Variable mixed-mode delamination in composite laminates under fatigue conditions: testing & analysis

La majoria de les fallades en elements estructurals són degudes a càrrega per fatiga. En conseqüència, la fatiga mecànica és un factor clau per al disseny d'elements mecànics. En el cas de materials compòsits laminats, el procés de fallada per fatiga inclou diferents mecanismes de dany que resulten en la degradació del material. Un dels mecanismes de dany més importants és la delaminació entre capes del laminat. En el cas de components aeronàutics, les plaques de composit estan exposades a impactes i les delaminacions apareixen facilment en un laminat després d'un impacte. Molts components fets de compòsit tenen formes corbes, superposició de capes i capes amb diferents orientacions que fan que la delaminació es propagui en un mode mixt que depen de la grandària de la delaminació. És a dir, les delaminacions generalment es propaguen en mode mixt variable. És per això que és important desenvolupar nous mètodes per caracteritzar el creixement subcrític en mode mixt per fatiga de les delaminacions. El principal objectiu d'aquest treball és la caracterització del creixement en mode mixt variable de les delaminacions en compòsits laminats per efecte de càrregues a fatiga. Amb aquest fi, es proposa un nou model per al creixement per fatiga de la delaminació en mode mixt. Contràriament als models ja existents, el model que es proposa es formula d'acord a la variació no-monotònica dels paràmetres de propagació amb el mode mixt observada en diferents resultats experimentals. A més, es du a terme un anàlisi de l'assaig mixed-mode end load split (MMELS), la característica més important del qual és la variació del mode mixt a mesura que la delaminació creix. Per a aquest anàlisi, es tenen em compte dos mètodes teòrics presents en la literatura. No obstant, les expressions resultants per l'assaig MMELS no són equivalents i les diferències entre els dos mètodes poden ser importants, fins a 50 vegades. Per aquest motiu, en aquest treball es porta a terme un anàlisi alternatiu més acurat del MMELS per tal d'establir una comparació. Aquest anàlisi alternatiu es basa en el mètode dels elements finits i virtual crack closure technique (VCCT). D'aquest anàlisi en resulten importants aspectes a considerar per a la bona caracterització de materials utilitzant l'assaig MMELS. Durant l'estudi s'ha dissenyat i construït un utillatge per l'assaig MMELS. Per a la caracterització experimental de la propagació per fatiga de delaminacions en mode mixt variable s'utilitzen diferents provetes de laminats carboni/epoxy essencialment unidireccionals. També es du a terme un anàlisi fractogràfic d'algunes de les superfícies de fractura per delaminació. Els resultats experimentals són comparats amb les prediccions del model proposat per la propagació per fatiga d'esquerdes interlaminars.

A correction to the analytical solution of the mixed-mode bending (MMB) problem

This paper addresses the analytical solution of the mixed-mode bending (MMB) problem. The first published solutions used a load separation in pure mode I and mode II and were applied for a crack length less than the beam half-span, a <= L. In later publications, the same mode separation was used in deriving the analytical solution for crack lengths bigger than the beam half-span, a > L. In this paper it is shown that this mode separation is not valid when a > L and in some cases may lead to very erroneous results. The correct mode separation and the corresponding analytical solutions, when a > L, are presented. Results, of force vs. displacement and force vs. crack length graphs, obtained using the existing formulation and the corrected formulation are compared. A finite element solution, which does not use mode separation, is also presented

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Finite element simulation of sandwich panels of laminated plaster and rockwool under mixed mode fracture

Sandwich panels of laminated gypsum and rock wool have shown large pathology of cracking due to excessive slabs deflection. Currently the most widespread use of this material is as vertical elements of division or partition, with no structural function, what justifies that there are no studies on the mechanism of fracture and mechanical properties related to it. Therefore, and in order to reduce the cracking problem, it is necessary to progress in the simulation and prediction of the behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability.

IdeaWall: Mixed mode distributed collaboration in enterprise environments

In early stages of design and modeling, computers and computer applications are often considered an obstacle, rather than a facilitator of the process. Most notably, brainstorms, process modeling with business experts, or development planning, are often performed by a team in front of a whiteboard. While "whiteboarding" is recognized as an effective tool, low-tech solutions that allow remote participants to contribute are still not generally available. This is a striking observation, considering that vast majority of teams in large organizations are distributed teams. And this has also been one of the key triggers behind the project described in this article, where a team of corporate researchers decided to identify state of the art technologies that could facilitate the scenario mentioned above. This paper is an account of a research project in the area of enterprise collaboration, with a strong focus on the aspects of human computer interaction in mixed mode environments, especially in areas of collaboration where computers still play a secondary role. It is describing a currently running corporate research project. © 2012 Springer-Verlag.

Mixed mode (I and II) crack tip fields in bulk metallic glasses

Stationary crack tip fields in bulk metallic glasses under mixed mode (I and II) loading are studied through detailed finite element simulations assuming plane strain, small scale yielding conditions. The influence of internal friction or pressure sensitivity on the plastic zones. notch deformation, stress and plastic strain fields is examined for different mode mixities. Under mixed mode loading, the notch deforms into a shape such that one part of its surface sharpens while the other part blunts. Increase in mode If component of loading dramatically enhances the normalized plastic zone size, lowers the stresses but significantly elevates the plastic strain levels near the notch tip. Higher internal friction reduces the peak tangential stress but increases the plastic strain and stretching near the blunted part of the notch. The simulated shear bands are straight and extend over a long distance ahead of the notch tip under mode II dominant loading. The possible variations of fracture toughness with mode mixity corresponding to failure by brittle micro-cracking and ductile shear banding are predicted employing two simple fracture criteria. The salient results from finite element simulations are validated by comparison with those from mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass.

Mixed-mode stress intensity factors for arbitrarily oriented cracks in cylindrical shells under axial pull and torsion

Results of photoelastic investigations conducted on cylindrical tubes (made of Araldite material) containing cracks oriented at 0°, 30°, 45°, 60° and 90° to the axis of the tube and subjected to axial and torsional loads are reported. The stress-intensity factors (SIFs) were determined by analysing the crack-tip stress fields. Smith and Smith's method [Engng Fracture Mech.4, 357–366 (1972)] and a new method developed by the authors by modifying Rakesh et al.'s method [Proc. 26th Congress of ISTAM, India (1981)] were employed to evaluate the mixed-mode SIFs.

A Harmonic Suppression Scheme for Open-End Winding Split-Phase IM Drive Using Capacitive Filters for the Full Speed Range

Voltage source inverter (VSI)-fed six-phase induction motor (IM) drives have high 6n +/- 1, n = odd-order harmonic currents. This is because these currents, driven by the corresponding harmonic voltages in the inverter output, are limited only by the stator leakage impedance, as these harmonics are absent in the back electromotive force of the motor. To suppress the harmonic currents, either bulky inductive harmonic filters or complex pulsewidth modulation (PWM) techniques have to be used. This paper proposes a harmonic elimination scheme using switched capacitor filters for a VSI-fed split-phase IM drive. Two 3-phase inverters fed from capacitors are used on the open-end side of the motor to suppress 6n +/- 1, n = odd-order harmonics. A PWM scheme that can suppress the harmonics as well as balance the capacitor voltage is also proposed. The capacitor fed inverters are switched so that the fundamental voltage is not affected, and the fundamental power is always drawn from the main inverters. The proposed scheme is verified with a detailed experimental study. The effectiveness of the scheme is demonstrated by comparing the results with those obtained by disabling the capacitor fed inverters.

A general methodology for calculating mixed mode stress intensity factors and fracture toughness of solder joints with interfacial cracks

Solder joints in electronic packages undergo thermo-mechanical cycling, resulting in nucleation of micro-cracks, especially at the solder/bond-pad interface, which may lead to fracture of the joints. The fracture toughness of a solder joint depends on material properties, process conditions and service history, as well as strain rate and mode-mixity. This paper reports on a methodology for determining the mixed-mode fracture toughness of solder joints with an interfacial starter-crack, using a modified compact mixed mode (CMM) specimen containing an adhesive joint. Expressions for stress intensity factor (K) and strain energy release rate (G) are developed, using a combination of experiments and finite element (FE) analysis. In this methodology, crack length dependent geometry factors to convert for the modified CMM sample are first obtained via the crack-tip opening displacement (CTOD)-based linear extrapolation method to calculate the under far-field mode I and II conditions (f(1a) and f(2a)), (ii) generation of a master-plot to determine a(c), and (iii) computation of K and G to analyze the fracture behavior of joints. The developed methodology was verified using J-integral calculations, and was also used to calculate experimental fracture toughness values of a few lead-free solder-Cu joints. (C) 2014 Elsevier Ltd. All rights reserved.

Mixed Mode Analysis of Obliquely Oriented Edge Cracked Semicircular Disk Under Compression

A new mixed-mode compression fracture specimen, obliquely oriented edge cracked semicircular disk (OECSD) is analyzed by extending pure opening mode configuration of edge cracked semicircular disk (ECSD) under Hertzian compression. Photoelastic experiments are conducted on two different specimens of OECSD of same size and different crack lengths and inclinations. Finite element method (FEM) is used to solve a number of cases of the problem varying crack length and crack inclination. FE results show a good match with experiments. Inclination of edge crack in OECSD can be so made as to obtain any mode-mixity ratio between zero and one and beyond for any crack length. The new specimen can be used for fracture testing under compression more conveniently than the existing ones in several ways.

An automatic algorithm for mixed mode crack growth rate based on drop potential method

A new automatic algorithm for the assessment of mixed mode crack growth rate characteristics is presented based on the concept of an equivalent crack. The residual ligament size approach is introduced to implementation this algorithm for identifying the crack tip position on a curved path with respect to the drop potential signal. The automatic algorithm accounting for the curvilinear crack trajectory and employing an electrical potential difference was calibrated with respect to the optical measurements for the growing crack under cyclic mixed mode loading conditions. The effectiveness of the proposed algorithm is confirmed by fatigue tests performed on ST3 steel compact tension-shear specimens in the full range of mode mixities from pure mode Ito pure mode II. (C) 2015 Elsevier Ltd. All rights reserved.

Prediction of mixed-mode cracking direction in random, short-fibre composite-materials

The prediction of cracking direction in composite materials is of significance to the design of composite structures. This paper presents several methods for predicting the cracking direction in the double grooved tension-shear specimen which gives mixed-mode cracking. Five different criteria are used in this analysis: two of them have been used by other investigators and the others are proposed by the present authors. The strain energy density criterion proposed by G.C. Sih is modified to take account of the influence of the anisotropy of the strength on the direction of crack. The two failure criteria of Tsai-Hill and Norris are extended to predict the crack orientation. The stress distributions in the near-notch zone are calculated by using the 8-node quadrilateral isoparametric finite element method. The predictions of all the criteria except one are in good agreement with the experimental measurement. In addition, on the basis of the FEM results, the size of the zone in which the singular term is dominant is estimated.

Additional response: Additional discussion of “Mixed mode ductile fracture using the strain energy density criterion”

boundary-layer flows, the skin friction and wall heat-transfer are higher and the