PSI - Issue 13

Mina Iskander et al. / Procedia Structural Integrity 13 (2018) 976–981 Iskander and Shrive/ Structural Integrity Procedia 00 (2018) 000 – 000

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stretching can break these bonds. The consequence of the relationship between interatomic bond force and interatomic spacing can be exemplified by considering a piece of solid concrete subjected to hydrostatic compression – deep in the ocean for example: the piece will never fail even at the deepest part as it is only under compression. However, the piece will fail easily if subject to tension. There has to be tension at the intermolecular level to break the bonds – even in compressive stress fields. This tension can be caused by the presence of a discontinuity (e.g. air bubble) which disturbs the stress field – whether it is tensile or compressive. Griffith (1921) recognized this point when he observed the tensile failure capacities for glass were lower than theoretical estimates and highly dependent on the size of the flaws in the material. Another difference between compressive and tensile fracture and their failure pattern is crack propagation. In uniaxial tension, failure is caused by a crack initiating at the highest stress concentration point and propagating uncontrollably. In contrast, in uniaxial compression, failure frequently develops through multiple cracks parallel to the direction of the applied stress, often propagating in a stable manner with the magnitude of the applied stress and stopping if no further loading occurs. Researchers interested in fracture mechanics have established a solid base of understanding of crack initiation and propagation in tensile stress fields. For mode 1 (opening) fracture, once the stress intensity defined in Eq. 1 reaches the fracture toughness of the material, the crack will propagate typically unstably. = √ (1) Stress intensity comes from the Westergaard (1939) solution for the stresses at the tip of an infinitely sharp crack perpendicular to the applied tensile stress. In terms of an ellipse, the semi-length, a, perpendicular to the tension is the dimension that matters, not the semi-height, b. Indeed, for a very sharp crack, b should essentially be zero, giving the infinitely thin crack perpendicular to the tension as shown in Fig. 1 (a). When the crack propagates (coloured in red in Fig. 1a), it does so perpendicular to the tension.

Fig. 1. (a) Infinitely thin crack perpendicular to tension; (b) Infinitely thin crack parallel to compression

Similar levels of understanding and ability to predict fracture in compressive stress fields have not been achieved. Consequently, most applications including design for compression remain essentially empirical. Therefore, the objective of our research is to understand the basic factors involved in the fracture of materials under uniaxial compression. Here, a 2D finite element model is presented for a specifically designed geometry (i.e. using a flaw) to produce a single crack in a uniaxial compressive stress field. We know that a crack will propagate parallel to the compression if the specimen is subject to uniaxial compression. However, if the crack is infinitely thin, there will be no difference in the strain energy between the uncracked and cracked states as shown in Fig. 1 (b). Thus, for a difference in strain energy to develop, to drive crack propagation in compression, it is necessary to consider a void with both width and length. Considering the stress-raising effects of voids in a medium subject to uniaxial compression, a circular void produces tension at its top and bottom of the same magnitude as the distant applied compressive stress. We thus begin our investigation modelling such voids, where we have made the medium wide enough and high enough that it is equivalent to a void in an infinite medium.