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

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 non-homogeneous 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

A micromechanical fracture analysis to investigate the effect of healing particles on the overall mechanical response of a self-healing particulate composite

A computational fracture analysis is conducted on a self‐healing particulate composite employing a finite element model of an actual microstructure. The key objective is to quantify the effects of the actual morphology and the fracture properties of the healing particles on the overall mechanical behaviour of the (MoSi2) particle‐dispersed Yttria Stabilised Zirconia (YSZ) composite. To simulate fracture, a cohesive zone approach is utilised whereby cohesive elements are embedded throughout the finite element mesh allowing for arbitrary crack initiation and propagation in the microstructure. The fracture behaviour in terms of the composite strength and the percentage of fractured particles is reported as a function of the mismatch in fracture properties between the healing particles and the matrix as well as a function of particle/matrix interface strength and fracture energy. The study can be used as a guiding tool for designing an extrinsic self‐healing material and understanding the effect of the healing particles on the overall mechanical properties of the material

Molding the Knowledge in Modular Neural Networks

Problem description. The learning of monolithic neural networks becomes harder with growing network size. Likewise the knowledge obtained while learning becomes harder to extract. Such disadvantages are caused by a lack of internal structure, that by its presence would reduce the degrees of freedom in evolving to a training target. A suitable internal structure with respect to modular network construction as well as to nodal discrimination is required. Details on the grouping and selection of nodes can sometimes be concluded from the characteristics of the application area; otherwise a comprehensive search within the solution space is necessary

A single grain approach applied to modelling recrystallization kinetics in a single-phase metal

A comprehensive model for the recrystallization kinetics is proposed which incorporates both microstructure and the textural components in the deformed state. The model is based on the single-grain approach proposed previously. The influence of the as-deformed grain orientation, which affects the stored energy via subgrain size and sub-boundary misorientation, is taken into account. The effects of the deformed grain geometry, the nucleation-site density, and the initial grain size prior to deformation on the recrystallization kinetics are assessed. The model is applied to the recrystallization kinetics of a cold-rolled AA1050 alloy

Cohesive-zone modelling of crack nucleation and propagation in particulate composites

A cohesive-zone approach is used to study the interaction between an approaching crack and a particle embedded in a matrix material as a function of the mismatch in elastic and fracture properties. Crack-particle interaction is a crucial issue governing fracture behavior of particle-dispersed materials. Special attention is given in the present work to the effect of the mismatch in fracture properties, namely fracture strength and energy, which has not been fully-explored in the literature. Based on extensive finite element simulations using cohesive elements, the basic fracture mechanisms governing the crack-particle interaction are identified, namely particle fracture, crack deflection and interface debonding. The details of the cracking sequences are elucidated and the role of secondary cracks is highlighted. The effect of pre-existing flaws on the fracture behavior is analyzed both for flaws inside the particle as well as flaws on the particle/matrix interface. Several flaw configurations in terms of size, orientation and location are considered. In addition, the effect of the mismatch between the matrix and the interface fracture properties is also considered for a wide range of adhesive characteristics. The results of the simulations are summarized in the form of several fracture maps for different configurations, whereby the main fracture mechanisms are identified in regions inside a two-dimensional space of strength and toughness mismatch between the particle and the matrix. It is observed that the mismatch in the fracture properties usually plays a more dominant role on the crack trajectory than the mismatch in elastic properties in a particle-dispersed system. Pre-existing flaws/defects in the particle and the interface are found to be one of the principal controlling factors that alter the crack propagation characteristics. These results can be used as a guideline for designing particulate composite system with a preferred fracture mechanism, namely matrix cracking, interface debonding or particle fracture

Detailed in situ hot stage transmission electron microscope observations of the localized pinning of a mobile ferrite-austenite interface in a Fe-C-Mn alloy by a single oxidic particle

The current study reports the detailed analysis of an observation of the local pinning of a slowly moving austenite-ferrite interface by a single nanosized oxidic particle. The observations were made during an in situ cyclic partial phase transformation experiment on a Fe-0.1C-1.0Mn alloy close to the inversion stage at which the interface migrates at a rather low velocity. The low velocity allowed capturing the interface pinning effect over a period of no less than 16 seconds. From our observations, it was possible to follow the progression of the pinning effect from the initial stages all the way through to the release of the interface. The pinning force exerted by the individual particle having a diameter of 140 nm on the austenite-ferrite interface was estimated as 175 nJ m−1, while the maximum pinning length was approximately 750 nm to either side of the particle, leading to an interface line tension of 170 nJ m−1. The observed pinning behavior is compared with the most relevant models in the literature

Position-dependent shear-induced austenite-martensite transformation in double-notched TRIP and dual-phase steel samples

While earlier studies on transformation-induced-plasticity (TRIP) steels focused on the determination of the austenite-to-martensite decomposition in uniform deformation or thermal fields, the current research focuses on the determination of the local retained austenite-to-martensite transformation behaviour in an inhomogeneous yet carefully controlled shear-loaded region of double-notched TRIP and dual-phase (DP) steel samples. A detailed powder analysis has been performed to simultaneously monitor the evolution of the phase fraction and the changes in average carbon concentration of metastable austenite together with the local strain components in the constituent phases as a function of the macroscopic stress and location with respect to the shear band. The metastable retained austenite shows a mechanically induced martensitic transformation in the localized shear zone, which is accompanied by an increase in average carbon concentration of the remaining austenite due to a preferred transformation of the austenite grains with the lowest carbon concentration. At the later deformation stages the geometry of the shear test samples results in the development of an additional tensile component. The experimental strain field within the probed sample area is in good agreement with finite element calculations. The strain development observed in the low-alloyed TRIP steel with metastable austenite is compared with that of steels with the same chemical composition containing either no austenite (a DP grade) or stable retained austenite (a TRIP grade produced at a long bainitic holding time). The transformation of metastable austenite under shear is a complex interplay between the local microstructure and the evolving strain fields

A nano-indentation study on the mechanical behaviour of the matrix material in an AA6061-Al2O3 MMC

The nano-indentation technique is a suitable technique to measure hardness and elastic moduli profiles of AA6061 reinforced with Al2O3 particles, since it allows measurements of mechanical properties on a micrometer range. To investigate possible local variations in mechanical behaviour of the matrix material due to precipitation reactions being affected by the presence of ceramic reinforcements, nano-indentation tests were done on both metal matrix composite (MMC) as well as unreinforced reference material, in three different heat treatment conditions. Matrix response depends on heat treatment condition, but is approximately equal for the MMC and the base reference alloy. Due to the various imposed heat treatments, magnesium enrichment around the ceramic particles was observed, but hardness and elastic modulus of this interfacial layer could not be measured. To confirm the preferential segregation of Mg near the particle/matrix interface, linescans were made with a Scanning Electron Microscope (SEM) equipped with EDS (Energy Dispersive Spectrum) facilities. The limited width of the Mg rich zone explains the absence of typical ''interphase'' indentations in this investigation. Hardly any differences in calculated elastic moduli and hardness values were found for the three heat treatment conditions investigated, when comparing results of AA6061 reference material with results of an AA6061 matrix in an MMC. This result is of great importance when modelling the mechanical behaviour of MMCs using the finite element method, since it permits the assumption that the MMC matrix material behaves similar to the same aluminium alloy without ceramic reinforcements

Review on some Stefan Problems for Particle Dissolution in Solid Metallic Alloys

This paper is a review of a suite of mathematical models of increasing complexity on particle dissolution in metallic alloys. This work deals with models for multi-component particle dissolution in multi-component alloys, where various chemical species diffuse simultaneously, and a two-dimensional model incorporating interfacial reactions as in the model of Nolfi [1]. The work is mathematically rigorous where asymptotic solutions and solution bounds are derived but is also of a practical nature as particle dissolution kinetics is modelled for industrially relevant conditions

Direct TEM observation of α/γ interface migration during cyclic partial phase transformations at intercritical temperatures in an Fe-0.1C −0.5Mn alloy

The kinetic behaviour of austenite/ferrite interfaces in a low carbon – 0.5 mass% Mn containing steel during Cyclic Partial Phase Transformation (CPPT) experiments has been investigated using hot stage Transmission Electron Microscopy (TEM). Individual interfaces were observed to display behaviour typical of CPPT experiments as recorded in macroscopic dilatometry experiments and demonstrated i) the “normal”, ii) inverse transformations and iii) a stagnant stage in which the interface migrates at a very low velocity as a result of the interface passing through a Mn enriched zone due to the preceding transformation. The length of the stagnant stage determined from the TEM observations shows excellent agreement with that measured from dilatometry and kinetic modelling, whilst the distance migrated from the interface shows some disparities which are primarily attributed to differences in assumptions about grain geometry and nucleation. No special interface features were observed when the interface changed direction and passed through the previously Mn-enriched zones. General observations on the interaction of the transformation interface with microstructural features are also reported