A simple calculation of strain-energy release rate for a non-linear double cantilever beam

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.

Download Full-text

Computation of mode I strain energy release rate of symmetrical and asymmetrical sandwich structures using mixed finite element

Frattura ed Integrità Strutturale ◽

10.3221/igf-esis.56.19 ◽

2021 ◽

Vol 15 (56) ◽

pp. 229-239

Author(s):

Amina Mohamed Ben Ali ◽

Salah Bouziane ◽

Hamoudi Bouzerd

Keyword(s):

Finite Element ◽

Energy Release Rate ◽

Energy Release ◽

Release Rate ◽

Strain Energy ◽

Strain Energy Release Rate ◽

Double Cantilever Beam ◽

Mixed Finite Element ◽

Strain Energy Release ◽

Mode I

The use of composite materials is on the rise in different engineering fields, the main advantage of these materials for the aerospace industry is their low weight for excellent mechanical qualities. The analysis of failure modes, such as delamination, of these materials has received great attention from researchers. This paper proposes a method to evaluate the mode I Strain Energy Release Rate (SERR) of sandwich structures. This method associated a two-dimensional mixed finite element with virtual crack extension technique for the analysis of interfacial delamination of sandwich beams. A symmetrical Double Cantilever Beam (DCB) and asymmetrical Double Cantilever Beam (UDCB) have been analyzed in this study. The comparison of the results obtained by this method and those found in the literature shows efficiency and good precision for the calculation of Strain Energy Release Rate (SERR).

Download Full-text

Bending and Fracture Properties of Small Scale Elastic Beams – A Nonlocal Analysis

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.152-154.1417 ◽

2012 ◽

Vol 152-154 ◽

pp. 1417-1426 ◽

Cited By ~ 1

Author(s):

Xiang Fang Li ◽

Bao Lin Wang

Keyword(s):

Energy Release Rate ◽

Energy Release ◽

Static Analysis ◽

Cantilever Beam ◽

Timoshenko Beam ◽

Release Rate ◽

Strain Energy ◽

Strain Energy Release Rate ◽

Strain Energy Release ◽

Beam Model

Using the nonlocal elasticity theory, this paper presents a static analysis of a microbeam according to the Timoshenko beam model. A fourth-order governing differential equation is derived and a general solution is suggested. For a cantilever beam at nanoscale subjected to uniform distributed loading, explicit expressions for deflection, rotation and strain energy are obtained. The nonlocal effect decreases the deflection and maximum stress distribution. With a double cantilever beam model, the strain energy release rate of a cracked beam is evaluated, and the results obtained show that the strain energy release rate is decreased (hence an increased apparent fracture toughness is measured) when the beam thickness is several times the material characteristic length. However, in the absence of a uniformly distributed loading, the nonlocal beam theory fails to account for the size-dependent properties for static analysis. Particularly, the nonlocal Euler-Bernoulli beam can be analytically obtained from the nonlocal Timoshenko beam if the apparent shear modulus is sufficiently large.

Download Full-text