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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.

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.

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.

A non-linear delamination fracture analysis of multilayered two-dimensional non-symmetric functionally graded beam configuration is developed.

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.

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.

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.

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.

This paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic model with an arbitrary number of parallel units is used for treating the relaxation. Each unit has one dashpot and two springs. A stress-strain-time relationship is derived for the case when the coefficient of viscosity in each unit of the viscoelastic model changes continuously with time. The beam exhibits continuous material inhomogeneity along the thickness. Thus, the moduli of elasticity and the coefficients of viscosity vary continuously in the thickness direction. The aim of the present paper is to obtain time-dependent solutions to the strain energy release rate that take into account the relaxation when the coefficient of viscosity changes with time.

Time-dependent solutions to the strain energy release rate are derived by considering the time-dependent strain energy and also by using the compliance method. The two solutions produce identical results.

The variation of the strain energy release rate with time due to the relaxation is analysed. The influence of material inhomogeneity and the crack location along the beam width on the strain energy release rate are evaluated. The effects of change of the coefficients of viscosity with time and the number of units in the viscoelastic model on the strain energy release rate are assessed by applying the solutions derived.

The time-dependent strain energy release rate for a longitudinal vertical crack in a beam under relaxation is analysed for the case when the coefficients of viscosity change with time.

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).

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.

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.

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.

This paper aims to analyze the elastic-plastic delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration.

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.

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.

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.

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.

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.

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.

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.

The purpose of this paper is to carry out a delamination fracture analysis of the three-dimensional functionally graded split cantilever beam (SCB) configuration.

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.

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.

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.

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.

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.

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.

Delamination fracture in the multilayered functionally graded SCB configuration was analysed with considering the non-linear material behaviour.

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.

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.

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.

The present study contributes for the understanding of delamination fracture in layered beams that exhibit non-linear material behaviour.

The purpose of this paper is to study theoretically the ability of the prestressed foam core composite sandwich Split Cantilever Beam (SCB) for generating mixed-mode II/III crack loading conditions (the mode II fracture was provided by prestressing the beam using imposed transverse displacements).

The concepts of linear-elastic fracture mechanics were used. The fracture behavior was studied in terms of the strain energy release rate. For this purpose, a three-dimensional finite element model of the prestressed sandwich SCB was developed. The virtual crack closure technique was applied in order to analyze the strain energy release rate mode components distribution along the crack front.

It was found that the distribution is non-symmetric. The analysis revealed that a wide mixed-mode II/III ratios range can be generated by varying the magnitude of the imposed transverse displacement. The influence of the sandwich core material on the mixed-mode II/III fracture behavior was investigated. For this purpose, three sandwich beam configurations with different rigid cellular foam core were simulated. It was found that the strain energy release rate decreases when the foam core density increases.

For the first time, a mixed-mode II/III fracture study of foam core composite sandwich beam is performed.