Enhancing the ability of strain energy release rate criterion for fracture assessment of orthotropic materials under mixed-mode I/II loading considering the effect of crack tip damage zone

Zahra Khaji and Mahdi Fakoor,Mahdi Fakoor 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.44 No.6

In this study, considering dissipated energy in fracture process zone (FPZ), a novel criterion based on maximum strain energy release rate (SER) for orthotropic materials is presented. General case of in-plane loading for cracks along the fibers is assumed. According to the experimental observations, crack propagation is supposed along the fibers and the reinforcement isotropic solid (RIS) concept is employed as a superior model for orthotropic materials. SER in crack initiation and propagation phases is investigated. Elastic properties of FPZ are extracted as a function of undamaged matrix media and micro-crack density. This criterion meaningfully links between dissipated energy due to toughening mechanisms of FPZ and the macroscopic fracture by defining stress intensity factors of the damaged zone. These coefficients are used in equations of maximum SER criterion. The effect of crack initiation angle and the damaged zone is considered simultaneously in this criterion and mode II stress intensity factor is extracted in terms of stress intensity factors of damage zone and crack initiation angle. This criterion can evaluate the effects of FPZ on the fracture behavior of orthotropic material. Good agreement between extracted fracture limit curves (FLC’s) and available experimental data proves the ability of the new proposed criterion.

Equivalent reinforcement isotropic model for fracture investigation of orthotropic materials

Mahdi Fakoor,Roham Rafiee,Shahab Zare 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.30 No.1

In this research, an efficient mixed mode I/II fracture criterion is developed for fracture investigation of orthotropic materials wherein crack is placed along the fibers. This criterion is developed based on extension of well-known Maximum Tensile Stress (MTS) criterion in conjunction with a novel material model titled as Equivalent Reinforced Isotropic Model (ERIM). In this model, orthotropic material is replaced with an isotropic matrix reinforced with fibers. A comparison between available experimental observations and theoretical estimation implies on capability of developed criterion for predicting both crack propagation direction and fracture instance, wherein the achieved fracture limit curves are also compatible with fracture mechanism of orthotic materials. It is also shown that unlike isotropic materials, fracture toughness of orthotic materials in mode I cannot be introduced as the maximum load bearing capacity and thus new fracture mechanics property, named here as maximum orthotropic fracture toughness in mode I is defined. Optimum angle between crack and fiber direction for maximum load bearing in orthotropic materials is also defined.

Investigation of composite coating effectiveness on stress intensity factors of cracked composite pressure vessels

Mahdi Fakoor,Seyed Mohammad Navid Ghoreishi,Nabi Mehri Khansari 대한기계학회 2016 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.30 No.7

The use of composite coating is among favorite reinforcement methods for repairing cracked pressure vessels. In the present study, the effects of mechanical properties and geometry of composite coatings on Stress intensity factors (SIF) is investigated. In this regard, after verification of modeling and analytical procedure, some 3D longitudinal and transverse semi-elliptical cracks in inner and outer layer of pressure vessels are modeled in FEM software. In addition, mechanical properties and thickness are adjustable. Then SIFs in throughout of the pressurized crack face were computed. Results indicate that critical crack occurred whenever inner longitudinal crack present in composite pressure vessel. Also, via 2 mm thickness of graphite/epoxy and glass/epoxy composite coatings, 55 and 43 percent reduction in Stress intensity factors (SIF) was observed, respectively. It is shown that increasing the thickness of the composite layers reduces stress intensity factor and hence can be considered as a suitable solution for reinforcement of the cracked pressure vessel in practical situations.

A Berry-Esseen Type Bound in Kernel Density Estimation for a Random Left-Truncation Model

Asghari, P.,Fakoor, V.,Sarmad, M. The Korean Statistical Society 2014 Communications for statistical applications and me Vol.21 No.2

In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if $Y{\geq}T$, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to $n^{-1/6}$ modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.

Aeroelastic investigation of a composite wind turbine blade

Rafiee, Roham,Fakoor, Mahdi Techno-Press 2013 Wind and Structures, An International Journal (WAS Vol.17 No.6

Static aeroelastic is investigated in a wind turbine blade. Imposed to different loadings, the very long and flexible structures of blades experience some changes in its preliminary geometry. This results in variations of aerodynamic loadings. An iterative approach is developed to study the interactions between structure and aerodynamics evaluating variations in induced stresses in presence of aeroelasticity phenomenon for a specific wind turbine blade. A 3D finite element model of the blade is constructed. Aerodynamic loading is applied to the model and deflected shape is extracted. Then, aerodynamic loadings are updated in accordance with the new geometry of the deflected blade. This process is repeated till the convergence is met. Different operational conditions consisting of stand-by, start-up, power production and normal shut-down events are investigated. It is revealed that stress components vary significantly in the event of power production at the rated wind speed; while it is less pronounced for the events of normal shut-down and stand-by.

Aeroelastic investigation of a composite wind turbine blade

Roham Rafiee,Mahdi Fakoor 한국풍공학회 2013 Wind and Structures, An International Journal (WAS Vol.17 No.6

Static aeroelastic is investigated in a wind turbine blade. Imposed to different loadings, the very long and flexible structures of blades experience some changes in its preliminary geometry. This results in variations of aerodynamic loadings. An iterative approach is developed to study the interactions between structure and aerodynamics evaluating variations in induced stresses in presence of aeroelasticity phenomenon for a specific wind turbine blade. A 3D finite element model of the blade is constructed. Aerodynamic loading is applied to the model and deflected shape is extracted. Then, aerodynamic loadings are updated in accordance with the new geometry of the deflected blade. This process is repeated till the convergence is met. Different operational conditions consisting of stand-by, start-up, power production and normal shut-down events are investigated. It is revealed that stress components vary significantly in the event of power production at the rated wind speed; while it is less pronounced for the events of normal shut-down and stand-by.

Mixed mode I/II fracture criterion to anticipate behavior of the orthotropic materials

Hannaneh Manafi Farid,Mahdi Fakoor 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.34 No.5

The new energy-based criterion, named Reinforcement Strain Energy Density (ReiSED), is proposed to investigate the fracture behavior of the cracked orthotropic materials in which the crack is embedded in the matrix along the fibers. ReiSED is an extension of the well-known minimum strain energy density criterion. The concept of the reinforced isotropic solid as an advantageous model is the basis of the proposed mixed-mode I/II criterion. This model introduces fibers as reinforcements of the isotropic matrix in orthotropic materials. The effects of fibers are qualified by defining reinforcement coefficients at tension and shear modes. These coefficients, called Reduced Stress (ReSt), provide the possibility of encompassing the fiber fraction in a fracture criterion for the first time. Comparing ReiSED fracture limit curve with experimental data proves the high efficiency of this criterion to predict the fracture behavior of orthotropic materials.

Bi-level optimization of laminated composite structures using particle swarm optimization algorithm

Parviz Mohammad Zadeh,Mahdi Fakoor,Mostafa Mohagheghi 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.4

This paper presents an efficient bi-level optimization technique to obtain the optimal stacking sequence for symmetric composite structures. The proposed approach involves two levels of modelling and optimization. The first level of the optimization procedure is used to minimize the weight of the composite structure. At this level, lamination parameters and the number of plies of specified angles (0, ±45 and 90 degree) are design variables, buckling load factor is treated as a constraint, and the weight of the structure is to be minimized using continuous-discrete particle swarm optimization algorithm. Next, at the second level the location of each ply orientation through the thickness (i. e. the layup of the panel) is found. At the second level, optimum stacking sequence is sought to maximize the load bearing capacity of the structure with respect to the buckling. The proposed methodology is applied to two test cases. Results show that the approach improves the buckling load factor of the structure without any weight penalty.

The influence of production inconsistencies on the functional failure of GRP pipes

Roham Rafiee,Mahdi Fakoor,Hadi Hesamsadat 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.19 No.6

In this study, a progressive damage modeling is developed to predict functional failure pressure of GRP pipes subjected to internal hydrostatic pressure. The modeling procedure predicts both first-ply failure pressure and functional failure pressure associated with the weepage phenomenon. The modeling procedure is validated using experimental observations. The random parameters attributed to the filament winding production process are identified. Consequently, stochastic simulation is conducted to investigate the influence of induced inconsistencies on the functional failure pressures of GRP pipes. The obtained results are compared to realize the degree to which random parameters affect the performance of the pipe in operation.

Mixed mode I/II fracture criterion to anticipate cracked composite materials based on a reinforced kinked crack along maximum shear stress path

Sadra Shahsavar,Mahdi Fakoor,Filippo Berto 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.39 No.6

In this paper, a fracture criterion for predicting the failure of the cracked composite specimens under mixed mode I/II loading is provided. Various tests performed on composite components reveal that cracks always grow along the fibers in the isotropic media. Using a new material model called reinforcement isotropic solid (RIS) concept, it is possible to extend the isotropic mixed mode fracture criteria into composite materials. In the proposed criterion, maximum shear stress (MSS) theory which is widely used for failure investigation of un-cracked isotropic materials will be extended to composite materials in combination with RIS concept. In the present study, cracks are oriented along the fibers in the isotropic material. It is assumed that at the onset of fracture, crack growth will be in a path where the shear stress has the highest value according to the MSS criterion. Investigating the results of this criterion and comparing with the available experimental data, it is shown that, both the crack propagation path and the moment of crack growth are well predicted. Available mixed mode I/II fracture data of various wood species are used to evaluate and verify the theoretical results.