Measurements of crack tip strain field in wood at the scale of growth rings

The fracture mechanisms of wood have often been interpreted on the scale of cell walls. Although this scale is important, the scale of growth rings needs to be considered in the same context. In the present study, the crack tip strain field of radial TR cracks at the scale of growth rings is measured by electronic speckle photography. The methodology is discussed in detail as well as the data reduction scheme. The tip is in the earlywood layer and the crack plane of the TR crack is perpendicular to the stiffer latewood layer. Increasing opening mode load is applied in-situ as the crack is observed by reflected light optical microscopy. Strains are measured on direct images of the microstucture. In contrast to some other methodologies, this allows direct correlation between strain field and microstructure. In the softer earlywood, tangential strains extend considerable distances in the tangential direction. Due to the stiff latewood, the strain is heavily constrained in the radial direction. This nature of the local strain field has been largely neglected, despite its obuius significance to TR crack growth mechanisms.     

Fracture phenomenology of a lithium-aluminium-silicate glass-ceramic

Crack propagation mechanisms in a lithium-aluminium-silicate glass-ceramic have been studied as a function of both initial flaw size and temperature. Using controlled surface cracks, the fracture stress at room temperature was found to conform to the Griffith flaw size dependence. Extrapolation suggests that processing flaws of the order of 6 to 8 m are strength-controlling in the material investigated. Two mechanistic regimes were manifest in the temperature dependence of the fracture stress. Up to 900° C, catastrophic transgranular crack propagation occurred from emplaced cracks. At 1000° C and above, subcritical crack growth occurred intergranularly and the extent of slow crack growth prior to catastrophic failure increased with increasing temperature. The influence of loading rate on slow crack growth and fracture stress was explored at 950 and 1100° C. Generally, the extent of slow crack growth decreased with increased loading rate until at a sufficiently high rate, catastrophic fracture occurred directly with no slow crack extension. These results are discussed in terms of the role of plastic accommodation in the crack extension process, a phenomenon which seems mechanistically dependent upon remnant amorphous (uncrystallized) phase at grain boundaries.     

Stability of arrays of multiple edge cracks

The creation and subsequent shedding of arrays of edge cracks is a natural phenomenon which occurs in heat-checked gun tubes, rapidly cooled pressure vessels and rock, dried-out mud flats, paint and concrete and in ceramic coatings and permafrost. The phenomenon covers five orders of magnitude in crack spacing and the driving mechanisms may include fast fracture, environmental cracking and fatigue crack growth. A simple model is developed which indicates that the shedding behaviour is governed by the behavior of individual cracks rather than global energy changes. The model predicts that all cracks will deepen until a crack-spacing/crack depth ratio (2h/a) of 3.0 is achieved, at which stage crack-shedding will commence. Two out of every three cracks will be shed, leading to a new (higher) crack spacing/crack depth ratio at which stage growth of all currently active cracks will be dominant. An approach based upon rapid, approximate methods for determining stress intensity provides good indications of behaviour provided near-surface stress gradients are not excessive. In cases where stress gradients are high it is shown that it is necessary to employ numerical techniques in calculating stress intensity. Two specific examples are presented, the first at very small scale (heat-check cracking in a gun tube, typical crack spacing 1 mm) and the second at very large scale (permafrost cracking, typical crack spacing 20 m). The predicted ratios for the proportion of cracks shed and for crack spacing/crack depth are in agreement with experimental evidence for gun tubes, concrete and permafrost. The ratios also appear to match experimental observations of “island delamination” in ceramic coatings and paint films.     

Mesoscopic modeling of crack arrestor delamination in Al–Li: primary crack shielding and {T}-stress effect

This work explores the effects of grain orientation and T-stress on crack-front shielding and delamination cracking in modern aluminum–lithium alloys. In the crack-arrestor configuration of interest here, a primary crack extends through the grain thickness while triggering delaminations over susceptible grain boundaries that lie normal to the plane of the primary crack. A three-dimensional, small-scale-yielding framework that employs a gradient-enhanced, crystal plasticity material model reveals key features of the strain/stress fields in a simulation of pancake-shaped grains with alternating orientation near a primary crack front. The alternating grain configurations exhibit a soft/stiff behavior and alternating out-of-plane, L–T shear stress—effects observed in recently-published experiments completed by the authors and others on various Al–Li alloys. Both texture effects contribute to highly localized driving forces for delamination cracking while concurrently shielding the primary crack. Moreover, texture does not act to shield the arrestor delamination planes, thereby favoring arrestor delamination development over primary crack growth. A compressive T-stress further enhances shielding of the primary crack—a result which aids in understanding marked differences in observed fracture behavior of tested M(T) and C(T) specimens of Al–Li alloys.     

Fatigue behaviour of friction stir welded AA2024‐T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024‐T3 aluminium alloy have been studied under constant load amplitude (increasing‐ΔK), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka's method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold ΔK values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K_C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non‐conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non‐conservative crack growth rate predictions next to K_C instability. At threshold ΔK values non‐conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.     

Multi-crack analysis of hydraulically pumped cone fracture in brittle solids under cyclic spherical contact

The evolution of surface damage in bilayers due to cyclic spherical indentation in the presence of incompressible lubricant is studied using an all-transparent glass/polycarbonate system as a model for more practical applications such as dental crowns and rolling contact fatigue. In situ observations and post-mortem material sectioning reveal that inner cone cracks evolve sequentially from the contact edge inward by slow growth in a process controlled by stress shielding from preceding cracks. The embryonic cracks are then accelerated by the action of fluid pressure into the flexural tensile stress at the lower part of the coating, where crossover fracture leading to delamination between the coating and substrate may ensue. A consistent FEM brittle fracture analysis incorporating multiple cracks, rate-dependent toughness and liquid pressure is used to follow the damage evolution in the coating. Crack trajectories are determined incrementally under the dual constraint K _I = K _II = 0, which maximize the tension at the crack tip upon the application of fluid pressure. The latter, evaluated at each increment with the aid of a fluid entrapment model, helps drive the leading crack past the compression zone beneath the contact via a hydraulic pump like action. In the early stages of fracture, the liquid pressure is reasonably well approximated by the Hertzian radial surface stress at the crack mouth. Fluid trapped in secondary cracks accentuate the compression beneath the contact. This helps squeeze more liquid into the tip of the leading crack in a zipping like action, which further enhance the crack driving force in the far field. The analytic predictions generally collaborate well with the tests.     

Investigation of fracture mechanism of 6063 aluminum alloy under different stress states

Fracture mechanisms in a 6063 aluminum alloy were investigated and analyzed carefully by in-situ tensile tests in SEM with a vacuum chamber. Specimens used were designed to produce different stress states. Studies indicated that with stress triaxiality (σ _m/σ _e) decreasing, the fracture modes changed from normal fracture to shear fracture and the fracture surfaces changed from the dimples and intragranular dominated fracture mode to the shear dominated fracture mode. The grain boundaries of the 6063 aluminum alloy were the weakest positions. In the case of high stress triaxiality, the grain boundary cracks were produced by normal stress or by the incompatibility of deformation between neighboring grains, and the normal stress dominated the crack propagation. In the case of low stress triaxiality, the boundary cracks were produced by the relative slipping of grains against neighboring grains, and the shear stress dominated the crack propagation. The final fracture of the specimens occurred by connections of cracks through transgranular cracking of the ligaments among these cracks.     

Cyclic fatigue of long and short cracks in alumina

The cyclic fatigue behaviour of long and microstructurally short cracks in a 10 μm grain-size alumina has been investigated. This material was found to be stress sensitive, a modest drop in applied stress resulting in a considerable lifetime enhancement. The growth of long cracks was studied using the circular compact tension geometry and was found to follow a Paris law behaviour. The crack path was entirely intergranular in this material with long fatigue crack growth governed by the degradation of crack-wake bridging. Short-crack growth was investigated using indented discs in a biaxial flexure geometry. Short cracks were observed to grow at lower values of applied ΔK than long cracks, increasing with crack length as bridging of the crack wake increased. The fatigue crack growth of AD90 alumina was also investigated by in situ testing within the specimen chamber of an SEM. The long-crack behaviour was found to be similar to the 10 μm grain-size alumina and other data reported in the literature. However, the crack path followed a mixture of transgranular and intergranular fracture and discontinuous in nature with frequent arrests. The crack-advancement mechanisms in these two alumina materials are different and affect the short-crack behaviour. However, in both cases the long-crack behaviour is dominated by crack-wake effects. This revised version was published online in November 2006 with corrections to the Cover Date.     

Tunneling radial cracks in layered structures from contact loading

Glass/epoxy laminates glued onto a compliant substrate are indented with a hard ball. The damage is characterized by a set of transverse cracks which pop out from the subsurface of the glass layers due to flexure and propagate stably in the radial direction with load in a bell-shape front under a diminishing stress field. Compliant interlayers, even extremely thin ones, are effective in inhibiting crossover fracture. This leads to crack tunneling and crack multiplication in the hard layers, which enhances energy dissipation and reduces the spread of damage relative to the basic bilayer configuration. The experiments show that the fracture in a given layer is well approximated by a power-law relation of the form c^3/2K_C/P = δ, where P, c, and K_C are the indentation load, crack length and fracture toughness, in that order, and δ an implicit function of the layer position and material and geometric variables, derived with the aid of available tunnel crack solutions.The model specimen studied provides a useful insight into the fracture behavior of natural, biological and synthetic layered structures from concentrated loading. The analysis shows that the crack arrest capability of a thin interlayer increases in proportion to the modulus misfit ratio between the layer and interlayer, and that the spread of radial cracks in a laminate of given thickness reduces in proportion to n^1/3, where n is the number layers in the laminate.     

Nucleation and propagation of fatigue cracks in Al-304 stainless steel laminate composite

A study has been made of fatigue crack nucleation and propagation in Al-stainless steel (30 vol%) laminate composites. A Paris type power relationship between the crack growth rate, da/dN, and the alternating stress intensity, K, was obtained over the crack growth rates ranging from 10^–7 to 10^–4 mm/cycle, with an exponentm of 2.7. The cracks nucleated first in Al strips and then in stainless steel strips accompanied by some interface decohesion. The fatigue crack propagated in two stages. In the first stage, where the Al-steel interface was largely intact, the crack propagated in a plane strain mode (flat fracture surface with striations, each striation consisting of a cluster of interstriations). In the second stage, where there occurred extensive Al-steel interface delamination and the concomitant loss of mutual constraint, the crack propagated in the plane stress mode (slant fracture with voids). The crack growth was faster in Al than that in steel since the apparent striation spacing was larger in the former than in the latter. No one to one correspondence existed between the apparent striation spacing and the macroscopic crack growth rate.Thus, although, microscopically, the crack front was not planar; macroscopically, it could be regarded as planar, and a Paris type power relationship did characterize the macroscopic fatigue crack growth in this laminate system over the applied stress amplitude studied. Comparing the fatigue crack growth rates among Al-steel laminate, commercial or pure aluminium and 304 stainless steel, the Al-steel laminate has the lowest crack growth rate. This plus the weight and cost saving benefits make Al-steel laminate quite attractive.     

Mode I cracks subjected to large T-stresses

There are several criteria for predicting brittle fracture in mode I and mixed mode loading. In this paper, the modified maximum tangential stress criterion originally proposed for mixed mode loading, is employed to study theoretically brittle fracture for mode I cracks. In particular, the effect of the non-singular term of stress, often known as the T-stress, on the angle of initiation of fracture and the onset of crack growth is explored. The T-stress component of the tangential stress vanishes along the crack line. Therefore, it is often postulated for linear elastic materials that the effect of T-stress on mode I brittle fracture can be ignored. However, it is shown here that the maximum tangential stress is no longer along the line of initial crack when the T-stress exceeds a critical value. Thus, a deviation in the angle of initiation of fracture can be expected for specimens having a large T-stress. It is shown that the deviation angle increases for larger values of T-stress. Theoretical results show that the apparent fracture toughness decreases significantly when a deviation in angle occurs. Earlier experimental results are used to corroborate the findings. The effect of large T-stresses is also explored for a crack specimen undergoing moderate scale yielding. The elastic-plastic investigation is conducted using finite element analysis. The finite element results reveal a similar deviation in the angle of maximum tangential stress for small to moderate scale yielding.     

An examination of mixed fatigue-tensile surface crack growth in rails

The fracture instability associated with alternating periods of fatigue and tensile growth of surface cracks was investigated in steel rails. Three different steels were tested. The instabilities commenced when the maximum stress intensity factor $\text{K}$ exceeded the fracture toughness $\text{K}{}_{\mathrm{IC}}$ and resulted in crack jump or total rail failure. The conditions for the establishment of fatigue-tensile crack jump and arrest are described. The load level, residual stresses, crack geometry and fracture toughness effects are analysed. The fatigue surface cracks were penetrated in both stress relieved and stress unrelieved rails. The effective stress intensity factors including the contribution of the applied load and residual stresses were calculated. For both the fatigue-tensile and tensile-fatigue transitions the stress intensity factors were almost the same with the value for the tensile-fatigue transition being slightly lower. Both calculated stress intensity factors were close to the fracture toughness $\text{K}{}_{\mathrm{IC}}$.     

Retardation and repair of fatigue cracks in a microcapsule toughened epoxy composite—Part II: In situ self-healing

Successful arrest and retardation of fatigue cracks is achieved with an in situ self-healing epoxy matrix composite that incorporates microencapsulated dicyclopentadiene (DCPD) healing agent and Grubbs’ first generation Ru catalyst. Healing agent is released into the crack plane by the propagating crack, where it polymerizes to form a polymer wedge, generating a crack tip shielding mechanism. Due to the complex kinetics of healing a growing crack, the resulting in situ retardation and arrest of fatigue cracks exhibit a strong dependence on the applied range of cyclic stress intensity ΔK_I. Significant crack arrest and life-extension result when the in situ healing rate is faster than the crack growth rate. In loading cases where the crack grows too rapidly (maximum applied stress intensity factor is a significant percentage of the mode-I fracture toughness value), a carefully timed rest period can be used to prolong fatigue life up to 118%. At moderate ΔK_I, in situ healing extends fatigue life by as much as 213%. Further improvements in fatigue life-extension are achieved by employing a rest period, which leads to permanent arrest at this moderate ΔK_I. At lower values of applied stress intensity factor, self-healing yields complete arrest of fatigue cracks providing infinite fatigue life-extension.     

Indentation fracture of WC-Co cermets

Indentation fracture of a series of well-characterized WC-Co cermets was studied with a Vickers diamond pyramid indenter. The resulting crack length-indentation load data were analysed in terms of relations characteristic of radial (Palmqvist) and fully developed radial/median (half-penny) crack geometries. The radial crack model gave a better fit to the data on all the alloys studied. Crack shapes determined by repeated surface polishing confirmed the radial nature of the cracks. An indentation fracture mechanics analysis based on the assumption of a wedge-loaded crack is shown to be consistent with the observed linear relation between the radial crack length and the indentation load. The analysis also predicts a simple relation among the fracture toughness (K _lc), the Palmqvist toughness (W) and the hardness (H) of the WC-Co alloys.     

A numerical analysis of failure characteristics of ductile layers in laminated composites

In this study, the failure of the ductile layers from collinear, multiple and delaminating cracks that occur in laminated composite systems was studied using a constitutive relationship that accounts for strength degradation resulting from the nucleation and growth of voids. The results indicate that, in laminated composites, void nucleation and growth ahead of the cracks occur at a much faster rate because of evolution of much higher stress values in the interface region. Except for short crack extensions, collinear and multiple cracks develop crack resistance curves similar to that seen for a crack in the ductile layer material as a homogenous isotropic cases. For delaminating crack cases, the fracture behaviour is strongly influenced by the delamination length. The resistance of the ductile layers to crack extension can be significantly reduced by short delamination lengths; however, for large delamination lengths the resistance to crack extension becomes greater than that seen for the ductile material. The results also show that, if the crack tip is at the interface, similar maximum stress values develop in the ductile layers as in the fracture test of the same ductile material, suggesting that ductile–brittle fracture transition behaviour of the ductile layers is dependent upon the extent of the cracks in the brittle layers and fracture characteristics of the brittle layers.     

Phenomenology of fracture in sintered alpha silicon carbide

Crack propagation mechanisms in a sintered alpha silicon carbide were studied as a function of initial flaw size, temperature, loading rate and applied stress. Surface cracks of controlled size were introduced using the microhardness indentation-induced-flaw (IIF) technique. At room temperature, the fracture stress was found to depend on initial crack size according to the Griffith relationship and extrapolation of the data indicated that processing flaws of 20 to 40m were strength controlling. The flexural strength was found to be independent of temperature (20 to 1400° C) and the fracture faces did not show the presence of subcritical crack growth (SCG). Preliminary results from stress rate testing also failed to show the presence of SCG in tests made at 1200° C in air. In contrast, flexural stress rupture tests carried out at 1200 and 1300° C in air using precracked specimens indicated the materials susceptibility to time-dependent deformation and showed the presence of SCG. Fractographic evidence for transgranular crack propagation during fast fracture (catastrophic failure) and intergranular crack propagation during SCG is presented.     

3D multiscale crack propagation using the XFEM applied to a gas turbine blade

This work presents a new multiscale technique to investigate advancing cracks in three dimensional space. This fully adaptive multiscale technique is designed to take into account cracks of different length scales efficiently, by enabling fine scale domains locally in regions of interest, i.e. where stress concentrations and high stress gradients occur. Due to crack propagation, these regions change during the simulation process. Cracks are modeled using the extended finite element method, such that an accurate and powerful numerical tool is achieved. Restricting ourselves to linear elastic fracture mechanics, the $J$ -integral yields an accurate solution of the stress intensity factors, and with the criterion of maximum hoop stress, a precise direction of growth. If necessary, the on the finest scale computed crack surface is finally transferred to the corresponding scale. In a final step, the model is applied to a quadrature point of a gas turbine blade, to compute crack growth on the microscale of a real structure.     

SMALL FATIGUE CRACK GROWTH IN A LOW CARBON STEEL UNDER TENSION–COMPRESSION AND PULSATING-TENSION LOADING

The growth behaviour of small fatigue cracks has been investigated in a low carbon steel under axial loading at the stress ratios R of –1 (tension-compression) and 0 (pulsating-tension). Crack closure was measured to evaluate the effects of stress ratio and stress level on small crack growth. Except for the accelerated growth at stress levels close to the yield stress of the material, at R=–1 small cracks grow faster than large cracks below a certain crack length, but at R= 0 the crack growth rates for small cracks are coincident with those for large cracks in the whole region of crack length investigated. The critical crack length, 2c_c, above which the growth behaviour of small cracks is similar to that of large cracks depends on stress ratio, being 1–2 mm at R=–1 and smaller than 0.7 mm at R=0. The 2c_c value at R=–1 agrees with that obtained under rotating bending (R=–1). The small crack data are closely correlated with large crack growth rates in terms of the effective stress intensity range, ΔK_eff; thus ΔK_eff is found to be a characterizing parameter for small crack growth including the growth at the higher stress levels.     

Deformation and fracture of cork in tension

Various properties related to the deformation and fracture of cork in tension were experimentally determined, including the Young's modulus, the stress and strain at fracture and the fracture toughnessK _Ic. The transverse isotropy of cork implies that there are three independent systems of mode I crack propagation andK _Ic was measured for each. The mechanisms of deformation and fracture were identified by SEM microscope observation ofin situ deformation and of the fracture surfaces and crack paths. Two fundamental mechanisms of fracture occur: crack propagation along the lateral cell walls in non-radial tension, withK _Ic = 94±16 kPam^1/2 and crack propagation by breaking the cell walls in radial tension withK _Ic=125±14 kPam^1/2. In radial tension, local fractures that do not propagate due to crack stopping were observed which lead to serrations in the tensile curves for that direction. The strain to fracture in this direction is considerably larger than in the perpendicular (non-radial) directions.     

Modeling mechanical stress and exfoliation damage in carbon fiber electrodes subjected to cyclic intercalation/deintercalation of lithium ions

Gradients in lithium ion concentration distribution in carbon fiber are accompanied by non-uniform fiber swelling leading to development of mechanical stresses. During lithium deintercalation these stresses may lead to initiation and growth of radial cracks in the fiber. The subsequent cycle of intercalation may result in arc-shaped cracks deviating from the tip of the radial cracks. These phenomena decrease the mechanical properties of fibers if used in structural batteries and reduce the charging properties of the battery by decreased diffusivity of lithium ions and by exfoliating layers on the fiber surface. The crack propagation and possible damage evolution scenarios are analyzed using linear elastic fracture mechanics. The crack geometry dependent ion concentration distributions and the elastic stress distributions were found using finite element software ANSYS.