Mixed Mode

Modh Measctha


It has been widely reported that the delamination toughness of adhesive joints and polymer matrix composites can vary considerably depending on the mode of loading. For this reason, extensive research has been aimed at devising fracture test methods based on beam-like geometries, which enable the testing of these joint systems under variable modes of loading. However, central to the analysis of these mixed mode test methods, is the definition of a consistent parameter for the characterisation of the mode mixity in the fracture process zone for a given geometry and loading arrangement. This has lead to the development of a number of contrasting analytical partitioning theories in literature which aim to address this problem. The most notable of these are the initial global analysis by Williams [1] and a subsequent local analysis by Hutchinson and Suo [2]. However, significant differences exist between the local and global approaches in the case of fracture in asymmetric geometries, and arguments have been put forward on various occasions supporting each [5, 6]. Recent numerical and experimental studies have suggested that the mode partition is in fact not just dependent on geometry and loading conditions, but also, in the case of asymmetric geometries, strongly dependent on the nature of the fracture process zone which develops during fracture [3, 4]. It has been observed numerically that, as the length of the damage region grows, the mode mixity tends from the local solution of Hutchinson and Suo towards the global solution of Williams. It has also been observed that this tendency from the local to the global solution seems to be controlled uniquely by the length of the fracture process zone relative to the size of the singular dominant region. These results highlight the limitations of the current analytical partitioning theories, which take only geometry and loading into consideration. Based on this observed unique dependency, which is obtained numerically, a new semi-analytical cohesive analysis (SACA) is proposed for partitioning. In this approach, cohesive zone lengths are estimated analytically and then used to obtain mode mixity from the observed unique dependency curve; this is carried out using an iterative procedure. It is found that this tendancy from local to global partitioning as a function of increasing cohesive zone length can be used to explain previously conflicting experimental results [7]. The general SACA partitioning approach has been coded into an excel macro to facilitate ease of use, and is available for download from the link below. This macro can be used to obtain more accurate damage dependent mode partitions using known substrate and cohesive properties. This work has been carried out in conjunction with an ESIS TC4 numerical round robin on mixed mode partitioning.

Further instructions are outlined in the excel file. Questions and comments regarding the use of the macro are also welcome, and should be sent to the email below.

E-mail: mark.conroy@ucdconnect.ie


[1] J.G. Williams, International Journal of Fracture Mechanics, 1988, 36, pp. 101-119.

[2] J.W. Hutchinson and Z. Suo, Advances in Applied Mechanics, 1992, 29, pp. 63-191.

[3] M. Conroy, A. Ivankovic, A. Karac and J. G. Williams, Mode Mixity in Beam Like Geometries: Global partitioning with cohesive zones, Proceedings of the 36th annual meeting of the Adhesion Society, Daytona Beach, FL, March 3-6 2013.

[4] M. Conroy, B.F. Sørensen and A. Ivankovic, Combined Numerical and Experimental Investigation of Mode Mixity in Beam Like Geometries, 37th annual meeting of the Adhesion Society, San Diego, CA, February 23-26 2014.

[5] F. Ducept, D. Gamby and P. Davies, Composite Science and Technology, 1999, 59, pp. 609-619.

[6] M. Charalambides, AJ Kinloch, W Wang, JG Williams, International Journal of Fracture, 1992, 54, pp. 269–291.

[7] M. Conroy and A. Ivankovic, Mixed Mode Partitioning in Beam Like Geometries: A Semi Analytical Cohesive Analysis, 38th annual meeting of the Adhesion Society, Savannah, GA, February 20-25 2015.


Please click on the link below to download mixed mode SACA macro


UCD Centre of Adhesion and Adhesives

School of Mechanical & Materials Engineering

University College Dublin