joint strength, one must have the stress distribution and a suitable failure criterion. The literature ... For each model proposed the compatible failure criteria are included to enable the user not ... The implemented models are described below.
Development of a software for the design of adhesive joints Lucas F. M. da Silva, Ricardo F. T. Lima, R. M. S. Teixeira and André T. Puga Department of Mechanical Engineering and Industrial Management, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
Abstract Adhesive joints are increasingly being used due to their improved mechanical performance and a better understanding of the mechanics of failure. To predict the joint strength, one must have the stress distribution and a suitable failure criterion. The literature contains many closed-form solutions for the stress distribution. However, the models are sometimes difficult to implement and use. The first objective of the present work was to compile existing models of increasing complexity in a user friendly software. Three main situations were considered: elastic adherends and adhesive, elastic adherends with nonlinear adhesive and nonlinear analyses for both adherends and adhesive. The adherends were both isotropic (metals) and anisotropic (composites). The joints considered are the single and double lap joints for most of the models. However, a sandwich model initially proposed by Crocombe can be used for any type of joint provided the boundary conditions are known. A newly developed model that can simulate the presence of two adhesives along the overlap is also implemented in the software. For each model proposed the compatible failure criteria are included to enable the user not only to have the stress distribution but also the failure load for a given joint/load scenario.
1.
Software description
The objective was to supply design engineers with a toolbox of methods for a better and easier analysis of adhesive joints. With a friendly interface this software allows the user to analyze the mechanical behavior of adhesive joints using a variety of mathematical models. For this effect a simple and intuitive web-interface was developed with a toolbox of methods and mathematical models, as shown schematically in Figure 1. The website was designed for multiple purposes: user input of joint problems data, automatic model selection (based on the problem data available), graphical plot visualization of stress distribution, and calculation of failure load and database access management. The user submits a problem data and the web-interface automatically selects the models that ‘fit’ the data given by the user. For example, if only the elastic properties of the adhesive and adherend are given, then only the models of Volkersen, Goland and Reissner and Bigwood and Crocombe can be used. Once the mathematical model calculations are finished, the results achieved are presented to the user via a plot based on graphical interface. The user can see a plot of the model results (for example the shear stress over the overlap). The datasheet version of the results is also available if the user wants to process the results in a different way. The models used in this project are implemented as computer programs following a simple set of rules:
1
the programs of the models are connected to the server (it may or may not be on the same machine); the programs of the models work using a black-box implementation (only the input and output formats are know); the programs of the models all use a normalized input/output set of rules. This design set allows pre-made programs, which follow the implementation format, to be incorporated in the project with minimum effort and retaining functionality.
2.
Models implemented
The software developed contains several mathematical models implemented, allowing the user to select the model more suitable for his analysis. The geometries suitable for analysis are the single and double lap joints. The model of Bigwood and Crocombe is more general and can simulate more complex joints such as T-joints or corner joints (see Figure 2 and Figure 3). The implemented models are described below. Volkersen [1] Volkersen’s analysis introduced the concept of differential shear. It assumes that the adhesive deforms only in shear but that the adherends can deform in tension, because they are considered elastic and not rigid. The solution given is more representative for linear geometric problems such as double lap joints. The shear stress in the adhesive is given. Goland and Reissner [2] Goland and Reissner’s analysis considers the nonlinear geometric problem effects due to the adherends rotation in the single lap joint. The model assumes that the adherends are integral, with an infinitely thin adhesive layer. Algebraic solutions for the elastic shear and peel adhesive stresses are available. Hart-Smith [3] Hart-Smith analysis gives a closed-form algebraic solution for the elastic shear and peel adhesive stresses. The same model can also consider adhesive shear stress plasticity using a bi-linear elastic-perfectly plastic approximation, keeping the peel stress elastic. This model takes into account the nonlinear adherends geometric problem, considering individual deformation of the upper and lower adherends in the overlap, and the adhesive layer between. Adams [4] This simple predictive model gives the adhesive global yielding and the adherend yielding. For substrates that yield, a plateau is reached for a certain value of overlap corresponding to the yielding of the adherend, the joint strength being easily predicted. For intermediate or brittle adhesives and non-yielding adherends, the analysis is less robust and the author suggests using the finite element method or a more complete analytical solution. Bigwood and Crocombe [5-6] Bigwood and Crocombe’s analysis can give a general elastic analysis, a simplified peel and shear analysis or a complex plastic analysis for the peel and shear stresses for either the adhesive or for both adhesive and adherends. The great advantage of the model of Bigwood and Crocombe is that it is a sandwich that can be used for any type
2
of joint provided the boundary conditions are known. The present software includes the general elastic analysis and the adhesive plasticity. The adherend plasticity is not implemented because of the complexity of the mathematic resolution. For that case, the model of Adams is simpler to use. Frostig [7] In Frostig’s analysis, the joint is divided into regions and the continuity requirements are derived for each region using the principle of virtual displacement to set the governing equations and boundary conditions. This model gives the elastic shear and peel stress in the adhesive. Composite materials can be modeled as well as the spew fillet. New models Some models described above were further developed to give the user a more general choice. The model of Bigwood and Crocombe was developed to include the case of composite materials. The model of Frostig was developed to include more than one adhesive along the overlap [8].
3.
Conclusions
A web-based software was developed for designing adhesive joints. Various analytical models were implemented in the software so that the user can get an easy answer for practically any type of situation. The main conclusions are: 1. Most of the models are applicable to single and double lap joints. However, the model of Bigwood and Crocombe can be used for any type of joint that contains a sandwich. 2. Elastic and plastic analyses whether in the adhesive or in the adherend can be carried out. 3. Isotropic as well as composite materials can be studied. 4. Adhesive joints with more than one adhesive are implemented. 5. The effect of the spew fillet can be assessed.
Acknowledgements The authors thank the University of Porto (project IPG96/2007) and the European Union (project Cordis FP6 31321) for supporting part of the work presented here.
References [1] Volkersen O. Luftfahrtforschung 1938; 15: 41. [2] Goland M Reissner E. Journal of Applied Mechanics 1944; 66: A17. [3] Hart-Smith LJ. NASA Contract Report 1973, NASA TR-11234. [4] Adams RD, Comyn J, Wake WC, Structural adhesive joints in engineering, 2nd ed. London: Chapman & Hall, 1997. [5] Bigwood DA, Crocombe AD. Int J Adhes Adhes 1989; 9: 229. [6] Bigwood DA, Crocombe AD. Int J Adhes Adhes 1990; 10: 31. [7] Frostig Y, Thomsen OT, Mortensen F. Journal of Engineering Mechanics 1999; 125: 1298. [8] das Neves PJC, da Silva LFM, Adams RD, J Adhesion Sci Technol, in press, 2008. 3
User
DataBase
Website
Mathematical model
C
Figure 1
MAXIMA
MAPLE
General description of the software developed.
a)
b)
c)
d) Figure 2
Types of joints that can be simulated by the software; a) single lap joint; b) double lap joint; c) T-joint; d) corner joint.
Figure 3
Bigwood and Crocombe’s diagram of adherend-adhesive sandwich under general loading.
4
