Planar Crack Propagation Research Articles

Role of the sample thickness in planar crack propagation

We study the effect of the sample thickness in planar crack front propagation in a disordered elastic medium using the random fuse model. We employ different loading conditions and we test their stability with respect to crack growth. We show that the thickness induces characteristic lengths in the stress enhancement factor in front of the crack and in the stress transfer function parallel to the crack. This is reflected by a thickness-dependent crossover scale in the crack front morphology that goes from from multiscaling to self-affine with exponents, in agreement with line depinning models and experiments. Finally, we compute the distribution of crack avalanches, which is shown to depend on the thickness and the loading mode.

Flaw Nucleation In A Brittle Open-Cell Kelvin Foam

Open-cell Kelvin foam is considered as a spatial lattice consisting of brittle elastic struts rigidly connected to each other at the nodal points. The lattice is subjected to remote uniaxial tensile loading, an initial imperfection is introduced and sequential break of the struts is observed. Different loading directions and material densities are examined and it is found that the broken struts form a plane flaw, which may be either a bridged or a usual crack. The possible crack propagation planes to be used in the fracture toughness analysis are determined.

Intralaminar and interlaminar fracture characterization in glued-laminated timber members using image analysis

This paper is concerned with the characterization of Mode I and Mode II fracture present in glued-laminated (glulam) timber members. In a typical glulam timber member, fracture can occur within each lamina (i.e., intralaminar fracture) or at the interface of two laminae (i.e., interlaminar fracture). Both the intralaminar and interlaminar fracture was investigated through an experimental study, where the double cantilever beam test for Mode I fracture and the end-notched flexure test for Mode II fracture were performed to a series of specimens. A salient feature of the intralaminar fracture in glulam timber members lies in the direction normal to the crack propagation plane. It is often the case that this direction neither coincides with the radial direction nor the tangential direction of the wood. Consequently for each intralaminar specimen tested, an image analysis was carried out to identify the relevant growth ring orientations, which were in turn represented by an angle. Analogous procedures were also utilized to associate three angles indicating growth ring orientations to each interlaminar specimen. After the specimen failure, crack tip morphology was analyzed by scanning electron microscopy micrographs. The critical loads used in the computation of the fracture energies were identified from the recorded load-versus-displacement curves. Further, statistical analyses were implemented to examine the obtained intralaminar Mode I and Mode II fracture energies with regard to different growth ring orientations.

Impacts of Thermal Annealing on Hydrogen-Implanted Germanium and Germanium-on-Insulator Substrates

Smart-cut and wafer bonding technology has been widely used in the germanium-on-insulator (GOI) fabrication. In this study, the damages formed in hydrogen implanted Ge, the surface blistering, and the GOI post-annealing processes were thoroughly investigated. The blistering of the hydrogen implanted Ge was carried out and compared with various thermal annealing temperatures ranging from 350 to 500°C. For the annealing temperature lower than 500°C, the Ge surface layer was found fully exfoliated with planar crack propagation. But at higher temperatures, discrete blisters were observed because of the very fast diffusion of the implanted hydrogen. Various post-annealing treatments, including annealing in vacuum or in N2 atmosphere were performed on the as-prepared GOI substrates. It was found that post-annealing in vacuum at 500°C improves the crystal quality of the GOI most effectively. As shown by X-ray diffraction (XRD) measurement, the full width at half maximum (FWHM) of the Ge peak was about 72.6 arc sec and almost all the residual stress was released.

Strategies for planar crack propagation based on the concept of material forces

This paper presents a computational framework for the simulation of planar crack growth (including kinking) driven by "material forces". An evolution law for the crack tip position is formulated, which is shown to give rise to different propagation strategies when subjected to certain assumptions on regularity. Three such strategies, that previously have been proposed in the literature in principle: Explicit Proportional Extension (EPE), Implicit Proportional Extension (IPE) and Maximum Parallel Release Rate (MPRR), are outlined and assessed. Based on the results of two numerical examples, it is concluded that the presented propagation strategies produce almost identical results and are robust with respect to time discretization.

In-situ observations of the effects of orientation and carbide on low cycle fatigue crack propagation in a single crystal superalloy

Based on in situ observations with scanning electron microscopy (SEM), we investigated the low cycle fatigue (LCF) propagation behaviors of a Ta-rich single crystal nickel-based superalloy at 550oC in vacuum. Specimens in three different orientations, i.e. [010], [011] and [111], were tested in stress-controlled tension-tension LCF tests with R=0.1. Slip traces can be observed ahead of the crack and distinct crystallographic fracture was dominated. By analysis on the surface slip traces and the crack propagation planes, the operated slip systems were examined to be octahedral slip and the active octahedral plane was identified in this context. The whole cracking process of small fatigue cracks were meticulously tracked and recorded. The evaluation of short crack growth rate for specimens in three orientations was carried out by fracture mechanics approach. The influence of crystallographic orientations on fatigue crack growth are analyzed and discussed. Especially, the interaction between the short crack and local microstructure such as the carbides ahead of the crack were analyzed, altering the propagation path as well as influencing the crack growth rate. The parameter of crack opening displacement was examined to correlate well the crack growth data in different orientations.

Helical crack-front instability in mixed-mode fracture

Planar crack propagation under pure tension loading (mode I) is generally stable. However, it becomes universally unstable with the superposition of a shear stress parallel to the crack front (mode III). Under this mixed-mode (I + III) loading configuration, an initially flat parent crack segments into an array of daughter cracks that rotate towards a direction of maximum tensile stress. This segmentation produces stepped fracture surfaces with characteristic 'lance-shaped' markings observed in a wide range of engineering and geological materials. The origin of this instability remains poorly understood and a theory with which to predict the surface roughness scale is lacking. Here we perform large-scale simulations of mixed-mode I + III brittle fracture using a continuum phase-field method that describes the complete three-dimensional crack-front evolution. The simulations reveal that planar crack propagation is linearly unstable against helical deformations of the crack front, which evolve nonlinearly into a segmented array of finger-shaped daughter cracks. Furthermore, during their evolution, facets gradually coarsen owing to the growth competition of daughter cracks in striking analogy with the coarsening of finger patterns observed in nonequilibrium growth phenomena. We show that the dynamically preferred unstable wavelength is governed by the balance of the destabilizing effect of far-field stresses and the stabilizing effect of cohesive forces on the process zone scale, and we derive a theoretical estimate for this scale using a new propagation law for curved cracks in three dimensions. The rotation angles of coarsened facets are also compared to theoretical predictions and available experimental data.

Cracking sheets: Oscillatory fracture paths in thin elastic sheets

When a blunt cutting tool is forced through a thin elastic sheet that is held along its lateral boundaries, a strikingly regular wavy cut can be left behind, examples of which are presented in Fig. 1. The thin film is brittle, hence it undergoes negligible irreversible deformation besides fracture. For tools much wider than the film’s thickness, the crack tip follows a highly reproducible nonsinusoidal oscillatory path. Each single period of this path consists of two smooth curves separated by a kink, at which there is a sharp change in the direction of curvature. Propagation is primarily quasistatic, at a speed comparable to that of the cutting tool but is interrupted by periodic bursts of dynamic propagation immediately after each kink. By decreasing either the size of the cutting tool down to widths comparable to the film thickness or the tool’s speed, the crack path eventually becomes straight. These oscillatory patterns are strikingly robust and even doing the experiment by hand yields surprisingly regular patterns. In Ref. 4 we have shown that the coupling of classical theories for elastic plates and for crack propagation can be reduced to a simple set of geometrical rules which explain this experimentally observed oscillatory crack behavior in thin brittle films. This was done by following a common approach in fracture theory: calculating the elastic energy of the system while taking into account the possible large outof-plane deformations of the film induced by the cutting tool. Griffith’s criterion for crack propagation was then applied. The principal ingredient of our 2D construction is therefore the coupling between crack propagation and large out-of plane deformations in the film. Geometry is, in general, known to play an important role in the theory of elastic rods, plates, and shells but, in the tearing of thin films, geometrical considerations acquire an unprecedented level of importance. This is a compelling example where a complex crack motion is entirely ruled by geometry.

Mechanical properties of single crystalline and glassy lithium triborate

AbstractMechanical properties of LiB3O5 single crystal plates with different orientation as well as of glass with the same composition have been investigated. The nano‐ (H) and microhardness (HM), the reduced Young's modulus (Er) and the crack behaviour of the samples were studied. Both hardness and Young's modulus of glass appeared smaller in comparison to corresponding single crystal data (H ∼ 7 – 8 GPa, HM ∼ 6 GPa, Er ∼ 70 – 80 GPa for glass and H ∼ 10 – 15 GPa, HM ∼ 6 –11 GPa, Er ∼ 93 – 155 GPa for single crystal). H, Er, and the plane of crack propagation proved orientation‐dependent. Cracks in the glass sample were not observed up to 0.49 N microindentation load, whereas for the single crystal the cracks appeared already at 0.098N. In single crystals the observed cleavage planes {211} and/or {412} are oriented nearly parallel to planes of B‐O rings. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental investigation on the propagation of fatigue cracks emanating from sharp notches

The effect of notch geometry on the propa- gation of fatigue cracks emanating from sharp V-shaped notches is investigated by means of an exper- imental campaign performed on Al-7075-T651 spec- imens carrying notches with opening angles of 45°, 90°, and 135°. The samples were tested using a servo- hydraulic machine under different loading directions and at several loading levels. The crack deflection in- duced by the variation in loading direction was deter- mined my measuring the kinking angle and by study- ing the crack propagation plane through fractographic analysis. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors were calculated using an ap- propriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. The in- fluence of KII on the crack propagation was discussed on the basis of theoretical and semi empirical models.

Quasi‐static crack propagation in plane and plate structures using set‐valued traction‐separation laws

AbstractWe introduce a numerical technique to model set‐valued traction‐separation laws in plate bending and also plane crack propagation problems. By using of recent developments in thin (Kirchhoff–Love) shell models and the extended finite element method, a complete and accurate algorithm for the cohesive law is presented and is used to determine the crack path. The cohesive law includes softening and unloading to origin, adhesion and contact. Pure debonding and contact are obtained as particular (degenerate) cases. A smooth root‐finding algorithm (based on the trust‐region method) is adopted. A step‐driven algorithm is described with a smoothed law which can be made arbitrarily close to the exact non‐smooth law. In the examples shown the results were found to be step‐size insensitive and accurate. In addition, the method provides the crack advance law, extracted from the cohesive law and the absence of stress singularity at the tip. Copyright © 2007 John Wiley & Sons, Ltd.

Mode-3 spontaneous crack propagation along functionally graded bimaterial interfaces

The effects of combining functionally graded materials (FGMs) of different inhomogeneous property gradients on the mode-3 propagation characteristics of an interfacial crack are numerically investigated. Spontaneous interfacial crack propagation simulations were performed using the newly developed spectral scheme. The numerical scheme derived and implemented in the present work can efficiently simulate planar crack propagation along functionally graded bimaterial interfaces. The material property inhomogeneity was assumed to be in the direction normal to the interface. Various bimaterial combinations were simulated by varying the material property inhomogeneity length scale. Our parametric study showed that the inclusion of a softening type FGM in the bimaterial system leads to a reduction in the fracture resistance indicated by the increase in crack propagation velocity and power absorbed. An opposite trend of increased fracture resistance was predicted when a hardening material was included in the bimaterial system. The cohesive tractions and crack opening displacements were altered due to the material property inhomogeneity, but the stresses ahead of the cohesive zone remained unaffected.

Mode-3 spontaneous crack propagation in symmetric functionally graded materials

The effects of spatially varying the material properties on the mode-3 planar crack propagation characteristics are numerically investigated. The spectral scheme that is available for homogeneous materials is modified to account for the symmetrically varying material properties. Crack propagation in hardening, softening and unsymmetric type of functionally graded have been simulated. A parametric study was performed by systematically varying the material inhomogeneity length scale. Our study indicated that softening and unsymmetric graded materials reduce the resistance to fracture, while a hardening material offers higher fracture resistance with increase in inhomogeneity. Only the transient phase of crack propagation speed was affected by the material property variation, irrespective of whether the material was hardening, softening or an unsymmetric type. The crack always reached a quasi-steady-state velocity, which remained unaffected by the material property inhomogeneity.

Cohesive zone modelling of wafer bonding and fracture: effect of patterning and toughness variations

Direct wafer bonding has increasingly become popular in the manufacture of microelectromechanical systems and semiconductor microelectronics components. The success of the bonding process is controlled by variables such as wafer flatness and surface preparation. In order to understand the effects of these variables, spontaneous planar crack propagation simulations were performed using the spectral scheme in conjunction with a cohesive zone model. The fracture-toughness on the bond interface is varied to simulate the effect of surface roughness (nanotopography) and patterning. Our analysis indicated that the energetics of crack propagation is sensitive to the local surface property variations. The patterned wafers are tougher (well bonded) than the unpatterned ones of the same average fracture-toughness.

PRIZE FOR BEST PAPER VOLUME 27

Fatigue & Fracture of Engineering Materials & StructuresVolume 28, Issue 6 p. 575-575 Free Access PRIZE FOR BEST PAPER VOLUME 27 First published: 05 May 2005 https://doi.org/10.1111/j.1460-2695.2005.00911.x Announcement in the International Journal: Fatigue and Fracture of Engineering Materials and Structures AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract has been awarded to Fatigue crack propagation in cast duplex stainless steels: thermal aging and microstructural effects V. Calonne, A. F. Gourges and A. Pineau Fatigue Fract. Engng. Mater. Struct. , 27 (1), pp . 31-44 Abstract The ferrite phase of cast duplex stainless steels becomes embrittled after thermal ageing, leading to a significant decrease in fracture properties. In the present paper, the influence of ageing and solidification structure on the fatigue crack growth rates (FCGRs) and on the fatigue crack growth mechanisms in a cast duplex stainless steel is studied. FCGRs measured at room temperature increase slightly after ageing at 400 °C, due to ferrite cleavage and to the resulting irregular shape of the crack front. The crack propagates without any preferential path by successive ruptures of ferrite and austenite phases. The macroscopic crack propagation plane depends on the crystallographic orientation of the ferrite grain. Secondary cracks can appear due to the complex solidification structure. This in turn influences the FCGR. The fatigue crack closure level decreases with increasing ageing. This can be explained by a decrease in the kinematic cyclic hardening of these materials. Volume28, Issue6June 2005Pages 575-575 RelatedInformation

On ductile fracture initiation toughness: Effects of void volume fraction, void shape and void distribution

This paper studies the effects of the initial relative void spacing, void pattern, void shape and void volume fraction on ductile fracture toughness using three-dimensional, small scale yielding models, where voids are assumed to pre-exist in the material and are explicitly modeled using refined finite elements. Results of this study can be used to explain the observed fracture toughness anisotropy in industrial alloys. Our analyses suggest that simplified models containing a single row of voids ahead of the crack tip is sufficient when the initial void volume fraction remains small. When the initial void volume fraction becomes large, these simplified models can predict the fracture initiation toughness ( J Ic) with adequate accuracy but cannot predict the correct J– R curve because they over-predict the interaction among growing voids on the plane of crack propagation. Consequently, finite element models containing multiple rows of voids should be used when the material has large initial void volume fraction.

Fatigue crack propagation in cast duplex stainless steels: thermal ageing and microstructural effects

ABSTRACTThe ferrite phase of cast duplex stainless steels becomes embrittled after thermal ageing, leading to a significant decrease in fracture properties. In the present paper, the influence of ageing and solidification structure on the fatigue crack growth rates (FCGRs) and on the fatigue crack growth mechanisms in a cast duplex stainless steel is studied. FCGRs measured at room temperature increase slightly after ageing at 400 °C, due to ferrite cleavage and to the resulting irregular shape of the crack front. The crack propagates without any preferential path by successive ruptures of ferrite and austenite phases. The macroscopic crack propagation plane depends on the crystallographic orientation of the ferrite grain. Secondary cracks can appear due to the complex solidification structure. This in turn influences the FCGR. The fatigue crack closure level decreases with increasing ageing. This can be explained by a decrease in the kinematic cyclic hardening of these materials.

Fracture toughness of human dentin.

The purpose of this study was to determine the fracture toughness (K(IC)) of human dentin and to test the null hypothesis that K(IC) is not affected by the orientation of dentinal tubules relative to the plane of crack propagation. Triangular prisms (4 x 4 x 4 x 8 mm) were obtained from human molars and tested using the notchless triangular prism (NTP) specimen K(IC) test. Dentin prisms were prepared so that the plane of crack propagation would have three different orientations relative to the orientation of dentinal tubules: perpendicular (PE), parallel aligned (PAA), and parallel transverse (PAT). The prepared specimens were secured in the specimen holder and loaded in tension until fracture or crack arrest. The maximum load recorded was used to calculate K(IC). There was no significant difference between the K(IC) of PAA specimens (1.97 +/- 0.17 MPa/m(1/2)) and PAT (2.02 +/- 0.18 MPa/m(1/2)). The K(IC) for the PE specimens (1.13 +/- 0.36 MPa/m(1/2)) was significantly lower. The SEM images of the fractured surfaces showed distinct differences that were correlated with the determined K(IC) values. The fractured surfaces of PAA and PAT specimens were rougher compared to PE specimens. Both the hyper mineralized peritubular dentin and the orientation of collagen fibrils surrounding the tubules could be responsible for the significant differences in K(IC). The results of this study identified a significant anisotropy of dentin with respect to its K(IC).

Effects of surface roughness and notch on fatigue properties for Ti–5Al–2.5Sn ELI alloy at cryogenic temperatures

To evaluate material risk caused by human-error, the effects of surface roughness and notch on the fatigue properties of Ti–5Al–2.5Sn ELI alloy have been investigated at cryogenic temperatures. Specimens with surface roughness changed by emery papers (Grade #600, #100) and notched specimens were prepared (Kt = 1.5; 3). The S–N curves shifted to higher stress level with a decrease of the test temperature.Regarding the effect of surface roughness, the fatigue strength of the #100-roughness specimens was a little lower than those of the #600-roughness specimens. Fatigue crack initiation sites of each surface roughness specimen at 4 K were found in the specimen interior (internal type fracture). On the other hand, the fatigue strength of the notched specimens was substantially lower than those of the surface roughness specimens. Although fatigue crack initiation sites of the Kt = 3 notched specimen were at the notch root (surface type fracture), those of the Kt = 1.5 notched specimen were in the specimen interior. The location of the fatigue crack initiation sites changed from the internal type fracture for Kt = 1.5 notched specimens to the surface type fracture for Kt = 3 notched specimens. Therefore, the Kt values of the internal fatigue crack initiation sites correspond between 1.5 and 3. The root area analysis, which is the size of the crack propagation plane as a shape parameter, the fatigue strength depends on the size (internal fatigue crack initiation site size). Fatigue properties of surface roughness and notched specimens at cryogenic temperatures were expected to be more improved when the grain size of the materials was minimized, i.e. fatigue crack initiation sites were minimized.

Electron backscattering diffraction analysis of secondary cleavage cracks in a reactor pressure vessel steel

An analysis of secondary cleavage cracks in the A 508 C1.3 bainitic steel has been carried out using electron backscattering diffraction (EBSD) and scanning electron microscopy (SEM). The crystallographic orientation in the vicinity of the secondary cracks was studied. Secondary cleavage crack propagation planes were identified to be {100}, {110}, {112} and {123}. The secondary cracks propagated mostly in the range of one crystallographic grain (bainitic packet) and were arrested on high-angle twist type boundaries or in the upper bainite carbide colonies. The size of cleavage facets on the fracture surface corresponds to the size of the bainitic packets.