Elastic Foundation Solution for the Energy Release Rate and Mode Partitioning of Sandwich Debonds by Use of the Timoshenko Beam Theory

2021 ◽  
Author(s):  
Siddarth Niranjan Babu ◽  
George Kardomateas
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Elastic Foundation ◽  
Timoshenko Beam ◽  
Release Rate ◽  
Beam Theory ◽  
Timoshenko Beam Theory

Analysis of Potential Energy Release Rate of Composite Laminate Based on Timoshenko Beam Theory

2007 ◽  
Vol 334-335 ◽  
pp. 513-516
Author(s):  
Kyohei Kondo
Keyword(s):  
Potential Energy ◽  
Energy Release Rate ◽  
Energy Release ◽  
Timoshenko Beam ◽  
Release Rate ◽  
Double Cantilever Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Beam Specimen ◽  
Cracked Beam

The Timoshenko beam theory is used to model each part of cracked beam and to calculate the potential energy release rate. Calculations are given for the double cantilever beam specimen, which is simulated as two separate beams connected elastically along the uncracked interface.

scholarly journals Analytical Energy Release Rate of Interfacial Crack in Composite Laminates

2019 ◽  
Vol 37 (1) ◽  
pp. 137-142
Author(s):  
Weiling Zheng ◽  
Longxi Zheng
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Composite Laminates ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Beam Theory ◽  
Three Point Bending ◽  
The Right

In order to study whether the interfacial crack will grow or not in the composite laminates, the energy release rate of a crack in three-point bending model was obtained by using the Timoshenko beam theory and local generalized forces. The results of energy release rate were validated by the finite element results. The results indicate that the energy release rate of left crack tip is equal to that of the right crack tip when the crack before the crack goes cross the loading point; after the crack goes cross the loading point, the energy release rate of the left crack tip increases and then decreases gradually, while the energy release rate of right crack tip decreases first and increases later; the energy release rate of left crack tip is equal to that of the right crack tip again when the crack is symmetric with the loading point.

Elastic Foundation Solution for the Energy Release Rate and Mode Partitioning of Face/Core Debonds in Sandwich Composites

2019 ◽  
Vol 86 (12) ◽  
Author(s):  
George A. Kardomateas ◽  
Niels Pichler ◽  
Zhangxian Yuan
Keyword(s):  
Energy Release Rate ◽  
Closed Form ◽  
Energy Release ◽  
Elastic Foundation ◽  
Release Rate ◽  
Sandwich Beam ◽  
Integral Approach ◽  
Closed Form Expression ◽  
Sandwich Composites ◽  
Sandwich Construction

Abstract The goal of this paper is to derive closed form expressions for the energy release rate and mode partitioning of face/core debonds in sandwich composites, which include loading in shear. This is achieved by treating a finite length sandwich beam as having a “debonded” section where the debonded top face and the substrate (core and bottom face) are free and a “joined” section where a series of springs (elastic foundation) exists between the face and the substrate. The elastic foundation analysis is comprehensive and includes the deformation of the substrate part (unlike other elastic foundation studies in the literature) and is done for a general asymmetric sandwich construction. A J-integral approach is subsequently used to derive a closed form expression for the energy release rate. In the context of this elastic foundation model, a mode partitioning approach based on the transverse and axial displacements at the beginning of the elastic foundation (“debond tip”) is proposed. The results are compared with finite element results and show very good agreement.

scholarly journals A Stretch/Bend Method for In Situ Measurement of the Delamination Toughness of Coatings and Films Attached to Substrates

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
M. Y. He ◽  
J. W. Hutchinson ◽  
A. G. Evans
Keyword(s):  
Residual Stress ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Beam Theory ◽  
Companion Paper ◽  
In Situ Measurement ◽  
Delamination Toughness ◽  
Slender Beams

A stretch/bend method for the in situ measurement of the delamination toughness of coatings attached to substrates is described. A beam theory analysis is presented that illustrates the main features of the test. The analysis is general and allows for the presence of residual stress. It reveals that the test produces stable extension of delaminations, rendering it suitable for multiple measurements in a single test. It also provides scaling relations and enables estimates of the loads needed to extend delaminations. Finite element calculations reveal that the beam theory solutions are accurate for slender beams, but overestimate the energy release rate for stubbier configurations and short delaminations. The substantial influence of residual stress on the energy release rate and phase angle is highly dependent on parameters such as the thickness and modulus ratio for the two layers. Its effect must be included to obtain viable measurements of toughness. In a companion paper, the method has been applied to a columnar thermal barrier coating deposited onto a Ni-based super-alloy.

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

2012 ◽  
Vol 152-154 ◽  
pp. 1417-1426 ◽  
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.

The Strain Energy Release Rate of a Bi-Material Beam with Interfacial Crack

2006 ◽  
Vol 306-308 ◽  
pp. 369-374 ◽  
Author(s):  
Shiuh Chuan Her ◽  
Wei-Bo Su
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Layer Structure ◽  
Interfacial Crack ◽  
Beam Theory ◽  
Strain Energy Release ◽  
Before And After

Multi-layer structures are common in electronic package especially for the micro devices manufactured via the semi-conductor processes or MEMS processes. Interfacial crack due to the delamination significantly weakens the multi-layer structure. It is desired to understand the interfacial fracture properties of the electronic packaging materials. In this research, three specimens named Doubled Cantilever Beam (DCB), End-Notched Flexure (ENF), and Four-Point-Bending are proposed to investigate the fracture toughness associated with mode I, mode II and mixed mode. Basing on the Euler-Bernoulli beam theory, the strain energy in a bi-layer beam is derived. The strain energy before and after the propagation of the interfacial crack are calculated, lead to the determination of the strain energy release rate. The analytical results of strain energy release rate derived in this investigation are compared with the numerical results obtained from finite element method. The effects of material properties and thickness between the adjacent layers of interfacial crack are examined through the parametric study.

The Effects of In-Service Induced Reduction of Bonding Quality on the Mode I, II, and I-II Fracture Toughness of CNT Nanocomposites

2016 ◽  
Author(s):  
Masoud Yekani Fard ◽  
Brian Raji ◽  
John M. Woodward ◽  
Aditi Chattopadhyay
Keyword(s):  
Fracture Toughness ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Accelerated Aging ◽  
Beam Theory ◽  
Mode I ◽  
Mode Ii ◽  
Initiation And Propagation ◽  
Calibration Methods

Tests were carried out to determine the interlaminar fracture toughness of stitch-bonded biaxial polymer matrix carbon nanotube nanocomposites for mode I, II, and I-II including durability effects. Analysis of the test specimens in terms of mode I energy release rates showed good agreement among Modified Beam Theory, Compliance Calibration, and Modified Compliance Calibration methods. End-Notched Flexure (ENF) and four point End-Notched Flexure (4ENF) tests gave very consistent crack initiation and propagation results for mode II fracture. The results show that the critical mode I energy release rate for delamination decreases monotonically with increasing mode II loading. The effects of accelerated aging (60°C and 90% Rh) on fracture properties were studied. Early accelerated aging (0–12 months) has the dominant diminishing effect on energy release rate initiation and propagation in composites and nanocomposites.

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