Cohesive Finite Element Method Research Articles

A Framework for Analyzing the Microstructure Level Thermomechanical Response Polymer Bonded Explosives

A framework for quantifying the thermomechanical response of polymer bonded explosives (PBX) at the microstructural level is developed using a cohesive finite element method (CFEM). This framework allows the contributions of individual constituents, fracture and frictional contact along failed crack surfaces to heating to be analyzed and tracked. Digitized micrographs of actual PBX materials and idealized microstructures with various distributions of grain sizes are used in the analysis. The analysis concerns impact loading of HMX/Estane with strain rates on the order of 104 – 105 s-1. Issues studied include large deformation, thermomechanical coupling, failure in the forms of microcracks in both bulk constituents and along grain/matrix interfaces, and frictional heating. The Estane matrix is described by a thermo-elasto-viscoelastic constitutive formulation, accounting for temperature dependence, strain rate sensitivity and strain hardening. The HMX crystals are assumed to be elastic under the conditions analyzed. Energy localization leading to formation of local hot spots as potential ignition sites is primarily due to the viscoelastic dissipation in the matrix in early stages of deformation and frictional heating along crack surfaces in later stages of deformation. Microstructure-response relations that can be used in the design of soft energetic composites are established.

Investigation of non-local cracking in layered stainless steel with nanostructured interface

A recent experiment of layered stainless steel with nanostructured interface has suggested that a brittle interface can lead to an overall structure with high ductility. Here a cohesive finite element method is employed to investigate the paradox of a brittle nanostructured interface (nanograined interface layer) and a ductile layered stainless steel. Parametric studies show that the more brittle the nanograined interface layer is, the more micro-cracks the nanograined interface layer has, and the more ductile the layered stainless steel is.

Formulation and Application of the Initially Rigid Cohesive Finite Element Method

AbstractThe presented procedure for cohesive crack propagation is based on an adaptive finite element (FE) implementation, which enables the introduction of cohesive surfaces in dependence on the current crack state. In contrast to already existing formulations, the focus of the present model lies on failure processes that can be described at quasi‐static conditions within an implicit framework. Furthermore, an extension for mesh independent crack propagation in terms of an additional mesh adaptive formulation is presented. By the evaluation of the failure criterion considering the preferred crack direction, a new crack tip coordinate is computed and the discretization is accordingly adjusted. The remaining mesh is modified for the new boundary representation. The application of the proposed method is shown by the numerical investigation of a concrete fracture specimen from an experimental research project. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Insights into the effects of tensile and compressive loadings on microstructure dependent fracture of trabecular bone

The micro-scale finite element models used in the past to understand yielding failure of trabecular bone have not addressed the microcrack formation and its effect on microstructure dependent fracture. An understanding of microcrack based failure mechanisms can be important to develop insights into response of trabecular bone to external loading before final failure. With this goal, we analyze tensile and compressive fracture failure at two different ages in two trabecular bone micrographs obtained from an ovine femur using a recently developed cohesive finite element method (CFEM) framework. The results and analyses indicate that examined trabecular microstructures are optimally designed for resisting compressive loading. Under tensile loading, initial damage in a microstructure is localized in a single random trabecula. Final microstructure failure occurs immediately after the failure of the trabecula. However, under compressive loading, failure of the first trabecula does not precede immediate complete failure of microstructure. Under compression the propagation fracture toughness (characterized by change in energy release rate as a function of crack density) increases with increase in crack density. However, under tension the propagation fracture toughness decreases with increasing crack density. The fracture mechanism remains unaffected by age variation. Effect of tissue property random variation on the variation in fracture strength diminishes under tension and increases under compression with increase in the age. Overall, results indicate that structural arrangement of the trabecular bone (besides the hierarchical chemical composition) can be an important contributor to its unique fracture resistance properties.

A cohesive finite element for quasi-continua

In this paper, a cohesive finite element method (FEM) is proposed for a quasi-continuum (QC), i.e. a contin- uum model that utilizes the information of underlying atomis- tic microstructures. Most cohesive laws used in conventional cohesive FEMs are based on either empirical or idealized constitutive models that do not accurately reflect the actual lattice structures. The cohesive quasi-continuum finite element method, or cohesive QC-FEM in short, is a step forward in the sense that: (1) the cohesive relation between interface traction and displacement opening is now obtained based on atomistic potentials along the interface, rather than empirical assumptions; (2) it allows the local QC method to simulate certain inhomogeneous deformation patterns. To this end, we introduce an interface or discontinuous Cauchy- Born rule so the interfacial cohesive laws are consistent with the surface separation kinematics as well as the atomistically enriched hyperelasticity of the solid. Therefore, one can sim- ulate inhomogeneous or discontinuous displacement fields by using a simple local QC model. A numerical example of a screw dislocation propagation has been carried out to dem- onstrate the validity, efficiency, and versatility of the method.

Analyses of the role of grain boundaries in mesoscale dynamic fracture resistance of SiC–Si 3N 4 intergranular nanocomposites

Silicon carbide (SiC)–silicon nitride (Si 3N 4) nanocomposites with SiC dispersions as well as Si 3N 4 matrix of mesoscale dimensions (∼1 μm) are considered to have exceptional strength attributed to interactions of SiC dispersions with Si 3N 4 grain boundaries (GBs). However, an account of GBs on the strength of these nanocomposites is not available. In order to analyze this issue, cohesive finite element method (CFEM) based mesoscale dynamic fracture analyses of SiC–Si 3N 4 nanocomposites with an explicit account of length scales associated with Si 3N 4 GBs, SiC particles, and Si 3N 4 grains are performed. Analyses indicate that primary mechanism of fracture in the nanocomposite microstructures is intergranular Si 3N 4 matrix cracking. GBs are responsible for crack deflection and accordingly damage is limited to a smaller geometric region in microstructures with GBs. On an average, a microstructure with GBs present is stronger than the corresponding microstructure with GBs removed. However, in cases where the second phase SiC particles are in the wake of microcracks the microstructure without GB becomes stronger against fracture in comparison to the corresponding one with GBs owing to the crack bridging effect caused by the second phase SiC particles.

Modeling of Dynamic Fracture and Damage in Two-Dimensional Trabecular Bone Microstructures Using the Cohesive Finite Element Method

Trabecular bone fracture is closely related to the trabecular architecture, microdamage accumulation, and bone tissue properties. Micro-finite-element models have been used to investigate the elastic and yield properties of trabecular bone but have only seen limited application in modeling the microstructure dependent fracture of trabecular bone. In this research, dynamic fracture in two-dimensional (2D) micrographs of ovine (sheep) trabecular bone is modeled using the cohesive finite element method. For this purpose, the bone tissue is modeled as an orthotropic material with the cohesive parameters calculated from the experimental fracture properties of the human cortical bone. Crack propagation analyses are carried out in two different 2D orthogonal sections cut from a three-dimensional 8 mm diameter cylindrical trabecular bone sample. The two sections differ in microstructural features such as area fraction (ratio of the 2D space occupied by bone tissue to the total 2D space), mean trabecula thickness, and connectivity. Analyses focus on understanding the effect of the rate of loading as well as on how the rate variation interacts with the microstructural features to cause anisotropy in microdamage accumulation and in the fracture resistance. Results are analyzed in terms of the dependence of fracture energy dissipation on the microstructural features as well as in terms of the changes in damage and stresses associated with the bone architecture variation. Besides the obvious dependence of the fracture behavior on the rate of loading, it is found that the microstructure strongly influences the fracture properties. The orthogonal section with lesser area fraction, low connectivity, and higher mean trabecula thickness is more resistant to fracture than the section with high area fraction, high connectivity, and lower mean trabecula thickness. In addition, it is found that the trabecular architecture leads to inhomogeneous distribution of damage, irrespective of the symmetry in the applied loading with the fracture of the entire bone section rapidly progressing to bone fragmentation once the accumulated damage in any trabeculae reaches a critical limit.

Analyses of the role of the second phase SiC particles in microstructure dependent fracture resistance variation of SiC-Si3N4 nanocomposites

One of the primary factors affecting the failure in high strength silicon carbide (SiC)–silicon nitride (Si3N4) nanocomposites is the placement of spherical nano-sized SiC particles in micro-sized Si3N4 grains. In order to analyze this issue, the cohesive finite element method (CFEM) based dynamic fracture analyses of SiC–Si3N4 nanocomposites at two different loading rates (0.5 and 2 m s−1) with an explicit account of the lengthscales associated with Si3N4 grain boundaries (GBs) (sizescale 100 nm), SiC particles (sizescale 200–300 nm), and Si3N4 grains (sizescale 0.8–1.5 µm) are performed. A range of CFEM meshes with selective placement of second phase particles placed exclusively along GBs, exclusively inside Si3N4 grains, and along GBs as well as inside Si3N4 grains are generated for analyses. Analyses of the damage progression and stress distribution as a function of microstructural morphology indicate that high strength and relatively small sized SiC particles act as stress concentration sites in Si3N4 matrix. The dominant mode of fracture in all microstructures, therefore, is intergranular Si3N4 matrix cracking. Crack density evolution and fracture energy dissipation results show loading rate dependence of failure with the role of phase morphology becoming prominent at the lower loading rate. Contrary to the belief that microstructures with second phase particles lying exclusively along GBs are the strongest against fracture, microstructures with SiC particles lying along GBs as well as inside Si3N4 grains in locations near GBs are found to be the strongest.

Microstructure dependent dynamic fracture analyses of trabecular bone based on nascent bone atomistic simulations

Trabecular bone fracture is closely related to the trabecular architecture, microdamage accumulation, and bone tissue properties. Primary constituents of trabecular tissue are hydroxyapatite (HA) mineralized type-I collagen fibers. In this research, dynamic fracture in two dimensional (2-D) micrographs of ovine (sheep) trabecular bone is modeled using the mesoscale cohesive finite element method (CFEM). The bone tissue fracture properties are obtained based on the atomistic strength analyses of a type-I collagen + HA interfacial arrangement using molecular dynamics (MD). Analyses show that the presented framework is capable of analyzing the architecture dependent fracture in 2-D micrographs of trabecular bone.

Bounds for element size in a variable stiffness cohesive finite element model

AbstractThe cohesive finite element method (CFEM) allows explicit modelling of fracture processes. One form of CFEM models integrates cohesive surfaces along all finite element boundaries, facilitating the explicit resolution of arbitrary fracture paths and fracture patterns. This framework also permits explicit account of arbitrary microstructures with multiple length scales, allowing the effects of material heterogeneity, phase morphology, phase size and phase distribution to be quantified. However, use of this form of CFEM with cohesive traction–separation laws with finite initial stiffness imposes two competing requirements on the finite element size. On one hand, an upper bound is needed to ensure that fields within crack‐tip cohesive zones are accurately described. On the other hand, a lower bound is also required to ensure that the discrete model closely approximates the physical problem at hand. Both issues are analysed in this paper within the context of fracture in multi‐phase composite microstructures and a variable stiffness bilinear cohesive model. The resulting criterion for solution convergence is given for meshes with uniform, cross‐triangle elements. A series of calculations is carried out to illustrate the issues discussed and to verify the criterion given. These simulations concern dynamic crack growth in an Al2O3 ceramic and in an Al2O3/TiB2 ceramic composite whose phases are modelled as being hyperelastic in constitutive behaviour. Copyright © 2004 John Wiley & Sons, Ltd.

Micromechanical Simulation of Dynamic Fracture Using the Cohesive Finite Element Method

Dynamic fracture in two-phase Al2O3/TiB2 ceramic composite microstructures is analyzed explicitly using a cohesive finite element method (CFEM). This framework allows the effects of microstructural heterogeneity, phase morphology, phase distribution, and size scale to be quantified. The analyses consider arbitrary microstructural phase morphologies and entail explicit tracking of crack growth and arbitrary fracture patterns. The approach involves the use of CFEM models that integrate cohesive surfaces along all finite element boundaries as an intrinsic part of the material description. This approach obviates the need for any specific fracture criteria and assigns models the capability of predicting fracture paths and fracture patterns. Calculations are carried out using idealized phase morphologies as well as real phase morphologies in actual material microstructures. Issues analyzed include the influence of microstructural morphology on the fracture behavior, the influence of phase size on fracture resistance, the effect of interphase bonding strength on failure, and the effect of loading rate on fracture.

Quasi–static studies of the deformation and failure of PBX 9501

This paper examines the influence of microstructure on the quasi–static failure of PBX 9501, a polymer–bonded explosive (PBX) manufactured for the Los Alamos National Laboratory in America. Optical microscopy has been used to examine qualitatively cracked and pristine material. Consequent on the manufacturing process, the explosive crystals display angular features and natural facets. In addition, considerable growth twinning, internal defects and voidage has been observed. These defects are found significantly to alter the failure path. In common with other PBXs, failure paths tend to run around the long straight edges of the explosive filler and avoid regions of fine filler and binder. Explosive crystals were found to fracture due either to cracks propagating from another region or internal defects. These observations are confirmed by the use of high–resolution moire interferometry. This sensitive optical technique allows the deformation of the sample to be measured up to and including the point of failure. By taking white–light micrographs that are in exact registration with the measured displacement maps, the influence of the underlying microstructure can be seen.