Stress analysis of hybrid joints of metal and composite plates via 3D-FEM

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 20, April 2013, pp Stress analysis of hybrid joints of metal and composite plates via 3D-FEM Kemal Aldaş a & Faruk Sen b * a Department of Mechanical Engineering, Aksaray University, Aksaray, Turkey b Department of Energy System Engineering, Mugla Sitki Kocman University, Mugla, Turkey Received 3 November 2011; accepted 31 January 2013 Three-dimensional finite element models are developed to investigate the effects of both tensile load and uniform temperature load on the stresses in hybrid joints. During the solution of the problem, finite element method (FEM) is preferred, as this method is very suitable for solving many engineering problems. An aluminum sheet is bonded a composite sheet. Hybrid joints are designed from both pinned joint and adhesively bonded single lap joint. The results pointed out that thermal high stresses occurred because of the different material properties of aluminum adherent, composite adherent and epoxy adhesive. If uniform temperature is applied to joint, stresses are higher than without thermal loading. Additionally, stresses are concentrated around the pin hole zone which is as very critical because of the high stresses. Keywords: Thermal stress analysis, single lap joint, composite joint, hybrid joint, FEM Application fields for composite materials are always expanding, from traditional application areas such as military aircraft to various engineering fields including commercial aircrafts, automobiles, robotic arms and even architecture 1. That s why mechanically fastened joints are frequently used in composite structures 2. They present a number of characteristics that make them well suited for joining composite laminates. For example, mechanically fastened joints are relatively inexpensive to produce and can be disassembled. However, mechanically fastened joints are a source of weakness and compliance because of the created stress concentrations 3. Since, the mechanical joint always requires fastener holes. Cutting the fastener holes creates local damage and stress concentration, and consequently, leads to a loss of structural strength 4. Meanwhile, adhesive bonding technology is commonly used in almost all the industries fields of the world and this is mainly due to its high strength-weight ratio, low cost and high efficiency nowadays 5. However, the design of safe and cost effective bonded joints is a main challenge. It forces on the engineer to have a good understanding of the effect of material and geometric parameters on the joint s strength 6. It is known that, the adhesive joints experience not only mechanical loads but also thermal loads in practice. Since the adhesive joints consist of materials with different mechanical and *Corresponding author (faruk.sen@deu.edu.tr) thermal properties, the thermal strains in the joint members might cause serious stresses 7. For instance, adhesive joints used in supersonic aircraft need to withstand low and high-temperatures, typically from- 55 o C (depending on altitude) to as much as 200 o C or more 8. Consequently, the most challenging problem faced by a design engineer is the possible weakness of the adhesive bond and the poor through- thickness strength of the adherents. One promising approach is to apply through thickness reinforcement using small diameter metallic or fibrous pins 9. Based on the literature survey result, many researchers have studied either adhesively bonded or pinned single lap joint, double lap joint etc. But, the analysis of hybrid joints used metal and composite sheets both adhesively bonded and pinned single lap joints under both thermal loads and tensile loads has been hardly investigated Firstly, a transient thermal analysis of an adhesively bonded and laser-spot welded joint was carried out based on a thermal model developed for the laser-spot welding of multilayered sheets using a pulsed Nd:YAG laser. The material non-linear properties of adhesive and sheets were considered using the non-linear finite element method in the thermal stress analysis 10. Nakano et al. 11 performed a thermal stress analysis of an adhesive butt joint which contained circular holes and rigid fillers in an adhesive and was under a nonuniform temperature field. The adherents were

2 ALDAS & SEN: STRESS ANALYSIS OF HYBRID JOINTS 93 assumed to be rigid and the adhesive was replaced with a finite strip having holes and rigid fillers in it and the thermal stress distribution in the adhesive was solved using a two-dimensional theory of elasticity. Morais et al. 12 studied the strength of stainless-steel joints bonded with two epoxy adhesives. The experimental program included tests on single-lap and butt joints, as well as thick-adherent and napkin ring shear tests. Nonetheless, FEM increased doubts on the true adhesive strengths, due to the complex stress state in joint tests and pressure-dependent adhesive performance. Notwithstanding some worries, FEM illustrated that failure could be fairly well predicted by a maximum shear strain criterion. Rastogi et al. 13 investigated thermal stresses in aluminum-tocomposite, symmetric, double-lap joints using FEM. The joint configuration considered aluminum adherent in combination with four different unidirectional laminated composite adherents subjected to uniform temperature loading. Silva and Adams 14 investigated a mixed adhesive joint. Experiments were applied for titanium/titanium and titanium/composite double lap joints. It was shown that, for a joint with dissimilar adherents, the combination of two adhesives gave a better performance over the temperature range than a high temperature adhesive alone. Silva and Adams 8 were also studied for adhesive joints with dual adhesives to be used over a wide temperature range theoretically. For this purpose, a numerical analysis was performed using finite element models to obtain the stress distribution in a mixed adhesive joint so as to find the best possible design of titanium/titanium and titanium/composite double lap joints. According to numerical analysis results, for a joint with dissimilar adherends, the combination of two adhesives gives a better performance over the temperature range considered than the use of a high-temperature adhesive alone, too. Sen 15 investigated thermal stresses in thermoplastic composites with a circular hole under uniform temperature loading. The elasticplastic stress analysis was performed using FEM. Sen and Aldas 16 developed a thermoplastic composite disc model with central hole using FEM. Linear temperature loadings was applied to disc for observing thermal stress distribution on it. Grassi et al. 17 offered a simple and efficient computational approach for analyzing the benefits of through-thickness pins for restricting debond failure in joints. It is suggested that the resulting model can be used to path the evolution of competing failure mechanisms, including tensile or compressive failure of the adherents, joint debonding (creating leak, for example, if the joint is in a pipeline), and ultimate failure associated with pin rupture or pullout. Pakdil et al. 18 analyzed the effect of preload moments on failure response of glass-epoxy laminated composite single bolted/pinned joints with hole clearance. To determine the effects of fastener geometry and stacking sequence of laminated plates on the bearing strength and failure mode, parametric analysis were performed, experimentally. Sayman et al. 19 investigated the effects of some preload moments on the bearing strength in fiber reinforced laminated composite single pinned/bolted-joints. The laminated plates were initially tested experimentally and then bearing strengths were calculated with maximum failure loads. Sen and Sayman 20 studied on the effects of the geometrical parameters such as the edge distance-to-hole diameter ratio (E/D), plate width-tohole diameter ratio (W/D) on the failure response of bolted-joint aluminum glass-epoxy sandwich composite plates. The failure modes and bearing strengths were obtained under different applied preload moments, experimentally. Briefly, previous studies were related to either pinned or adhesively bonded single joint, but stress analysis of hybrid joint based these joints has not been investigated using FEM. The scope of this study, a stress analysis of hybrid joint based on pinned joint and adhesively bonded aluminum and composite joint. For this purpose, three dimensional finite element models were created to obtain stresses caused both tensile loading and temperature loading. Materials and Methods In this study, a hybrid joint was considered as shown in Fig. 1. An aluminum sheet as lower adherent and aluminum metal matrix composite sheet were combined with both epoxy adhesive and single pin. The hybrid joint was provided using combination of pinned joint and adhesively bonded joint. The Fig. 1 The schematic view of hybrid joint

3 94 INDIAN J ENG. MATER. SCI., APRIL 2013 epoxy resin was selected for adhesively bonded process. It is generally used in many real applications due to good bonding properties. Furthermore, it is known that epoxies have excellent combination of mechanical properties, corrosion resistance, dimensionally stable, good adhesion, relatively inexpensive and good electrical properties 21. The thickness of both aluminum adherent and composite adherent were 2 mm, whereas the thickness of epoxy adhesive was 0.2 mm. Nevertheless, the lengths of each adherents and adhesive were 100 mm and 50 mm, respectively. The length of bonding surface of adhesive with adherents was 50 mm. Since the problem was assumed as three dimensional, the width of both adherents and adhesive was 25 mm. Meanwhile, pin diameter was preferred as 5 mm. Consequently, for pinned joint, both the edge distance-to-hole diameter ratio (E/D) and plate widthto-hole diameter ratio (W/D) were designed as 5. Seeing as some previous experimental studies suggested that the best E/D and W/D ratios were 5 for single pinned joints 22,23. Since, these ratios supply higher values of bearing strengths and bearing failure mode which is the desired failure mode for single pinned joint get rid of catastrophic failure of pinned joints. Physical properties of aluminum adherent and epoxy adhesive are listed in Table 1 10, whereas the mechanical properties of aluminum metal matrix composite are given in Table In this work, the composite material was selected as aluminum metal matrix reinforced with steel fibers, since load carrying capacity of this composite are higher than some other type of composite which is polymer matrix composite as an example. Moreover, fiber reinforced metal laminate has high fracture toughness and resistance to fatigue crack propagation. These properties are required in critical structures such as fuselage, lower wing skin and tail skins of aircraft 25. It is assumed that material properties were not changed depending on applied uniform temperature, since the analyses were not performed at higher temperatures. The finite element method (FEM) was used to obtain stresses. For this purpose, three dimensional FEM models were developed. Meanwhile, in previous studies, most researchers used 2D rather than 3D FEM models because the 2D models are computationally efficient, but the results from 2D models can be misleading, especially for thermal loading conditions 26. During the modeling and solution processes, ANSYS 27 code was used, since it is acknowledged as powerful software for both scientific studies and commercial applications. SOLID45 element type was preferred, for the duration of the mesh generation process. The geometry, node locations, and the coordinate system for this element are illustrated in Fig SOLID45 element is used for the 3-D modeling of solid structures. The element is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. Additionally, the element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities 27. FEM structure of the hybrid single-lap joint is drawn in Fig. 3. The detail of mesh structure is also shown in Fig. 3. This figure represents that the good mapped mesh structure was built on the model including pin hole zone and adhesive layer, perfectly. It is known that if it is possible, mapped mesh structure should be built because of some advantages comparing to the free Table 1 Physical properties of aluminum and epoxy adhesive [10] Property Aluminum Epoxy Density, ρ (kg/m 3 ) Specific heat, c p (J/kgK) Thermal conductivity, k (W/mK) Elasticity modulus, E (GPa) Poisson s ratio, υ Thermal expansion coefficient, α (µm/m o C) Table 2 Mechanical properties of aluminum metal matrix composite material [24] E 1 (MPa) E 2 (MPa) G 12 (MPa) ν 12 α 1 (1/ o C) α 2 (1/ o C) ,29 18,5x x10-6 Fig. 2 SOLID45 element type [27]

4 ALDAS & SEN: STRESS ANALYSIS OF HYBRID JOINTS 95 Fig. 3 FEM structure and mesh details of hybrid single-lap joint Fig. 4 Half model and node definitions for evaluating the results around pin hole mesh, for a fine FEM solution. Moreover, a mapped mesh is limited in terms of the element shape it contains and the pattern of the mesh 27,28. As clarified previously, the hole must be required when the pin, bolt, rivet etc. are used in the structure for mechanical joint. For that reason, mesh structure is very significant around the hole zone especially due to stress concentrations at this area. On the other hand, the generation of mapped mesh is very hard if the model has hole. Nevertheless, the desired mapped mesh was developed in this study by the author. Besides, the refine mesh was made around the pin hole zone, adhesive layer and their near areas as seen in detail views in Fig. 3. Consequently, elements and nodes were created in the 3Dmodel end of the meshing process. As seen from Fig. 1, the hybrid joint was symmetric according to y- direction. Therefore, a half part of the whole hybrid joint structure was modeled due to the symmetry of it (Fig. 4a). This modeling advantage provided to decrease both element and node numbers and the solution time. After the modeling and meshing process, solution process was completed in two steps based on loading conditions. In first step, the tensile load was applied on the half model as pinned condition. For this intention, one side of the model fixed for all directions and a pressure was applied on other side as 10 MPa for providing tensile load. The pinned condition was carried out hole surface. Thereby, the hybrid joint model was conditioned as under only tensile loading. In the second step, the uniform temperature load was applied on the half model with tensile loads. Thus, both tensile load and thermal load were applied on the model. Since, in practice adhesive joints can suffer thermal loads as well as structural loads too. These thermal loads play an important role in the strength of the adhesively bonded joint 29. The reference temperature was assumed as 25 o C. The

5 96 INDIAN J ENG. MATER. SCI., APRIL 2013 magnitude of applied uniform temperature was as 55 o C. Results and Discussion Due to the superior evaluating of results, node and path definitions are essential around the pin hole zone, especially. Seeing as stress concentrations are observed on this area because of the existence of hole. Node definitions and paths are shown in Fig. 4. This figure point out that four important paths are defined from θ=0 o to θ=180 o. The path AB is defined on the top surface of the composite (upper adherent) and it is called composite upper surface. The path CD is between composite and epoxy adhesive layer. This path is called both composite lower surface and epoxy upper surface. Similarly, the path EF is between epoxy adhesive layer and aluminum plate (lower adherent) and it is named as both epoxy lower surface and aluminum upper surface. Lastly, the path GH is located bottom surface of the aluminum which is named as aluminum lower surface in graphs. Normal and shear stress distributions related to defined four paths without thermal loads are plotted in Fig. 5. According to this figure, stresses for x-direction (σ x ) are higher than y-direction (σ y ) particularly. The magnitudes of stresses on adhesive layer are lower than both aluminum and composite sheets. But, the higher values of stresses are calculated on composite upper surface (path AB). When θ=90 o, the stresses are reached highest values for each paths. The stresses occurred as tensile form except aluminum lower surface, when θ=90 o, too. In other words, any failure may be started from θ=90 o located nodes because of higher stresses on them. These tensile stresses are decreased after θ=90 o and changed as compressive form between θ=135 o and θ=180 o. This result is very suitable with some previous experimental studies for single pinned joints 22,23. Consequently, these stress distributions may cause net tension failure when θ=90 o, whereas they may create bearing failure between θ=135 o and θ=180 o like previous experimental studies 22,23. According to Fig. 5c shear stresses is also very important for this hybrid joint because of their higher values. It is known that shear stresses reason debonding between adhesive layer and adherent layers. In brief, the highest values of stresses without thermal loading are calculated as MPa for x-direction, MPa for y-direction, MPa for shear stresses. All of them were calculated on composite upper surface (path AB) when θ=90 o. Fig. 5 Stress distributions around pin hole on defined paths without thermal loads Normal and shear stress distributions related to defined four paths with thermal loads are shown in Fig. 6. Since, the solution was completed in two stages as mentioned previously. It is seen from this figure, the magnitudes of stresses on each adherent are increased strictly. It is valid both normal stresses and shear stresses. In other words, the stresses on epoxy layer, aluminum and composite plates are raised after applied thermal loading. But maximum values of stresses can be changed between upper and

6 ALDAS & SEN: STRESS ANALYSIS OF HYBRID JOINTS 97 lower surfaces of each adherent after thermal loading. The occurrence of stresses for each path in Fig. 6 is seen like Fig. 5 except path GH (aluminum lower surface). The form of stresses on it are compressive form between θ=45 o and θ=135 o in Fig. 5, whereas it is seen as tensile form between θ=0 o and θ=135 o in Fig. 6. Additionally, the highest values of stresses are calculated on path GH in Fig. 6, while the highest values are computed path AB in Fig. 5. It means that, applying of extra thermal load with tensile load on hybrid joint cause highest stresses on aluminum lower surface with changing form from compressive form to tensile form or tensile form to compressive form. The highest calculated values of stresses under both tensile and thermal double loading conditions are calculated as MPa for x-direction, MPa for y- direction, MPa for shear stresses on aluminum lower surface (path GH) when θ=90 o. It can be said uniform applying of thermal loading increased all stresses if whole joint is considered. The reason of this result is based from the different thermal expansion coefficients of the aluminum and epoxy adhesive as seen in Tables 1 and 2. Because of good understanding loading conditions which are tensile and tensile plus thermal loadings, stress distributions for x-direction on aluminum adherent, composite adherent and epoxy layer are plotted in Figs 7-9, respectively. According to Fig. 7, thermal stresses both lower surface and upper surface of aluminum adherent are increased after thermal loading. The stress form is also changed after θ=45 o for lower surface. When θ=90 o, the stress form without thermal loading is compressive while it is changed tensile form after thermal loading. It is also calculated uppermost value at θ=90 o on lower surface. Similarly highest compressive stresses are obtained for lower surface of aluminum adherent. Figure 8 points out that the stresses are increased after applying of thermal loading on composite lower surface, although it is decreased after performing of thermal load on composite upper surface. The occurrences of tensile and compressive stresses for composite adherent are seen similar with aluminum, Fig. 6 Stress distributions around pin hole on defined paths with thermal loads Fig. 7 Stress distributions on aluminum adherent

7 98 INDIAN J ENG. MATER. SCI., APRIL 2013 Fig. 8 Stress distributions on composite adherent Fig. 9 Stress distributions on epoxy adhesive layer Fig. 10 Stress distributions on epoxy adhesive layer for x-direction generally. Additionally, tensile stresses are also higher than compressive stresses for composite adherent. As seen from Fig. 9, the magnitudes of stresses lower than both aluminum and composite adherents. The uppermost value of stress on adhesive layer is calculated as 8.45 MPa tensile and MPa compressive on upper surface after applying thermal load. Stresses are increased after thermal loading for both lower surface and upper surface of the epoxy. This result is also valid both tensile and compressive stresses. Contrary to aluminum and composite adherents, the uppermost values between tensile and compressive stresses are not higher than each other. Meanwhile, the highest tensile stresses are calculated when θ=90 o, whereas the highest compressive stresses are computed when θ=90 o. Lastly, the occurrence of stresses on aluminum and composite adherents are seen similar, generally (Figs 7-8), although it is very

8 ALDAS & SEN: STRESS ANALYSIS OF HYBRID JOINTS 99 Fig. 11 von Mises stress distributions on epoxy adhesive layer different for epoxy layer (Fig. 9). The difference is very important after thermal loading especially, since it understand that the differences thermal expansion coefficients between aluminum and composite adherents and epoxy are very important creating of the stresses on a hybrid joint constructed from different adherents. It is known that ANSYS software provides color contours for each part of the joint for good evaluating of the results. Nonetheless, the stress distribution on adhesive layer is very vital for adhesively bonded joints. For that reason, stress distribution for x- direction and von Mises stress distribution related to with/without thermal loadings on adhesive layer are shown in Figs 10 and 11 via color contours, respectively. It is clearly seen that the values of stresses on epoxy adhesive are increased with applying thermal load. For instance, the highest von Mises stress MPa without thermal loads, whereas it is calculated as MPa with thermal loading. This increasing is also valid for σ x as shown Fig. 10. Furthermore, stresses are created as compressive form which is pinned contact surface from after θ=90 o to θ=180 o. However, the highest tensile stress is calculated when θ=90 o. The magnitudes of maximum tensile stresses are higher than maximum compressive stresses. Conclusions In this study, a numerical stress analysis was performed for a hybrid joint constructed both adhesively bonded and pinned single lap joint for aluminum and composite adherent via 3D-FEM. According to analyses results some significant remarks can be concluded as; stresses with thermal loading are calculated higher than without thermal loading. Different thermal and mechanical properties of aluminum, composite and epoxy adhesive cause high stresses on the hybrid joint. Owing to the existence of the pin hole, stresses are particularly concentrated pin hole zone both adherents and adhesive. When θ=90 o, stresses are observed as tensile form, after the θ=90 o to θ=180 o which is the pin contact surface stresses are obtained as compressive form. It is known, tensile stresses may cause net-tension failure and compressive stresses may reason bearing failure in pinned joints, thus obtained stress distribution is appropriate with reported experimental studies.

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