Increase In Crack Growth Resistance Research Articles

Pinning cracks by microstructure design in brittle materials

In this work, we explore the possibility of controlling toughening mechanisms in brittle materials through microstructure design to enhance their resistance to crack growth. First, a computational framework is established using the distinct element method (DEM) with J integral implemented to simulate complex crack propagation and characterize the effective fracture energy of brittle materials. The fracture behavior of a soda-lime glass plate containing pre-existing voids under tensile loading is simulated, and toughening mechanisms associated with the existence of voids, including blunting-induced pinning and deflection-induced pinning, are identified in brittle materials. Then we seek to modulate the fracture toughness of brittle materials by introducing either randomly distributed voids or sinusoidally distributed voids and controlling the pinning events. Our findings reveal that randomly distributed voids with different volume fractions induce only modest toughening in brittle materials. Sinusoidally distributed voids with specific amplitude and wavelength trigger both crack blunting and deflection in the vicinity of voids, increasing the probability of crack pinning and leading to a significant increase in crack growth resistance. Moreover, we identify the critical conditions for the “embrittlement-toughening transition” and “maximized toughening”. Finally, we discuss the difference between void toughening for brittle materials and ductile materials due to distinct toughening mechanisms activated, and also extend the toughening strategy to nacre-like materials. The stairwise herringbone structure is demonstrated to be a promising candidate for structure optimization due to unique stiffness, strength, and toughness.

Transformation-toughened zirconia: An overview

Zirconia is a “metastable” ceramic, consisting of monoclinic, tetragonal, and cubic phases. Partially stabilized zirconia is preferred choice for dental use since they offer the opportunity to fabricate prosthesis which is not available with other ceramic materials. Phase transformation in zirconia ceramics represents one of the most remarkable innovations in the ceramic field. This phase transformation can have desirable consequences, increase in crack growth resistance which is referred to as “phase transformation toughening”. However, the phase-induced volumetric transformation can also have disastrous consequences, if not properly controlled. This article provides information on crystallography of zirconia and the main characteristics of the tetragonal to monoclinic transformationand also discusses the positive (transformation toughening) and negative aspects (ageing/LTD) of the tetragonal to monoclinic transformation.

Increasing crack growth resistance for through-thickness matrix cracking and its role in suppressing ply cracking in thin-ply laminates

A new analysis is proposed, and verified, to quantitively explain the recent experimental observations of a transition from unstable to slow, stable through-thickness crack growth in cross-ply laminates, as the ply thickness is decreased to 40 µm. The approach is prompted by the observed stable rise of crack opening under increasing applied strain in micromechanical model simulations. Estimates of the energy release rates associated with these crack opening profiles clearly indicate an increasing value of crack growth resistance with crack extension, i.e. an R-curve effect. To verify that the thickness dependence of the matrix crack growth behaviour can be attributed to an R-curve effect, the R-curves were independently determined by micromechanical modelling and employed to predict the progression of through-thickness cracking in constrained plies of various thicknesses. These predictions are shown to agree closely with the reported experimental observations. The benefit of this new approach is that only one simulation is required to generate the R-curve, instead of requiring separate simulations for each ply thickness, thus considerably reducing the computational burden. This is particularly valuable for parametric studies to investigate the dependence on various material properties. As an illustrative example, the effects of changing the fracture energy of the epoxy matrix and the volume fraction of fibres present in the composite were investigated, and simple linear relationships were identified for both the steady-state value of the crack-growth resistance and the crack extension required to reach the steady state. Such relationships can further reduce the computational cost of micromechanical modelling, especially when the relevant material properties may not be available from direct measurements but can be reasonably estimated, as for cryogenic applications.

Effect of vacuum smelting method on the quality of pipe steel of northern application

Pipe metal of Northern application must meet increased requirements of strength properties, low-temperature ductility, cold resistance and weldability. Cracks, skins, flaws, roll-ins and other defect are not allowed on the surface of pipes. The fulfillment of the requirements substantially can be provided by the process of steel smelting by a vacuum remelting method. Study of the effect of 03ХГ grade pipe steel smelting in vacuum and without vacuum on its contamination by nonmetallic inclusions and resistance against hydrogen cracking was accomplished. The smelting of ingots of adjusted chemical composition was carried out in a vacuum induction furnace ZG-0.06L. To imitate the process of hot roughing rolling, hydraulic press П6334 of 250 t force was used. Finishing rolling was carried out at reversible hot rolling mill 500 duo, combined with a controlled cooling facility. It was determined, that the samples, smelted in vacuum, had insignificant number of nonmetallic inclusions and withstand the test of resistance against hydrogen cracking; cracks were not detected on them. After testing on resistance against hydrogen cracking of the samples smelted without vacuum, cracks were discovered, located on both the surface and central layers amounting to 600 mm and 1700 mm length correspondently. It was shown, that steel smelting in vacuum allows to reach a high degree of the steel purity, results in increased crack growth resistance and in decreased number of nonmetallic inclusions in the pipe steel of Northern application.

Strain-induced crystallisation in natural rubber: a thermodynamically consistent model of the material behaviour using a multiphase approach

Strain-induced crystallisation (SIC) is the phenomenon of elastomers to experience a pronounced nonlinearity under large deformations of several hundred percentages of strain, which is advantageous for industrial applications due to the resulting positive properties such as increasing crack growth resistance and fatigue behaviour. The overall objective of the current study is the constitutive modelling of the material behaviour of natural rubber when stretched uniaxially. Initially, unfilled natural rubber is considered. Cyclic traction experiments in which crystallinity, elongation and stresses are simultaneously measured are found in the literature. The same vulcanisate is used to conduct additional experiments in the present laboratory. The experimental investigations focus on uniaxial tension tests, conducted with a variety of parameters such as time and stretch rate. The current work presents an approach to model the SIC phenomenon. The model considers thermoelasticity and crystallisation. The approach of the hybrid free energy is used to derive constitutive equations and to meet thermomechanical consistency. However, the effect of temperature is not the focus of the current work. Furthermore, the contribution of a mixing energy is represented in the free energy. The derivation of this mixing entropy is explained in detail by making use of different assumptions and approaches, e.g. the consideration of ideal mixtures. Here, a one-dimensional constitutive model for strain-crystallising rubber is developed, which can be extended with a micro-sphere approach (concept of representative directions) to a full thermodynamically consistent anisotropic model.

Influence of Grain Size Distribution on Ductile Intergranular Crack Growth Resistance

AbstractThe influence of grain size distribution on ductile intergranular crack growth resistance is investigated using full-field microstructure-based finite element calculations and a simpler model based on discrete unit events and graph search. The finite element calculations are carried out for a plane strain slice with planar grains subjected to mode I small-scale yielding conditions. The finite element formulation accounts for finite deformations, and the constitutive relation models the loss of stress carrying capacity due to progressive void nucleation, growth, and coalescence. The discrete unit events are characterized by a set of finite element calculations for crack growth at a single-grain boundary junction. A directed graph of the connectivity of grain boundary junctions and the distances between them is used to create a directed graph in J-resistance space. For a specified grain boundary distribution, this enables crack growth resistance curves to be calculated for all possible crack paths. Crack growth resistance curves are calculated based on various path choice criteria and compared with the results of full-field finite element calculations of the initial boundary value problem. The effect of unimodal and bimodal grain size distributions on intergranular crack growth is considered. It is found that a significant increase in crack growth resistance is obtained if the difference in grain sizes in the bimodal grain size distribution is sufficiently large.

Fracture behavior of carbon fiber reinforced polymer composites: An optical study of loading rate effects

Crack initiation and growth in single-edge notched unidirectional T800s/3900-2 CFRP laminates are studied under stress wave and quasi-static loading conditions. An optical technique called reflection-mode Digital Gradient Sensing is also extended to study fracture mechanics of CFRP by using it in conjunction with ultrahigh-speed photography to perform full-field measurement of crack-tip deformations in the pre- and post-crack initiation regimes. DGS is capable of measuring two orthogonal surface slopes in the crack-tip vicinity as angular deflection of light rays. A method for extracting crack-tip parameters – the instantaneous crack speed and stress intensity factor (SIF) histories – associated with the stationary and propagating cracks using measured surface slopes is presented. The effect of fiber orientation in the range 0°–60° relative to the initial notch and two loading rates are investigated. Nominally mode-I fracture occurs when the fiber orientation is 0° whereas mixed-mode fractures ensue in others. Besides crack initiation occurrence at higher loads as fiber orientation increases, the SIF histories imply strong fiber bridging at low fiber orientations under quasi-static conditions. Furthermore, this CFRP shows significant loading rate dependence during crack growth. Unlike stress wave loading conditions, an increasing crack growth resistance immediately after crack initiation is seen under quasi-static conditions.

The importance of microstructural variations on the fracture toughness of human dentin

The crack growth resistance of human dentin was characterized as a function of relative distance from the DEJ and the corresponding microstructure. Compact tension specimens were prepared from the coronal dentin of caries-free 3rd molars. The specimens were sectioned from either the outer, middle or inner dentin. Stable crack extension was achieved under Mode I quasi-static loading, with the crack oriented in-plane with the tubules, and the crack growth resistance was characterized in terms of the initiation (Ko), growth (Kg) and plateau (Kp) toughness. A hybrid approach was also used to quantify the contribution of dominant mechanisms to the overall toughness. Results showed that human dentin exhibits increasing crack growth resistance with crack extension in all regions, and that the fracture toughness of inner dentin (2.2 ± 0.5 MPa·m0.5) was significantly lower than that of middle (2.7 ± 0.2 MPa·m0.5) and outer regions (3.4 ± 0.3 MPa·m0.5). Extrinsic toughening, composed mostly of crack bridging, was estimated to cause an average increase in the fracture energy of 26% in all three regions. Based on these findings, dental restorations extended into deep dentin are much more likely to cause tooth fracture due to the greater potential for introduction of flaws and decrease in fracture toughness with depth.

Stable and unstable fracture of thin brittle disks under a ball-on-3-balls loading

Ball-on-3-balls tests carried out on a coarse-grained alumina exhibited typical features of stable crack extension well-known for macroscopic cracks in materials with an increasing crack growth resistance. In order to interpret this effect unexpected for small natural cracks, stress intensity factors of semi-elliptical surface cracks were computed by application of the procedure proposed by Cruse and Besuner. For these computations an analytical description for the stress distribution in the disk under ball-on-3-balls loading was applied. The stresses strongly decrease with increasing distance from the disk centre. It can be concluded from the results that natural small cracks can propagate stably due to this decrease.

On the R-curve behavior of human tooth enamel

In this study the crack growth resistance behavior and fracture toughness of human tooth enamel were quantified using incremental crack growth measures and conventional fracture mechanics. Results showed that enamel undergoes an increase in crack growth resistance (i.e. rising R-curve) with crack extension from the outer to the inner enamel, and that the rise in toughness is a function of distance from the dentin enamel junction (DEJ). The outer enamel exhibited the lowest apparent toughness (0.67 ± 0.12 MPa m 0.5), and the inner enamel exhibited a rise in the growth toughness from 1.13 MPa m 0.5/mm to 3.93 MPa m 0.5/mm. The maximum crack growth resistance at fracture (i.e. fracture toughness ( K c)) ranged from 1.79 to 2.37 MPa m 0.5. Crack growth in the inner enamel was accompanied by a host of mechanisms operating from the micro- to the nano-scale. Decussation in the inner enamel promoted crack deflection and twist, resulting in a reduction of the local stress intensity at the crack tip. In addition, extrinsic mechanisms such as bridging by unbroken ligaments of the tissue and the organic matrix promoted crack closure. Microcracking due to loosening of prisms was also identified as an active source of energy dissipation. In summary, the unique microstructure of enamel in the decussated region promotes crack growth toughness that is approximately three times that of dentin and over ten times that of bone.

Aging and the reduction in fracture toughness of human dentin

An evaluation of the crack growth resistance of human coronal dentin was performed on tissue obtained from patients between ages 18 and 83. Stable crack extension was achieved over clinically relevant lengths ( 0 ≤ a ≤ 1 mm ) under Mode I quasi-static loading and perpendicular to the nominal tubule direction. Results distinguished that human dentin exhibits an increase in crack growth resistance with extension (i.e. rising R -curve) and that there is a significant reduction in both the initiation (K o) and plateau (K p ) components of toughness with patient age. In the young dentin ( 18 ≤ age ≤ 35 ) there was a 25% increase in the crack growth resistance from the onset of extension (K o=1.34 MPa m 0.5) to the maximum or “plateau” toughness (K p=1.65 MPa m 0.5). In comparison, the crack growth resistance of the old dentin ( 55 ≤ age ) increased with extension by less than 10% from K o =1.08 MPa m 0.5 to K p =1.17 MPa m 0.5. In young dentin toughening was achieved by a combination of inelastic deformation of the mineralized collagen matrix and microcracking of the peritubular cuffs. These mechanisms facilitated further toughening via the development of unbroken ligaments of tissue and posterior crack-bridging. Microstructural changes with aging decreased the capacity for near-tip inelastic deformation and microcracking of the tubules, which in turn suppressed the formation of unbroken ligaments and the degree of extrinsic toughening.

Effect of Aging on Crack Initiation and Propagation of Ni-Base Super Alloy 718

In order to investigate the effect of aging condition on initiation and propagation properties of a fatigue crack, rotating bending fatigue tests were carried out using partially notched specimens of Ni-base supper alloy, Alloy 718, at 500℃. Aging conditions selected were the under-aged and the over-aged conditions with nearly the same hardness. Fatigue strength of the over-aged alloy was higher than that of the under-aged one in wide life region till 108 cycles. Moreover, fatigue strength at 500℃ was larger than that at room temperature in both alloys. Most of fatigue life was occupied by the growth life of a small crack in both alloys. The main reason for higher fatigue strength of the over-aged alloy was an increase in crack growth resistance. Many slip bands were observed on the specimen surface of the over-aged alloy in comparison with results of the under-aged one. This related to the difference in crack growth resistances in both alloys.

Mode-II shielding-curve of Al2O3 from measurement of cone crack angles

Many ceramic materials exhibit the effect of an increasing crack growth resistance during crack extension. Especially in the case of coarse-grained materials, cracks generally follow the grain boundaries, leave the original crack plane and produce a crack-face roughness. In the theoretical analysis forces transmitted by local links between the two crack faces are smoothed and replaced by so-called continuous bridging stresses acting against the crack opening. As the consequence of such bridging stresses, there exists a shielding stress intensity factor term that shields the crack tip partially from the applied loads. This effect as a reason for the occurrence of R-curves is well documented in literature for cracks under pure mode-I loading conditions [1]. In addition it has to be expected that crack-face interactions will also affect crack extension under pure or superimposed mode-II loading as for instance outlined in literature for frictional crack-face interactions [2–4]. In [5] it was outlined that the shear tractions generated under small mode-II load contributions may cause a disappearing effective crack-tip stress intensity factor KII,tip. Also the externally applied mode-II stress intensity factor KII,appl can be reduced by the mode-II shielding so that a disappearing KII,tip can occur. The distribution of the intensity of crack-face interlocking has the same consequences on the bridging tractions normal to the crack face rbr as for the tangentially transferred tractions sbr. At the same distance from the crack tip where the bridging interactions disappear, both the shear and the normal stresses must vanish. Under the assumption of the same traction versus displacement characteristics, the two stresses are proportional sðxÞ 1⁄4 k rbrðxÞ ð1Þ

Tear Toughness Evaluation of High-Quality Squeeze-Cast and Rheocast Aluminium Alloy Castings

Cast plates of A356 aluminum alloy with different thickness were fabricated by rheocasting and squeeze casting. Tear tests were performed on the as-cast and heat-treated products (T5 and T6), and effects of solidified structure and heat treatment on unit crack propagation energy (UEp) were examined. Increased cooling rate (corresponding to a decrease in plate thickness) resulted in refined solidified structure and enlarged UEp values for as-cast samples. For both rheocast and squeeze-cast samples, both spheroidized eutectic Si particles and age-hardened α-Al matrix by T6 treatment were effective for increasing UEp. UEp of the squeeze-cast sample was higher than that of the rheocast sample. Observation of crack growth path and fracture surface revealed that the tear toughness of the present cast alloy was controlled by distribution of eutectic solidified region in the cast structure, which provided a preferential crack growth path. The discontinuous distribution for the squeeze-cast sample is considered to be beneficial for increasing crack growth resistance rather than the continuous arrangement of the network-like eutectic region for the rheocast sample. Relatively small UEp was obtained for the T6 treated rheocast sample collected from the 6 mm thickness plate. This is attributable to the volume fraction of the eutectic solidified region in the sample being larger than others under the present experimental conditions.

Toughening of wood particle composites—Effects of sisal fibers

AbstractSisal fibers were added to wood particle composites to enhance their toughness. The selected matrix was a commercial styrene diluted unsaturated polyester thermoset resin. Fracture tests were carried out using single‐edge notched beam geometries. Stiffness, strength, critical stress intensity factor KIQ, and work of fracture Wf of notched specimens were determined. The incorporation of sisal fibers into wood particle composites significantly changed the fracture mode of the resulting hybrid composite. For the neat matrix and the wood particle composites, once the maximum load was reached, the crack propagated in a catastrophic way. For hybrid composites, fiber bridging and pull‐out were the mechanisms causing increased crack growth resistance. Addition of a 7% wt of sisal fibers almost doubled the KIQ value of a composite containing 12% wt of woodflour. Moreover, the Wf increased almost 10‐fold, for the same sample. In general, the two composite toughness parameters KIQ and Wf increased when the fraction of sisal fibers was increased. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 1982–1987, 2006

ＡＣ４ＣＨアルミニウム合金レオキャスト材およびスクイズキャスト材の引裂靭性

Cast plates of the AC4CH aluminum alloy with different thickness were fabricated by rheocasting and squeeze casting. Tear tests were performed for the as cast and heat treated products (T5 and T6) and effects of solidified structure and heat treatment on the unit crack propagation energy (UEp) were examined. Increase of the cooling rate (corresponding to the decrease in plate thickness) resulted in refined solidified structure and enlarged UEp values for as cast samples. Both spheroidized eutectic Si particles and age-hardened α-Al matrix by T6 treatment were effective to increase UEp for both rheocast and squeeze cast samples. UEp of the squeeze cast was larger than that of the rheocast. Observation of crack growth path and fracture surface revealed that the tear toughness of the present cast alloy was controlled by distribution of eutectic solidified region in the cast structure, which provided a preferential crack growth path. The discontinuous distribution for the squeeze cast is considered to be beneficial for increase in crack growth resistance rather than the continuous arrangement of the network-like eutectic region for the rheocast. Relatively small UEp was obtained for the T6 treated rheocast sample collected from the 6 mm thickness plate. This was caused by the fact that the volume fraction of the eutectic solidified region in the sample was larger than others under the present experimental condition.

Three dimensional microstructural effects on plane strain ductile crack growth

Ductile crack growth under mode I, plane strain, small scale yielding conditions is analyzed. Overall plane strain loading is prescribed, but a full 3D analysis is carried out to model three dimensional microstructural effects. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model the material. Two populations of second-phase particles are represented, large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. The larger inclusions are represented discretely and the effects of different three dimensional distributions on the crack path and on the overall crack growth rate are analyzed. For comparison purposes, a two dimensional distribution of cylindrical inclusions is analyzed. Crack growth occurs off the initial crack plane in all 3D computations, whereas straight ahead crack growth occurs with the two dimensional cylindrical inclusions. As a consequence, the three dimensional distributions of spherical inclusions exhibit an increased crack growth resistance as compared to the two dimensional distribution of cylindrical inclusions.

Effect of Nb on the mechanical properties of Ti/Al2O3 composite

Ti/Al2O3 composite with improved mechanical properties was synthesized by the spark plasma sintering. The effect of Nb on the microstructure of the composite was analyzed by TEM, SEM and so on. The experimental results indicate that the bending strength, fracture toughness, micro-hardness and relative density of the composite are 897.29MPa, 17.38MPa·m1/2, 17.13GPa and 99.24% respectively when adding 1.5vol Nb. The bending strength is improved by reason of forming dislocation ring and transfering fracture mode from integranular to mixture fracture of intergranular and transgranular. The crack propagating is mainly the deflection bridging. It indicates a reduction of crack driving force and an increase in crack growth resistance, which results in toughness enhanced.

Nonpropagating incipient cracks from sharp notches under fatigue

Growing incipient cracks from sharp notches can stop completely even when the remote applied stress amplitude remains constant. As the crack lengthens, the crack-tip driving force, the stress intensity factor, should increase for a constant remote applied stress, yet, arrest occurs. For this reason, the fatigue stress concentration factor K f differs from the conventional stress concentration factor K t for sharp notches. The arrest has been attributed to increased crack growth resistance as an incipient crack lengthens. The increased resistance has been related to plasticity-induced crack closure, which builds up with crack-wake plasticity during crack growth. In this paper we present a different concept based on our unified approach that considers the existence of two fatigue thresholds rather than one. It is shown that nonpropagation of incipient crack occurs when the total stress intensity factor falls below the long crack growth threshold value in terms of K max. Total stress intensity results from both the remote applied stress and the local internal stress. Even when the remote applied load is constant, the local internal stress can decrease sharply as the incipient crack grows away from the notch tip. Notch-tip plasticity contributes to the changes in the internal stresses. Using extensive data from the literature, it is shown that it is the decreasing crack-tip driving force with length that causes the crack arrest phenomenon. Crack growth under tension–tension, tension–compression, and compression–compression fatigue are all accounted for on the basis of gradient in the internal stresses.

Mixed-mode, high-cycle fatigue-crack growth thresholds in Ti–6Al–4V: II. Quantification of crack-tip shielding

The role of crack-tip shielding in influencing mixed-mode (mode I+II) fatigue-crack growth thresholds for large, through-thickness cracks in a Ti–6Al–4V turbine blade alloy is examined under high-cycle fatigue loading conditions, i.e., at a loading frequency of 1000 Hz in ambient temperature air for load ratios ( K min/ K max) of R=0.1–0.8. Techniques are developed to quantify crack-tip shielding with respect to both the mode I and mode II applied loading, enabling an estimation of the shielding-corrected, crack-driving forces actually experienced at the crack tip ( ΔK I,TH,eff and ΔK II,TH,eff or ΔG TH,eff). In Part I, it was shown that when the crack-driving force is characterized in terms of the range in strain-energy release rate, ΔG, which incorporates contributions from both the applied tensile and shear loading, the mixed-mode (I+II) fatigue-crack growth resistance increases monotonically with the ratio ΔK II/ ΔK I. When the fatigue-crack growth thresholds are expressed in terms of the near-tip (shielding-corrected) crack-driving force, this increase in crack-growth resistance with increasing mode mixity is markedly reduced. Moreover, for all mode mixities investigated, the near-tip mixed-mode fatigue threshold is lower than the applied (global) value, with the effect being particularly pronounced under shear-dominant loading conditions. These observations illustrate the prominent role of crack-tip shielding for the mixed-mode loading of fatigue cracks with crack-wake dimensions large compared with microstructural size scales; specifically, they indicate that the elevation of the ΔG TH fatigue-crack growth threshold with increasing applied mode mixity is largely due to a shear-induced enhancement of crack-tip shielding.