Membrane mode enhanced cohesive zone element

PurposeIn certain cases, traction–separation laws do not reflect the behaviour sufficiently so that thin volumetric elements, Internal Thickness Extrapolation formulations, bulk material projections or various other approaches are applied. All of them have disadvantages in the formulation or practical application.Design/methodology/approachDamage within thin layers is often modelled using at cohesive zone elements (CZE). The constitutive behaviour of cohesive zone elements is usually described by traction–seperation laws (TSLs) that consider the (traction separation) relation in normal opening and tangential shearing direction. Here, the deformation (separation) as well as the reaction (traction) are vectorial quantities.FindingsIn this contribution, a CZE is presented that includes damage from membrane modes.Originality/valueMembrane mode-related damaging effects that can be seen in physical tests that could not be simulated with standard CZEs are well captured by membrane mode–enhanced cohesive zone elements.

Binary Black Hole Merger: Mass-Separation Relation and Intermediate Mass Black Holes

Intermediate Mass Black Holes (IMBHs) are an elusive category of black holes in the mass range of 100 to 100000 Solar Masses. Binary IMBHs might form due to mergers of Globular Clusters, Pair Instability Supernovae, and in Young Massive Star Clusters. In this Research Note, merger timescale, constraints on the separation based on the timescale, and other parameters of Binary IMBHs are calculated analytically and are discussed. The calculations were conducted using Newtonian and Einstienian dynamics. The timescale of a Binary IMBH system to reach maximum gravitational wave amplitude is also calculated ad discussed. We also present the relation between the combined Mass of a Binary Black Hole (BBH) System and the Separation between two BHs required for a BBH system to merge within a given timescale tc, solely due to Gravitational Radiation is a function of the total mass of the system. In this article, tc is set equal to Hubble time tH. Now, the relation obtained is essentially the relation between separation of a BBH system (collide within tH) and its Mass. The calculations were conducted for all three categories of Black Holes: Stellar, Intermediate, and Supermassive. Time ahead, the relation might be used for determining whether a BBH merger would be observational. The relation is also solved for Intermediate Mass Black Holes (IMBHs), and and tc separation for collision within tH was calculated.

A double cantilever beam incorporating cohesive crack modeling for superconductors

In this paper, a double cantilever beam (DCB) specimen incorporating cohesive crack is developed for superconductors which have potential applications in high temperature superconducting cables in space solar power station. The cohesive interface is introduced along the crack front of the DCB model under electromagnetic force. The load-separation relation (i.e. the crack opening displacement) is used as the fracture mechanics parameter and the corresponding curves during fracture process are obtained and verified by the finite element numerical method. Results show that the presence of tensile electromagnetic force makes crack propagate easily. Superconductors with small cracks have good adaptability to the oscillation of magnetic fields while that with large cracks are easier to fracture during the descent of the magnetic field. In addition, the ductility ratio of the cohesive interface can significantly increase the fracture strength. The length of fracture zone decreases as the crack length increases.

Cohesive Zone Modeling of Stable Crack Propagation in Highly Ductile Steel

A recent cohesive zone model is applied to the simulation of crack extension in austenitic stainless steel under large scale yielding conditions. The shape of the corresponding exponential traction-separation-relation can be modified in a wide range. In order to investigate the sensitivity regarding the cohesive zone parameters, a systematic parametric study is performed. The shape of the traction-separation envelope has a minor effect on the results compared to the cohesive strength and the work of separation. The aim is to fit experimental data by an appropriate choice of these parameters. Therefore, not only force-displacement curves should be used, but also crack growth resistance curves should be employed. A promising strategy for parameter identification is derived.

Snap Transitions of Pressurized Graphene Blisters

Blister tests are commonly used to determine the mechanical and interfacial properties of thin film materials with recent applications for graphene. This paper presents a numerical study on snap transitions of pressurized graphene blisters. A continuum model is adopted combining a nonlinear plate theory for monolayer graphene with a nonlinear traction–separation relation for van der Waals interactions. Three types of blister configurations are considered. For graphene bubble blisters, snap-through and snap-back transitions between pancake-like and dome-like shapes are predicted under pressure-controlled conditions. For center-island graphene blisters, snap transitions between donut-like and dome-like shapes are predicted under both pressure and volume control. Finally, for the center-hole graphene blisters, growth is stable under volume or N-control but unstable under pressure control. With a finite hole depth, the growth may start with a snap transition under N-control if the hole is relatively deep. The numerical results provide a systematic understanding on the mechanics of graphene blisters, consistent with previously reported experiments. Of particular interest is the relationship between the van der Waals interactions and measurable quantities in corresponding blister tests, with which both the adhesion energy of graphene and the equilibrium separation for the van der Waals interactions may be determined. In comparison with approximate solutions based on membrane analyses, the numerical method offers more accurate solutions that may be used in conjunction with experiments for quantitative characterization of the interfacial properties of graphene and other two-dimensional (2D) membrane materials.

Multiscale modeling of organic-inorganic interface: From molecular dynamics simulation to finite element modeling

ABSTRACTBi-layer material systems are found in various engineering applications ranging from nanoscale components, such as thin films in circuit boards, to macroscale structures, such as adhesive bonding in aerospace and civil infrastructure. They are also found in many natural and biological materials such as nacre or bone. The structural integrity of a bi-layer system depends on properties of both the interface and the constitutive materials. In particular, interfacial delamination has been observed as a major integrity issue. Here we present a multiscale model, which can predict the macroscale structural behavior at the interface between organic and inorganic materials, based on a molecular dynamics (MD) simulation approach combined with the metadynamics method used to reconstruct the free energy surface (FES) between attached and detached states of the bonded system. We apply this technique to model an epoxy-silica system that primarily features non-bonded and non-directional van der Waals and Coulombic interactions. The reconstructed FES of the epoxy-silica system derived from the molecular level is used to quantify the traction-separation relation at epoxy-silica interface. In this paper, two different approaches in deriving the traction-separation relation based on the reconstructed FES are described. With the derived traction-separation relation, a finite element approach using cohesive zone model (CZM) can be implemented such that the structural behavior of epoxy-silica interface at the macroscopic length scale can be predicted. The prediction from our multiscale model shows a good agreement with experimental data of the interfacial fracture toughness. The method used here provides a powerful new approach to link nano to macro for complex heterogeneous material systems.

Measurement of Cohesive Laws and Related Problems

Cohesive modelling provides a simple method to introduce a process region in models of fracture. It is computationally attractive since it blends into the structure of finite element programmes for stress analysis. The development of computational methods and applications of cohesive modelling has accelerated during recent years. Methods to measure cohesive laws have also been developed. One class of such methods is based on the path-independence of the J-integral. By choosing a path encircling the cohesive zone, J can be shown to be given by the area under the traction-separation relation for the cohesive zone. Using an alternative path, J can in some cases be directly related to the applied load and deformation with relatively modest or no assumptions on the material behaviour. Thus, the cohesive law can be measured. Methods to measure cohesive laws for different specimen geometries are presented. The methods are used to measure the cohesive law in peel, shear and mixed-mode for an adhesive layer. A new method to measure cohesive laws in shear is presented. The method is shown to give accurate data with a much smaller test specimen than earlier methods.

A Study of Thermal Fracture in Functionally Graded Thermal Barrier Coatings Using a Cohesive Zone Model

This work describes the application of two-dimensional finite element models with a cohesive zone to study quasi-static crack extension in functionally graded Yttria stabilized Zirconia (YSZ)-Bond Coat (BC) alloy (NiCoCrAlY) thermal barrier coatings (TBC). Crack growth under a single heating-cooling cycle simulating a laser thermal shock experiment is considered. The traction-separation relations for YSZ and BC alloy are coupled to yield a traction-separation relation for the individual layers of the graded TBC. Results from laser thermal shock experiments are then used for a systematic evaluation of the material properties in this traction-separation relation. The effective work of separation for YSZ-BC alloy composites, which is indicative of the material’s fracture toughness, is then computed. The model is then used to predict the surface thermal fracture response in a graded TBC having an architecture different from the coatings that were used to evaluate the cohesive properties. These model predictions are then compared with results from laser thermal shock experiments.