Crack propagation at material interfaces: I. Experimental technique to determine crack profiles

The analysis of the strength of adhesively bonded joints depends to a large degree on concepts of linear fracture mechanics. This discipline rests on appropriate fracture criteria and their evaluation in terms of the linearized theory of (visco) elasticity. We document here the technique and the instrumentation that allows close experimental scrutiny of the linearity assumption as well as an exploration of criteria for interfacial unbonding.     

Crack propagation under mode II dominance at stainless steel–epoxy interfaces with residual stresses and micro-scale roughness

This report describes investigations of grain boundary groove effects on mode II dominated interface fracture. The study focused on a specific interface between stainless steel and an epoxy adhesive. First, a finite element model was developed to simulate residual stresses and crack propagation. Second, the simulation results were compared with the experimental results from a previous study (Kanerva et al., 2013. Eng. Fract. Mech. 99, 147-158). Additional measurements were performed using atomic force microscopy. Based on the simulation, a 100-fold toughening effect due to the grain boundaries was determined. Implementation of flaws, in the form of interfacial voids, decreased the toughening effect by 35% and increased the mode II dominance significantly. The work underlines the practical importance of complete wetting by the adhesive and its necessary adherence to the grain boundary groove walls.     

Theoretical investigation of an elliptical crack in thermopiezoelectric material. Part II: Crack propagation

Propagation behavior of an elliptical crack in thermopiezoelectric material subjected to a uniform temperature is investigated in this paper. The three-dimensional strain energy density formulation is used to determine the direction of crack propagation and the shape of the initial fracture increment. It is found that the elliptical crack grows coplanarly under this particular load case but not normal to the crack front. The elliptical crack tends to become a circular one when thermal loading is applied.     

Crack propagation in the power-law nonlinear viscoelastic material

I.IntroductionCrazingdamageisacommonphenon1enonoffractureofpolymericmaterials.Theformationofcrazezoneisamid-stateinthefractureprocessofthematerialsfromperfectstatetofaiIurc.Microscopically,inthisregionthereexistssomefibrilslinkingthetwocracksurfacesandres…     

Coupling between flow and diffusion at polymer/polymer interfaces: large amplitude oscillatory shear experiments

 Coupling between flow and diffusion at symmetric polymer/polymer interfaces has been investigated. Polystyrene/polystyrene sandwich assemblies were subjected to large-amplitude oscillatory shear (LAOS) using a sliding-plate rheometer (SPR) and the stress was monitored as a function of time. The results were treated using a new model combining Wagner's model with the theory of Doi and Edwards. The model explicitly expresses the influence of the strain and stress amplitudes frequency and time on the self-diffusion process. The apparent self-diffusion coefficient was found to increase with welding time, in agreement with our previous results obtained using small-amplitude oscillatory shear measurements. However, it was found in the present case that the self-diffusion coefficient depends strongly on the strain and stress amplitudes and frequency, and its steady state value was found to be larger than that determined from small-amplitude oscillatory shear measurements. It appears that the large strain oscillatory shear field continuously increases the density of chain ends at the interface and thus increases the flux of mass transport. Received: 30 January 2001 Accepted: 12 June 2001     

Intersonic crack propagation along interfaces: Experimental observations and analysis

The isochromatic fringe patterns surrounding an intersonically propagating interface crack are developed and characterized using the recently developed stress field equations. A parametric investigation is conducted to study the influence of various parameters such as the crack-tip velocity and the contact coefficient on the isochromatic fringe patterns. It has been observed that the crack-tip velocity has a significant effect on the size and shape of isochromatic fringe patterns. The contact coefficient, on the other hand, does not affect the fringe pattern significantly. The paper also presents a numerical scheme to extract various parameters of interest such as the series coefficients of the stress field, the contact coefficient and the dissipation energy. The results show that the crack growth is highly unstable in the intersonic regime, and the energy dissipation decreases monotonically with increasing crack-tip velocity. The experimental data fit well with the recently proposed fracture criterion for intersonic interfacial fracture.     

Subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone

A recent experimental study has demonstrated the attainability of intersonic shear crack growth along weak planes in otherwise homogeneous, isotropic, linear elastic solids subjected to remote loading conditions (Rosakis et al., Science 284 (5418) (1999) 1337). The relevant experimental observations are summarized briefly here and the conditions governing the attainment of intersonic crack speeds are examined. Motivated by experimental observations, subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone is subsequently analyzed. A cohesive law is assumed, wherein the cohesive shear traction is either a constant or varies linearly with the local sliding rate. Complete decohesion is assumed to occur when the crack tip sliding displacement reaches a material-specific critical value. Closed form expressions are obtained for the near-tip fields. With a cohesive zone of finite size, it is found that the dynamic energy release rate is finite through out the intersonic regime. Crack tip stability issues are addressed and favorable speed regimes are identified. The influence of shear strength of the crack plane and of a rate parameter on crack propagation behavior is also investigated. The isochromatic fringe patterns predicted by the analytical solution are compared with the experimental observations of Rosakis et al. (1999) and comments are made on the validity of the proposed model.     

Effects of characteristic material lengths on mode III crack propagation in couple stress elastic–plastic materials

The asymptotic fields near the tip of a crack steadily propagating in a ductile material under Mode III loading conditions are investigated by adopting an incremental version of the indeterminate theory of couple stress plasticity displaying linear and isotropic strain hardening. The adopted constitutive model is able to account for the microstructure of the material by incorporating two distinct material characteristic lengths. It can also capture the strong size effects arising at small scales, which results from the underlying microstructures. According to the asymptotic crack tip fields for a stationary crack provided by the indeterminate theory of couple stress elasticity, the effects of microstructure mainly consist in a switch in the sign of tractions and displacement and in a substantial increase in the singularity of tractions ahead of the crack-tip, with respect to the classical solution of LEFM and EPFM. The increase in the stress singularity also occurs for small values of the strain hardening coefficient and is essentially due to the skew-symmetric stress field, since the symmetric stress field turns out to be non-singular. Moreover, the obtained results show that the ratio η introduced by Koiter has a limited effect on the strength of the stress singularity. However, it displays a strong influence on the angular distribution of the asymptotic crack tip fields.     

Crack size and speed interaction characteristics at micro-, meso- and macro-scale

The motivation to examine physical events at even smaller size scale arises from the development of use-specific materials where information transfer from one micro- or macro-element to another could be pre-assigned. There is the growing belief that the cumulated macroscopic experiences could be related to those at the lower size scales. Otherwise, there serves little purpose to examine material behavior at the different scale levels. Size scale, however, is intimately associated with time, not to mention temperature. As the size and time scales are shifted, different physical events may be identified. Dislocations with the movements of atoms, shear and rotation of clusters of molecules with inhomogeneity of polycrystals; and yielding/fracture with bulk properties of continuum specimens. Piecemeal results at the different scale levels are vulnerable to the possibility that they may be incompatible. The attention should therefore be focused on a single formulation that has the characteristics of multiscaling in size and time. The fact that the task may be overwhelmingly difficult cannot be used as an excuse for ignoring the fundamental aspects of the problem.Local nonlinearity is smeared into a small zone ahead of the crack. A “restrain stress” is introduced to also account for cracking at the meso-scale.The major emphasis is placed on developing a model that could exhibit the evolution characteristics of change in cracking behavior due to size and speed. Material inhomogeneity is assumed to favor self-similar crack growth although this may not always be the case. For relatively high restrain stress, the possible nucleation of micro-, meso- and macro-crack can be distinguished near the crack tip region. This distinction quickly disappears after a small distance after which scaling is no longer possible. This character prevails for Mode I and II cracking at different speeds. Special efforts are made to confine discussions within the framework of assumed conditions. To be kept in mind are the words of Isaac Newton in the Fourth Regula Philosophandi:

“Men are often led into error by the love of simplicity which disposes us to reduce things to few principles, and to conceive a greater simplicity in nature than there really is … We may learn something of the way in which nature operates from fact and observation; but if we conclude that it operates in such a manner, only because to our understanding that operates to be the best and simplest manner, we shall always go wrong.”––Isaac Newton

Crack front shape effects on propagation stability in thermosetting polyesters

Fracture mechanics testing of the resistance of a polymer to slow crack growth often reveal it to be a unique function of crack speed. However, several thermosetting polyesters, tested using the Double Torsion (DT) and Tapered Double Cantilever Beam (TDCB) techniques, seem unable to sustain stable propagation over particular, isolated ranges of crack velocity with specimen-dependent limits. The meaning of ‘propagation stability’ in this context is discussed, distinguished from the static stability concept normally used, and applied using Liapunov criteria. The corresponding hypothesis that isolated unstable regimes symptomise locally-falling sectors of the resistance versus crack speed crack speed characteristic is supported by an observed crack shape influence, due to which DT tests are inherently more stable than TDCB ones.     

Analyzing the propagation of a plane wave in a microcomposite material taking inertial interaction into account

The influence of inertial interaction on the coefficient describing the redistribution of the amplitude of a plane wave is analyzed. Two new wave effects in fibrous microcomposites are revealed: abrupt change in the amplitude of the first mode in the matrix and the absence of the second mode in fibers in some frequency range Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 94–98, November 2008.     

Asymmetrical dynamic propagation problems on mode Ⅲ interface crack

By the application of the theory of complex functions, asymmetrical dynamic propagation problems on mode Ⅲ interface crack are studied. The universal representations of analytical solutions are obtained by the approaches of serf-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.     

Asymmetrical dynamic propagation problems on mode III interface crack

By the application of the theory of complex functions, asymmetrical dynamic propagation problems on modeⅢinterface crack are studied. The universal representations of analytical solutions are obtained by the approaches of self-similar function. The problems researched can be facilely transformed into Riemann-Hilbert problems and analytical solution to an asymmetrical propagation crack under the condition of point loads and unit-step loads, respectively, is acquired. After those solutions were used by superposition theorem, the solutions of arbitrarily complex problems could be attained.     

Crack propagation in concrete: Linear elastic fracture mechanics and boundary element method

Crack propagation in concrete is investigated by application of Linear Elastic Fracture Mechanics (LEFM) and the Boundary Element Method (BEM). Acoustic Emission (AE) measurement is made for detecting the load level at which unstable crack initiation occurs in a notched beam under bending. The corresponding critical stress intensity factor K_Ic does not vary appreciably with notch depth. This result is in contrast to that found by the conventional procedure.The critical stress intensity factor K_Ic is employed to analyze the process of crack propagation in an arbitraty direction. The BEM prediction is in good agreement with the experiments.The detection and assessment of crack initiation in concrete structures is of considerable technical interest.     

System-size effect on the friction at liquid-solid interfaces

The friction at the liquid-solid interfaces is widely involved in various phenomena ranging from nanometer to micrometer scales. By the molecular dynamic(MD)simulation, the friction properties of liquid-solid interfaces at the molecular level are calculated via the Green-Kubo relation. It is found that the system size will influence the value of the friction coefficient, especially for the solid surfaces with the larger polar charge. The value of the friction coefficient decreases with the incre...     

Wave propagation in an unconsolidated granular material: A micro-mechanical approach

We provide a theoretical analysis to support the presence of both slow and fast compression waves in an unconsolidated, fully saturated, granular material. We derive the constitutive relation for such an aggregate based upon a micro-mechanics analysis. In doing this, we take in account the coupling between the solid particles and fluid. As a consequence of this coupling, the lubrication layer provides a connection between particles, both when they are separating and when they are compressing. The predictions of the speed and attenuation of the fast compression waves compare well with experimental data over the range of frequencies for which the nonlinear dissipation associated with the relative velocities between solid and fluid is negligible. Slow waves are also predicted without comparison, because of the absence of clear experimental data. Predictions of the speed and attenuation for the shear wave are also provided and show a good agreement with experimental data when surface roughness is taken into account.     

Logarithm strain singularity at tip of mode I growing crack in elasticand perfectly-plastic material

Reanalyzed in detail is the stress and strain distribution near the tip of a Mode I steadily growing crack in an elastic and perfectly-plastic material. The crack tip region is divided into five angular sectors, one of which is singular in character and represents a rapid transition zone that becomes a line of strain discontinuity in the limit as crack tip is approached. It is shown for an incompressible material (ν=0.5) under plane strain that the local strain in all the angular sectors possesses the same logarithm singularity, i.e., In r where r is the radial distance measured from the crack tip. This result also prevails for the compressible material ( v < 0.5) and resolves a long standing controversy concerning the strain singularity in the sector just ahead of the crack tip.     

Growth of a mode II crack in an orthotropic plate made of a viscoelastic composite material

The growth of a straight mode II crack in a viscoelastic orthotropic plate is examined. The plate material is modeled by a viscoelastic anisotropic medium. The shear displacement in the fracture process zone is determined as a function of time using the corresponding elastic solution, the Volterra principle, and the method of operator continued functions. The time dependence of the crack length is constructed as integral equations of three phases of stable growth. The solution of these equations gives kinetic curves __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 89–97, September 2006.