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.

Non-linear delamination fracture analysis by using power-law hardening

2016 ◽  
Vol 12 (1) ◽  
pp. 80-92 ◽  
Author(s):  
Victor Iliev Rizov
Keyword(s):  
Power Law ◽  
Strain Curve ◽  
Fracture Analysis ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Content Type ◽  
Elastic Plastic ◽  
Linear Fracture ◽  
Delamination Fracture ◽  
Non Linear

Purpose – The purpose of this paper is to perform a theoretical analysis of non-linear delamination fracture in cantilever beam opened notch (CBON) configuration. It is assumed that the non-linear mechanical behavior of the CBON can be described by using a stress-strain curve with power-law hardening. Design/methodology/approach – The fracture analysis is carried-out by applying the integration contour independent J-integral. For this purpose, a model based on the technical beam theory is used. Equation is derived for determination of the CBON specimen curvature in elastic-plastic stage of deformation. The equation is solved by using the MatLab program system. Solutions of the J-integral are obtained at linear-elastic as well as elastic-plastic behavior of the CBON. The influence of the power-law exponent on the non-linear fracture is evaluated. Findings – The analysis reveals that the J-integral value increases when the exponent of the power-law increases. The solution obtained here is very useful for parametric analyses of the non-linear fracture behavior, since the simple formulas derived capture the essentials of the fracture response. Practical implications – Beside for parametric investigations, the solution obtained here can also be applied for calculating the critical J-integral value at non-linear behavior using experimentally determined critical fracture load at the onset of crack growth from the initial crack tip position in the CBON configuration. Originality/value – An analysis is performed of the non-linear fracture in the CBON configuration by applying the J-integral approach, assuming that the mechanical response can be modeled using a stress-strain curve with power-law hardening.

scholarly journals Analytical Study of Elastic-Plastic Fracture in the Crack-Lap Shear Multilayered Beam Configuration

2018 ◽  
Vol 48 (4) ◽  
pp. 61-77
Author(s):  
Victor Rizov
Keyword(s):  
Analytical Study ◽  
Mechanical Response ◽  
Fracture Behaviour ◽  
Stress Strain ◽  
Lap Shear ◽  
Linear Fracture ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Non Linear ◽  
Multilayered Beam

Abstract This paper reports an analytical study of delamination fracture in the Crack-Lap Shear (CLS) multilayered beam configuration with taking into account the material non-linearity. A delamination crack was located arbitrary along the beam height. It was assumed that the CLS mechanical response can be described by using a power-law stress-strain relation. It should be mentioned that each layer may have different material constants in the stress-strain relation. Besides, the thickness of each layer may be different. The classical beam theory was applied in the present study. The non-linear fracture behaviour was analyzed by the J-integral. Analytical solutions of the J-integral were obtained for homogeneous as well as for multilayered CLS beams. In order to verify the solutions obtained, analyses of the strain energy release rate were developed with considering material non-linearity. Material properties and crack location effects on the non-linear fracture behaviour were investigated. The analysis revealed that the J-integral value increases when the material non-linearity is taken into account. It was found also that the J-integral value decreases with increasing the lower crack arm thickness. The approach developed here is very convenient for parametric fracture analyses. The solutions derived can be used for optimization of the CLS multilayered beams with respect to their fracture performance.

Delamination analysis of a layered elastic-plastic beam

2017 ◽  
Vol 8 (5) ◽  
pp. 516-529 ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Fracture Behaviour ◽  
Strain Curve ◽  
Integral Approach ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Content Type ◽  
Elastic Plastic ◽  
Lap Shear ◽  
Delamination Fracture ◽  
Non Linear

Purpose The purpose of this paper is to perform a theoretical analysis of delamination fracture behaviour of the Crack Lap Shear layered beam configuration taking into account the material non-linearity. A delamination crack located arbitrarily along the beam height was considered in this study. Design/methodology/approach The beam mechanical behaviour was described by using the Ramberg-Osgood stress-strain relation. Fracture was analysed by applying the J-integral approach. Besides by using symmetric Ramberg-Osgood stress-strain curve, fracture was investigated also by Ramberg-Osgood stress-strain curve that is not symmetric with respect to tension and compression. The J-integral solutions were verified by performing elastic-plastic analyses of the strain energy release rate. Findings The effects of crack location and material properties on the non-linear fracture behaviour were evaluated. It was found that the material non-linearity leads to increase of the J-integral values. Therefore, the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members composed by layered materials. The analytical solutions derived are very useful for parametric investigations of delamination fracture with considering the material non-linearity. The results obtained can be applied for optimisation of the beam structure with respect to fracture performance. Originality/value The present study contributes for the understanding of delamination fracture in layered beams that exhibit non-linear material behaviour.

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.

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.

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.

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