Literature Review On The Reliability Analysis Of Composite Structures
Recently, the application of the adhesive joints has been increased dramatically in different industries including aerospace, automotive, shipbuilding. Enhancement in the strength of structures and fatigue life is the most important advantages of adhesive joints which makes them more popular than typical joints such as bolts and welding. However, the main drawback of these typical joining methods is that they are not suitable for bonding the dissimilar materials such as composite and metals. This is due to the fact that this joining method may cause the formation of some local damages at the interface between metal and composite which are named debonding. When the stress of interface exceeds the strength of the adhesive layer due to the loading condition, the initial crack starts to grow and consequently, the debonding happens. Debonding leads to the degradation in the strength and stiffness of the structure and reducing in its life. Another disadvantage of debonding formation is that it may intensify the stress concentration in the load-bearing plies and produce local instability. To comprehensive practical study of adhesive joints, the reliability analysis of these types of structures seems to be necessary. In order to describe the behavior of real structural systems, consideration of uncertainty in system parameters is inevitable.
In recent decades, the reliability analysis of composite structures has been addressed significantly by researchers. Uncertainty in composite materials usually appears due to the variation in distribution of external loads, boundary conditions, geometry of the structure, material properties such as fiber and matrix properties and operational conditions and leads to the random behavior of structures.
Since metal-composite adhesive joints contain many sources of uncertainty such as the mechanical properties of composite and metal, it is important to investigate the debonding behavior of these structures due to the effect of random variables in a probabilistic framework. Lu et al. proposed the reliability-based design optimization (RBDO) for the adhesive bonded steel-concrete composite beam with considering probabilistic and non-probabilistic uncertainties. In addition, Alia et al. investigated the reliability of aluminum-composite adhesive joint for mode II with using Weibull distribution. Delbariani-Nejad et al. proposed an approach to analyze the reliability of composite laminates in the presence of the most common and catastrophic failure mode in macro-scale, i.e. delamination under mode I, mode II, and mixed mode I/II by the use of energy based method. Importance of debonding failures in metal-composite adhesive bonded joints provokes many researchers to investigate the problem, using the experimental and numerical approaches.
Cheuk et al , studied the fatigue crack growth in Aluminum-Boron adhesive joints using experimental and numerical approaches. Fatigue tests were done under tensile loading and crack length was measured with using the optical methods. According to the obtained results, it was claimed that the main reason for fatigue failure of metal-composite double-lap joints is the tensile loading mode due to the peel stress.
Derwnko , proposed a function for normal and frictional stresses of the interface in Aluminum-Glass/Epoxy composite adhesive joints. The results showed that the stress between adhesive layer and aluminum is more than 90% of stress between adhesive layer and composite.
Rudawska evaluated the joint's shear strength in Titanium sheet–Aramid/epoxy composite and Aluminumsheet–Aramid/epoxy composite using experimental and and numerical approaches. Results revealed that the shear strength in Titanium sheet–Aramid/epoxy composite is nearly 2.8 times higher than an Aluminum sheet–Aramid/epoxy composite. In addition, it was concluded that the numerical analysis is a useful alternative tool for prediction of failure modes with respect to the impossible experimental tests.
Valenza et al. investigated the influence of several parameters on the mechanical behavior and failure modes of the Aluminum-GFRP adhesive bonded joints. In order to improve the adhesion strength between the adherents, two different methods used: variation of the adhesive thickness and pre-treating the metal surface with Silane coupling agent, γ-glycidoxypropyltrimethoxysilane (γ-GPS). Results showed the chemical pre-treatments of the metal surface with the γ-GPS saline coupling agent is the best tool to improve the mechanical performances of metal to composite hybrid joints bonded with an epoxy adhesive.
Andre et al. studied the adhesive strength of Steel-CFRP structures in mode I and mode II and mixed mode (I/II) using numerical and experimental approaches. DCB specimens, Single Side Shear (SSS) specimens and reinforced bending specimens used for mode I, mode II and mixed mode (I/II) respectively. The adhesive layer’s thickness in all specimens were 2.4 mm. FE results forDCB and SSS Showed a good agreement with Experimental results but in reinforced bending specimen,large deviation from experimental results observed.
Anyfantis proposed a FE model for prediction of the debonding in the Steel-CFRP adhesive bonded joints. Additionally, a numerical parametric study was conducted to investigate the effect of the overlap length and the thickness of the adherents on the strength of the joints. The results showed that the failure load is increased significantly, as the overlap length tends to 40 mm and beyond that point, the failure load reach a plateau. In addition, it was observed that in the cases involve thin metal substrates, the efficiency of adherent is much better than the cases that involve thick metal substrates.
Khosravan and mehrabadi investigated the fracture event of Aluminum-CFRP adhesive bonded joints in loading mode I and used Double Cantilever Beam (DCB) test to evaluate the fracture toughness in this mode. They also applied the Virtual Crack Closure Technique (VCCT) and J-integral approaches to investigate the deboning growth numerically. Good agreement between the experimental tests and numerical analyses demonstrated the effectiveness of the proposed experiment and numerical methods.
Hosseini et al. studied the progressive debonding in wind turbine blade constructed Aluminum-GFRP subjected to cyclic loading using numerical simulation and experimental test. The required mechanical properties for numerical simulation such as fracture toughness in mode I, mode II, mixed mode (I/II) as well as Paris-law coefficients were characterized by performed experiments. It was illustrated that the maximum length of the deboned area after a typical overloading is about 8% of the total height of the root and it would increase to about 40% of the total height after a 1-month normal operation.
Wang et al. employed an advanced hybrid joining technique to manufacture double lap joints between an aerospace titanium alloy (Ti6Al4V) and a carbon fiber reinforced epoxy composite. A digital image correlation (DIC) technique was used to monitor the strain field and also detecting failure modes in specimens.
Freitas et al. , investigated the adhesion quality of composite-to-metal bonded joints under salt spray aging conditions. The peel specimens were exposed to salt spray for 30 and 90 days. The results revealed that the adhesion performance under the peeling load of the joints is decreased progressively with enhancement of the aging time.
Sun et al. , studied the influence of adherent thickness and adherent materials on the fracture characteristics of single-lap adhesive joints. DIC analysis was used to capture full-field strain information and strain evolution. Results showed that the joint strength is increased with the adherent’s thickness regardless of the joint types, but it was not linearly proportional to the thickness of the adherents. Considering the mentioned research works, it is evident that there is no any exclusive study on the probabilistic analysis of debonding growth in adhesive bonded joints with dissimilar material. As a result, the present paper is concerned with the reliability analysis of debonding growth in metal-composite adhesive joints under mode I, mode II and mixed mode I/II loading. To this end, an approach, which has been developed and utilized by Delbariani-Nejad et al. for the first time is employed. To achieve this goal, after conducting standard experiments on the metal-composite adhesive joints in mode I and mode II, in order to obtain the probability density function of random variables such as fracture toughness of metal-composite adhesive joints related to the mode I, mode II and Mixed mode (I/II), the reliability analysis methods are applied. The first and second order reliability methods (FORM and SORM) are used to attain the probability of debonding growth. Then, for the verification of results, a Monte Carlo simulation (MCS) is applied.
Later on, through utilizing the concept of energy release rate as well as its existing analytical solutions for pure mode I, pure mode II, and mixed mode (I/II) and the corresponding interlaminar fracture toughnesses, limit state functions (LSF) are formulated based on energy release rate in the aforementioned modes, and thereby the probabilistic analysis of debonding growth in metal-composite adhesive joints is conducted. To obtain the statistical characterization of uncertainty source (mean values and coefficients of variation), experimental and numerical investigations are performed on debonding behavior of Steel–Glass/Epoxy adhesive bonded joint. In order to calculate the fracture toughness, in mode I and mode II, DCB and ENF specimens are used respectively. Then, suitable data reduction method is used for calculation of the fracture toughness in mode I and mode II. Furthermore, all experimental tests are simulated in ABAQUS software and then analyzed using the Cohesive Zone method (CZM) based on linear traction separation law (LTSL). Finally, the FE results are verified by experimental results.
It is worth noting that, in this paper, the effect of initial debonding length on the probability of debonding growth for each mode is obtained. It is worthwhile to state that the effects of loading modes including mode I, mode II and mixed mode I/II loading on the reliability of cracked structures have been investigated by Delbariani-Nejad and Nazari using the concept of stress intensity factor of metal structures. They also recommended that further researches to be done regarding the effects of different loading modes on the reliability of laminates under delamination/debonding mode, which is one of the main goals of the present paper. Therefore, by comparing reliability in mode I, mode II and mixed mode (I/II) along with using mixed mode ratio (MMR) parameter, the effect of loading modes on the reliability of debonding growth in metal-composite adhesive joints is investigated. Furthermore, the sensitivity analysis is performed to characterize the most effective random variables on the probability of debonding growth in each of the mentioned modes.
