Fatigue crack propagation characteristics of high‐tensile steel wires for bridge cables

The viability of single edge cracked sheet test method for rapidly determining the crack propagation characteristics of steel wires was investigated. First, fatigue tests under 3 different stress ratios were conducted on the sheet specimens which were manufactured from a kind of widely used cable wires. The test data were analysed, and the crack growth rates of sheet specimens were constructed by Walker model. Then, a series of fatigue tests were performed on notched round‐bar specimens to verify the predictability of Walker model parameters. Moreover, the experimental results obtained in different studies on crack propagation characteristics of steel wires were discussed. The results show that the crack propagation characteristics of sheet specimens behave a certain dependence on depth. The sheet crack growth laws can be well used to predict the fatigue life of notched bar specimens when the mechanical heterogeneity is considered. For bridge cable steels, the rational values for the exponent parameter of Paris law, m, should be close to 3.     

层状Ti3SiC2陶瓷的组织结构及力学性能

利用热压烧结TiH₂,Si和C粉获得了致密度大于98%的层状Ti₃SiC₂陶瓷。利用压痕法,在不同的载荷下测定了材料的维氏硬度, 发现其硬度值随载荷的增加而降低,在最大载荷30kg时,硬度值为4GPa。压痕对角线没有发现径向裂纹的出现。 这归因于多重能量吸收机制——颗粒的层裂、裂纹的扩展、颗粒的变形等。利用三点弯曲法和单边切口梁法测定了材料的强度和韧性分别为270MPa和6.8MPa·m1/2。Ti₃SiC₂材料的断口表现出明显的层状性质,大颗粒易于发生层裂和穿晶断裂,小颗粒易被拔出。当裂纹沿平行于Ti₃SiC₂基面的方向扩展造成颗粒的层裂,当裂纹沿垂直于基面的方向扩展时,裂纹穿过颗粒的同时,在颗粒内部发生偏转,使裂纹的扩展路径增加。裂纹的扩展路径类似人们根据仿生结构设计的层状复合材料。裂纹在颗粒内的多次偏转、裂纹钉扎以及颗粒的层裂和拔出等是材料韧性提高的主要原因。此外,在室温下得到的荷载-位移曲线,说明Ti₃SiC₂材料不象其它陶瓷材料的脆性断裂,而是具有金属一样的塑性。     

A New Procedure for Mode I Fracture Characterization of Cement‐Based Materials

Fracture characterization under mode I loading of a cement‐based material using the single‐edge‐notched beam loaded in tree‐point‐bending was performed. A new method based on beam theory and crack equivalent concept is proposed to evaluate the Resistance‐curve, which is essential to determine fracture toughness with accuracy. The method considers the existence of a stress relief region in the vicinity of the crack, dispensing crack length monitoring during experiments. A numerical validation was performed by finite element analysis considering a bilinear cohesive damage model. Experimental tests were performed in order to validate the numerical procedure. Digital image correlation technique was used to measure the specimen displacement with accuracy and without interference. Excellent agreement between numerical and experimental load–displacement curves was obtained, which validates the procedure.     

Experimental investigation on low cycle fatigue and fracture behaviour of a notched Ni‐based superalloy at elevated temperature

In order to investigate the effects of stress concentration on low cycle fatigue properties and fracture behaviour of a nickel‐based powder metallurgy superalloy, FGH97, at elevated temperature, the low cycle fatigue tests have been conducted with semi‐circular and semi‐elliptical single‐edge notched plate specimens at 550 and 700 °C. The results show that the fatigue life of the notched specimen decreases with the increase of stress concentration factor and the fatigue crack initiation life evidently decreases because of the defect located in the stress concentration zone. Moreover, the plastic deformation induced by notch stress concentration affects the initial crack occurrence zone. The angle α of the crack occurrence zone is within ±10° of notch bisector for semi‐circular notched specimens and ±20° for semi‐elliptical notched specimens. The crack propagation rate decreases to a minimum at a certain length, D, and then increases with the growth of the crack. The crack propagation rate of the semi‐elliptical notched specimen decelerates at a faster rate than that of the semi‐circular notched specimen because of the increase of the notch plasticity gradient. The crack length, D, is affected by both the applied load and the notch plasticity gradient. In addition, the fracture mechanism is shown to transition from transgranular to intergranular as temperature increases from 550 to 700 °C, which would accelerate crack propagation and reduce the fatigue life.     

On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture

In this paper, strong discontinuities embedded in finite elements are used to model discrete cracking in quasi-brittle materials. Special attention is paid to (i) the constitutive models used to describe the localized behaviour of the discontinuities, (ii) the enforcement of the continuity of the crack path and (iii) mixed-mode crack propagation. Different constitutive relations are adopted to describe the localized behaviour of the discontinuities, namely two damage laws and one plasticity law. A numerical algorithm is introduced to enforce the continuity of the crack path. In the examples studied, an objective dissipation of energy with respect to the mesh is found. Examples of mode-I and mixed-mode crack propagation are presented, namely a double notch tensile test and a single-edge notched beam subjected to shear. In the former case different crack patterns are obtained depending on the notch offset; in the latter case special emphasis is given to the effect of shear on the global structural response. In particular, both the peak load and the softening response of the structure are related to the amount of shear tractions allowed to develop between crack faces. The results obtained are compared to experimental results. As a general conclusion, it is found that crack path continuity allows for the development of crack patterns similar to those found in experiments, even when reasonably coarse meshes are used.     

Modelling on crack propagation behaviours at concrete matrix‐aggregate interface

A numerical model is proposed to simulate crack propagation at concrete matrix‐aggregate interface. One single aggregate surrounded by concrete matrix is taken to demonstrate the behaviours of crack penetration into concrete matrix and crack growth along the interface. Influences of side‐edge constraint, aggregate direction, and interface fracture energy on the crack propagation behaviours are respectively investigated. The results show that, tensile constraint on the side edge, a smaller angle between tensile axis and aggregate, and higher fracture energy lead to a higher rupture strength of the interface. Once the interface crack starts to grow, it propagates to the two ends of aggregate major axis drastically and further penetrates into the matrix. Nevertheless, these factors have no appreciable influence on crack propagation path. By mapping interface crack into major axis, ordinary crack is generated. Using the above simplification, modelling of multiple crack propagation in concrete is efficiently achieved.     

Experimental Investigations of Fracture Process in Concrete by Means of X‐ray Micro‐computed Tomography

The paper describes investigation results on fracture in notched concrete beams under quasi‐static three‐point bending by the X‐ray micro‐computed tomography. The two‐dimensional (2D) and three‐dimensional image procedures were used. Attention was paid to width, length, height and shape of cracks along beam depth. In addition, the displacements on the surface of concrete beams during the deformation process were measured with the 2D digital image correlation technique in order to detect strain localisation before a discrete crack occurred. The 2D fracture patterns in beams were numerically simulated with the finite‐element method using an isotropic damage constitutive model enhanced by a characteristic length of micro‐structure. Concrete was modelled as a random heterogeneous four‐phase material composed of aggregate, cement matrix, interfacial transitional zones and air voids. The advantages of the X‐ray micro‐computed tomography were outlined.     

Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.     

Prediction on fatigue life of U‐notched PMMA plate

In this paper, fatigue life prediction of U‐notched polymethyl methacrylate (PMMA) plate is numerically investigated based on the combination of fatigue damage mechanism and fatigue crack propagation mechanism. First, strength and stiffness degeneration criterions during the fatigue process are established on the basis of nonlinear progressive damage evolution, and the fatigue crack initiation life is estimated. Second, fatigue crack propagation phase is analysed through virtual crack closure technique. The fatigue crack propagation life before totally fracture is also predicted. Finally, finite element models of PMMA plate weakened by lateral symmetric U‐notch are built up using ABAQUS, and the total fatigue life of notched plate is calculated by combining the crack initiation life with the crack propagation life. These results will play an important role for evaluating the fatigue life of U‐notched PMMA plate.     

Application of the cohesive zone model for analysing the edge crack propagation of steel sheet in the cold rolling process

In the cold rolling process, the expansion and coalescence of micro‐defects can make steel sheet quality descend and create edge crack in the steel sheet. And the edge crack can cause the strip rupture completely. In this research, the cohesive zone model (CZM) was used to analyse the initiation and propagation of edge crack in the cold rolling process with the non‐reversing two‐high mill. A bi‐linear traction–separation law was utilized which is primarily given by the CZM parameters including the cohesive stress, T, and the cohesive energy, Γ. Compared with other popular models such as the Gurson–Tvergaard–Needleman (GTN) model, the CZM presents certain advantages because it requires a smaller number of parameters to be defined. Comparison results of the experiments and simulation illustrated that the CZM can provide accurate prediction for the propagation of edge crack in the cold rolling process. Parametric analysis was carried out and showed that the extent of the crack propagation increases with the increasing of the reduction ratio.     

A contact algorithm for frictional crack propagation with the extended finite element method

We present an incremental quasi‐static contact algorithm for path‐dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows for the modeling of frictional contact independent of the FE mesh. Standard Coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity. The contact constraint is borrowed from non‐linear contact mechanics and embedded within a localized element by penalty method. Newton–Raphson iteration with consistent linearization is used to advance the solution. We show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called ‘LATIN’ for frictional crack propagation. Numerical examples include simulation of crack initiation and propagation in 2D plane strain with and without bulk plasticity. In the presence of bulk plasticity, the problem is also solved using an augmented Lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution. Copyright © 2008 John Wiley & Sons, Ltd.     

Equivalent crack based mode II fracture characterization of wood

This paper reports a numerical study of the end notched flexure Pinus pinaster wood specimen. The main objective was to validate a data reduction method based on the equivalent crack concept, in order to avoid well-known difficulties in monitoring crack propagation. A cohesive linear softening damage model based on developed interface elements was used to simulate crack propagation. The equivalent crack proposed was related to the fracture process zone, whose effect on the perceived critical strain energy release rate was assessed. The equivalent crack was incorporated in a compliance-based beam method, which provided accurate values of the mode II critical strain energy release rate, G_IIc. Furthermore, compliance-based beam method does not require crack measurements during end notched flexure tests and additional tests to obtain elastic properties.     

How cracks propagate in a vitreous dense biopolymer material

Crack propagation in vitreous biopolymer material is studied considering numerical and experimental aspects. Finite Element computation is performed to predict crack propagation in starch material. Maximum dilatational strain energy criterion is used as a criterion for crack propagation. Model validation is undertaken considering notched specimens with a hole under tensile loading. The experimental results show that the crack path is affected by the presence of the defect, which allows adequate testing of the crack propagation criterion under a mixed mode. The predicted results show that the selected criterion anticipates adequately the crack propagation in vitreous starch under linear elastic conditions.     

An improved crack tracking algorithm with self-correction ability of the crack path and its application in a continuum damage model

In this paper, a new procedure for predicting the crack propagation and fracture behavior in quasi-brittle materials is presented based on continuum damage mechanics. Several crack tracking algorithms are widely used for failure analysis, among which the local tracking algorithm is very simple and easy to implement with low computational cost. However, in the prediction of crack growth with the traditional local tracking algorithm, it can be often seen that the sharp changes in the crack path such as U-turns can occur. An improved local tracking algorithm with self-correction ability of the crack path is proposed to overcome these difficulties of the traditional crack tracking algorithms. A continuum damage model, in addition to the present crack tracking algorithm, can greatly enhance the performance of failure prediction in quasi-brittle materials. The present approach has the advantages that it can well predict the crack propagation path and can avoid mesh size and mesh bias dependence without the embedment of discontinuities or nodal enrichment. The present model is incorporated into ANSYS by the ANSYS Parameter Design Language to simulate the initiation and propagation of the discrete crack in engineering applications. The numerical results by this model are compared with the ones by the extended finite element method and experiments, and good agreements are achieved.     

Mode I Fracture Toughness of CNT‐Reinforced PMMA

The influence of carbon nanotube (CNT) concentration on the fracture toughness of poly(methyl methacrylate) (PMMA) was examined on single‐edge V‐notched‐beam (SEVNB) specimens. Six groups of SEVNB specimens containing 0.5, 1, 2, 4, 8.5 wt% of CNTs and neat PMMA as a reference were tested. First, a notch was introduced into the specimens by a specially made disk whose edge is V‐shaped with a 30^° angle and a 30 μm tip width. As suggested by an American Society for Testing and Materials Standard for polymers, induction of a natural crack was attempted, without success. Therefore, fracture toughness values were determined with the ‘sharp’ machined notch by means of a calibration formula. These were compared to values obtained using a stress concentration factor and found to differ by less than 3%. The latter calculation takes into account the geometry of the notch. Results showed a decrease in the fracture toughness values with an increase in the CNT concentration. For specimens in which a natural crack was attempted, referred to as a razor‐cut notch, a significant increase in the apparent fracture toughness was observed, as a result of the induced damage.     

High speed fracture in brittle materials: Supersonic crack propagation

Microcircuit resistance grids were deposited on the surface of glass and glass-ceramic single edge notched beam (SENB) specimens. The individual strips were as small as ~ 10 μm in width. The specimens were broken in bending and the signal from the grids was captured using a waveform recorder. It was observed that the crack began to propagate with a nonzero initial velocity provided the initial notch was blunt. With continued crack propagation, the crack velocity decreased. In specimens with sharp notches, the crack began propagating with a near zero velocity and the velocity increased with increasing crack length. In some glass specimens with blunt notches, the initial crack velocity was found to be considerably greater than the sound velocity thereby showing that supersonic crack propagation can occur.     

Experimental fatigue crack growth analysis and modelling in part‐through circumferentially pre‐cracked pipes under pure bending load

In the present work, an attempt has been made to study the fatigue crack growth in a part‐through circumferentially notched pipe specimen. It has been observed that under four‐point bend cyclic load, the crack propagates in a transverse plane in the radial direction initially followed by propagation in the circumferential direction. The crack extension in the circumferential direction resulted crack growth retardation in the radial direction. This behaviour of the fatigue crack growth has been modelled, and a fatigue life prediction methodology based on an exponential model has been applied for prediction of fatigue crack growth.     

Analysis of the crack growth propagation process under mixed-mode loading

In the present paper, a computational model for crack growth analysis under Mode I/II conditions is formulated. The focus is on two issues – crack path simulation and fatigue life estimation. The finite element method is used together with the maximum principal stress criterion and the crack growth rate equation based on the equivalent stress intensity factor. To determine the mixed-mode stress intensity factors, quarter-point (Q-P) singular finite elements are employed. For verification purposes, a plate with crack emanating from the edge of a hole is examined. The crack path of the plate made of 2024 T3 Al Alloy is investigated experimentally and simulated by using the finite element method with the maximum tangential stress criterion. Then, the validation of the procedure is illustrated by applying the numerical evaluation of the curvilinear crack propagation in the polymethyl methacrylate (PMMA) beam and the Arcan specimen made of Al Alloy for which experimental results are available in the literature. In order to estimate fatigue life up to failure of the plate with crack emanating from the edge of a hole, the polynomial expression is evaluated for the equivalent stress intensity factor using values of stress intensity factors obtained from the finite element analysis. Additionally, the fatigue life up to failure of the Arcan specimen is analyzed for different loading angles and compared with experimental data. Excellent correlations between the computed and experimental results are obtained.     

Fracture behavior of notched specimens of TiAl alloys

Fracture behavior of a two-phase TiAl alloy was investigated using notched specimens. Fracture surfaces and metallographic sections of surviving notch in double notched specimens are observed. The fracture process of notched specimens of TiAl alloys was described as that several inter-lamellar cracks initiate and extend directly from the notch root and propagate preferentially along the interfaces between lamellae and stop at various obstacles. With increasing applied load, cracks connect with each other and propagate further by translamellar cracks. The toughening mechanisms, which make the main crack difficult to propagate or cause it to be stopped, could be reducing the driving force for crack propagation. The higher toughness of near fully lamellar microstructure than that of finer duplex microstructure is attributed to the path of crack propagation. On the fracture surfaces of the finer duplex microstructure, more low-energy-spending interlamellar fracture facets are observed, which means that it is easier for crack to bypass a fine duplex lamellar grain with lamellae perpendicular to the main crack and to take a interlamellar path.     

Influence of sub-micrometer notches on the fracture of single crystal silicon thin films

The influence of notches on the fracture of single crystal silicon thin films was investigated. The tests were conducted on notched and smooth tensile specimens micromachined on a silicon wafer. The specimen geometry was 100 μm long, 50 μm wide and 5 μm thick. For the notched specimen, a V‐shaped sub‐micrometer notch was introduced on one edge of it by using a focused ion beam (FIB) process. The notch lengths ranged from 0.07 to 1.3 μm. Four types of specimens with different surfaces and tensile orientations were tested. The smooth specimens showed scattered fracture strengths and ‘collapsed’ fractures. For the restrictive‐shaped notches, the critical length was 0.5 μm. The short‐notched (<0.5 μm) specimens also showed ‘collapsed’ fractures, and the stress concentrations on notch tips decreased their fracture strengths. For the long‐notched (>0.5 μm) specimens, the notch was equivalent to a crack in the Griffith model and the crack mainly propagated on {111} cleaved planes.