Periodic Reporting for period 1 - MOLAY-STRUDEL (Modelling mixed-mode rate-dependent delamination in layered structures using geometrically nonlinear beam finite elements)
Reporting period: 2016-10-01 to 2018-05-31
The project addressed the characterisation of the fracture resistance in layered structures, with special focus on debonding of adhesive joints or delamination of composite laminates, which are very important issues particularly for the aerospace and automotive industry. For these problems, several industrial standards have been released. For a mode-I (opening) case a ’double-cantilever-beam’ (DCB) is mostly used (Fig. 1). For a mode mode-II (sliding) case the ‘end-notched flexure’ (ENF) specimen is often used (Fig. 2). For a mixed-mode case, a simple test uses the ‘mixed-mode-fracture’ (MMF) specimen (Fig. 3). Peel tests are also used in some cases (Fig. 4).
Current standards are mostly based on linear elastic fracture mechanics (LEFM). They also need the measurement of the crack length, which is a main obstacle to their adoption by the industry. Moreover, many authors and indeed even textbooks question the validity of LEFM for the case of ductile adhesives and suggest that alternative approaches, including J-integral and cohesive-zone models (CZMs), better account for ductile behaviour of adhesive before fracture.
Indeed, CMZs are widely used to simulate delamination because they are easy to implement in a finite-element (FE) model and are able to accurately model the deformability and damage of the adhesive before failure. In many cases, the rate-dependence of the process (i.e. dependence on the loading speed) cannot be ignored and has been recently incorporated within CZMs by a number of authors, with important contributions given by the host researcher before this project.
The main aim of the project was to revisit the current standards to overcome the above-mentioned issues, taking advantage of the fact that, because of their simple geometry, the specimens used in these tests can be modelled using relatively simple FE models (beam models). For the same level of complexity and accuracy, these models can simulate delamination tests faster than any available models (e.g. 2D and 3D models).
The specific objectives, which can be found in the detailed technical report and in the DoA, can be summarised in less technical terms as follows:
(a) Develop a new software code for the computer-aided simulation of the above mentioned tests by using computationally efficient FE models accounting for mode I, mode II and mixed-mode crack growth, as well as for rate dependence.
(b) Conduct experimental tests using DCB, ENF, MMF and peel-test adhesive-joint specimens, at a sufficient number of different speeds to characterise the rate dependence of the adhesive.
(c) Validate the numerical models against the experimental results.
(d) Develop a friendly graphic user interface (GUI) for the code, with a view to promoting the developed models as new tools for the characterisation of fracture resistance of layered structures in the industry.
Current standards are mostly based on linear elastic fracture mechanics (LEFM). They also need the measurement of the crack length, which is a main obstacle to their adoption by the industry. Moreover, many authors and indeed even textbooks question the validity of LEFM for the case of ductile adhesives and suggest that alternative approaches, including J-integral and cohesive-zone models (CZMs), better account for ductile behaviour of adhesive before fracture.
Indeed, CMZs are widely used to simulate delamination because they are easy to implement in a finite-element (FE) model and are able to accurately model the deformability and damage of the adhesive before failure. In many cases, the rate-dependence of the process (i.e. dependence on the loading speed) cannot be ignored and has been recently incorporated within CZMs by a number of authors, with important contributions given by the host researcher before this project.
The main aim of the project was to revisit the current standards to overcome the above-mentioned issues, taking advantage of the fact that, because of their simple geometry, the specimens used in these tests can be modelled using relatively simple FE models (beam models). For the same level of complexity and accuracy, these models can simulate delamination tests faster than any available models (e.g. 2D and 3D models).
The specific objectives, which can be found in the detailed technical report and in the DoA, can be summarised in less technical terms as follows:
(a) Develop a new software code for the computer-aided simulation of the above mentioned tests by using computationally efficient FE models accounting for mode I, mode II and mixed-mode crack growth, as well as for rate dependence.
(b) Conduct experimental tests using DCB, ENF, MMF and peel-test adhesive-joint specimens, at a sufficient number of different speeds to characterise the rate dependence of the adhesive.
(c) Validate the numerical models against the experimental results.
(d) Develop a friendly graphic user interface (GUI) for the code, with a view to promoting the developed models as new tools for the characterisation of fracture resistance of layered structures in the industry.
As for the first objective, a very fast and robust code has been implemented, initially with a rate-independent CZM. This led to breakthrough contributions, partly unplanned, discussed in the next section. We also derived two types of closed-form solutions for DCB models that usually require more complex and time-consuming solution procedures. The significance of these solutions is discussed in the next section, too. The implementation of rate dependence for mode-I delamination or debonding has been completed. The extension to mixed mode is in a very advanced state of implementation. The developed code takes into account the possibility of large displacements and rotations, and therefore represents an important step forward also towards the analysis of peel tests, but there has been no time to address the specific issues related to the extreme deformations occurring within a peel test.
The second objective has been met for DCB, ENF and MMF tests (Figs. 5-8), but not for peeling tests. A total of 96 tests were conducted on joints made of aluminium arms bonded with the epoxy adhesive Araldite 2015, at 6 loading speeds between 0.1 and 5000 mm/min. More details are reported in the technical report, but it is useful to note that the rate dependence of results is clear and, despite some scatter, the results show sufficient consistency to be published and used for validation of our numerical models.
As for the third objective, the rate-dependent mode-I model has been successfully validated, whereas for mode II and mixed mode validation will be conducted once the numerical model is completed.
The 4th objective has been fully met, in that the software code has been linked to a friendly GUI designed for the practical use in the industry, with parametric input. The GUI is in the final phase of testing and it will be made available for download on the project website.
The dissemination activities of the project have been conducted according to plan. One article has been published on International Journal of Solids and Structures. Two articles submitted to Composites Part B and on International Journal of Fracture are still under review. Two more journal articles are in preparation.
The researcher presented the work at 7 conferences and organised a mini-symposium at ECCM-ECFD 2018, held in Glasgow in June 2018. A project website has been developed also with links to the published articles and data underpinning them.
The second objective has been met for DCB, ENF and MMF tests (Figs. 5-8), but not for peeling tests. A total of 96 tests were conducted on joints made of aluminium arms bonded with the epoxy adhesive Araldite 2015, at 6 loading speeds between 0.1 and 5000 mm/min. More details are reported in the technical report, but it is useful to note that the rate dependence of results is clear and, despite some scatter, the results show sufficient consistency to be published and used for validation of our numerical models.
As for the third objective, the rate-dependent mode-I model has been successfully validated, whereas for mode II and mixed mode validation will be conducted once the numerical model is completed.
The 4th objective has been fully met, in that the software code has been linked to a friendly GUI designed for the practical use in the industry, with parametric input. The GUI is in the final phase of testing and it will be made available for download on the project website.
The dissemination activities of the project have been conducted according to plan. One article has been published on International Journal of Solids and Structures. Two articles submitted to Composites Part B and on International Journal of Fracture are still under review. Two more journal articles are in preparation.
The researcher presented the work at 7 conferences and organised a mini-symposium at ECCM-ECFD 2018, held in Glasgow in June 2018. A project website has been developed also with links to the published articles and data underpinning them.
The fast FE code allowed us to prove that the range of validity of LEFM is wider than what is stated in fracture mechanics text books. This is a fundamental breakthrough, which was also supported by a novel and rigorous theoretical analysis. We were able for the first time to find the relation between the critical energy release rate, Gc, used in LEFM, and the critical value of the J integral, Jc, often recommended for problems with ductile interfaces. Contrary to what is stated by many authors, the difference between Gc and Jc is not related to the size of the cohesive zone, but to the extent to which the damage process translates in a steady-state fashion during crack propagation. We also demonstrated that, for most cases of practical interest, LEFM-based closed-form formulae that do not require the measurement of the crack length can be used with an error typically well below 1%.
The derivation of a novel general closed-form solutions for a DCB specimen with a CZM used on the interface is also a valuable novel contribution, considering that solutions of such problems have been known as being computationally demanding and time-consuming. The proposed method provides the solution in a fraction of a second for any type of adhesive. The further derivation of a much simpler closed-form solution resulted then in a novel simple mathematical formula for the fracture resistance of a DCB test, which is a simpler and more accurate alternative to all method used so far in industrial standards.
As for the experimental results obtained, they cover a spectrum of mode-mixity and loading speeds not approached by any other work reported in the literature. The two other articles in preparation will not only document the experimental results but also present the validation of the new rate-dependent models developed.
Last but not least, the software developed, also thanks to the friendly GUI, is a very practically useful tool that can be used to extend the impact of our work to real-life applications in the industry. No similar tool is available to the best of our knowledge.
The derivation of a novel general closed-form solutions for a DCB specimen with a CZM used on the interface is also a valuable novel contribution, considering that solutions of such problems have been known as being computationally demanding and time-consuming. The proposed method provides the solution in a fraction of a second for any type of adhesive. The further derivation of a much simpler closed-form solution resulted then in a novel simple mathematical formula for the fracture resistance of a DCB test, which is a simpler and more accurate alternative to all method used so far in industrial standards.
As for the experimental results obtained, they cover a spectrum of mode-mixity and loading speeds not approached by any other work reported in the literature. The two other articles in preparation will not only document the experimental results but also present the validation of the new rate-dependent models developed.
Last but not least, the software developed, also thanks to the friendly GUI, is a very practically useful tool that can be used to extend the impact of our work to real-life applications in the industry. No similar tool is available to the best of our knowledge.