A cohesive-zone crack healing model for self-healing materials

Abstract

A cohesive zone-based constitutive model, originally developed to model fracture, is extended to include a healing variable to simulate crack healing processes and thus recovery of mechanical properties. The proposed cohesive relation is a composite-type material model that accounts for the properties of both the original and the healing material, which are typically different. The constitutive model is designed to capture multiple healing events, which is relevant for self-healing materials that are capable of generating repeated healing. The model can be implemented in a finite element framework through the use of cohesive elements or the extended finite element method (XFEM). The resulting numerical framework is capable of modeling both extrinsic and intrinsic self-healing materials. Salient features of the model are demonstrated through various homogeneous deformations and healing processes followed by applications of the model to a self-healing material system based on embedded healing particles under nonhomogeneous deformations. It is shown that the model is suitable for analyzing and optimizing existing self-healing materials or for designing new self-healing materials with improved lifetime characteristics based on multiple healing events.

Modelling the fracture behaviour of thermal barrier coatings containing healing particles

“…Within the context of self-healing TBC systems, few modelling studies have addressed the effect of the healing particles on the TBC properties and the thermomechanical response [29,30]. The effect of the healing particles on the fracture mechanisms and the mechanical properties of a particulate composite representing a self-healing TBC microstructure were studied using cohesive element-based finite element analysis in [31][32][33]. However, one critical aspect that has not been analysed in detail pertains to the mismatch in thermo-elastic properties coupled to a mismatch in fracture properties.…”

Modeling Self-Healing Mechanisms in Coatings: Approaches and Perspectives

“…On the other hand, cohesive formulations of the evolving crack ease the treatment of damage and healing. Relatively straight forward formulations of the traction-displacement function allow to capture changes in the mechanical performance of materials due to fatigue and healing [48,50] and repeated healing events [51], though the actual healing step is not taken into account (a phenomenological law for the curing degree of the polymerization of liquid healing agents was used in [50] to establish the dimensions and mechanical properties of the healed material). Therefore, it seems clear that the path to improve the predictive power of these models demands the incorporation of the transport and reaction of healing agents, either from the capillary flow of liquid agents [66] or the diffusive transport and reaction of dissolved species [54].…”

“…Thus, crack growth is inhibited only at fast healing kinetics, and for a prescribed healing kinetics, better results are obtained for longer rest periods. Ponnusami et al [51] apply a cohesive damage model to analyze the effects of repeated healing events in the mechanical performance of the material. Following the same notation as in [51], we have that the first loading cycle induces a damage D [1](0) in the original material that can be estimated as the ratio of the dissipated energy G d and the cohesive energy G c , D [1]…”

“…Furthermore, results also indicate a deterioration of the load carrying capacity when the degree of crack filling reduces. Ponnusami et al [51] interpret the filling efficiency as a geometrical factor (i.e., the ratio of the crack volume filled with healing agent). However, in a fully coupled healing model, the filling efficiency should be deduced from the the mobilization and reaction of the healing agents.…”

Determination of fracture strength and fracture energy of (metallo-) ceramics by a wedge loading methodology and corresponding cohesive zone-based finite element analysis

“…Within the finite element framework, the cohesive relation was implemented using zero-thickness cohesive elements. These elements were inserted along the inter-element boundaries to capture the onset and evolution of the fracture process (see, e.g., [26,27] for more details). In the present analysis, cohesive elements are inserted at the interfaces of all bulk elements in the regions where crack (s) are expected to initiate and propagate, in particular at the chevron and groove.…”