Modeling ductile to brittle transition temperature of functionally graded steels by fuzzy logic

In this article, a model based on fuzzy logic (FL) for predicting ductile to brittle transition temperature of functionally graded steels in both crack divider and crack arrester configurations has been presented. Functionally graded steels containing graded ferritic and austenitic regions together with bainite and martensite intermediate layers were produced by electroslag remelting. For purpose of building the model, training and testing using experimental results from 140 specimens produced from two basic composites were conducted. The used data as inputs in FL models are arranged in a format of six input parameters that cover the FGS type, the crack tip configuration, the thickness of graded ferritic region, the thickness of graded austenitic region, the distance of the notch from bainite or martensite intermediate layer, and temperature. According to these input parameters, in the FL, the ductile to brittle transition temperature of each FGS specimen was predicted. It has been found that FL model will be valid within the ranges of variables. The training and testing results in the FL model have shown a strong potential for predicting the ductile to brittle transition temperature of each FGS specimen.     

Simulation of impact energy in functionally graded steels by mechanism-based strain gradient plasticity theory

Charpy impact energy of functionally graded steels composed of graded ferritic or austenitic layers which were produced by electroslag remelting in both crack divider and crack arrester configurations has been modeled by finite element method. The yield stress of each layer was related to the density of the dislocations of that layer and by assuming Holloman relation for the corresponding stress-strain curve, tensile strength and tensile strain of that layer were determined. Cubic elements were joined together to build the standard Charpy impact specimen. The data used for each cubic element in finite element modeling was the predicted stress-strain curve obtained from strain gradient plasticity theory. After applying the impact loading, a relatively good agreement between experimental results and those obtained from simulation was observed.     

Simulation Charpy impact energy of functionally graded steels by modified stress-strain curve through mechanism-based strain gradient plasticity theory

In the present work, Charpy impact energy of functionally graded steels produced by electroslag remelting composed of graded ferritic or austenitic layers in both crack divider and crack arrester configurations has been modeled by finite element method. The yield stress of each layer was related to the density of the statistically stored dislocations of that layer and assuming by Holloman relation for the corresponding stress-strain curves, tensile strengths of the constituent layers were determined via numerical method. By using load-displacement curves acquired from instrumented Charpy impact tests on primary specimens, the obtained stress-strain curves from uniaxial tensile tests were modified. The data used for each layer in finite element modeling were predicted modified stress-strain curves obtained from strain gradient plasticity theory. A relatively good agreement between experimental results and those obtained from simulation was observed.     

Modeling fracture toughness of ferritic and austenitic functionally graded steel based on the strain gradient plasticity theory

Functionally graded ferritic and austenitic steels were produced through electroslag refining by setting the austenitic stainless steels and plain carbon steel with appropriate thickness as electrode. Fracture toughness of the specimen in terms of J_IC was studied and modeled regarding the mechanism-based strain gradient plasticity theory. The yield stress of each layer was related to the density of the dislocations of that layer and assuming Holloman relation for the corresponding stress–strain curves, tensile strengths of the constituent layers were determined via numerical method. Fracture toughness of each layer was related to the corresponding area under stress–strain curve of that layer and finally by applying the rule of mixtures, fracture toughness of functionally graded steels was determined. The obtained results of the proposed model are in good agreement with the experimental ones.     

Some studies on the impact behavior of banded microalloyed steel

Microalloyed steels are used in automobile industries, offshore platforms and in structural applications. It is essential to establish a relation between service consition such as temperature, loading rate and fracture behavior of the steel. Impact study on new material is very handy to understand the mechanicl properties in a rapid and inexpensive way. The present investigation aims to assess impact toughness (CVN), ductile brittle transition temperature (DBTT, 25J), and initiation dynamic fracture toughness (J_ld*) of the indigenously developed microallayed seel. The steel has shown banding with alternate layers of ferrite and pearlite. The banding concentration (ferrite bands per mm) has been altered by heat treatment. Presence of banding has given spikes and splits in impact fracture. Change in banding concentration has affected DBTT of the steel, upper shelf energy and the extent of splitting. A model of crack divider with respect to the present microstructure has been analyzed. Banding in divider orientation improves the impact as well as initiation dynamic fracture toughness of the steel. The effect of temperature on splitting is also discussed. Splits in fractured surface disappear with decreasing temperature and higher numbers of splits yield lower toughness. Further, initiation dynamic fracture toughness is calculated for all temperatures and correlated with impact toughness.     

Thermo-mechanical behavior of a viscoelastic FGMs coating containing an interface crack

In this paper the plane thermo-mechanical behavior of a crack in a viscoelastic functionally graded materials (FGMs) coating with arbitrary material properties bonded to a homogeneous substrate is studied. In order to avoid the complex forms that describe the viscoelastic properties of FGMs, a multi-layered model for the FGMs coating is developed. The compliance and thermal conductivity in the multi-layered model linearly vary in each layer. In this mixed boundary value problem, the system is reduced to singular integral equations and solved numerically with the Lobatto-Chebyshev collocation technique. Using the correspondence principle and Laplace transform, the problem of an interface crack between a homogeneous substrate and a viscoelastic FGMs is solved. Some numerical examples are given to demonstrate the accuracy, efficiency and versatility of the multi-layered model. The numerical results confirm that the fracture toughness of materials can be greatly improved by the graded variation of material parameters. It is also confirmed that the specific variation of material parameters greatly influences the fracture behavior of viscoelastic FGMs coating.     

Evaluation of R-curve behavior of ceramic-metal functionally graded materials by stable crack growth

This paper deals with the fracture toughness and R-curve behavior of ceramic-metal functionally graded materials (FGMs). A possibility of stable crack growth in a three-point-bending specimen is examined based on the driving force and resistance for crack growth in FGMs, and the distribution of fracture toughness or R-curve behavior is evaluated on FGMs fabricated by powder metallurgy using partially stabilized zirconia (PSZ) and stainless steel (SUS 304). The materials have a functionally graded surface layer (FGM layer) with a thickness of 1 mm or 2 mm on a SUS 304 substrate. Three-point-bending tests are carried out on a rectangular specimen with a very short crack in the ceramics surface. On the three-point-bending test, a crack is initiated from a short pre-crack in unstable manner, and then it propagates in stable manner through the FGM layer with an increase in the applied load. From the relationship between applied load and crack length during the stable crack growth in the FGM layer, the fracture toughness is evaluated. The fracture toughness increases with an increase in a volume fraction of SUS 304 phase.     

The effects of functionally graded material structure on wear resistance and toughness of repaired weldments

To perform a long lasting, crack-free repair welding on ultrahigh strength steels, the filler metal must be chosen and applied properly. Avoiding several short-term repairs or replacements, the repaired weldment should reveal comparative characteristics such as wear resistance, toughness and hardness to base metal. In the present study, a novel functionally graded material have been introduced to obtain enhanced wear resistance and hardness at surface as well as improved fracture toughness at fusion line of repaired weldments. A comparative study of wear resistance of repaired weld metals has been carried out by pin-on-disk apparatus at 5 N normal load and 0.14 ms⁻¹ sliding speed. Fracture toughness of weld metal was also evaluated by charpy absorbed fracture energy tests and scanning electron microscopy fractograghs. The results show that by employing functionally graded layers, toughness was enhanced significantly while retaining the surface wear resistance.     

Impact Energy of Functionally Graded Steels with Crack Divider Configuration

Functionally graded steels were produced via electroslag remelting process using the primary electrodes of plain carbon and austenitic stainless steels. Charpy impact energy of as-prepared specimens was measured in the form of crack divider. The obtained results show that the impact energy of the specimens depends on the type and the volume fraction of the present phases. Based on the rule of mixtures, a mathematical model, which correlates the impact energy of functionally graded steels to the impact energ...     

Transient anti-plane crack problem of a functionally graded piezoelectric strip bonded to elastic layers

Summary. This paper examined the dynamic electromechanical behavior of a crack in a functionally graded piezoelectric layer bonded between two elastic layers under the combined anti-plane mechanical shear and in-plane electric impacts. Fourier cosine transforms are used to reduce the problem to the solution of a set of singular integral equations. It is found that the impermeable crack condition is more reasonable than the permeable crack condition to analyze the influence of electric loading, and the energy density factor is more acceptable than the energy release rate to be used as the fracture criterion. In addition, numerical results are also presented to show the influences of the crack position, electromechanical combination factor and material gradient parameter on the fracture behavior.     

A local approach model for cleavage fracture and crack extension direction of functionally graded materials

A local approach model has been developed for structural assessment of functionally graded materials in which the yield strength and the fracture toughness vary spatially. While the yield strength of the material at any point is taken to be deterministic, the local cleavage toughness is statistically distributed following a two-parameter Weibull model. The model is intended to determine the crack extension direction and failure probabilities of cleavage failure for a stationary pre-crack in a functionally graded material. The effect of independent variation in yield strength and toughness is discussed as a precursor to validating the model using a temperature gradient problem in which the yield strength and toughness are coupled through the temperature. The model is shown to closely reproduce experimental observations from cleavage fracture tests on mild steel subject to a controlled temperature gradient normal to the crack.     

UNSTABLE FATIGUE CRACK PROPAGATION AND FATIGUE FRACTURE TOUGHNESS OF STEELS

This paper presents the results of fatigue crack growth and fatigue fracture toughness studies of a high-pressure vessel steel with particular emphasis on the influence of heat treatment, low temperatures, plastic prestraining, the stress ratio and specimen dimensions. It has been shown that steels in an embrittled state, caused primarily by thermal treatment and low-temperatures, exhibit unstable fatigue crack growth which is characterized by alternate crack jumps (cleavage zones) and zones of fatigue crack growth. The fatigue fracture toughness, which corresponds to the first crack jump, and final fracture can be appreciably lower (i.e. up to 50%) than the static fracture toughness under plane strain conditions at the corresponding temperature. An analysis has been performed of unstable and stable fatigue crack growth and a model of unstable crack propagation is proposed which accounts for the observed experimental behaviour.     

Computational modeling of crack propagation in real microstructures of steels and virtual testing of artificially designed materials

A computational approach to the optimization of service properties of two-phase materials (in this case, fracture resistance of tool steels) by varying their microstructure is developed. The main points of the optimization of steels are as follows: (1) numerical simulation of crack initiation and growth in real microstructures of materials with the use of the multiphase finite elements (MPFE) and the element elimination technique (EET), (2) simulation of crack growth in idealized quasi-real microstructures (net-like, band-like and random distributions of the primary carbides in the steels) and (3) the comparison of fracture resistances of different microstructures and (4) the development of recommendations to the improvement of the fracture toughness of steels. The fracture toughness and the fractal dimension of a fracture surface are determined numerically for each microstructure. It is shown that the fracture resistance of the steels with finer microstructures is sufficiently higher than that for coarse microstructures. Three main mechanisms of increasing fracture toughness of steels by varying the carbide distribution are identified: crack deflection by carbide layers perpendicular to the initial crack direction, crack growth along the network of carbides and crack branching caused by damage initiation at random sites.     

梯度复合材料裂纹扩展路径和起裂载荷的有限元分析

为了模拟功能梯度材料(FGM)在工程应用中可能会出现的断裂问题并计算相应的开裂载荷,通过编写用户自定义UEL子程序将梯度扩展单元嵌入到ABAQUS软件中模拟功能梯度材料的物理场,并编写交互能量积分后处理子程序计算裂纹尖端的混合模式应力强度因子(SIF),采用最大周向应力准则编写子程序计算裂纹的偏转角,并模拟了裂纹扩展路径,计算了裂纹的起裂载荷。讨论了材料梯度参数对裂纹扩展路径以及起裂载荷的影响规律。通过与均匀材料的对比,验证了功能梯度材料断裂性能的优越性。研究表明:外载平行于梯度方向时,垂直梯度方向的初始裂纹朝着等效弹性模量小的方向扩展,且偏转角在梯度指数线性时出现峰值,并随着组分弹性模量比的增加而变大;当外载和初始裂纹均平行于梯度方向时,材料等效弹性模量和断裂韧性的增加或者梯度指数的减小都导致起裂载荷变大。     

功能梯度材料的断裂与屈曲驱动断裂的简化分析

作为一类先进的复合材料,功能梯度材料(FGM)能综合利用多种材料的物理性能,同时材料性质的连续变化也使其具有许多优越的力学性能。本文对功能梯度材料中平行于界面的裂纹的断裂参数进行了计算,并分析了梯度变化的薄膜在压应力作用下的屈曲驱动扩展。研究结果表明:功能梯度材料能有效地减小界面中的应力集中及它对材料中缺陷的作用,从而不同程度地提高了材料的强度和韧性。     

Microhardness profile prediction of a graded steel by strain gradient plasticity theory

In the present study, the Vickers microhardness profile of functionally graded steel austenitic steel produced by electroslag remelting process has been investigated. To produce functionally graded steels, two different slices from plain carbon steel and austenitic stainless steels were spot welded and used as electroslag remelting electrode. Functionally graded steel containing graded layers of austenite may be fabricated via diffusion of alloying elements during remelting stage. Vickers microhardness profile of the specimen has been obtained experimentally and modeled with mechanism-based strain gradient plasticity theory. In this regard, the density of the statistically stored dislocations and that of geometrically necessary dislocations was related to the Vickers microhardness profile of each layer. The experimental results are in good agreement with those obtained from the theory.     

The effect of the interaction of cracks in orthotropic layered materials under compressive loading

The non-classical problem of fracture mechanics of composites compressed along the layers with interfacial cracks is analysed. The statement of the problem is based on the model of piecewise homogeneous medium, the most accurate within the framework of the mechanics of deformable bodies as applied to composites. The condition of plane strain state is examined. The layers are modelled by a transversally isotropic material (a matrix reinforced by continuous parallel fibres). The frictionless Hertzian contact of the crack faces is considered. The complex fracture mechanics problem is solved using the finite-element analysis. The shear mode of stability loss is studied. The results are obtained for the typical dispositions of cracks. It was found that the interacting crack faces, the crack length and the mutual position of cracks influence the critical strain in the composite.     

Paper multilayer with a fracture toughness of steel

We demonstrate in this paper that commercially available printing paper can reach very high fracture toughness, comparable to that of steel, simply due to a special arrangement of the paper sheets with respect to the crack. Fracture mechanics experiments are conducted on single sheets of paper as well as on multilayer specimens in crack divider and crack arrester configuration. It is demonstrated that an arrangement in crack arrester configuration leads to an increase of the fracture toughness by a factor ten. An explanation of the effect is given and the transferability to other materials is discussed.     

On a moving dielectric crack in a piezoelectric interface with spatially varying properties

This paper provides a comprehensive theoretical analysis of a finite crack propagating with constant speed along an interface between two dissimilar piezoelectric media under inplane electromechanical loading. The interface is modeled as a graded piezoelectric layer with spatially varying properties (functionally graded piezoelectric materials, i.e., FGPMs). The analytical formulations are developed using Fourier transforms and the resulting singular integral equations are solved with Chebyshev polynomials. Using a dielectric crack model with deformation-dependent electric boundary condition, the dynamic stress intensity factors, electric displacement intensity factor, crack opening displacement (COD) intensity factor, and energy release rate are derived to fully understand this inherent mixed mode dynamic fracture problem. Numerical simulations are made to show the effects of the material mismatch, the thickness of the interfacial layer, the crack position, and the crack speed upon the dynamic fracture behavior. A critical state for the electromechanical loading applied to the medium is identified, which determines whether the traditional impermeable (or permeable) crack model serves as the upper or lower bound for the dielectric model considering the effect of dielectric medium crack filling.