Measurement of the Total Energy Release Rate for Cracks in PZT Under Combined Mechanical and Electrical Loading

2007 ◽  
Vol 74 (6) ◽  
pp. 1197-1211 ◽  
Author(s):  
H. Jelitto ◽  
F. Felten ◽  
M. V. Swain ◽  
H. Balke ◽  
G. A. Schneider
Keyword(s):  
Total Energy ◽  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Electric Fields ◽  
Release Rate ◽  
Total Energy Release ◽  
Custom Made ◽  
Poling Direction ◽  
Total Energy Release Rate

Four-point-bending V-notched specimens of lead zirconate titanate (PZT) poled parallel to the long axis are fractured under conditions of controlled crack growth in a custom-made device. In addition to the mechanical loading electric fields, up to 500V∕mm are applied parallel and anti-parallel to the poling direction, i.e., perpendicular to the crack surface. To determine the different contributions to the total energy release rate, the mechanical and the piezoelectric compliance, as well as the electrical capacitance of the sample, are recorded continuously using small signal modulation/demodulation techniques. This allows for the calculation of the mechanical, the piezoelectric, and the electrical part of the total energy release rate due to linear processes. The sum of these linear contributions during controlled crack growth is attributed to the intrinsic toughness of the material. The nonlinear part of the total energy release rate is mostly associated to domain switching leading to a switching zone around the crack tip. The measured force-displacement curve, together with the modulation technique, enables us to determine this mechanical nonlinear contribution to the overall toughness of PZT. The intrinsic material toughness is only slightly dependent on the applied electric field (10% effect), which can be explained by screening charges or electrical breakdown in the crack interior. The part of the toughness due to inelastic processes increases from negative to positive electric fields by up to 100%. For the corresponding nonlinear electric energy change during crack growth, only a rough estimate is performed.

An Analytical Crack-Tip Element for Layered Elastic Structures

1995 ◽  
Vol 62 (2) ◽  
pp. 294-305 ◽  
Author(s):  
B. D. Davidson ◽  
Hurang Hu ◽  
R. A. Schapery
Keyword(s):  
Total Energy ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Plate Theory ◽  
Crack Tip ◽  
Total Energy Release ◽  
Linear Elastic ◽  
Crack Tip Element ◽  
Total Energy Release Rate

A previously developed linear elastic crack-tip element analysis is reviewed briefly, and then extended and refined for practical applications. The element provides analytical expressions for total energy release rate and mode mix in terms of plate theory force and moment resultants near the crack tip. The element may be used for cracks within or between homogeneous isotropic or orthotropic layers, as well as for delamination of laminated composites. Classical plate theory is used to derive the equations for total energy release rate and mode mix; a “mode mix parameter,” Ω, as obtained from a separate continuum analysis is necessary to complete the mode mix decomposition. This parameter depends upon the elastic and geometrical properties of the materials above and below the crack plane, but not on the loading. A relatively simple finite element technique for determining the mode-mix parameter is presented and convergence in terms of mesh refinement is studied. Specific values of Ω are also presented for a large number of cases. For those interfaces where a linear elastic solution predicts an oscillatory singularity, an approach is described which allows a unique, physically meaningful value of fracture mode ratio to be defined. This approach is shown to provide predictions of crack growth between dissimilar homogeneous materials that are equivalent to those obtained from the oscillatory field solution. Application of the approach to delamination in fiber-reinforced laminated composites is also discussed.

scholarly journals Mixed Mode Partition in one Dimensional Fractures

2011 ◽  
Vol 462-463 ◽  
pp. 616-621 ◽  
Author(s):  
Simon Wang ◽  
Christ Harvey
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Energy Flow ◽  
Coefficient Matrix ◽  
Total Energy Release ◽  
One Dimensional ◽  
Axial Forces ◽  
Unique Pair ◽  
Total Energy Release Rate

Taking a double cantilever beam (DCB) as a representative of one dimensional fracture, a unique pair of pure fracture modes I and II are successfully found in the absence of axial forces, which are orthogonal to each other with respect to the coefficient matrix of the energy release rate. Although the pair are pure modes there still exist interactions between them. The interactions result in energy flow between the two modes and are successfully determined. With the presence of axial forces, there are two independent pure modes I and two independent pure modes II, which are orthogonal to each other as well. They are found and used to partition the total energy release rate.

Fatigue crack propagation in short-fiber reinforced plastics

2015 ◽  
Author(s):  
K. Tanaka ◽  
K. Oharada ◽  
D. Yamada ◽  
K. Shimizu
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Propagation Rate ◽  
Propagation Rate ◽  
Short Fiber ◽  
Total Energy Release ◽  
R Ratio ◽  
Total Energy Release Rate

The influence of fiber orientation on the crack propagation behavior was studied with single edgenotched specimens which were cut from an injection-molded plate of short-fiber reinforced plastics of polyphenylenesulphide (PPS) reinforced with 30wt% carbon fibers. Specimens were cut at five fiber angles relative to the molding direction, i.e. ??= 0° (MD), 22.5°, 45°, 67.5°, 90° (TD). Fracture mechanics parameters derived based on anisotropic elasticity were used as a crack driving force. Macroscopic crack propagation path was nearly perpendicular to the loading axis for the cases of MD and TD. For the other fiber angles, the crack path was inclined because the crack tended to propagate along inclined fibers. For mode I crack propagation in MD and TD, the resistance to crack propagation is improved by fiber reinforcement, when the rate is correlated to the range of stress intensity factor. The crack propagation rate, da/dN, was slowest for MD and fastest for TD. For each material, the crack propagation rate is higher for larger R ratio. The effect of R ratio on da/dN diminished in the relation between da/dN and the range of energy release rate, ?GI. Difference among MD, TD and matrix resin becomes small when da/dN correlated to a parameter corresponding the crack-tip radius, H?GI, where H is compliance parameter. Fatigue cracks propagated under mixed loading of mode I and II for the fiber angles other than 0° and 90°. The data of the crack propagation rate correlated to the range of total energy release rate, ?Gtotal, lie between the relations obtained for MD and TD. All data of crack propagation tend to merge a single relation when the rate is correlated to the range of total energy release rate divided by Young’s modulus.

On Crack Growth in Composite Cylindrical Shells

1999 ◽  
Author(s):  
Hayder A. Rasheed ◽  
John L. Tassoulas
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Cylindrical Shells ◽  
Applied Pressure ◽  
Fluid Pressure ◽  
Laminated Composite ◽  
Stable Crack Growth ◽  
Composite Cylindrical Shells

Abstract Interfacial defects, in the form of cracks or layer separation, may occur in composite cylindrical shells during the manufacturing process, transportation or service life. Such defects are expected to affect the integrity of laminated composite structural elements and may reduce their capacity to resist the applied loads. In this article, the growth of pre-existing cracks in moderately thick composite cylinders is studied for the case of externally applied fluid pressure. The cracks considered separate thick layers, which are unlikely to buckle locally prior to the final collapse of the structural component. The potential of growth is assessed by computing the energy release rate. It is found that any initial out-of roundness imperfection introduces a shear force at the crack tip by causing the cross section to ovalize slightly. The energy release rate is found to vary exponentially with the applied pressure, when geometric nonlinearities are considered. The analysis is applied to a carbon/glass-fiber hybrid composite tube and the parameters influencing growth are examined. Crack length, through the thickness location, circumferential location relative to the ovalization orientation and the amount of imperfection are found to control the nature of growth. Unstable as well as stable crack growth and arrest cases are observed for various combinations of these parameters.

On Global Energy Release Rate of a Permeable Crack in a Piezoelectric Ceramic

2003 ◽  
Vol 70 (2) ◽  
pp. 246-252 ◽  
Author(s):  
S. Li
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Piezoelectric Ceramic ◽  
Piezoelectric Materials ◽  
Dielectric Medium ◽  
Crack Model ◽  
Permeable Crack ◽  
Global Energy

A permeable crack model is proposed to analyze crack growth in a piezoelectric ceramic. In this model, a permeable crack is modeled as a vanishing thin, finite dimension, rectangular slit with dielectric medium inside. A first-order approximation solution is derived in terms of the slit height, h0. The main contribution of this paper is that the newly proposed permeable crack model reveals that there exists a realistic leaky mode for electrical field, which allows applied electric field passing through the dielectric medium inside a crack. By taking into account the leaky mode effect, a correct estimation of electrical and mechanical fields in front of a crack tip in a piezoelectric ceramic is obtained. To demonstrate this new finding, a closed-form solution is obtained for a mode III permeable crack under both mechanical as well electrical loads. Both local and global energy release rates are calculated based on the permeable crack solution obtained. It is found that the global energy release rate derived for a permeable crack is in a broad agreement with some known experimental observations. It may be served as a fracture criterion for piezoelectric materials. This contribution reconciles the outstanding discrepancy between experimental observation and theoretical analysis on crack growth problem in piezoelectric materials.

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