Showing papers on "Fracture mechanics published in 2012"

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling

Abstract: SUMMARY In 3D fracture modeling, the complexity of the evolving crack geometry during propagation raises challenges in stress analysis because the accuracy of results mainly relies on the accurate description of the crack geometry. In this paper, a numerical framework is developed for 3D fracture modeling where a meshless method, the element-free Galerkin method, is used for stress analysis and level sets are used accurately to describe and capture crack evolution. In this framework, a simple and general formulation for associating the displacement jump in the field approximation with an arbitrary 3D curved crack surface is proposed. For accurate closure of the crack front, a tying procedure is extended to 3D from its original use in 2D in the previous paper by the authors. The benefits of level sets in improving the results accuracy and reducing the computational cost are explored, particularly in the model refinement and the confinement of the displacement jump. Issues arising in level sets updating are discussed and solutions proposed accordingly. The developed framework is validated with a number of 3D crack examples with reference solutions and shows strong potential for general 3D fracture modeling. Copyright © 2012 John Wiley & Sons, Ltd.

Patterning by controlled cracking

Abstract: Propagating cracks—normally associated with material failure and viewed as undesirable—can be controlled in a film/substrate system, opening up new possibilities for nanofabrication and atomic-scale patterning. Crack propagation is usually associated with materials failure, and as such is to be avoided. In the right place, however, crack formation can be useful. A team based in South Korea has developed a technique that harnesses crack initiation, propagation and termination to create patterns in a silicon nitride thin film deposited on top of a silicon substrate. Nam et al. introduce into the substrate notches that concentrate stress to initiate cracks spontaneously during deposition; they also define three modes of crack propagation and prepare multistep structures in the silicon substrate to terminate propagation at specific locations. They even bend cracks in a way that resembles the refraction of light. This concept opens up new possibilities for nanofabrication and patterning using fracture mechanics in applications such as nanotechnology and micro-scale fluidic devices. Crack formation drives material failure and is often regarded as a process to be avoided1,2,3. However, closer examination of cracking phenomena has revealed exquisitely intricate patterns such as spirals4, oscillating5,6,7 and branched7 fracture paths and fractal geometries8. Here we demonstrate the controlled initiation, propagation and termination of a variety of channelled crack patterns in a film/substrate system9,10,11 comprising a silicon nitride thin film deposited on a silicon substrate using low-pressure chemical vapour deposition. Micro-notches etched into the silicon substrate concentrated stress for crack initiation, which occurred spontaneously during deposition of the silicon nitride layer. We reproducibly created three distinct crack morphologies—straight, oscillatory and orderly bifurcated (stitchlike)—through careful selection of processing conditions and parameters. We induced direction changes by changing the system parameters, and we terminated propagation at pre-formed multi-step crack stops. We believe that our patterning technique presents new opportunities in nanofabrication and offers a starting point for atomic-scale pattern formation12, which would be difficult even with current state-of-the-art nanofabrication methodologies.

Extended isogeometric analysis for simulation of stationary and propagating cracks

Abstract: SUMMARY A novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is presented for fracture analysis of structures. The extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational B-splines as basis functions for both the solution field approximation and the geometric description, and it can reproduce crack tip singular fields and discontinuity across a crack. IGA has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two-dimensional isotropic media. Concepts of the extended FEM are used in IGA to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip. Crack discontinuity is represented by the Heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions. Also, the Lagrange multiplier method is used to impose essential boundary conditions. Moreover, the subtriangles technique is utilized for improving the accuracy of integration by the Gauss quadrature rule. Several two-dimensional static and quasi-static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed-mode stress intensity factors are compared with analytical and extended FEM results. Copyright © 2011 John Wiley & Sons, Ltd.

Discontinuous crack-bridging model for fracture toughness analysis of nacre

Abstract: Studying the structure–property relation of biological materials can not only provide insight into the physical mechanisms underlying their superior properties and functions but also benefit the design and fabrication of advanced biomimetic materials. In this paper, we present a microstructure-based fracture mechanics model to investigate the toughening effect due to the crack-bridging mechanism of platelets. Our theoretical analysis demonstrates the crucial contribution of this mechanism to the high toughness of nacre. It is found that the fracture toughness of nacre exhibits distinct dependence on the sizes of platelets, and the optimized ranges for the thickness and length of platelets required to achieve higher fracture toughness are given. In addition, the effects of such factors as the mechanical properties of the organic phase (or interfaces), the effective elastic modulus of nacre, and the stacking pattern of platelets are also examined. Finally, some guidelines for the biomimetic design of novel materials are proposed based on our theoretical analysis.

Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation

Abstract: The modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations of complex crack topologies including branching. This drawback can be overcome by a diffusive crack modeling based on the introduction of a crack phase field as proposed in Miehe et al. (Comput Methods Appl Mech Eng 19:2765–2778, 2010a; Int J Numer Meth Eng 83:1273–1311, 2010b), Hofacker and Miehe (Int J Numer Meth Eng, 2012). In this work, we summarize basic ingredients of a thermodynamically consistent, variational-based model of diffusive crack propagation under quasi-static and dynamic conditions. It is shown that all coupled field equations, in particular the balance of momentum and the gradient-type evolution equation for the crack phase field, follow as the Euler equations of a mixed rate-type variational principle that includes the fracture driving force as the mixed field variable. This principle makes the proposed formulation extremely compact and provides a perfect basis for the finite element implementation. We then introduce a local history field that contains a maximum energetic crack source obtained in the deformation history. It drives the evolution of the crack phase field. This allows for the construction of an extremely robust operator split scheme that updates in a typical time step the history field, the crack phase field and finally the displacement field. We demonstrate the performance of the phase field formulation of fracture by means of representative numerical examples, which show the evolution of complex crack patterns under dynamic loading.

Effect of defects on fracture strength of graphene sheets

Abstract: With a hexagonal monolayer network of carbon atoms, graphene has demonstrated exceptional electrical and mechanical properties. In this work, the fracture of graphene sheets with Stone–Wales type defects and vacancies were investigated using molecular dynamics simulations at different temperatures. The initiation of defects via bond rotation was also investigated. The results indicate that the defects and vacancies can cause significant strength loss in graphene. The fracture strength of graphene is also affected by temperature and loading directions. The simulation results were compared with the prediction from the quantized fracture mechanics.

A finite fracture mechanics model for the prediction of the open-hole strength of composite laminates

Abstract: A new model based on finite fracture mechanics is proposed to predict the open-hole tensile strength of composite laminates. Failure is predicted when both stress-based and energy-based criteria are satisfied. The material properties required by the model are the ply elastic properties, and the laminate unnotched strength and fracture toughness. No empirical adjusting parameters are required. Using experimental data obtained in quasi-isotropic carbon–epoxy laminates it is concluded that the model predictions are very accurate, resulting in improvements over the traditional strength prediction methods. It also is shown that the proposed finite fracture mechanics model can be used to predict the brittleness of different combinations of materials and geometries.

The Meaning, Selection, and Use of the Peridynamic Horizon and Its Relation to Crack Branching in Brittle Materials

Abstract: This note discusses the peridynamic horizon (the nonlocal region around a material point), its role, and practical use in modelling. The objective is to eliminate some misunderstandings and misconceptions regarding the peridynamic horizon. An example of crack branching in a nominally brittle material (homalite) is addressed and we show that crack branching takes place without wave interaction. We explain under what conditions the crack propagation speed depends on the horizon size and the role of incident stress waves on this speed.

Characterization of the fracture toughness of micro-sized tungsten single crystal notched specimens

Abstract: Fracture experiments using micrometer-sized notched cantilevers were conducted to investigate the possibility of determining fracture mechanical parameters for the semi-brittle material tungsten. The experiments were also used to improve the understanding of semi-brittle fracture processes for which single crystalline tungsten serves as a model material. Due to the large plastic zone in relation to the micrometer sample size, linear elastic fracture mechanics is inapplicable and elastic-plastic fracture mechanics has to be applied. Conditional fracture toughness values J Q were calculated from corrected force vs. displacement diagrams. Crack growth was accessible by direct observation of in-situ experiments as well as with the help of unloading compliances. As a further tool, fracture toughness can be determined via crack tip opening displacement. The micro samples behave more ductile and exhibit higher fracture toughness values compared to macro-sized single crystals and fail by stable crack propagation.

Monitoring mechanical damage in structural materials using complimentary NDE techniques based on thermography and acoustic emission

Abstract: This work deals with nondestructive evaluation (NDE) of the fracture behavior of metallic materials by combining thermographic and acoustic emission (AE) characterization. A new procedure, based on lock-in infrared (IR) thermography, was developed to determine the crack growth rate using thermographic mapping of the material undergoing fatigue. The thermography results on crack growth rate were found to be in agreement with measurements obtained by the conventional compliance method. Furthermore, acoustic emission was used to record different cracking events. The rate of incoming signals, as well as qualitative features based on the waveform shape, was correlated with macroscopically measured mechanical parameters, such as load and crack propagation rate. Additionally, since the failure modes have distinct AE signatures, the dominant active fracture mode was identified in real time. The application of combined NDE techniques is discussed for characterizing the damage process which leads to catastrophic failure of the material, thereby enabling life prediction in both monolithic aluminum alloys and aluminum alloy/SiC particle (SiCp) reinforced composites.

Analysis of Fracture Toughness and Crack Propagation of Ti6Al4V Produced by Selective Laser Melting

Abstract: This paper describes and analyzes fracture toughness and crack propagation of selective laser molten (SLM) components made from Ti6Al4V powder particles The main goal of this research is to gain more insight in the fracture mechanisms of this relatively new material and to improve the static and dynamic behavior of cracked SLM-Ti components At first, the SLM process parameters are optimized until the relative material density equals 997% This is close to the relative density of vacuum arc remelted mill annealed standard oxygen titanium which is used as a reference for all experiments A distinctive difference in phase morphology and texture of the microstructure is noticed between the SLM and the reference titanium The fine acicular martensite phase of the SLM-Ti results in more brittle behavior and inferior fracture toughness On the other hand, the fine grained microstructure leads to a large number of grain boundaries acting as obstacle points for crack propagation Consequently, crack growth properties do not significantly differ between both Microstructural analysis of the crack growth and final failure areas on the fractured surfaces is performed to study the failure mechanisms in more detail