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.

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.

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.

scholarly journals Analyses of delaminations in non-linear elastic multilayered inhomogeneous beam configurations

2020 ◽  
Vol 40 (3) ◽  
pp. 65-77
Author(s):  
Victor Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Cross Section ◽  
Release Rate ◽  
Strain Energy ◽  
Fracture Behavior ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Linear Elastic ◽  
Delamination Fracture

This paper presents investigation of delamination fracture behavior of multilayered non-linear elastic beam configurations by using the Ramberg-Osgood stress-strain relation. It is assumed that each layer exhibits continuous material inhomogeneity along the width as well as along thickness of the layer. An approach for determination of the strain energy release rate is developed for a delamination crack located arbitrary along the multilayered beam height. The approach can be applied for multilayered beams of arbitrary cross-section under combination of axial force and bending moments. The layers may have different thickness and material properties. The number of layers is arbitrary. The approach is applied for analyzing the delamination fracture behavior of a multilayered beam configuration subjected to four-point bending. The beam has a rectangular cross-section. The delamination crack is located symmetrically with respect to the beam midspan. The strain energy release rate is derived assuming that the modulus of elasticity varies continuously in the cross-section of each layer according to a hyperbolic law. In order to verify the solution to the strain energy release rate, the delamination fracture behavior of the multilayered non-linear elastic four-point bending beam configuration is studied also by applying the method of the J-integral. The solution to the strain energy release rate derived in the present paper is used in order to perform a parametric study of delamination.

On the Axial Rigidity of a Perforated Strip and the Strain Energy Release Rate in a Centrally Notched Strip Subjected to Uniaxial Tension

1964 ◽  
Vol 86 (4) ◽  
pp. 693-697 ◽  
Author(s):  
R. G. Forman ◽  
A. S. Kobayashi
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Uniaxial Tension ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Theoretical Studies ◽  
Correction Factors ◽  
Elasticity Solutions

This paper presents theoretical studies on the axial rigidities in strips with circular and elliptical perforations and subjected to uniaxial tension. Greenspan’s original derivations on these axial rigidities [2] were improved by using the elasticity solutions by Howland [6] and Ishida [7] for infinite strips with circular and elliptical perforations, respectively. Finally, the correction factors for centrally notched strips subjected to uniaxial tension were rederived from the above results following the energy approach by Irwin and Kies [3].

Nonlinear Approach for Strain Energy Release Rate in Micro Cantilevers

2010 ◽  
Author(s):  
Arash Kheyraddini Mousavi ◽  
Seyedhamidreza Alaie ◽  
Maheshwar R. Kashamolla ◽  
Zayd Chad Leseman
Keyword(s):  
Surface Roughness ◽  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Rigid Substrate ◽  
Micro Cantilever

An analytical Mixed Mode I & II crack propagation model is used to analyze the experimental results of stiction failed micro cantilevers on a rigid substrate and to determine the critical strain energy release rate (adhesion energy). Using nonlinear beam deflection theory, the shape of the beam being peeled off of a rigid substrate can be accurately modeled. Results show that the model can fit the experimental data with an average root mean square error of less than 5 ran even at relatively large deflections which happens in some MEMS applications. The effects of surface roughness and/or debris are also explored and contrasted with perfectly (atomically) flat surfaces. Herein it is shown that unlike the macro-scale crack propagation tests, the surface roughness and debris trapped between the micro cantilever and the substrate can drastically effect the energy associated with creating unit new surface areas and also leads to some interesting phenomena. The polysilicon micro cantilever samples used, were fabricated by SUMMIT V™ technology in Sandia National Laboratories and were 1000 μm long, 30 μm wide and 2.6 μm thick.

Influence of Loading History on Delamination in Multilayered Beam with Creep

2021 ◽  
Vol 1046 ◽  
pp. 23-28
Author(s):  
Victor Iliev Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Time Dependent ◽  
External Loading ◽  
Loading History ◽  
Multilayered Beam

The present paper deals with an analytical study of the time-dependent delamination in a multilayered inhomogeneous cantilever beam with considering of the loading history. The multilayered beam exhibits creep behaviour that is treated by using a non-linear stress-strain-time relationship. The material properties are continuously distributed along the thickness and length of the layers. The external loading is applied in steps in order to describe the loading history. The analysis reveals that during each step of the loading, the strain energy release rate increases with time. The influences of crack length and location on the time-dependent strain energy release rate are also investigated.

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