The effect of initial notch shape of compact specimen on fatigue pre-cracking and fracture toughness testing

The circular notched compact specimens, along with standard specimens having straight or chevron notch are provided for fatigue and fracture toughness testings in order to study the crack observation capability during fatigue pre-cracking, skewness of the crack front, and the resulting fracture toughness K_Q. The test results indicated that circular notched specimens significantly facilitate the crack observation during fatigue testing as the cracks initiate on both surfaces of the specimen. No remarkable differences were observed on geometries of the fatigue crack front obtained and the resulting fracture toughness among these three types of specimen. The macroscopic observation of beach marks on the fracture surfaces revealed that, in the present material Ti-6Al-4V (ELI), the advance of only 1.3% of the whole crack length corresponded to the load level at which fracture toughness K_Q was evaluated.     

The fracture behaviour of specimens with a notch tip partly in the base metal of strength mis-match welded joints

The relevant parameter for the safe service of a welded structure is the critical crack tip opening displacement (CTOD). This value is dependent on the microstructure present along the front of the fatigue pre-crack, which is also in the same locality where the strength mis-matching has a substantial influence. In the case of a specimen containing a through thickness notch, embedded partly in the heat affected zone and partly in the base metal, the fracture behaviour strongly depends on a portion of the ductile base metal and the size and distribution of the mis-matching factor along the vicinity of the crack front. Therefore, if local brittle zones are located in the process zone the ductile base metal cannot prevent pop-in instability, but it can reduce it to an insignificant level during the fracture toughness testing and it can provide higher critical CTOD values.     

Fracture toughness of foams with tetrakaidecahedral unit cells using finite element based micromechanics

Fracture toughness of open-cell foams consisting of tetrakaidecahedral unit cells is predicted by simulating crack propagation using a finite element (FE) based micromechanical model. The inputs to the model are the geometric parameters required to model the repeating unit cell and tensile strength of the foam ligament or strut. Cracks are created by removing certain number of cells pertaining to a crack length. The FE model consists of a local micro-scale region surrounding the crack tip. For an assumed stress intensity factor, the displacements along the boundary of the local model are calculated based on linear elastic fracture mechanics for orthotropic materials. The stresses in the ligaments ahead of the crack tip calculated from this micro-model in conjunction with the tensile strength of the strut material are used to predict fracture toughness. A parametric study with different micro-model sizes and different crack lengths is performed to check for convergence of predicted Mode-I, Mode-II and mixed mode fracture toughness values. The effect of applying rotations as additional boundary conditions along with translational displacement boundary conditions on the predicted fracture toughness values is also studied.     

Roughness of a mode I in-plane crack front propagating along a heterogeneous cohesive interface

The roughness of the crack front of an interfacial crack propagating along a weak plane in a heterogeneous disordered medium has been repeatedly studied both experimentally and numerically. For an interfacial toughness varying randomly on the interface, the front is self-affine. Quite often, however, the calculated roughness exponent differs from the experimental estimate. Several theoretical models have been employed up to now in the numerical simulations (elastic line depinning, random fuse and spring or beam models). In this paper we present finite element simulations (FEA) of the macroscopic mode-I static propagation of a crack front along a planar interface of an elastic or elastic-plastic coating adhered to a rigid substrate. The interfacial elements separate obeying a cohesive law, their toughness spatially fluctuating at random. The cohesive elements here employed allow for taking into account local I + II + III mixed-opening mode, i.e., allow for mode mixity at the local level. Our results indicate that for a given macroscopic toughness the crack front roughness is strongly sensitive to both the local cohesive law and the local fracture criterion.     

Fracture analyses and experimental results of crack growth under general mixed mode loading conditions

In this paper detailed results of 3D finite element (FE) and mixed mode analyses of different fracture specimens are presented and discussed. Special interest is taken in 3D and mode coupling effects to be found in strain energy release rate (SERR) results along crack fronts, in particular adjacent to corners, where a crack front intersects a free surface of a specimen. It will be shown that these effects stay small if they are related to Poisson’s ratio but that they can also be considerably pronounced if they are related to the global deformation behaviour of the specimen. The computational fracture analysis is based on the calculation of separated energy release rates (SERRs) by the aid of the modified virtual crack closure integral (MVCCI)-method in order to calculate the local SERR-distributions along the crack front. Furthermore some qualitative experimental results will show the influence of these variable mixed mode I, II and III loading conditions along the crack front on crack initiation and on the further development of 3D crack growth in the specimens.     

Delamination cracking in advanced aluminum-lithium alloys - Experimental and computational studies

Delamination cracking in advanced aluminum-lithium (Al-Li) alloys plays a dominant role in the fracture process. With the introduction of these materials into components of aerospace structures, a quantitative understanding of the interplay between delamination cracking and macroscopic fracture must be established as a precursor to reliable design and defect assessment. Delamination cracking represents a complex fracture mechanism with the formation of transverse cracks initially on the order of the grain size. In this work, interrupted fracture toughness tests of C(T) specimens, followed by incremental polishing, reveal the locations, sizes and shapes of delamination cracks and extensions of the primary macrocrack. These observations suggest that delamination crack sizes scale with loading of the primary crack front expressed in terms of J/σ₀. Using a 3-D, small-scale yielding framework for Mode I loading, a companion finite element study quantifies the effects of prescribed delamination cracks on local loading along the macroscopic (primary) crack and ahead of the delamination cracks. An isotropic hardening model with an anisotropic yield surface describes the constitutive behavior for the 2099-T87 Al-Li alloy plate examined in this study. The computational results characterize the plastic zone size, the variation of local J ahead of the macrocrack front and the stress state that serves to drive growth of the macrocrack and delamination crack. The computational studies provide new, quantitative insights on the observed increase in toughness that has been observed during fracture experiments caused by delamination cracks that divide the primary crack front.     

陶瓷材料断裂韧性与缺口半径 Ⅱ 断裂韧性估算方法

在陶瓷材料裂纹尖端存在一个断裂过程区，当断裂过程区内平均应力达到断裂强度时，裂纹扩展。本文由理论推导结合实验数据，得到了新断裂过程区的大小是平均晶粒直径的四倍。并由平均应力断裂模型，给出了陶瓷材料断裂韧性和缺口半径及平均晶粒直径之间的关系式，由此关系式可以用宽缺口试件测出的断裂韧性去估算陶瓷材料的本质断裂韧性。     

Analysis of steady-state ductile crack growth along a laser weld

The fracture toughness in an elastic-plastic material joined by a laser weld is analyzed for steady-state crack growth along the weld. The analysis is performed for laser welds in steel. Laser welding gives high mismatch between the yield stress within the weld and that in the base material, due to the fast thermic cycle that the material undergoes in welding. The material is described by J ₂-flow theory, and the analysis is performed using a special numerical algorithm, in which the finite element mesh remains fixed relative to the tip of the growing crack, so that the material moves through the mesh. Fracture is modelled by using a cohesive zone criterion in front of the crack tip along the fracture zone. It is found that in general a thinner laser weld gives a higher interface toughness. Furthermore, it is shown that the preferred path of the crack is in the base material slightly outside the weld; a phenomenon also observed in experiments.     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.     

A PROBABILISTIC MODEL FOR LOWER-SHELF FRACTURE TOUGHNESS—THEORY AND APPLICATION

When fitting parametric distributions to fracture toughness data, one will often encounter the situation where there are few data available. In such a situation, additional information obtained from a theoretical model can prove to be of value. A theoretical model is described here, which predicts that lower-shelf fracture toughness follows a 2-parameter Weibull distribution with a shape parameter equal to 2 or 4 (depending on the units used for fracture toughness), the scale parameter being determined by the crack front length and a material constant. A rule-of-thumb is given for determining when it is an advantage to use this theoretical information, and when it is best to fit a parametric distribution on the basis of the available data alone.     

Film cracking and debonding in a coated fiber

A fracture mechanics based methodology for the determination of interface fracture toughness from crack spacing in a thin coated fiber is presented. The coating (film) may be regarded as the matrix material in typical experiments employing this configuration. Matrix crack spacing is considered to be the result of a competitive process between matrix segmentation and interface debonding which are assumed to be governed by critical energy release rate criteria. Matrix cracks are assumed to form by the process of channeling in the circumferential direction and steady state conditions are assumed at the matrix crack front in the channeling direction. Energy release rates are determined using domain integral procedures in conjunction with the finite element method. The minimum crack spacing is obtained as a function of applied stress for different values of interface fracture toughness. A methodology to relate the saturated crack spacing to interface fracture toughness is developed. Interfaces are classified into three categories: weak, intermediate and strong. It is shown that in experiments of this type, quantitative information about the interface fracture toughness can be obtained for intermediate interfaces while qualitative information may be obtained for weak and strong interfaces.     

Near the static fatigue limit in glass

Fracture surfaces formed near the crack growth threshold in soda-lime-silicate glass are examined by atomic force microscopy. Cracks held below the apparent crack growth threshold for 16 h alter their mode of growth. The fracture plane changes from a flat surface to one that exhibits substantial out of plane growth. The direction of crack growth changes from 3° to 5° to the original growth direction. However, the change in growth direction is not uniform along the crack front; some portions of the front propagate at +3° to +5°, while adjacent portions propagating at –3° to –5° to the original growth direction. Thus, the crack is no longer flat, but becomes wavy after the 16 h hold period. This out of plane growth may be partially explained in terms of a crack growth model developed by Chuang and Fuller, which predicts an enhancement in the corrosion rate on the flank of a crack at stresses below the stress corrosion threshold. Alternatively, the unevenness of the crack plane after the hold period may be a consequence of a modification of the fracture toughness of the glass as a consequence of leaching.     

On size effect of cleavage cracking in polycrystalline thin films

A crack trapping model is developed for the fracture resistance of high-angle grain boundaries in free-standing brittle thin films, based on which a new size effect is predicted. In addition to the crystallographic misorientations, the grain boundary toughness is also dependent on the film thickness, primarily due to the geometrically necessary crack front branching.     

The interfacial fracture characteristics of bimaterial and sandwich blister specimens

The interfacial crack initiation characteristics of bimaterial and sandwich strip blister specimens were compared. Interface cracks were grown along glass/epoxy interfaces and the corresponding loads, normal crack opening displacements (NCOD) and crack front geometries were measured. Finite element analyses were used to compare NCOD, extract fracture parameters and examine near front stress fields. On the small scale of crack extension that could be measured, the bimaterial specimens exhibited resistance curve behavior whereas none could be resolved in the sandwich specimens. The phase angle dependence of toughness in the bimaterial specimens was similar to that obtained in previous blister tests but was much steeper than has otherwise been measured. The toughness of the glass/epoxy interface in the sandwich specimen decreased with decreasing epoxy thickness in spite of the fact that it was never completely spanned by plastic zones.     

Numerical investigation to prevent crack jumping in Double Cantilever Beam tests of multidirectional composite laminates

During the experimental characterization of the mode I interlaminar fracture toughness of multidirectional composite laminates, the crack tends to migrate from the propagation plane (crack jumping) or to grow asymmetrically, invalidating the tests.The aim of this study is to check the feasibility of defining the stacking sequence of Double Cantilever Beam (DCB) specimens so that these undesired effects do not occur, leading to meaningful onset and propagation data from the tests. Accordingly, a finite element model using cohesive elements for interlaminar delamination and an intralaminar ply failure criterion are exploited here to thoroughly investigate the effect of specimen stiffness and thermal residual stresses on crack jumping and asymmetric crack growth occurring in multidirectional DCB specimens.The results show that the higher the arm bending stiffness, the lower the tendency to crack jumping and the better the crack front symmetry. This analysis raises the prospect of defining a test campaign leading to meaningful fracture toughness results (onset and propagation data) in multidirectional laminates.     

Fracture toughness of laminated steels

Lamination occurs spontaneously in the transverse direction in many commercially available steel plates, if the transverse stresses are sufficiently high. Previous investigations have indicated that lamination is often accompanied by an improvement in the fracture toughness of the plate material. In the vicinity of the crack tip, the stress concentration is so large that the bond between adjacent layers will break before crack propagation sets in. If these layers are sufficiently thin, a state of plane stress is approached near the crack tip. In the present study, the influence of layer thickness and bond strength on the fracture toughness is investigated. It is shown that lamination does improve the toughness, if certain conditions in these variables are fulfilled. This offers a possibility to build up structures with high yield stress and high fracture toughness at the same time, since the permissible defect size to prevent unstable crack growth need not be uncomfortably small.     

Effects of mode mix upon fracture behavior of a solder joint

Results of fracture experiments of brass/solder/brass sandwich CTS (Compact Tension-Shear) specimens are presented together with observations of the crack propagation behavior and the fractographs. The fracture behaviors of the interface crack are analyzed by the finite element method with a modified boundary layer formulation. Several fracture mechanisms and the corresponding criteria are examined. And the crack growth behavior and fracture toughness are predicted. As the results various crack growth procedures such as the crack jump to another interface on the opposite side, the nucleation of a new crack far from the initial crack front, and the asymmetric relation of fracture toughness versus mode mix J _c– can be successfully explained. The fractographs, the crack growth behaviors, and stress-strain distribution along the interface are inter-related.     

Grain Boundary-induced Shielding of Ni-base Single Crystals: Experimental and Analytical Study

1.IotroductionGrainandgrainboundaryarethetwoelemen-taryaspectsofthefractureofalloys.Somepreviousstudiessuchastheselfconsistenttheorycanonlyre-vealthemacroresponsesofthedeformationandfrac-tureofalloys.Increasingresearchinteresthasbeendirectedtowardsstudyingfractureofthebicrystals.Aspreviouslyindicated,itistheinteractionofthecrackwiththegrainwhichdeviatesfromthepredic-tions'basedonLEFMI1'2].Thereisagrainboundary-inducedshieldingeffectl31.Moreover,suchresearchmaythrowlightonthedesignofmaterial…     

木材断裂解离分形特征与分形断裂力学模型研究

目的 以椴木为研究对象,研究冲击载荷作用下椴木试件的断裂解离形貌特征和断裂力学特性,建立适用于木材原料断裂解离的分形断裂力学模型,并对其断裂解离力学行为进行描述。方法 对椴木试件进行冲击加载试验,分析试件断口的形貌特征和断裂力学特性,构建适用于木材原料断裂解离的分形断裂力学模型。结果 椴木试件横向冲击断裂断口裂纹形状和断口形貌特征比纵向冲击复杂,横、纵向冲击断裂断口均具有分形特征;椴木试件纵向冲击断裂韧性均值是横向冲击断裂韧性均值的1.112倍,椴木试件横、纵向冲击断口的分形维数均值分别为2.063 5和2.075 1,椴木试件横、纵向冲击韧性与其断口分形维数之间存在线性正相关关系,拟合优度分别为0.778 7和0.812 2;构建的木材原料断裂解离临界解离应力和断裂韧性的分形断裂力学模型也适用于脆性材料。结论 在木材原料冲击断裂解离时,木材原料初始裂纹长度越短,断裂解离断口越粗糙复杂,木材原料断裂解离所需要的能量越大;当裂纹沿着与冲击加载力方向垂直成大约1.055rad方向扩展时所需的能量最小,木材原料最易沿该方向进行断裂解离。     

Crack trapping effect of persistent grain boundary islands

In the polycrystalline Fe–Si alloy, when a cleavage front transmits from one grain to another, it first penetrates stably across the grain boundary at a number of breakthrough points (BTPs) that distribute along the front quasi‐periodically. As the critical energy release rate is reached, unstable crack jump occurs and the persistent grain boundary islands (PGBI) between the BTPs are left behind the verge of propagating, bridging across the crack flanks, which leads to a 10–30% increase in fracture resistance. In this article, this process is investigated through an energy analysis. The influence of the size/spacing ratio of PGBI on the grain boundary toughness is discussed in detail.