FAnTe­Stick - Enhanced life­time predic­tion of bonded joints through simu­la­tion

Dear reader,

In this blog article, we intro­duce you to one of our research projects in which we are active: FAnTe­Stick. You will get an overview of the project, the moti­va­tion behind it as well as the chal­lenges, tech­nical devel­op­ments and the insights gained so far. In this and future arti­cles on the FAnTe­Stick project, we will show you how the failure and fatigue behav­iour of bonded fibre composite compo­nents can be predicted using targeted testing and calcu­la­tion methods. Based on these results, durable, sustain­able composite struc­tures can be devel­oped.

Enjoy reading!

Intro­duc­tion & Moti­va­tion

An impor­tant aspect in compo­nent devel­op­ment is the eval­u­a­tion of the connec­tion between compo­nents to ensure their struc­tural integrity and thus the reli­a­bility of the overall system. To achieve a reli­able and strong connec­tion between fibre composite compo­nents, two joining tech­niques are usually used: conven­tional mechan­ical fasteners (e.g. screws and rivets) and/​or adhe­sive bonding. The latter offers numerous, promising advan­tages, such as lower stress concen­tra­tions in the joining area, the possi­bility of joining different mate­rials, flex­i­bility in the design as well as high damage toler­ance and good fatigue behav­iour.

However, bonded joints usually contain micro-cracks and isolated voids (air pockets) in the adhe­sive layer, which inevitably occur during the manu­fac­turing process or assembly of the joint. Since the pres­ence of such defects can compro­mise the strength of the loaded joint, it is neces­sary to eval­uate the frac­ture and fatigue behav­iour as well as the failure mech­a­nisms to ensure safe design of bonded struc­tures.

The FAnTe­Stick project is being carried out in coop­er­a­tion with our research partner, the Leibniz Insti­tute for Composite Mate­rials (IVW) in Kaiser­slautern. The aim is to develop a prac­tical calcu­la­tion method for predicting the service life of bonded joints in fibre composite struc­tures. The analysis of the bonded joint is carried out with the help of analyt­ical and numer­ical approaches devel­oped within the project, as well as with data from exper­i­mental tests carried out in parallel.

Frac­ture mechanics calcu­la­tion of bonded joints

Conven­tional methods for designing and analysing a compo­nent work with stress or strain-based strength concepts. In this approach, a mate­rial failure is defined when the occur­ring stress or strain exceeds the material’s ultimate/​yield stress or ulti­mate strain, which is defined based on the chosen failure crite­rion. The manu­fac­turing-related flaws in adhe­sive layers lead to the forma­tion and prop­a­ga­tion of cracks. Such cracks lead to local stress concen­tra­tions, which can result in mate­rial failure before the expected nominal strength limit deter­mined by conven­tional testing.

Frac­ture mechanics is used to under­stand and predict the failure of mate­rials due to these flaws. Frac­ture mechanics is a field of engi­neering and mate­rials science that studies the behav­iour of cracks and defects in mate­rials under external loads. The concept of strain energy release rate (SERR) is used for the assess­ment as it is a measure of the energy required to prop­a­gate a crack. The SERR repre­sents the energy lost per unit area of a newly formed frac­ture surface during the frac­ture process.

Frac­ture mechanics is an effec­tive tool for char­ac­ter­ising the failure of mono­lithic mate­rials as well as bonded joints. To eval­uate the frac­ture behav­iour, the bonded struc­tures are subjected to a wide range of tensile (mode I) and shear stresses (mode II) as well as mixed stresses (mode I+II). There­fore, it is essen­tial to exper­i­men­tally char­ac­terise the entire range of tests in order to obtain the so-called frac­ture enve­lope.

In addi­tion to the exper­i­mental eval­u­a­tion, a numer­ical calcu­la­tion model was created using the finite element method (FEM) to simu­late the frac­ture behav­iour. Finite element analysis offers a cost-effec­tive, virtual solu­tion for frac­ture mechanics eval­u­a­tion that reduces the cost and time required for further exper­i­mental inves­ti­ga­tions.

For the simu­la­tion of crack initi­a­tion and prop­a­ga­tion under mechan­ical loading, several numer­ical approaches have been devel­oped within the frame­work of FEM. Among the avail­able approaches, the Virtual Crack Closure Tech­nique (VCCT) orig­i­nally proposed by Rybicki and Kanninen [1] was selected as it is an already well researched method for simu­lating crack growth at inter­faces. VCCT is based on linear elastic frac­ture mechanics (LEFM) and assumes that the strain energy required to enlarge a crack by a given amount is equal to the strain energy required to close it to its orig­inal length.

Results

The sample prepa­ra­tion and the tests were carried out by the IVW in Kaiser­slautern. So far, the quasi-static tests for Mode I, Mixed Mode and Mode II loads have been eval­u­ated. Figure 1 shows the Double Cantilever Beam (DCB) test for the eval­u­a­tion of Frac­ture Mode I.

The DCB test shows that the crack spreads in the middle of the adhe­sive layer, which means a cohe­sive failure. This frac­ture behav­iour is exactly what we expected in the obser­va­tion. There­fore, it is possible to deter­mine the SERR for the bonded joint under peel load (mode I) with this test.

Consid­ering the same boundary condi­tions as in the exper­i­mental test, the numer­ical simu­la­tion was performed using the VCCT approach and the result is shown in Figure 2.

It can be seen that the simu­la­tion and test results show very similar frac­ture behav­iour. For further illus­tra­tion, the load-displace­ment curves are plotted in Figure 3.

The simu­la­tion with the VCCT approach has shown that the frac­ture behav­iour, i.e. crack initi­a­tion and prop­a­ga­tion, can be predicted with high accu­racy compared to the exper­i­mental results. There­fore, the numer­ical simu­la­tion is vali­dated for frac­ture mode I. The same proce­dure was carried out for mixed mode (I + II) and mode II, and good results were also obtained.

Summary

Exper­i­mental tests were carried out, the results of which were used as input for the numer­ical simu­la­tion. After the eval­u­a­tion and vali­da­tion of the simu­la­tion results, a frac­ture enve­lope curve was created. With the calcu­la­tion method used in this project, it is there­fore possible to predict the failure limits for the entire load range of mode I, mixed mode I+II and mode II.

In the current work package, we are looking at assessing the devel­op­ment of fatigue damage, i.e. the process by which damage accu­mu­lates and progresses over time in the bonded joint subjected to cyclic loading. This is crucial for the assess­ment of fatigue life.

A phenom­e­no­log­ical approach is used, based on the stiff­ness degra­da­tion of the bonded struc­ture. Through the knowl­edge gained in the research project, ranging from exper­i­mental methods to numer­ical simu­la­tions, we can help you improve your product design. Improved failure and fatigue predic­tion leads to more safety and longer life of your bonded joints. This, in turn, ensures lower repair and main­te­nance costs and and increases the reli­a­bility of your prod­ucts and the satis­fac­tion of your customers. satis­fac­tion of your customers.

As an alter­na­tive approach to the VCCT method, addi­tional inves­ti­ga­tions based on cohe­sive zone models (CZM) are now being analysed to further improve the model­ling of the frac­ture behav­iour. Here, stresses in the area of the crack tip are calcu­lated via so-called inter­face or cohe­sive zone elements.

In the next article on the FAnTe­Stick project, you will learn more about the eval­u­a­tion of cycli­cally stressed bonded joints and their fatigue behav­iour. Stay tuned!