A novel double-spring analytical model for hybrid GLARE joints: Model development, validation, parameter study and global sensitivity analysis

https://doi.org/10.1016/j.ijmecsci.2020.105606Get rights and content

Highlights

  • The deformation of hybrid GLARE joints can be well predicted by the novel double-spring model.

  • Based on the Monte Carlo simulation and global sensitivity analysis, the influences of uncertainty and probability assembly factors on hybrid joints are quantitatively investigated.

  • The role that various jointed factors play in the mechanical responses of hybrid GLARE joints are discussed in detail.

  • The results can provide effective guidance for the design and assembly of hybrid GLARE joints.

Abstract

It is significant to theoretically evaluate the mechanical properties of hybrid (bonded/bolted) GLARE joint, especially under the condition of multiple assembly uncertainties. This work develops a double-spring analytical model that predicts the deformation of hybrid joints under the quasi-static load to solve this critical problem in the fabrication process of hybrid joints. Besides the mechanical properties of bolt, the stiffness of adhesive layers is introduced in this novel model in which the factors such as geometrics, properties of adhesive layer, bolt-hole clearance, laminate properties, contact condition, relaxation of pre-torque and types of materials are discussed in detail. Meanwhile, a Monte Carlo simulation (MCS) and a variance-based method are used to calculate their global sensitivity indices that have the ability to quantify the relative importance of those assembly factors in load distribution between the bolt and adhesive layer, fracture displacement at the initial stage and other mechanical properties. It is found that bolt-hole clearance, geometrics of laminate and properties of adhesive layer are the top three sensitive factors, the qualities of which must be strictly controlled in the process of fabrication. This model is able to provide a powerful approach for the future design of hybrid joints to achieve higher reliability and load capacity.

Introduction

Composite materials have been widely adopted in the aerospace industry [1], [2], [3], due to high stiffness-weight and strength-weight ratios. Glass fiber reinforced aluminum (GLARE) laminate as a kind of hybrid composites that consist of aluminum alloy and glass fiber reinforced polymer layers have been broadly used in airframe structures such as Airbus A380 [4,5]. Although these materials display advantages in terms of capacity, their assembly is a key problem that limits the development. Mechanical fastening as a low-cost and reliable method has become the primary mode of connection. However, the bolted hole is a potential weak point, which can influence the loading capacity and the lifetime of structures [6], [7], [8], [9]. Therefore, developing more advanced jointed technologies can improve the ultimate strength and reliability of jointed structures [10,11].

The hybrid joint combining adhesive layer and bolt can provide more excellent mechanical properties than bolted joints or bonded joints [12], because the adhesive and bolt can carry the external load jointly [13]. Research techniques for hybrid joints could be divided into simulation, the lap-joint design and the development of analytical models [14], [15], [16]. Commercial FEM software as an efficient and economical approach has been applied to study the adhesive layers through cohesive elements that can well simulate the debonding of adhesive layer. Besides, the investigations of numerical model including multiscale modeling, the simulation of contact conditions and judgement of failure mode could provide us efficient instruments to analyze the adhesive bonded joints [17], [18], [19]. Lelias et al. [20] developed an extended semi-analytical formulation for the stress analysis of bonded joints. Pardon et al. [21] investigated the constraint effect on adhesive joint fracture by modeling the adhesive joint in which the elastic-plastic properties of adhesive and adherends were considered. In order to improve the joint qualities, Moreira et.al [22] also enhanced the bonded interface for single lap joint by using laser treatment surfaces.

From the literature reviews, little attention has been paid on the effect of uncertainty or probabilistic parameters on mechanical behavior of hybrid joints. Because there are many parameters that could not be controlled precisely during the process of preparation including error of bolt-hole clearance, relaxation of bolted pre-torque and so on. Besides the improvement of mechanical properties of hybrid joints through the design of lap joint and characteristic analysis before fabricating joints, the ultimate capacity of hybrid joints sometimes relies on the assembly technology. The bolt-hole clearance between bolted shank and hole could change the bolted 90% of properties. Due to the uncertainty assembly process, it is necessary to conduct the reliability analysis of composite structure joints, which determined the service life of structures. Besides the structural reliability affected by jointed geometric parameters, the probabilistic failure prediction of composite laminates is a research hotspot which has been investigated by Khashaba [23]. In the calculation process, mathematic analytical model of hybrid joints must be developed in order to implement the probabilistic prediction. To bolted joints, a spring-based model was introuduced by Tate et.al [24] to analysis the load-displacement behavior of structure. With the development of composite materials, Nelson [25] studied the bolted composite joints by using spring-based model, and McCarthy et.al [26] improved this spring-based model considering the effect of clearance, friction and bolted pre-torque. Then, there were some researchers investigating the global sensitivity and probabilistic of load distribution and failure of bolted joints [27], [28], [29] based on this spring-based model. Kelly [30] investegated the influence of variable parameters on load-displacement of hybrid joints by finite element methods. The sensitivity indices of adhesive material, adhesive thickness and laminate geometris were ranked according the sensitivity analysis. He just varied only one parameter at a time without considering the varying mutiple parameters at a time. Therefore, this study can be classified in the local sensitivity analysis, which did not take into account the influence of all variable parameters. Bodjona and Larry [31] investigated the global sensitivity of design factors based on Global Hybrid Joint Method (GHJM), which was also modified from ABAQUS FEM model. These researches illustrated the effect of geometry, adhesive thickness and plastic deformation of adhesive layer on the hybrid joints. But they did not consider the fracture of adhesive layer and the effect of uncertainty assembly factors during the fabrication process.

According to the reference [32], when the adhesive layer and fastener work together, the structural strength could be enhanced. However, the adhesive layer only plays a role at the initial stage, and the effect of adhesive layer would vanish when it is damaged entirely. Based on original achievements [33], the mechanical properties of hybrid joints relay on numerous factors including bolt-hole clearance, bolted pre-torque, structural geometries and so on. The single-lap, single-bolt hybrid jointed configurations consist of GLARE laminates, fasteners and the adhesive layer (J-272-A adhesive, Heilongjiang Institute of Petrochemical, China), which are the objects of research shown in Fig. 1. The GLARE3A is fabricated using three 2024-T3 aluminum alloy plates and four HS4 glass fiber/epoxy reinforced pre-pregs with stacking sequence [Al/0°/90°/Al/90°/0°/Al]. Each aluminum alloy has the thickness of 0.4 mm and GFRP layer has 0.15 mm, yielding a total GLARE thickness of 1.8 mm. Because only elastic deformation of GLARE laminate is considered, the GLARE laminate is simplified based on classical laminate theory (CLT), which is used to calculate the properties of equivalent homogenized laminate [34].The constituent material properties are listed in Table 1 [32]. The properties of fasteners, including steel nut, washers and ∅6 bolt, are also listed in Table 1 as fundamental parameters used in the model analysis.

In the fabrication process, it is hard to guarantee that the bolt-hole clearance can be a constant parameter during the manufacturing process [8,26]. With service time increasing, the bolted pre-torque can relax [35], which is also an uncertainty parameter. The other parameters including the material properties, contacting condition of joints, the manufacturing error of fasteners and different structural geometries can vary within a certain range. However, the contribution of variable input parameters on the results will be different. Therefore, a variance-based global sensitivity analysis is conducted based on DS model proposed in this research, which can provide the baseline for actual applications in the future.

In this study, a novel analytical model for hybrid (bonded/bolted) joint taking into account all uncertain assembly factors was developed, which could predict initial load-displacement behavior of hybrid joint under axial quasi-static load. The mechanical response including the phenomenon of load-dropping at the initial stage observed in experiments can be well predicted by this model. Then, based on the analytical model, the effects of uncertain assembly factors on the mechanical properties of hybrid GLARE joint are investigated by using a Monte Carlo simulation and a variance-based global sensitivity analysis.

Section snippets

The introduction of double-spring model

Before developing the novel double-spring model, two sets of quasi-static tensile experiments were conducted on bolted joint and hybrid joint in order to obtain their different mechanical responses. All experiments were carried out on the universal test machine INSTRON 5569 with a load limitation of 50 kN and loading rate of 1 mm/min. A spring model is used to describe the mechanical response of bolted GLARE joint including slope-1, slope-2 and a sliding section as shown in Fig. 2(a)-(b), which

Global sensitivity analysis method for uncertain assembly parameters

In general, it is difficult to precisely control the manufacturing process of hybrid GLARE joints, which causes a considerable uncertainty in the hybrid joints. Therefore, it is essential to conduct global sensitivity analyses of assembly parameters affecting the properties of hybrid GLARE joints. The flow chart of analytical process is given in Fig. 7 that may be divided into three parts including the generation of uncertain parameters, computation of mechanical response based on the proposed

Results and discussions

The established DS model in this research is created and computed in MATLAB program. Through the parameter studies, the influence of assembly factors on mechanical properties of hybrid joints is found. It is also worth noting that the global sensitivity analysis is helpful for engineers to improve the assembly quality of structures by ranking the sensitive factors.

Conclusion

The contribution of this work is developing a novel double-spring model for hybrid GLARE joints under the axial quasi-static load. Meanwhile, the developed model validated by the experiments well predicts the mechanical properties of hybrid GLARE joints.

Through parameter studies, it can be found that all factors are divided into two categories based on the influence on ultimate capacity or fracture displacement of hybrid joints. The ultimate capacity of hybrid joints at the initial stage is

CRediT authorship contribution statement

Peifei Xu: Conceptualization, Data curation, Formal analysis, Writing - original draft, Methodology, Investigation. Zhengong Zhou: Supervision, Funding acquisition, Project administration, Writing - review & editing. Tianzhen Liu: Methodology, Validation, Investigation, Writing - review & editing. Xiaojun Tan: Methodology, Validation. Shidong Pan: Funding acquisition, Project administration.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is supported by National Natural Science Foundation of China [grant numbers: 11572101, 11572104]

References (48)

  • E. Paroissien et al.

    Simplified stress analysis of hybrid (bolted/bonded) joints

    Int J Adhes Adhes

    (2017)
  • Q. Luo et al.

    Analytical solutions for adhesive composite joints considering large deflection and transverse shear deformation in adherends

    Int J Solids Struct

    (2008)
  • B.R.K. Blackman et al.

    The fracture behaviour of adhesively-bonded composite joints: effects of rate of test and mode of loading

    Int J Solids Struct

    (2012)
  • K. Matouš et al.

    Multiscale cohesive failure modeling of heterogeneous adhesives

    J Mech Phys Solids

    (2008)
  • G. Carbone et al.

    Analysis of the adhesive contact of confined layers by using a Green’s function approach

    J Mech Phys Solids

    (2008)
  • Q.D. Yang et al.

    Numerical simulations of adhesively-bonded beams failing with extensive plastic deformation

    J Mech Phys Solids

    (1999)
  • G. Lelias et al.

    An extended semi-analytical formulation for fast and reliable mode I/II stress analysis of adhesively bonded joints

    Int J Solid Struct

    (2015)
  • T. Pardoen et al.

    Constraint effects in adhesive joint fracture

    J Mech Phys Solids

    (2005)
  • R.D.F. Moreira et al.

    Mode ii fracture toughness of carbon–epoxy bonded joints with femtosecond laser treated surfaces

    Int J Mech Sci

    (2018)
  • U.A. Khashaba et al.

    Failure and reliability analysis of pinned-joints composite laminates: effects of stacking sequences

    Compos Part B

    (2013)
  • C.T. Mccarthy et al.

    An analytical model for the prediction of load distribution in highly torqued multi-bolt composite joints

    Compos Struct

    (2011)
  • F. Liu et al.

    A failure-envelope-based method for the probabilistic failure prediction of composite multi-bolt double-lap joints

    Compos Part B

    (2019)
  • J. Xiang et al.

    An improved spring method for calculating the load distribution in multi-bolt composite joints

    Compos Part B

    (2017)
  • H.-.S. Li et al.

    A probabilistic analysis for pin joint bearing strength in composite laminates using subset simulation

    Compos Part B

    (2014)
  • Cited by (0)

    View full text