Speaker
Description
The failure criterion proposed by Christensen is a two-parameter failure criterion with two sub-criteria [1]. The criterion applies to all isotropic non-porous materials ranging from ductile materials like aluminum over polymers and cast iron to brittle materials like concrete or rocks. It contains the von Mises criterion as the limit case for ideally ductile materials and the Rankine criterion for perfectly brittle materials. Additionally, the Christensen criterion allows to define a failure index, indicating the failure mechanism. Although the failure criterion demonstrates good alignment with experimental results [1] and a wide range of applicability, it has only been applied to a few materials [2, 3]. This may be attributed to the difficulty of evaluation with its two sub-criteria as well as the lack of existing implementations in Finite Element Software. In this work, we propose a method to overcome these disadvantages by deriving a single failure index for the Christensen failure criterion. The index is defined analogously to failure indices for composite laminae, which, if it exceeds the value of 1, defines the onset of material failure, characterized as either the onset of plastic deformation or brittle failure. The failure index, being defined in a linear manner, provides an indication of material utilization. This is achieved with an algorithm utilizing the principal stress space in spherical coordinates. Then, under the same angles, the radius of the stress state can be related to the radius of the failure surface to compute a failure index. Additionally, a methodology for identifying the corresponding failure number by projection onto the failure surface is proposed. Both the failure index and the failure number are implemented in the Finite Element Software Simulia ABAQUS. This allows for an efficient use of the failure index. In a case study, the Christensen criterion is compared to the von Mises criterion. Using a three-point bending test with a notched specimen made of the polymer PEEK, the difference in failure load and failure location are analyzed.
References:
[1] R. M. Christensen, The theory of materials failure, Oxford University Press, USA (2013)
[2] A. Krainer, et al., A semi-passive beam dilution system for the FCC-ee collider, EPJ Techniques and Instrumentation 9.1 (2022): 3
[3] Oikonomopoulou, Faidra, et al. Interlocking cast glass components, exploring a demountable dry-assembly structural glass system, Heron 63.1/2 (2018): 103-138
