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1

Facture energy of bonded joints with 2D elastic adhesive layer

Budzik M., Jumel J., Shanahan M. M.

Advances in Materials Science

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2010

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Vol. 10, nr 3(25)

4-16

EN

When bonded joint is subjected to mode I fracture loading, the adhesive joints analytical solutions treats the adhesive layer, usually, as not existing or 1D Hook elastic layer. In the case of 1D elastic layer, represented as Hooks spring element, is acting, only, in direction contrary to the applied load. Basing on the information yielded from sensitive laser profilometry technique, where deflections of bonded part of the joint were measured, within this contribution, 2D Finite Element Method model is introduced. The FEM allows adhesive layer to be simulated as two perpendicular-acting Hook's springs, thus in-plane shear compliance is enabled. Subsequently, appropriate analysis were carried out. Results, in terms of plate deflection, were compared with laser profilometry technique and common analytical solutions. It is concluded that linear 1D model is not sufficient for the asymmetric bonded joint configuration since the adhesive resists actively also in the in-plane shearing direction. Omitting shearing compliance effect can lead to valuable misinterpretation of the fracture energy, up to 20% in cases studied, and thus, cannot be ignored. Finally, power law based, correction factors are given promising fast and reliable data correction.

2

Crack arrest saturation model under combined electrical and mechanical loadings

Bhargava R. R., Setia A.

Journal of Achievements in Materials and Manufacturing Engineering

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2009

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Vol. 37, nr 2

544-548

EN

Purpose: The investigation aims at proposing a model for cracked piezoelectric strip which is capable to arrest the crack. Design/methodology/approach: Under the combined effect of electrical and mechanical loadings applied at the edges of the strip, the developed saturation zone is produced at each tip of the crack. To arrest further opening of the crack, the rims of the developed saturation zones are subjected to in-plane cohesive, normal uniform constant saturation point electrical displacement. The problem is solved using Fourier integral transform method which reduces the problem to the solution of Fredholm integral equation of the second kind. This integral equation in turn is solved numerically. Findings: The expressions are derived for different intensity factors and energy release rate. A qualitative analysis of the parameters affecting the arrest of opening of the crack and fatigue crack growth with respect to strip thickness and material constants are presented graphically. Research limitations/implications: The investigations are carried out by considering the material electrical brittle. Consequently, the zones protrude along the straight lines ahead of the crack tips. And further, the small scale electrical yielding conditions are used. Practical implications: Piezoelectric materials are widely getting used nowadays, even in day to day life like piezoelectric cigarette lighter, children toys etc. And, its advance used in technology like transducers, actuators has been already in progress. So, the aspect of cracking of piezoelectric materials are of great practical importance. Originality/value: The piezoelectric material under the combined effect of electrical and mechanical loadings gives the assessment of electrical displacement which is required to arrest the crack. The various useful interpretations are also drawn from the graphs.

3

Uwagi dotyczące wyznaczania odporności na rozwarstwienia struktur dwumateriałowych

Czarnocki P.

Kompozyty

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2004

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R. 4, nr 10

200-204

PL

Wyniki wielu badań wskazują, iż wartość krytyczna współczynnika uwalniania energii jest funkcją proporcji obciążeń realizujących I i II sposób rozwoju pęknięcia (SRP), często definiowanej przy pomocy kąta fazowego (1). W przypadku delaminacji na granicy warstw z tego samego materiału procedura jego wyznaczania jest prosta. W przypadku rozwarstwienia separującego warstwy z różniących się materiałów występują komplikacje, gdyż kąt fazowy staje się funkcją stałych sprężystych materiałów warstw oraz odległości r od czoła pęknięcia. Konsekwencje pominięcia tych zależności są ciągle dyskutowane. Przytaczane są argumenty przemawiające zarówno za, jak i przeciw takiemu postępowaniu. Wydaje się, iż dodatkowych argumentów w tej dyskusji mogą dostarczyć wyniki badań, rzucające światło na to, jak dalece na interpretacje wyników testów odporności na rozwarstwienie na granicy warstw z różnych materiałów wpływa przyjęcie, iż [beta]=0, rozpatrywane na tle rozrzutów wyników eksperymentalnych. W tym celu rezultaty badań odporności na delaminację laminatu węglowo-epoksydowego opracowano za pomocą dwu metod. W pierwszej z nich kąt fazowy wyznaczono, korzystając z metody pracy zaniknięcia szczeliny, wykorzystującej do wyznaczenia WUE siły i przemieszczenia węzłowe. Druga z wykorzystanych metod była modyfikacją poprzedniej, zaproponowaną przez Bjerken i Persson i bazującą na zależności podanej przez Malysheva i Salganika, wiążącej moduł zespolonego współczynnika intensywności naprężeń ze współczynnikiem uwalniania energii. Badania eksperymentalne wykonano, korzystając z metody zaproponowanej przez Reedera, a opartej na procedurze separacji składowych współczynnika uwalniania energii zaproponowanej przez Williamsa. Otrzymane wyniki (rys. 4) wskazują, iż w odniesieniu do badanego laminatu, zawierającego rozwarstwienie na granicy warstw wzmocnionych pod kątem 0° i 90°, przyjęcie uproszczenia [beta]=0, z praktycznego punktu widzenia, jest bez znaczenia, gdyż rozrzut właściwości wytrzymałościowych laminatu znacznie przekracza różnice wyników, które uproszczenie to powoduje.

EN

Results of number of experimental investigations indicate that the toughness of laminate is a function of the mode mixed ratio, often expressed by phase angle (1). In a case of interface delamination separating layers of the same materials the procedure of determining thc phase angle is simple. If delamination separates layers of different materials, the procedure is more complicated since the phase angle is a function of the material elastic constants and distance from the delamination tip (2). The possbility of neglecting this dependence has been discussed for years and rational argumeuts have been put forward both supporting and contradicting the idea. Perhaps some helpful conclusion could be drown from comparing the changes in results caused by these two approaches against the discrepancy of experimental results due to stochastic variation in strength of tested interfaces. For this purpose two methods of determining the phase angle were applied. The first was based on the virtual crack closure method proposed by Rybicki and Kanninen which allows for direct determination of GI and GII from the nodal forces and displacement obtained by FE analysis. The second was the modification of that of Rybicki's. It was recently proposed by Bjerken and Persson. This method is based on Malyshev and Salganik's expression relating the modulus of the complex stress intensity factor to strain energy release rate (3). The sought phase angle is determined form (9) equating the arguments of complex strain energy release rate and complex stress intensity factor in (5). The expression was modified such that it was possible to take advantage of the results coming from the FEM as in the case of Rybicki's method. The experimental results were obtained from testing 0/90 layer interface of the carbon fibre/epoxy laminate (Figs. 1, 2). The tests were carried out with the help of the method proposed by Reeder, based on Williams's global mode separation procedure. The results are presented in Fig. 4. It is clearly visible that the differences resulting in k from accounting for real value of [beta] and making simplifying assumption that [beta]=O become practically meaningless comparing to stochastic differences in toughness of the interface.

4

The planar crack problem for a dielectric medium in a uniform electric field

Shindo Y., Narita F.

Archives of Mechanics

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2004

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Vol. 56, nr 6

447-463

EN

The theory for dielectric materials is applied to solve the planar problem of a Griffith crack in an infinite isotropic dielectric body subjected to a far-field tension and a uniform electric field. Fourier transforms are used to reduce the mixed boundary value problem to two simultaneous dual integral equations. The integral equations are then solved exactly, and the stress intensity factor and energy release rate under Mode I and Mode II loadings are expressed in closed form.

5

Energy Release Rate Due to Propagation of Conducting Crack in Elastic Dielectric

Kurlandzka Z.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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1999

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Vol. 47, nr 1

1-14

EN

Basing on the results published in the earlier papers by the author, an extension of the Irvin criterion for the case of conducting crack, propagating in elastic dielectric influenced by strong electromagnetic field is derived. The criterion includes beside the mechanical stress intensity coefficients, which appear in the purely mechanical case, the electromagnetic stress intensity coefficients and the electric an magnetic field intensity coefficients.