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 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.

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.

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.

Characteristics of Fracture Mechanics for Crack Tip near the Interface between Steel and Concrete in Composite Structures

2007 ◽  
Vol 348-349 ◽  
pp. 841-844 ◽  
Author(s):  
Shan Suo Zheng ◽  
Lei Li ◽  
Shun Li Che ◽  
Lei Zeng ◽  
Jie Zheng
Keyword(s):  
Composite Structure ◽  
Composite Structures ◽  
Great Influence ◽  
Crack Tip ◽  
Strain Energy Release ◽  
Schematic Model ◽  
J Integral ◽  
Mechanical Behaviors ◽  
Crack Location ◽  
Path Independence

Steel-concrete composite structures are widely used in high buildings for its excellent seismic behaviors, whereas faults or cracks, which have great influence on interfacial mechanical behaviors of structural members, inevitably form near the interface between steel and concrete during the process of molding. Therefore, it is necessary to study the mechanical characteristics of the crack tip near the interface. In this paper, the application scope of the path-independence of J-integral in steel-concrete composite structure with a crack is discussed. According to the conservation law of J-integral for the steel-concrete composite structure with a crack parallel to the interface, a hypothesis that the value of strain energy release rate (SERR) of the mode-$fracture is independent of the crack location when the crack is parallel and close to the interface is put forwarded. And this hypothesis is verified through finite element method (FEM). A schematic model for a skew crack near the steel-concrete interface is provided. The variation law of SERR with the Dundur’s parameters and the angle between crack direction and interface are calculated by FEM. At last, calculating method of the stress intensity factor as well as the SERR for a skew crack near the interface is suggested. All these may contribute to further investigation on interfacial mechanical behaviors for steel-concrete composite structure.

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.

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.

Fracture Characteristics for Crack Tip near the Interface between Steel and Concrete in Composite Structures

2010 ◽  
Vol 97-101 ◽  
pp. 1701-1704
Author(s):  
Mei Xiong
Keyword(s):  
Composite Structure ◽  
Composite Structures ◽  
Great Influence ◽  
Crack Tip ◽  
Strain Energy Release ◽  
Schematic Model ◽  
J Integral ◽  
Mechanical Behaviors ◽  
Crack Location ◽  
Path Independence

Steel-concrete composite structures are widely used in high buildings for its excellent seismic behaviors, whereas faults or cracks, which have great influence on interfacial mechanical behaviors of structural members, inevitably form near the interface between steel and concrete during the process of molding. Therefore, it is necessary to study the mechanical characteristics of the crack tip near the interface. In this paper, the application scope of the path-independence of J-integral in steel-concrete composite structure with a crack is discussed. According to the conservation law of J-integral for the steel-concrete composite structure with a crack parallel to the interface, a hypothesis that the value of strain energy release rate (SERR) of the mode-I fracture is independent of the crack location when the crack is parallel and close to the interface is put forwarded. And this hypothesis is verified through finite element method (FEM). A schematic model for a skew crack near the steel-concrete interface is provided. The variation law of SERR with the Dundur’s parameters and the angle between crack direction and interface are calculated by FEM. At last, calculating method of the stress intensity factor as well as the SERR for a skew crack near the interface is suggested. All these may contribute to further investigation on interfacial mechanical behaviors for steel-concrete composite structure.

The Configurational Force Concept in Elastic-Plastic Fracture Mechanics−Instructive Examples

2009 ◽  
Vol 417-418 ◽  
pp. 297-300 ◽  
Author(s):  
R. Schöngrundner ◽  
Otmar Kolednik ◽  
Franz Dieter Fischer
Keyword(s):  
Driving Force ◽  
Plastic Material ◽  
Shielding Effect ◽  
Integral Approach ◽  
J Integral ◽  
Configurational Force ◽  
Crack Driving Force ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Elastic Plastic Materials

This paper deals with the determination of the crack driving force in elastic-plastic materials and its correlation with the J-Integral approach. In a real elastic-plastic material, the conventional J-integral cannot describe the crack driving force. This problem has been solved in Simha et al. [1], where the configurational force approach was used to evaluate in a new way the J-integral under incremental plasticity conditions. The crack driving force in a homogeneous elastic-plastic material, Jtip, is given by the sum of the nominally applied far-field crack driving force, Jfar, and the plasticity influence term, Cp, which accounts for the shielding or anti-shielding effect of plasticity. In this study, the incremental plasticity J-integral and the crack driving force are considered for a stationary and a growing crack.

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