occurs when the aluminum omega profile walls undergo local buckling, the numerical model of 3 PB deformation of the analyzed structural element is efficient and shows good accuracy with the experimental findings, and thus provides detailed knowledge of its mechanical response over the full range of loading conditions, starting from the elastic response, through the initialization of bending collapse and degradation, local folding and cracking, and up to the final phase of bending collapse.
Acknowledgment This work was financially supported by the Ministry of Science and Higher Education, Poland under statutory research project No S/20/ 2018.
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