Mode II Fracture of Functionally Graded Beams Exhibiting Material Non-Lynearity

2017 ◽  
Vol 863 ◽  
pp. 317-322
Author(s):  
Victor Iliev Rizov
Keyword(s):  
Strain Energy Release ◽  
Functionally Graded ◽  
Integral Approach ◽  
Mode Ii ◽  
Graded Materials ◽  
Mode Ii Fracture ◽  
Crack Location ◽  
Linear Fracture ◽  
Non Linear ◽  
Beam Height

A non-linear analysis of the mode II fracture in functionally graded materials was developed by using a beam configuration with two longitudinal cracks located symmetrically with respect to the centroid. The beam mechanical behaviour was described by a non-linear stress-strain relation. The non-linear fracture was studied by the J-integral approach. An analysis of the strain energy release rate was conducted with considering the material non-linearity in order to verify the J-integral non-linear analytical solution derived. The solution obtained is very convenient for parametric studies of mode II fracture in functionally graded beams exhibiting material non-linearity. The effects of material properties and crack location along the beam height on the non-linear fracture were evaluated. The results can be used for optimization of the beam structures with respect to the fracture performance.

Non-linear delamination in two-dimensional functionally graded multilayered beam

2018 ◽  
Vol 9 (5) ◽  
pp. 646-663
Author(s):  
Victor Rizov
Keyword(s):  
Mechanical Behaviour ◽  
Fracture Behaviour ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Integral Approach ◽  
Two Dimensional ◽  
Content Type ◽  
Crack Location ◽  
Delamination Fracture ◽  
Non Linear

Purpose A delamination fracture analysis of two-dimensional functionally graded multilayered end-loaded split beam configuration with non-linear mechanical behaviour of material is conducted. The beam is made of an arbitrary number of longitudinal layers. Perfect adhesion between layers is assumed. The material is two-dimensional functionally graded in the cross-section of each layer. Also, each layer has individual thickness and material properties. A delamination crack is located arbitrary along the beam height. The paper aims to discuss these issues. Design/methodology/approach The delamination fracture behaviour is investigated analytically in terms of the strain energy release rate by analysing the balance of the energy. An additional analysis of the delamination fracture is performed by applying the J-integral approach for verification. Findings The solutions derived are used to evaluate the effects of crack location, material gradients and material non-linearity on the delamination fracture behaviour of end-loaded split beam. The effect of material gradient on the distribution of the J-integral value along the crack front is elucidated too. Originality/value Delamination in the multilayered functionally graded end-loaded split beam exhibiting non-linear mechanical behaviour of the material is analysed assuming that the material property is distributed non-linearly in both thickness and width directions in each layer.

scholarly journals The elastic-plastic delamination analysis of layered beam configurations

2019 ◽  
Vol 39 (2) ◽  
pp. 165-173
Author(s):  
Victor Rizov
Keyword(s):  
Analytical Solutions ◽  
Strain Energy Release ◽  
Integral Approach ◽  
J Integral ◽  
Elastic Plastic ◽  
Crack Location ◽  
Layered Beams ◽  
Delamination Fracture ◽  
Non Linear ◽  
Point Bend

The elastic-plastic delamination fracture in layered beams was studied theoretically. Two Four Point Bend (FPB) beam configurations (the Double Leg Four Point Bend (DLFPB) and the Single Leg Four Point Bend (SLFPB)) were analyzed. An elastic-plastic constitutive model with power law hardening was used in the analysis. Fracture behavior was studied by applying the J-integral approach. The analytical solutions of the J-integral were obtained at characteristic levels of the external load. The solutions obtained were verified by analyzing the strain energy release rate with taking into account the material non-linearity. The variation of J-integral value in a function of crack location along the beam dept was investigated. The effect of material non-linearity on the fracture was evaluated. The analysis revealed that the J-integral value decreased with increasing the lower crack arm thickness. It was also found that the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members and components made of layered materials. The analytical solutions obtained are very useful for non-linear investigations, since the simple formulae derived capture the essentials of non-linear fracture in the layered beams under consideration.

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

Non-linear fracture in bi-directional graded shafts in torsion

2019 ◽  
Vol 15 (1) ◽  
pp. 156-169 ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Fracture Behaviour ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Content Type ◽  
Linear Elastic ◽  
Stress Strain Relation ◽  
Non Linear

Purpose The purpose of this paper is to develop an analysis of longitudinal fracture behaviour of a functionally graded non-linear-elastic circular shaft loaded in torsion. It is assumed that the material is functionally graded in both radial and longitudinal directions of the shaft (i.e. the material is bi-directional functionally graded). Design/methodology/approach The Ramberg–Osgood stress-strain relation is used to describe the non-linear mechanical behaviour of the functionally graded material. The fracture is studied in terms of the strain energy release rate by analysing the balance of the energy. The strain energy release rate is obtained also by differentiating of the complementary strain energy with respect to the crack area for verification. Findings Parametric studies are carried out in order to evaluate the influence of material gradients in radial and longitudinal directions, the crack location in radial direction and the crack length on the fracture behaviour of the shaft. It is found that by using appropriate gradients in radial and longitudinal directions, one can tailor the variations of material properties in order to improve the fracture performance of the non-linear-elastic circular shafts to the externally applied torsion moments. Originality/value A longitudinal cylindrical crack in a bi-directional functionally graded non-linear-elastic circular shaft loaded in torsion is analysed by using the Ramberg–Osgood stress-strain relation.

scholarly journals Lengthwise fracture analyses of functionally graded beams by the Ramberg-Osgood equation

2018 ◽  
Vol 38 (3) ◽  
pp. 309-320 ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Energy Release Rate ◽  
Mechanical Behavior ◽  
Energy Release ◽  
Cross Section ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Non Linear

The basic purpose of the present paper is to develop lengthwise fracture analyses of the functionally graded Symmetric Split Beam (SSB) configurations which exhibit non-linear mechanical behavior of the material. The SSB is loaded in pure bending. A lengthwise crack is located symmetrically with respect to the beam's mid-span. The crack is located arbitrary along the width of the beam's cross-section. Thus, the crack arms have different widths. The material is linearly and functionally graded along the height of the beam's cross-section. The material non-linearity is treated by the Ramberg-Osgood equation (this is one of the basic novelties introduced in this paper). The fracture is analyzed in terms of the strain energy release rate by applying three approaches. First, the strain energy release rate is derived by considering the balance of the energy. The strain energy release rate is obtained also by using the complementary strain energy. The fracture is analyzed also by the J-integral. The results obtained by the three approaches are identical which proves the correctness of the lengthwise fracture analyses developed in the present paper. A parametric study is carried-out in order to examine the influences of the material gradient, the lengthwise crack location along the beam's width, and the non-linear mechanical behavior of the functionally graded material on the fracture in the SSB configuration.

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