The Damage Tolerance of a Sandwich Panel Containing a Cracked Honeycomb Core

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
I. Quintana Alonso ◽  
N. A. Fleck
Keyword(s):  
Finite Element ◽  
Sandwich Panel ◽  
Finite Element Simulations ◽  
Analytical Models ◽  
Tensile Fracture ◽  
Linear Elastic ◽  
Statistical Variation ◽  
Wall Strength ◽  
Elastic Fracture ◽  
Weibull Theory

The tensile fracture strength of a sandwich panel, with a center-cracked core made from an elastic-brittle diamond-celled honeycomb, is explored by analytical models and finite element simulations. The crack is on the midplane of the core and loading is normal to the faces of the sandwich panel. Both the analytical models and finite element simulations indicate that linear elastic fracture mechanics applies when a K-field exists on a scale larger than the cell size. However, there is a regime of geometries for which no K-field exists; in this regime, the stress concentration at the crack tip is negligible and the net strength of the cracked specimen is comparable to the unnotched strength. A fracture map is developed for the sandwich panel with axes given by the sandwich geometry. The effect of a statistical variation in the cell-wall strength is explored using Weibull theory, and the consequences of a stochastic strength upon the fracture map are outlined.

SIFs for Radial Cracks in Annular Discs Under Internal and External Shrinkage Pressure and Constant Angular Velocity

2007 ◽  
Author(s):  
A. Sakhaee-Pour ◽  
A. R. Gowhari-Anaraki ◽  
S. J. Hardy
Keyword(s):  
Finite Element ◽  
Angular Velocity ◽  
Constant Angular Velocity ◽  
Coefficient Of Determination ◽  
Linear Elastic ◽  
Crack Configuration ◽  
Wide Range ◽  
Elastic Fracture ◽  
Radial Cracks

Finite element method has been implemented to predict stress intensity factors (SIFs) for radial cracks in annular discs under constant angular velocity. Effects of internal and external uniform pressure on the SIFs have also been considered. Linear elastic fracture mechanics finite element analyses have been performed and results are presented in the form of crack configuration factors for a wide range of components and crack geometry parameters. These parameters are chosen to be representative of typical practical situations. The extensive range of crack configuration factors obtained from the analyses is then used to develop equivalent prediction equations via a statistical multiple non-linear regression model. The accuracy of this model is measured using a multiple coefficient of determination, R2, where 0 ≤ R2 ≤ 1. This coefficient is found to be greater than or equal to 0.98 for all cases considered in this study, demonstrating the quality of the model fit to the data. These equations for the SIFs enable designers to predict fatigue life of the components easily.

Fatigue analysis of groove weld with steel bar backing by fracture mechanics finite elements

1988 ◽  
Vol 15 (4) ◽  
pp. 524-533 ◽  
Author(s):  
Farid Taheri ◽  
Aftab A. Mufti
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Stress Ratio ◽  
Stress Range ◽  
Cyclic Life ◽  
Linear Elastic ◽  
Steel Bar ◽  
Elastic Fracture ◽  
Number Of Cycles ◽  
Cycles To Failure

The purpose of this paper is to analyze the fatigue crack growth rate in groove weld with backing steel bar. The linear elastic fracture mechanics approach is used. This approach is coded in a special purpose fracture mechanics package FAST. By using FAST, the structure is modeled and analyzed by its finite element module FAST-I, and the cyclic life is estimated by its crack propagation module FAST-II.An example recently studied by Baker and Kulak is investigated by the FAST program. The S–N curve (stress range versus number of cycles to failure) obtained by FAST is compared with the curve presented by Baker and Kulak. Key words: Engineering, finite element, fracture mechanics, fatigue, steel, stress intensity factor, numerical, computer analysis, weld, stress ratio, enriched element.

The static response of axisymmetric conical shells exhibiting bistable behavior

2021 ◽  
pp. 1-24
Author(s):  
Yair Luxenburg ◽  
Sefi Givli
Keyword(s):  
Finite Element ◽  
Radial Displacement ◽  
Functional Dependence ◽  
Building Blocks ◽  
Rigid Rotation ◽  
Finite Element Simulations ◽  
Analytical Models ◽  
Geometrical Parameters ◽  
Bistable Behavior ◽  
Conical Shells

Abstract Belleville springs are widely used in variety of mechanical systems. Recent advances in the field of multi-stable structures suggest that these conical axisymmetric washers may be extremely useful as bistable building-blocks for multi-stable architected metamaterials. In this paper, we examine the ability of existing analytical models to accurately predict the bistable behavior of Belleville springs, namely a non-monotonous force-displacement relation with two branches of positive stiffness separated by a branch of negative stiffness. By comparing to results of finite-element simulations, we find that current analytical models may suffer from significant inaccuracies associated with the assumption of rigid rotation. According to this assumption, adopted by all analytical models of Belleville springs, the cross-section of the spring rotates without bending, i.e. maintains zero curvature as the spring deforms. Motivated by this insight, we relax the rigid-rotation assumption and approximate the radial displacement field by a linear relation in terms of the distance from the spring axis. We find, based on extensive finite-element simulations, that the functional dependence of the radial displacement on the geometry of the springs is indifferent to the stage of deformation and can be expressed in terms of three geometrical parameters. These findings enable us to derive closed-form expressions that are simple and straight-forward to use, yet are significantly more accurate than existing analytical models.

Application of the Finite Element Method to Linear Elastic Fracture Mechanics

1991 ◽  
Vol 44 (10) ◽  
pp. 447-461 ◽  
Author(s):  
Leslie Banks-Sills
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Fracture Mechanics ◽  
Displacement Field ◽  
Three Dimensional ◽  
Linear Elastic Fracture Mechanics ◽  
The Finite Element Method ◽  
Linear Elastic ◽  
Elastic Fracture

Use of the finite element method to treat two and three-dimensional linear elastic fracture mechanics problems is becoming common place. In general, the behavior of the displacement field in ordinary elements is at most quadratic or cubic, so that the stress field is at most linear or quadratic. On the other hand, the stresses in the neighborhood of a crack tip in a linear elastic material have been shown to be square root singular. Hence, the problem begins by properly modeling the stresses in the region adjacent to the crack tip with finite elements. To this end, quarter-point, singular, isoparametric elements may be employed; these will be discussed in detail. After that difficulty has been overcome, the stress intensity factor must be extracted from either the stress or displacement field or by an energy based method. Three methods are described here: displacement extrapolation, the stiffness derivative and the area and volume J-integrals. Special attention will be given to the virtual crack extension which is employed by the latter two methods. A methodology for calculating stress intensity factors in two and three-dimensional bodies will be recommended.

A Measure for the Fracture Toughness of Cement Based Materials

1984 ◽  
Vol 42 ◽  
Author(s):  
Y. S. Jenq ◽  
S. P. Shah
Keyword(s):  
Fracture Toughness ◽  
Finite Element ◽  
Direct Method ◽  
Maximum Load ◽  
Nonlinear Finite Element ◽  
Linear Elastic ◽  
Cement Based Materials ◽  
Notch Length ◽  
Elastic Fracture ◽  
A Direct Method

It is frequently reported that the higher the strength of cement based materials, the more brittle is their behavior. It could he useful to quantitatively express the degree of brittleness. Many attempts [1–13] have been made to use linear elastic fracture mechanis (LEFM) to quantitatively express the degree of brittleness. For example, by testing notched beams one can calculate, using the formulas developed from LEFM, a quantity called fracture toughness and termed KIC from the measured maximum load and the initial notch-length. Unfortunalely, it has been observed that K thus calculated is dependent on the dimension of the beams. Many researchers have attempted to analyze this size dependency. Such approaches are usually quite cumbersome and are often based on expensive nonlinear finite element programs. In this paper a direct method is suggested to calculate two size-independent fracture toughness parameters from the experimental results. The method was developed based on tests on notched-beams of different mix proportions and different sizes.

A Practical Approach to Implementing Linear Elastic Fracture Mechanics in Gas Turbine Rotor Disk Analyses

2015 ◽  
Author(s):  
Scott Keller
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Gas Turbine ◽  
Crack Growth ◽  
Turbine Rotor ◽  
Linear Elastic Fracture Mechanics ◽  
Linear Elastic ◽  
Rotor Disk ◽  
Elastic Fracture ◽  
Growth Analyses

The failure of vital components is not uncommon in the gas turbine industry. In the event excessive degradation occurs within a component, e.g. extensive cracking in a turbine blade or vane, solutions exist to either repair or replace defective parts. Such parts are readily accessible and mostly exchangeable in the field, limiting the amount of outage time and assessment required for defective parts. When more critical components exhibit extreme wear or cracking, e.g. a crack in a rotor disk, repairs typically necessitate a complete rotor destack and refurbishment or have the potential to require the replacement of individual disks. In extreme cases, defects found in rotor disks can be known to retire an entire compressor or turbine rotor. The OEM solution of replacing disks puts a substantial cost on the customer, thus providing an incentive for characterization and advanced analyses to determine the residual life in critical rotating components. Considered an advanced analysis, linear elastic fracture mechanics (LEFM) provides the theory and fundamental structure to conduct crack growth analyses in components that exhibit nominally elastic behavior. Successful implementation of LEFM requires extensive characterization of the material, engine operating boundary conditions, and high fidelity finite element models. Upon the detection of a flaw, whether an internal or external indication, the results from finite element analyses can be used to derive the crack tip stress field and subsequent crack tip driving parameters. These parameters are then utilized in a comprehensive crack propagation model, calibrated to temperature- and load-dependent material data, to determine the number of cycles to unstable propagation. As a result, the remaining life of a component with a given indication is readily obtained, enabling our engineering team to provide a thorough life assessment of critical rotating components. An overview of the linear elastic fracture mechanics crack growth analyses conducted is presented, with a special emphasis on compressor and turbine disks.

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