Effect of hydrostatic pressure on the viscosity of failure of polymeric materials

Conclusions A setup and method were developed for studying the effect of hydrostatic pressure on the characteristics of the crack resistance of polymeric materials. The viscosity of failure of material K-4I based on butyl rubber was determined in a wide range of rates of crack propagation and hydrostatic pressures. It was found that an increase in the hydrostatic pressure increases the resistance to crack propagation in a polymeric material. The pressure-time analogy method, where the dependences of the viscosity of failure on the rate of crack growth are parallelly shifted to the value of the pressure-time shift and a generalized curve is formed, can be used for taking the effect of the pressure into consideration.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 973–977, November–December, 1986.     

Interlaminar fracture and low-velocity impact of carbon/epoxy composite materials

The interlaminar fracture and the low-velocity impact behavior of carbon/epoxy composite materials have been studied using width-tapered double cantilever beam (WTDCB), end-notched flexure (ENF), and Boeing impact specimens. The objectives of this research are to determine the essential parameters governing interlaminar fracture and damage of realistic laminated composites and to characterize a correlation between the critical strain energy release rates measured by interlaminar fracture and by low-velocity impact tests. The geometry and the lay-up sequence of specimens are designed to probe various conditions such as the skewness parameter, beam volume, and test fixture. The effect of interfacial ply orientations and crack propagation directions on interlaminar fracture toughness and the effect of ply orientations and thickness on impact behavior are examined. The critical strain energy release rate was calculated from the respective tests: in the interlaminar fracture test, the compliance method and linear beam theory are used; the residual energy calculated from the impact test and the total delamination area estimated by ultrasonic inspection are used in the low-velocity impact test. Results show that the critical strain energy release rate is affected mainly by ply orientations. The critical strain energy release rate measured by the low-velocity impact test lies between the mode I and mode II critical strain energy release rates obtained by the interlaminar fracture test. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 195–214, March–April, 2000.     

The onset of mixed-mode intralaminar cracking in a cross-ply composite laminate

The intralaminar fracture toughness of a unidirectionally reinforced glass/epoxy composite is determined experimentally at several mode I and mode II loading ratios. The crack propagation criterion, expressed as a quadratic form in terms of single-mode stress intensity factors (alternatively, linear in terms of energy release rates), approximates the test results reasonably well. The mixed-mode cracking criterion obtained is used to predict the intralaminar crack on set in a cross-ply glass/epoxy composite under off-axis tensile loading. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 785–794, November–December, 2008.     

Toughening effect of ferroelectric ceramics induced by domain switching and dislocations

The multi-scale analysis of fracture toughness of ferroelectric ceramics under complicate mechanical–electrical coupling effect is carried out in this paper. The generalized stress intensity factor (SIF) arising from spontaneous strains and polarization transformation in switching domain zones is accurately obtained by using an extended Eshelby theory. Taking BaTiO₃ ferroelectric ceramic for example, it is discovered that the crack propagation can be induced by domain switching arising from negative electrical field when the crack surface is parallel to the isotropic plane, and the obtained critical electric displacement intensity factor (EDIF) approximates closely to that obtained by the Green’s function method. Additionally, as pinning dislocations and slip dislocations can strongly influence properties of ferroelectric devices and induce the property degradation, it is necessary to investigate the dislocation toughening effects on fatigue and fracture mechanisms. The results show that the dislocation shielding and anti-shielding effects on mode II SIF, mode I SIF and EDIF are obviously different when a dislocation locates at a position near the crack tip. Through the calculation of the critical applied EDIF for crack propagation by using mechanical energy release rate (MERR) theory, it is discovered that the slip angles obviously influence fracture toughness, and the mode II SIF arising from dislocation has little influence on fracture toughness, however, the mode I SIF and EDIF arising from dislocation have great influences on fracture toughness.     

Limiting state of a multilayered nonlinearly elastic long cylindrical shell under the action of nonuniform external pressure

The buckling of a long multilayered nonlinearly elastic shell made of different materials and subject to the action of external pressure is investigated. The load is not hydrostatic and greatly varies in value and direction. Neglecting the effect of end fastening of the shell, the problem is reduced to an analysis of the loss of load-carrying ability of a ring of unit width separated from the shell. The solution is based on a variational method of mixed type formulated for heterogeneous nonlinearly elastic bodies, taking into account the geometrical nonlinearity, in a combination with the Rayleigh–Ritz method. The initial analysis is reduced to solving the Cauchy problem for a nonlinear ordinary differential equation resolved for the derivative. Numerically, using the Runge–Kutta method, the effect of the number of layers and of the parameter of nonuniformity of the external pressure on the critical buckling force is revealed. The urgency and importance of the problem are connected with the research of reserves in the saving of materials with a simultaneous possibility of increasing the load-carrying ability of a structure.     

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.     

Buckling of stepped composite columns

The stability of elastic columns subjected to axial pressure is studied. An elastic multistepped column with rectangular cross sections are considered assuming that at the re-entrant corners of the column stable cracks are located. The influence of a crack on the loss of stability of the column is described by means of local flexibility and the function of compliance coupled with the stress intensity factor, which is known from the linear elastic fracture mechanics. A column with a single step is studied in more detail. The influence of crack location and length on the buckling load is assessed numerically. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 87–100, January–February, 2006.     

Dynamics of a bridged crack in a discrete lattice

The paper addresses a problem of partial fracture of a latticeby a propagating fault modelling a crack bridged by elasticfibres. It is assumed that the strength of bonds within thelattice alternates periodically, so that during the dynamiccrack propagation only weaker bonds break, whereas the strongerbonds remain intact. The mathematical problem is reduced tothe functional equation of the Wiener–Hopf type, whichis solved analytically. The load–crack speed dependenceis presented, which also has implications on the stability analysisfor the bridged crack propagating within the lattice. In particular,we address the evaluation of the dissipation rate, which isfound to be strongly dependent on the crack speed. In this latticemodel, our results also cover the case of the supercriticalcrack speed.     

Numerical crack path prediction considering orthotropic effects and experimental verification

For a reliable prediction of crack paths, on the one hand the accurate calculation of crack tip loading quantities is inevitable, on the other hand orthotropic features of the fracture toughness need to be taken into account. The interplay of crack tip loading and material response due to fracture is still unclear and seems to have a crucial effect on crack path predictions. Numerical tools for the accurate calculation of crack tip loading quantities using path-invariant J-integrals and interaction integrals (I-integral) are presented. Here, global approaches are beneficial when considering crack tips approaching other crack faces or internal boundaries. Curved crack faces have to be taken into account and special treatment regarding crack face integrals is necessary. Experimental investigations are carried out at standard CT-specimens of rolled aluminum alloy Al-7075 exhibiting a directional orthotropy of the fracture toughness. Considering that property, the numerically predicted crack paths based on FE calculations show very good agreement with subcritically grown paths obtained from experiments. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strength and fracture properties of advanced SiC-based fibers

The tensile strength and the fracture properties of advanced SiC-based fibers were characterized, and an extensive fractographic analysis was conducted to correlate their mechanical behavior and microstructure. Tensile tests re vealed that the strength of Hi-Nicalon™ and Hi-Nicalon™ Type S fibers was sensitive to a critical flaw. The inspection of fracture surfaces revealed that the fracture of these fibers originated mainly at the critical flaw, which was surrounded by an obvious mirror zone. The Tyranno™-SA fiber showed a transcrystalline fracture behavior. The different fracture behavior observed in this work could be related to different fabrication processes and compositions at the grain boundary. For the Hi-Nicalon™ and Hi-Nicalon™ Type S fibers, the critical flaw size was linearly related to the mirror size. By using the linear fracture mechanics, the fracture toughness and the critical fracture energy of the fibers were estimated. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 759–770, November–December, 2006.     

Modelling of cracks on different scales in ferroelectric materials

In this work we study contributions to the effective fracture toughness of ferroelectric materials arising from effects on macroscopic and mesoscopic scales of the system. On the macroscopic scale, the crack in a ferroelectric material is modeled taking into account an extended theory of stresses at interfaces in dielectric solids [1-3]. We predict several new effects, such as the “poling effect”, “collinear effect” and the coupling of a Mode-II shear loading and the Mode-I SIF. Further, on the mesoscopic scale, we study the influence of polarization switching limited to the fracture process zone (small scale switching) on the fracture toughness. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.     

Initiation of Cracks in Griffith’s Theory: An Argument of Continuity in Favor of Global Minimization

The initiation of a crack in a sound body is a real issue in the setting of Griffith’s theory of brittle fracture. If one uses the concept of critical energy release rate (Griffith’s criterion), it is in general impossible to initiate a crack. On the other hand, if we replace it by a least energy principle (Francfort–Marigo’s criterion), it becomes possible to predict the onset of cracking in any circumstance. However this latter criterion can appear too strong. We propose here to reinforce its interest by an argument of continuity. Specifically, we consider the issue of the initiation of a crack at a notch whose angle ω is considered as a parameter. The result predicted by the Griffith criterion is not continuous with respect to ω, since no initiation occurs when ω>0 while a crack initiates when ω=0. In contrast, the Francfort–Marigo’s criterion delivers a response which is continuous with respect to ω, even though the onset of cracking is necessarily brutal when ω>0. The theoretical analysis is illustrated by numerical computations.     

Properties of unidirectional GFRPs based on an epoxy resin modified with polysulphone or an epoxyurethane oligomer

The mechanical properties of unidirectional GFRPs based on an ED-22 epoxy resin were investigated. The resin was modified with a PSK-1 polysulphone or a PEF-3a epoxyurethane oligomer. Triethanolaminotitanate or diaminodiphenilsulphone was used as a hardener. The modification did not improve the mechanical properties of GFRPs in quasi-static loading; but in a low-speed impact loading, the shear strength of epoxypolysulphone GFRPs with 20 wt.% PSK-1 increased by 20–25%. For all the GFRPs investigated, the shear strength grew linearly with the logarithm of loading rate. The introduction of the modifiers increased the fracture toughness considerably: by 100 and 70% for GFRPs modified with 20 wt.% PSK-1 and 50 wt.% PEF-3a, respectively. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp.739–758, November–December, 2006.     

On the influence of the distance between edges of cracks on brittle fracture

We study the influence of the shape of a hole (cavity or crack) in an elastic plane on brittle fracture. We use a modified method of solving macrocrack problems. The results obtained are generalizations of known problems. One figure. Two tables. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 26–30, 1991.     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

Fracture analysis of a high-strength concrete and a high-strength steel-fiber-reinforced concrete

This paper addresses the use of R-curves to study the fracture behavior of high-strength concrete and steel-fiber-reinforced concrete subjected to crack ing in a three-point bending configuration. The R-curves are modeled through an effective approach based on the equations of linear-elastic fracture mechanics (LEFM), which relates the applied load to the fundamental displacements of notched-through beams loaded monotonically. It is initially shown that, for quasi-brittle materials, the R-curves responses can be evaluated in a quasi-analytical way, using the load-crack mouth opening, the load-load line displacement, or exclusively the displacement responses obtained experimentally. Afterward, the methodology is used to obtain the fracture responses of high-strength and fiber-reinforced concretes, up to the final stages of rupture. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 701–710, September–October, 2007.     

Experimental study of fracture toughness and energy in composite materials

The paper presents an experimental investigation of fracture characteristics of composite materials. The post-peak response of the load-crack opening displacement of notched specimens is used to evaluate the fracture energy associated with progressive matrix damage and crack growth. Effects of fiber orientation and other geometric characteristics on fracture parameters are studied. The load versus crack opening displacement as well as crack length, fracture toughness, and energy versus the number of loading cycles are obtained for different specimens. Based on the experimental results of this study, concepts of the fracture mechanics are applied to evaluate the evolution of fracture toughness and energy.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Department of Mechanical & Industrial Engineering, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 323–332, May–June, 1998.     

Failure of particulate reinforced polymers

In this presentation, a review is given on the main effects of mineral particulate fillers (with an aspect ratio of about unity) on the deformation and fracture of amorphous and semicrystalline thermoplastic and thermosetting polymers. Elastomeric modifiers, polymer blends, and filled elastomers are not considered here. Fillers are generally used to reduce cost as well as the thermal sensitivity of mechanical properties of the matrix material and to improve, if possible, the strength and toughness. The addition of particulate fillers influences all stages of the fabrication and use of the resulting composites. We focus on the effects of a stiff second phase on elastic moduli, matrix structure, and on deformation, creep, and failure mechanisms. As the main mechanisms, particle-matrix debonding, void formation, and matrix microshear yielding are identified. Toughness is less sensitive to the quality of adhesion since particle-matrix debonding and formation of voids can be tolerated. If well controlled, debonding contributes to deformation (formation of voids should be well distributed in space and time). Reference is also made to the surprising and positive effect of CaCO₃ particles on the toughness and impact resistance of HDPE, which increases at small interparticle distances due to interfacial effects on lamellar growth in the ligament area. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 305–316, March–April, 2000.