Fracture Mechanics Quantities Research Articles

Signatures of fatigue crack growth from acoustic emission repeaters

Since the discovery of fatigue phenomena, scientific research has constantly sought to understand and anticipate the failure of materials due to fatigue to mitigate unforeseen accidents and malfunctions in various technical fields. Numerous studies using acoustic emission (AE) – a key method in non-destructive testing – have shown a correlation between acoustic activity and fatigue damage. However, these measurements suffer from the non-specific nature of AE signals, which may be due to various physical sources. To investigate further the mechanisms of AE emission associated with fatigue, we study the groups of acoustic signals generated by fatigue cracking in metals. These so-called acoustic multiplets are characterized by highly correlated waveforms, are repeatedly triggered over many successive loading cycles at nearby stress levels and originate from a single location. These acoustic signatures produced during the propagation of fatigue cracks in alloys are automatically detected by a dedicated algorithm, grouped into multiplets and analyzed to understand the physical mechanisms from which they originate. By synchronizing their detection with digital image correlation measurements of fracture mechanics quantities, the investigation of this acoustic emission phenomenon shows that two mechanisms are at the origin of the multiplets: repeated local friction over fracture surfaces, and incremental crack propagation in the Paris regime, probably due to the reactivation of crack tip plasticity at each cycle. These two multiplet types serve as acoustic signatures, distinctly indicating the existence and propagation of a fatigue crack.

Fracture mechanics characterization of mortar nanocomposites reinforced with carbon nanotubes

The objective of this paper is to provide a fracture mechanics characterization of mortar nanocomposites reinforced with multiwall carbon nanotubes (MWCNTs). The critical stress intensity factor, KIc, the strain energy release rate, GIc, the effective crack length, ac, and the crack tip opening displacement, CTODc are determined using three-point bend specimens. It was established that reinforcement of mortar with MWCNTs provides excellent improvement in the above fracture mechanics quantities.

Three-dimensional fields in an infinite transversely isotropic magneto-electro-elastic space with multiple coplanar penny-shaped cracks

This paper investigates the Mode-I crack problem that a three-dimensional infinite space of transversely isotropic multi-ferroic composite medium is weakened by multiple coplanar penny-shaped cracks under uniform mechanical, electric and magnetic loadings. These cracks are arbitrarily distributed in an isotropic plane of the material. Four kinds of idealized electro-magnetic crack boundary conditions, which assume a crack to be electrically permeable (or impermeable) and magnetically permeable (or impermeable), are adopted, and all the possible combinations of these electro-magnetic crack boundary conditions are considered. An approximate three-dimensional solution of the field variables and expressions of some important fracture mechanics quantities are proposed, by virtue of Kachanov’s method and the generalized potential theory method. Numerical examples for some particular configurations of cracks are presented. Based on a two-crack system, the validity of the present solution is checked by comparing the results with their counterparts from a finite element simulation. Interaction of cracks is investigated as well, by taking the crack size and distance between two cracks as factors. From the phenomena shown in the numerical examples, a reduced solution and an empirical method for evaluating generalized stress intensity factors are proposed.

Three-dimensional closed-form solution to elliptical crack problem in magneto-electro-elasticity: Electrically and magnetically induced Maxwell stress boundary condition

An elliptical mode-I crack problem in an infinite multi-ferroic composite material with transverse isotropy under remote uniform mechanical, electric and magnetic loadings is analyzed. The electro-magnetically semi-permeable crack boundary condition and Maxwell stress on the crack faces caused by the electric and magnetic fields are considered, which makes the problem nonlinear. On the basis of the general solution for multi-ferroic composite materials and modern potential theory method, the nonlinear integro-differential boundary equations are established and solved analytically. The field variables in the three-dimensional space and some important fracture mechanics quantities, are obtained in explicit forms. From numerical examples, it is found that the combination of the applied electric and magnetic loadings should be in a elliptical region in the electric displacement-magnetic induction coordinate plane to keep the crack open. Furthermore, in the vicinity of the center of this region, the electro-magnetically semi-permeable crack boundary condition without the Maxwell stress could provide relatively accurate results. Otherwise, the Maxwell stress would have a significant influence, and thus should not be neglected.

Mechanism and modeling of fatigue crack initiation and propagation in the directionally solidified CM186 LC blade of a gas turbine engine

First-stage blades of gas turbines are elements positioned after the combustion chamber and are responsible for extracting energy from high temperature and high pressure gas. One of the common problems of mechanical components, particularly gas turbine blades, is fatigue cracking which usually occurs under variable loading due to the start and shutdown process and vibrations. Low-cycle fatigues are caused by the stress induced by high centrifugal force due to high rotational speed and thermal loads triggered by temperature gradients in startup and shutdown of gas turbine, as well as operation at critical environmental conditions. The present study aimed at presenting the mechanism and modeling of fatigue crack initiation and propagation in CM186 LC directional solidified material of a first-stage gas turbine blade. To investigate the crack initiation point, a finite element study was carried out using ABAQUS software package. The stress distribution of the blade was calculated in accordance with engine conditions and the fatigue crack growth was then predicted by using ZENCRACK fracture mechanics code. Moreover, the Paris model was used in this study to estimate the fatigue life. The stress intensity factors (KI & KII) of individual mode and fracture mechanics quantities were calculated from CTOD and J-Integral methods, followed by the computation of crack growth direction on the basis of maximum energy release rate criterion.

Small scale fracture mechanics of ductile materials: Advantage of fatigue precracks and comparison of J-integral evaluations

Conducting fracture mechanics at small scales and extrapolating the behavior to larger length scales is a powerful tool to analyze materials and components with limited volumes of investigation. A critical requirement for this technique is the validity of the test methods at these scales on one hand, but also that the measured fracture mechanical quantities are independent of specimen size. To check whether the fracture toughness is size dependent we evaluated the fracture toughness of a ductile alloy at two length scales. Furthermore, we also investigated the influence of fatigue precracks compared to ion cut notches that are widely used at the micro scale.

Miniaturized fracture experiments to determine the toughness of individual films in a multilayer system

Recently, the miniaturization of devices in the field of microelectronics has become more and more important. This also implies an increased complexity of the devices, where multilayer thin film systems play a major role. The use of various material combinations leads to the development of residual stresses, potentially causing cracks. Therefore, to prevent failures a thorough understanding of material properties such as the fracture toughness at small scales is indispensable, as these may differ significantly from bulk values. In this study we use miniaturized fracture tests to investigate the fracture behaviour of Cu–W–Cu and W–Cu–W trilayer thin film systems, having a thickness of 500 nm per individual W or Cu layer. The films are subjected to differences in elastic properties and residual stress gradients that both influence the fracture behaviour and thus have to be included in all considerations. We demonstrate that for the W layers a valid J-integral can be evaluated. However, we find that the presented advanced treatment does not allow the extraction of valid fracture mechanical quantities for the Cu layers, pointing out the need to develop a more sophisticated approach for ductile materials.

Verification of Linear Dependence of Plastic Zone Size on J-Integral for Mixed-Mode Loading

Determination of fatigue crack growth characteristics under shear-mode loading is a rather complicated problem. To increase an efficiency and precision of such testing, special specimens enabling simultaneous propagation of shear cracks under II, III and II+III loading modes started to be used rather recently. However, a description of crack growth rate in terms of appropriate fracture mechanics quantities demands a precise assessment of plastic zone size under various shear-mode loading levels. This contribution is focused on the numerical elasto-plastic analysis of stress-strain field at the crack tip in specimens made of a pure polycrystalline (ARMCO) iron loaded by mixed mode II+III. The dependence of plastic zone size on theJ-integral value described the wide region of loading. The results reveal that formixed mode II+III the small scale yielding conditions are fulfilled in the region where plastic zone size is smaller than 1/10 of the total crack length.

Fatigue crack growth prediction in a gas turbine casing

Some gas turbines casings are very susceptible to involve cracking in critical points. According to studies, thermal fatigue specified as the main reason of creation of cracks. This approach is to predict the fatigue life of the detected crack on the edge of eccentric pin hole of a heavy duty gas turbine casing, which is one of the most probable positions for crack initiation and propagation. The crack position and direction was determined, by using non-destructive tests. Distribution of outer surface temperature was measured by using thermography method and for the measurement of inner surface ten thermocouples were installed inside the casing wall. The temperature data was applied as boundary condition in finite element simulation by using Abaqus software. Stress distribution of the casing was calculated in accord to engine work cycle and then, fatigue crack growth was predicted by using ZENCRACK fracture mechanics code. The analysis results showed that the crack growth rate will decrease gradually and after periods of time while stress intensity factor values will reach the Threshold value, the crack propagation will stop. CTOD and J-Integral methods were implemented for calculating the fracture mechanics quantities and Paris model was used to estimate the fatigue life.

Specimens for Simultaneous Mode II, III and II+III Fatigue Crack Propagation: Elasto-Plastic Solution of Crack Tip Stress-Strain Field

Determination of fatigue crack growth characteristics under shear-mode loading is a rather complicated problem. To increase an efficiency and precision of such testing, special specimens enabling simultaneous propagation of shear cracks under II, III and II+III loading modes started to be used rather recently. K-calibration of these specimens was performed and, after unique pre-crack and heat-treatment procedures, effective thresholds in several metallic materials could be measured. However, a description of crack growth rate in terms of appropriate fracture mechanics quantities demands a precise assessment of plastic zone size under various shear-mode loading levels. This contribution is focused on the numerical elasto-plastic analysis of stress-strain field at the crack tip in specimens made of a pure polycrystalline (ARMCO) iron. The results reveal that the small scale yielding conditions are fulfilled in the near-threshold region. Starting from ΔK values approximately two times higher than the threshold, however, the ΔKJ or ΔJ approach should already be utilized. Probably the most interesting result of the analysis lies in a simple procedure that enables us to separate individual loading components ΔKJ,II and ΔKJ,III, applied in the mixed-mode II+III part of the specimen, by comparing elasto-plastic and elastic solutions.

T-stress based short crack growth model for fretting fatigue

The aim of this work is to model short crack growth under fretting fatigue loading conditions by considering a criterion based on linear elastic fracture mechanics quantities, which also accounts for the first non-singular terms of the asymptotic expansion, namely the T-stresses. The Modes I and II Stress Intensity Factors and the T-stresses were computed by the finite element method under plane strain hypothesis. To assess the model fretting fatigue tests were carried out using two cylindrical fretting pads, which were loaded against a flat dogbone tensile test piece, both made of a Ti–6Al–4V titanium alloy. The model was capable to correctly estimate short crack arrest and to find the threshold fretting conditions separating failure from infinite life (here defined by tests which reached one million cycles). An optimization technique was implemented to the numerical model so that it could also estimate crack path.

Fatigue initiation and propagation behavior in bulk-metallic glasses under a bending load

Understanding how to predict the fatigue lifetimes of bulk-metallic glass (BMG) materials is crucially important for their selection as structural alloys. In our paper, the nature of likely fatigue mechanisms for BMGs is revealed. Fatigue cracks, arising from machining/polishing damage, were experimentally observed to initiate from shear bands near defects. At the crack tip, a plastic-zone creation is observed through the formation of many shear bands, and the fatigue crack is found to propagate along these shear bands. The size of the plastic zone can be characterized by fracture-mechanics quantities, and each fatigue cycle is seen to produce a fine striation instead of a single coarse one. We propose a shear-band mechanism to explain the characteristics of the observed fatigue cracking. Numerical computations, based on linear-elastic-fracture mechanics, yield reasonably good agreement with experiments. Our findings are significant to predict the fatigue lifetimes of these materials.

Electrostatic tractions at crack faces and their influence on the fracture mechanics of piezoelectrics

The influence of electrostatic tractions acting upon crack faces on the fracture mechanical quantities in piezoelectric materials under electromechanical loading is investigated. The physical background are the mechanical and dielectric equilibria at an interface between two dielectric domains and related mechanical stresses. The model is applied to a crack problem, where a dielectric interface exists between the solid material and the insulating crack medium. The analytical solution for a crack in an infinite piezoelectric body accounting for intrinsic charges and electrostatic stresses on the crack faces gives insight into the influence of crack boundary conditions on the field intensity factors. Varying loading conditions and the dielectric permittivity of the flaw yields a parameter range in which induced crack surface tractions are relevant. Then, the calculation of the J-integral for thermodynamically consistent crack boundary conditions is discussed. The line integral along the crack faces is replaced by a simple jump term. This approach comes out to be exact only for a simplified model of the electrostatic tractions.

Crack analyses in three-dimensional piezoelectric structures by the BEM

The aim of this paper is the modeling of cracks in three-dimensional piezoelectric structures by means of boundary elements. A single region, direct collocation boundary element code has been implemented, where the anisotropic, piezoelectric fundamental solutions for the coupled electromechanical field problem are calculated applying the Radon transform. For the discretization of the boundary, continuous as well as discontinuous boundary elements with quadratic shape functions are used. The crack itself is modeled by special crack front elements accounting for the r12-behavior of the displacements and electric potentials and the r-12-singularity of the tractions and electric displacements around the crack front. Once the piezoelectric field problem has been solved, fracture mechanics quantities are calculated as mechanical and electrical field intensity factors. Thereby, the properties of the introduced crack tip elements are utilized, i.e., by performing a limiting process over the elements in the ligament. The developed BEM-techniques are applied to three-dimensional example problems. The results are in good agreement with known solutions.

Finite element analysis of a notch root semi-elliptical crack in single crystal superalloy

In this article, the stress/strain concentrations at a notch and the J integral of a semi-elliptical crack embedded at the notch root in a single notch bar of single crystal (SC) superalloy PWA 1480 are studied, using finite element method (FEM). Two material orientations, [0 0 1]/[1 0 0] and [0 0 1]/[1 1 0] (loading/notch directions), have been evaluated to study the effect of material anisotropy on the aforementioned fracture mechanics quantities. In the present study, only the case of mode I cracking is considered with a tensile load applied in the longitudinal direction of the notched bar. The elastic–perfectly-plastic condition is assumed for the material, such a behavior would particularly occur at the notch root. Coupling the elastic–perfectly-plastic condition with the Hill’s function for the yield potential, the material model considers anisotropic yielding but without strain hardening at the post-yield stage. Four load cases for three different crack sizes with the same aspect ratio are analyzed. The effect of material anisotropy on both J integral and crack tip opening displacement (CTOD) are discussed and compared with that of isotropic materials. A correlation is also established between the J integrals of a semi-elliptical crack and that of a through-the-thickness crack evaluated based on the continuously distributed dislocation theory.

Response of a Cracked Cantilever Beam to Free and Forced Vibrations

Cracks present in machine parts affect their vibrational behaviour like the fundamental frequency and the resonance. In this paper, the resonance response of a cracked cantilever rectangular beam has been studied based on fracture mechanics quantities like strain energy release rate, stress intensity factor and compliance. The spring stiffness and the fundamental frequency decrease with increase in crack length. The amplitude of vibration increases and the occurrence of resonance gets shifted with increase in crack length.

Messunsicherheiten bestimmen

UNCERT - Codes of Practice for the Determination of Uncertainties in Mechanical Tests of Metallic Materials. Mechanical testing labs are increasingly recommended to include the uncertainties affecting the measured data into the test reports. But, still there is a lack of special procedures for determination of uncertainties. Up till now, such procedures only exist for the tensile test, the creep rupture test and the hardness test. In order to close this gap, the project UNCERT was initiated within the Standards, Measurement and Testing Programme of CEC. UNCERT provides appropriate procedures as Codes of Practice for 17 types of tests, e. g. tensile, hardness, charpy impact, creep, bend, HCF, LCF-test, determination of fracture mechanical quantities, residual stress measurement by the hole drilling method etc. All procedures have already been drafted and included in a Manual of Codes of Practice. In this contribution reports the general procedure of uncertainty determination is described and its application in the Codes of Practice is shown for the tensile test and the residual stress measurement.

An intergranular creep crack growth model based on grain boundary sliding

An intergranular crack growth model is developed to describe the effect of microstructural features such as grain size, grain boundary precipitates, and serrated grain boundaries on creep crack growth under grain boundary sliding (GBS) conditions. The model considers quantitatively that several deformation mechanisms contribute to the stress redistribution ahead of the crack tip through a stress relaxation process. The crack tip region is divided into three zones: (a) the intragranular-deformation-controlled stress relaxation zone, (b) the GBS-controlled stress relaxation zone, and (c) the elastic region. Intergranular creep crack growth is considered to occur as a result of the GBS-controlled process in all cases. The derived creep crack growth model shows a complex dependence of the creep crack growth rate (CCGR) on fracture mechanics quantities, such as C(t) (the path-independent energy integral with its steady-state value as C*) and K (the stress intensity factor). For creep-brittle materials, the model predicts that the CCGR depends on K to the power of 2 and this is verified experimentally; however, when environmental effects contribute to the crack growth process, the power exponent will increase. A semiempirical factor is introduced to account for the effects of oxidation on CCGR.

Creep-fatigue crack growth in austenitic stainless steel centre cracked plates at 650°C. Part I: experimental study and interpretation

Experimental data on fatigue or creep-fatigue crack growth on large components at high temperature are of primary importance to validate or develop further existing defect assessment procedures and leak before break methods. This paper addresses in the first part a detailed presentation of a creep-fatigue experiment consisting of a wide plate subjected to cyclic bending loads. The specimen consists of a large 316L(N) austenitic stainless steel plate containing a wide semi-elliptical surface notch, machined in the centre of the specimen. The test is conducted at a temperature of 650°C. Over 3000 cycles with a one hour holdtime at the peak load of the cycle were applied to the plate allowing to obtain a significant amount of crack growth, both on the surface and through the thickness of the plate. In the second part, a first interpretation of the experimental results is proposed. It is based on global fracture mechanics quantities estimated from a linear elastic analysis. The results are compared with those obtained from similar plate specimens but for continuous fatigue loading conditions. A good correlation of the experimental results is obtained with observations made on small scale laboratory specimens.

Instrumentierter Kerbschlagbiegeversuch

The German DVM-group on Instrumented Impact Testing has recently finished a round-robin test. Seventeen participants performed about 400 instrumented Charpy tests with a German reactor pressure vessel steel at four different temperatures. The specimens were prepared with standardized V-notches, spark-eroded crack-similar slits or fatigued cracks. Besides standardized material data, like e.g. the Charpy energy, especially characteristic forces and partial energies were determined and thereon based evaluations of fracture mechanical quantities were performed. The results of the participants showed an excellent agreement. A high accuracy of the force measurement was observed. Therefore, these results support current international activities to standardize the instrumented Charpy test.