Non-linear fracture analysis of multilayered two-dimensional graded beams

2018 ◽  
Vol 14 (2) ◽  
pp. 387-399
Author(s):  
Victor Rizov
Keyword(s):  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Fracture Behaviour ◽  
Strain Energy Release ◽  
Fracture Analysis ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Content Type ◽  
Delamination Fracture ◽  
Non Linear

Purpose The purpose of this paper is to present an analytical study of the delamination fracture behaviour of a multilayered two-dimensional functionally graded cantilever beam configuration. A delamination crack is located arbitrary along the height of the beam cross-section. The layers have different thicknesses and material properties. Perfect adhesion is assumed between layers. The material is functionally graded in both thickness and width directions in each layer. Besides, the material of the beam exhibits non-linear-elastic behaviour. Design/methodology/approach The delamination fracture behaviour is analysed in terms of the strain energy release rate. The J-integral approach is applied in order to verify the analysis of the strain energy release rate developed in the present paper. Findings The influence of material properties, the crack location along the height of the beam cross-section and the non-linear behaviour of the material on the delamination fracture is examined. Originality/value A non-linear delamination fracture analysis of multilayered two-dimensional non-symmetric functionally graded beam configuration is developed.

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.

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.

Non-linear elastic delamination of multilayered functionally graded beam

2017 ◽  
Vol 13 (3) ◽  
pp. 434-447 ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Analytical Solution ◽  
Energy Release Rate ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Content Type ◽  
Delamination Fracture ◽  
Non Linear

Purpose The purpose of this paper is to perform an analytical study of non-linear elastic delamination fracture in the multilayered functionally graded split cantilever beam (SCB) configuration. The SCB studied may have an arbitrary number of vertical layers. The material in each layer is functionally graded along the layer thickness. Also, the material properties may be different in each layer. The analytical solution derived was applied for parametric investigations in order to evaluate the effects of material properties and delamination crack location on the non-linear fracture behaviour. Design/methodology/approach The delamination fracture was studied in terms of the strain energy release rate. The SCB mechanical response was described by using a power-law stress-strain relation. A non-linear analytical solution for the strain energy release rate was derived by considering the SCB complementary strain energy. In order to verify the solution, an additional analysis of the strain energy release rate was developed by considering the complementary strain energy in the beam cross-sections ahead and behind the crack front. Findings The effects of material gradient, crack location along the beam width and non-linear material behaviour on the delamination fracture were evaluated. The analytical solution derived is useful for parametric studies of non-linear fracture in multilayered functionally graded beams. Originality/value Delamination fracture in the multilayered functionally graded SCB configuration was analysed with considering the non-linear material behaviour.

Fracture analysis of a three-dimensional functionally graded beam

2018 ◽  
Vol 9 (1) ◽  
pp. 93-106 ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Fracture Behaviour ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Beam Width ◽  
Functionally Graded ◽  
Content Type ◽  
Delamination Fracture

Purpose The purpose of this paper is to carry out a delamination fracture analysis of the three-dimensional functionally graded split cantilever beam (SCB) configuration. Design/methodology/approach The fracture behaviour was studied analytically in terms of the strain energy release rate by applying methods of linear elastic fracture mechanics. It was assumed that the material is functionally graded along the beam width, height and length. The strain energy release rate was derived by analysing the stress and strain state in the beam cross-sections ahead and behind the crack front. An additional analysis of the strain energy release rate was performed by considering the beam strain energy for verification. Findings The influence of material gradient along the beam width, height and length on the delamination fracture behaviour was investigated. The effect of crack length was analysed too. The analytical approach developed is very useful for parametric fracture investigations. The results obtained in the present study can be applied for optimisation of three-dimensional functionally graded beam systems in their design with respect to delamination fracture behaviour. Originality/value An analytical approach for studying the delamination fracture in the SCB configuration that is functionally graded along the beam width, height and length was developed.

Analytical Study of Delamination in Multilayered Two-Dimensional Functionally Graded Non-Linear Elastic Beams

2017 ◽  
Vol 34 (4) ◽  
pp. 495-504
Author(s):  
V. I. Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Cross Section ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Delamination Fracture

AbstractThe present paper is focused on the delamination fracture in a multilayered two-dimensional functionally graded beam configuration which exhibits non-linear behavior of the material. The beam is loaded by two longitudinal forces applied at the beam free ends. The beam contains a delamination crack which is located symmetrically with respect to the beam mid-span. The delamination is studied analytically in terms of the strain energy release rate. TheJ-integral approach is applied for verification of the analysis of the strain energy release rate. The solution derived is valid for a beam made of an arbitrary number of layers. It is assumed that each layer has individual thickness and material properties. Also, the material is two-dimensional functionally graded in the cross-section of each layer. The solution obtained can be applied for a delamination crack located arbitrary along the height of the beam cross-section. It is shown that the solution is very convenient for investigating the influences of material gradients and crack location on the delamination fracture behavior. The results obtained can be used for optimization of multilayered two-dimensional functionally graded structural members and components with respect to their delamination fracture performance.

Elastic-plastic delamination of multilayered graded four-point bending beam

2018 ◽  
Vol 15 (1) ◽  
pp. 166-172 ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Content Type ◽  
Four Point Bending ◽  
Delamination Fracture

Purpose This paper aims to analyze the elastic-plastic delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration. Design/methodology/approach The mechanical response of beam is described by a power-law stress-strain relation. The fracture is studied analytically in terms of the strain energy release rate by considering the beam complimentary strain energy. The beam can have an arbitrary number of layers. Besides, each layer may have different thickness and material properties. Also, in each layer, the material is functionally graded along the beam width. A delamination crack is located arbitrary between layers. Thus, the crack arms have different thickness. Findings The analysis developed is used to elucidate the effects of crack location, material gradient and non-linear behaviour of material on the delamination fracture. It is found that the material non-linearity leads to increase in the strain energy release rate. Therefore, the non-linear behaviour of material should be taken into account in fracture mechanics-based safety design of structural members and components made of multilayered functionally graded materials. The analysis revealed that the strain energy release rate can be effectively regulated by using appropriate material gradients in the design stage of multilayered functionally graded constructions. Originality/value Delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration is studied in terms of the strain energy release rate by taking into account the material non-linearity.

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.

Delamination of Multilayered Functionally Graded Beams with Material Nonlinearity

2018 ◽  
Vol 18 (04) ◽  
pp. 1850051 ◽  
Author(s):  
V. Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Functionally Graded ◽  
Material Nonlinearity ◽  
Functionally Graded Beam ◽  
Delamination Fracture

Delamination fracture in multilayered functionally graded, split cantilever beams is analyzed with account taken of the nonlinear behavior of the material. The fracture is studied analytically in terms of the strain energy release rate. The mechanical behavior of the material is described by a power-law stress–strain relation that is not symmetric for tension and compression. The beam can have an arbitrary number of vertical layers of different thickness. Each layer can have different material properties. Besides, the material in each layer is functionally graded along the layer thickness. Also, the delamination fracture can occur at any interface. The strain energy release rate is derived by analyzing the complementary strain energy of the beam. The solution obtained is applied to elucidating the effects of crack location, material gradient and material nonlinearity on the delamination fracture behavior of multilayered functionally graded beam configuration. It is found that the material nonlinearity leads to increase of the strain energy release rate, which implies that the material nonlinearity should be taken into account in the fracture mechanics based safety design of multilayered functionally graded structural members and components.

Non-linear study of delamination cracks in multilayered beams

2016 ◽  
Vol 12 (4) ◽  
pp. 678-692
Author(s):  
Victor Rizov
Keyword(s):  
Analytical Solutions ◽  
Fracture Behaviour ◽  
Fracture Analysis ◽  
Stress Strain ◽  
Content Type ◽  
Material Constants ◽  
Linear Fracture ◽  
Delamination Fracture ◽  
Non Linear ◽  
Multilayered Beam

Purpose The purpose of this paper is to deal with an analytical investigation of delamination fracture in the mixed-mode bending (MMB) multilayer beam configurations taking into account the material non-linearity. Design/methodology/approach The J-integral approach was applied in fracture analysis. The beam layers non-linear mechanical response was described by using a power-law stress-strain relation with four material constants. Analytical solutions of the J-integral were derived by using the technical beam theory. The fracture analysis developed is valid for MMB beams whose layers may have different thicknesses. Also, the values of material constants in the non-linear stress-strain equation may be different for each layer. Findings The effect of material constants, crack location and layer thicknesses on the non-linear fracture was evaluated. The analytical solutions obtained are very suitable for parametric studies of non-linear fracture behaviour. The approach developed here can be used for optimization of multilayered beam structures with respect to the delamination fracture performance. The present study can also be useful for the understanding of fracture in multilayered beams exhibiting material non-linearity. Originality/value For the first time, an analytical study was performed of the delamination fracture behaviour of the MMB multilayered beam configuration taking into account the material non-linearity.

scholarly journals Fracture analysis of a nonhomogeneous beam with two concentric cylindrical longitudinal cracks

2021 ◽  
Vol 41 (3) ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Cross Section ◽  
Release Rate ◽  
Strain Energy ◽  
Radial Direction ◽  
Strain Energy Release Rate ◽  
Fracture Behaviour ◽  
Strain Energy Release ◽  
Longitudinal Cracks

This paper is concerned with the analysis of the fracture behaviour of a nohomogeneous cantilever beam with two concentric longitudinal cracks. The beam has a circular cross-section with linearly varying radius along the beam length. Moreover, the beam exhibits continuously varying material inhomogeneity in the radial direction. The fracture is analyzed in terms of strain energy release rate assuming nonlinear mechanical behaviour of the material. For this purpose, solutions for the strain energy release rate are derived by considering the energy balance. Two cantilever beam configurations with different lengths of longitudinal cracks are analysed. Moreover, the two cracks are arranged arbitrarily in the radial direction. The longitudinal fracture behaviour of the beam is also analysed by considering the complementary strain energy for verification. The strain energy release rate solutions are used to investigate the influence of varying radius of the cross section along the length of the beam on the longitudinal fracture behaviour. The effects of crack lengths and the location of the two concentric cracks in the radial direction on fracture are also studied. The influences of the loading conditions of the beam and the inhomogeneity of the material in the radial direction on the fracture behaviour are also evaluated.

Sign in / Sign up

Export Citation Format

Share Document