Crack Tip Mechanics Research Articles

Unravelling the lamellar size-dependent fracture behavior of fully lamellar intermetallic [formula omitted]-TiAl

Strengthening of metals by incorporating nano-scale coherent twin boundaries is one of the important breakthroughs of recent years in overcoming the strength-ductility trade-off. To this effect, also twin boundaries in nano-lamellar lightweight Ti-Al alloys promise a great potential, but their contribution to the deformation and fracture behavior needs to be better understood for designing optimal microstructures. To this end, we carry out linear elastic fracture mechanics informed large-scale atomistic simulations of fully lamellar microstructures consisting of the so-called ”true twin” boundaries in γ-TiAl. We find that nano-scale lamellae are not only effective in improving the fracture toughness and crack growth resistance, but also that the lamellar size controls the crack tip mechanisms. We identify a critical lamella thickness in the region between 1.64 and 3.04 nm, above which the crack tip events are primarily dislocation-based plasticity and the critical fracture initiation toughness exhibits an increasing trend with decreasing lamella size. Below the critical thickness, a decline in fracture toughness is observed and the crack tip propagation mechanisms are quasi-brittle in nature, i.e. the cleavage of atomic bonds at the crack tip is accompanied by plasticity events, such as twin-boundary migration and dislocation nucleation. A layer-wise analysis of the unstable stacking fault energy, the energy barrier for dislocation nucleation, that the critical thickness is of a similar value as the distance from the twin boundary at which bulk properties are restored.

Crack tip fields and fracture resistance parameters based on strain gradient plasticity

The crack tip mechanics of strain gradient plasticity solids is investigated analytically and numerically. A first-order mechanism-based strain gradient (MSG) plasticity theory based on Taylor’s dislocation model is adopted and implemented in the commercial finite element package ANSYS by means of a user subroutine. Two boundary value problems are considered, a single edge tension specimen and a biaxially loaded plate. First, crack tip fields are characterized. Strain gradient effects associated with dislocation hardening mechanisms elevate crack tip stresses relative to conventional plasticity. A parametric study is conducted and differences with conventional plasticity predictions are quantified. Moreover, the asymptotic nature of the crack tip solution is investigated. The numerical results reveal that the singularity order predicted by the first-order MSG theory is equal or higher to that of linear elastic solids. Also, the crack tip field appears not to have a separable solution. Moreover, contrarily to what has been shown in the higher order version of MSG plasticity, the singularity order exhibits sensitivity to the plastic material properties. Secondly, analytical and numerical approaches are employed to formulate novel amplitude factors for strain gradient plasticity. A generalized J-integral is derived and used to characterize a nonlinear amplitude factor. A closed-form equation for the analytical stress intensity factor is obtained. Amplitude factors are also derived by decomposing the numerical solution for the crack tip stress field. Nonlinear amplitude factor solutions are determined across a wide range of values for the material length scale l and the strain hardening exponent N. The domains of strain gradient relevance are identified, setting the basis for the application of first-order MSG plasticity for fracture and damage assessment.

Anisotropic failure behavior of ordered intermetallic TiAl alloys under pure mode-I loading

Whether a metallic material fractures by brittle cleavage or by ductile rupture is primarily governed by the competition between cleavage and dislocation emission at the crack tip. The linear elastic fracture mechanics (LEFM) based criterion of Griffith, respectively the one for dislocation emission of Rice, are sufficiently reliable for determining the possible crack tip propagation mechanisms in isotropic crystalline metals. However, the applicability of these criteria is questionable when non-cubic, anisotropic solids are considered, as e.g. ordered intermetallic TiAl phases, where slip systems are limited and elastic anisotropy is pronounced. We study brittle versus ductile failure mechanisms in face-centered tetragonal TiAl and hexagonal Ti3Al using large-scale atomistic simulations and compare our findings to the predictions of LEFM-based criteria augmented by elastic anisotropy. We observe that the augmented Griffith and Rice criteria are reliable for determining the direction dependent crack tip mechanisms, if all the available dislocation slip systems are taken into account. Yet, atomistic simulations are necessary to understand crack blunting due to mixed mechanisms, or shear instabilities other than dislocation emission. The results of our systematic study can be used as basis for modifications of the Griffith/Rice criteria in order to incorporate such effects.

Numerical simulation of fatigue crack growth based on accumulated plastic strain

Fatigue crack growth (FCG) is simulated here by node release, which is made when the accumulated plastic strain reaches a critical value. The numerical procedure is very robust, showing a very fast stabilization and independence relatively to the load considered for node release. A critical accumulated plastic strain of 110% was obtained for the 2024-T351 aluminium alloy, comparing the experimental value of da/dN for a crack length of 26.5 mm and a stress ratio of 0.1, with plane strain numerical predictions. This critical value was used to predict da/dN for different crack lengths. The da/dN-ΔK curve was found to be linear in log-log plot with a slope m = 2.4, which is lower than the slope m = 3.6 presented by the experimental results. The difference is attributed to crack tip mechanisms activated at relatively high loads. The variation of stress ratio and stress state did not affect the da/dN-ΔK curves, which indicates that the effect of these parameters is not linked to crack tip plastic deformation. FCG rate was also predicted for the 7050-T6 aluminium alloy and the 18Ni300 maraging steel, and slopes m = 3.09 and 2.70, respectively, were obtained for da/dN-ΔK curves. The predictions obtained for the steel agreed well with experimental results.

Effect of crack length on tip field of 304 stainless steel SCC

Stress corrosion cracking (SCC) is one of the key issues affecting the long-term safe operation of high temperature pressure vessels and pipeline. In this paper, the effect of crack length on the SCC crack tip field of austenitic 304 stainless steel is studied by using a compact tensile specimen. Firstly, the finite element model of SCC crack tip creep is established by using ABAQUS, and the crack tip creep and creep to crack tip mechanics are analyzed. The influence of different crack lengths on crack tip creep and creep rate was studied. It can be obtained by numerical simulation analysis software. The high creep variable area is mainly concentrated in the near crack tip region. The crack length has a great influence on the SCC crack tip creep field. With the continuous expansion of the austenitic 304 stainless steel crack, crack tip creep variables and creep rates are also increasing. It provides a theoretical reference for the safety evaluation and analysis of high temperature pressure vessels and pipelines.

A unified method to solve higher order asymptotic crack-tip fields of mode I, mode II and mixed mode I/II crack in power-law creeping solids

A higher order asymptotic analysis with separable variable form is presented in this paper for crack tip mechanics fields under mixed mode creep conditions. By defining a second order mode mixity factor, higher order term solutions are investigated by solving the boundary value problem. The solution procedure is validated first and then the characteristics of various kinds of second order asymptotic solutions for mixed I/II creep crack tip field are presented and discussed. The angular distribution functions of the second order stress and the stress exponent for various cases are given. Detailed relations between the amplitudes of the second order term and the first order term are also discussed. The method and solutions given in this paper encompass the higher order term solutions of pure mode I, pure mode II and mixed mode I/II.

Hydrogen-induced cracking of an aluminum single crystal: An atomistic simulation

The purpose of this paper is to examine the effect of hydrogen on the crack tip mechanism of an Al single crystal. A (121)[11¯1] (plane/front) crack system model with a varying hydrogen concentration was investigated based on a molecular dynamics (MD) framework employing an angular-dependent interatomic potential (ADP). The incipient crack tip event was analyzed using a mixed-mode displacement solution for mode-I and mode-II crack tip fields. The critical stress intensity factor for the onset of the crack tip deformation event was evaluated. A detailed description based on a von Mises atomic shear strain analysis revealed that the presence of hydrogen near a crack tip significantly inhibited the activities of emitted partial dislocations. The hydrogen locking of dislocations near a crack tip was found to facilitate the local amorphization of the crack tip, which considerably reduced the critical stress intensity factor for the onset of crack growth. The effect of the loading mode on the atomic-scale mechanism of the hydrogen embrittlement (HE) was further analyzed, and the explicit dependence of in-plane shear loading was observed.

Simulation of anisotropic crack tip deformation processes and particle interactions in toughened polymers

This study develops a finite element-based simulation of submicrometer crack tip deformation processes in polymers to investigate local toughening effects. An initial study of how these processes interact with stiff inclusions is presented to enable further investigation of particulate toughening. Crack tip and process zone mechanisms, including polymer chain disentanglement, directional chain realignment with consequent anisotropy, and crack propagation, are considered in a dedicated user-defined material law. Such processes are generally homogenized on higher scale continuum levels analyses, but direct simulation can provide insight into toughening mechanisms that have been widely observed but not fully explained. The user material law herein was employed in a parametric study to investigate the relative importance of (1) the extent of local inelastic polymer chain realignment and (2) consequent anisotropic hardening of the realigned polymer chains. In order to explore the interaction of fracture processes with nanometer-scale inclusions, silica particles with varied spacing were also included in the simulations. The interaction between local stress concentration and energy dissipation mechanisms has been quantified. It is shown that in neat polymers, local yielding is the dominant toughening effect accounting for over 90% of the local energy absorption, whereas local stiffening alone would decrease toughness. Stiff inclusions were shown to generally decrease toughness, except in cases where local yielding greatly outweighs local stiffening effects. Roughly 45% increase in toughness was shown for a 250-nm particle spacing that balances the acceleration of elastic failure with the formation of a larger local yield zone size. This demonstrates the utility of employing dedicated material laws to microstructural scale analyses in providing design targets in material design.

Synchrotron X-ray diffraction based method for stress intensity factor evaluation in the bulk of materials

A generalised approach for determining the stress intensity factor in the bulk of non-transparent materials is presented. The new approach combines experimental elastic strain data, measured with powerful synchrotron X-ray diffraction, with an elastic model based on Williams’ series development. The stress intensity factor is calculated using a multi-point over-deterministic method where the number of experimental data points is higher than the number of unknowns describing the elastic field surrounding the crack-tip. The tool is tested on X-ray strain measurements collected on a bainitic steel. In contrast to surface techniques the approach provides insights into the crack tip mechanics deep within the sample and makes full use of the plastic zone data. Satisfactory results are obtained with 1 term in the series development and a smaller region of interest. By increasing the number of terms, it is possible to improve the accuracy in the SIF predictions but this requires a larger region of interest.

Multi-approach study of crack-tip mechanics on aluminium 2024 alloy

This work presents a comprehensive study for characterising the crack-tip mechanics and fatigue crack propagation in an Aluminium 2024-T351 alloy. It combines information obtained from three different sources: full-field displacement information from digital image correlation, analytical modelling of the crack-tip field and SEM fractographies. The displacement data measured around the crack-tip are fitted to a Williams’ series development in order to evaluate singular and non-singular terms of the crack-tip field. The procedures also allows rigid body motion to be corrected and the crack-tip coordinates and crack orientation to be estimated. Fatigue striations from the fracture surface were analysed with SEM in order to estimate the crack growth rate for different boundary conditions. Representation of all the results together with the Paris law data of the alloy allows the procedures to be cross-validated and to fit with a good agreement micro-scale measurements with continuum mechanics estimations.

Evaluation of crack-tip fields from DIC data: A parametric study

In the past two decades, crack-tip mechanics has been studied increasingly using full-field techniques. Within these techniques, Digital Image Correlation (DIC) has been most widely used due to its many advantages, to extract important crack-tip information, including Stress Intensity Factor (SIF), crack opening displacement, J-integral, T-stress, closure level, plastic zone size, etc. However, little information is given in the literature about the experimental setup that provides best estimations for the different parameters. The current work aims at understanding how the experimental conditions used in DIC influence the crack-tip information extracted experimentally. The influence of parameters such as magnification factor, the position of the images with respect the crack-tip and size of the subset used in the correlation is studied. The influence is studied in terms of SIF by using Williams’ model. In this regard, cyclic loading on a fatigue crack in a compact tension (CT) specimen, made of aluminium 2024-T351 alloy, has been applied and the surface deformation around the crack-tip has been examined. The comparison between nominal and experimental values of KI showed that the effect of subset size on the measured KI is negligible compared to the effect of the field of view and the position of the area of interest.

Some experimental observations of crack-tip mechanics with displacement data

In the past two decades, crack-tip mechanics has been increasingly studied with full-field techniques. Within these techniques, Digital Image Correlation (DIC) has been most widely used due to its many advantages, to extract important crack-tip information, including Stress Intensity Factor (SIF), Crack Opening Displacement, J-integral, T-stress, closure level, plastic zone size, etc. However, little information is given in the literature about the experimental setup that provides best estimations for the different parameters. The current work aims at understanding how the experimental conditions used in DIC influence the crack-tip information extracted experimentally. The influence of parameters such as magnification factor, size of the images, position of the images with respect the crack-tip and size of the subset used in the correlation is studied. The influence is studied in terms of SIF and T-stress by using Williams’ model. The concept of determination of the K-dominance zone from experimental data has also explored. In this regard, cyclic loading on a fatigue crack in a compact tension (CT) specimen, made of aluminium 2024-T351 alloy, has been applied and the surface deformation ahead of the crack tip has been examined. The comparison between theoretical and experimental values of KI showed that the effect of subset size on the measured KI is negligible compared to the effect of size of the image.

Application of CTOD in Atomistic Modeling of Fracture

In atomistic modeling of fracture, most examinations are based on the Griffith energy, calculated from the surface energy, and the stress intensity factor derived from continuum mechanical formulations. Both approaches, however, reflect continuum mechanics and lack the direct connection to the atomistic crack tip mechanisms, and it is thus appealing to examine if Crack Tip Opening Displacement, CTOD, can be a meaningful physical parameter in atomistic modeling of material failure.In this presentation we first review our previous examinations of the crack tip displacements from fracture of single crystal silicon. We there established a procedure to determine the deformation zone ahead of the crack tip, based on CTOD90degree and CTODblunting, and demonstrated that CTOD could give a realistic estimate of the fracture toughness.The same procedure has then been applied on iron, loaded by a Modified Boundary Layer (MBL) model. In this case the crack flanges were not straight, and we were not able to extrapolate the flanges and define the center of rotation. However, by directly measure the deformed zone ahead of the crack tip, we could obtain realistic estimates of the fracture toughness via the CTOD.

Deterministic Formulation of the Effect of Stress Intensity Factor on PWSCC of Ni-Base Alloys and Weld Metals

The fundamental correlations such as crack growth rate (CGR) versus K for primary water stress corrosion cracking (PWSCC) of nickel-base alloys in simulated pressurized water reactor environments are quantified with the theoretical model based on the combination of crack tip mechanics and oxidation kinetics. Materials reliability program (MRP) proposed a CGR disposition curve in a report MRP 55 for PWSCC of thick-section Alloy 600 materials. This deterministic CGR equation has been adopted by Section XI Nonmandatory Appendix O of the ASME Boiler and Pressure Code for flaw evaluation. MRP also proposed a CGR disposition curve in a report MRP 115 for PWSCC of Alloy 82/182/132 weld metals. Stress intensity factor (K), temperature and thermal activation energy are included in both MRP 55 and MRP 115 reports. Both MRP 55 and MRP 115 are engineering-based. The results of mechanism-based modeling are compared with the screened experimental data for typical PWSCC systems of nickel-base alloys and the consistence is observed.

Multiscale simulations of mixed-mode fracture in bcc-Fe

Mixed-mode fracture of bcc-Fe has been investigated using the quasicontinuum method with an embedded atom method potential. A modified boundary layer approach has been employed to simulate a semi-infinite crack and to investigate the influence of the degree of mode II and mode III loading on the crack tip mechanisms. The analyses have been carried out with four crystallographic orientations and different degrees of mixed-mode loading. The results show that the critical stress intensity factor and the mechanisms at the crack tip are sensitive to both the crystallographic orientation and the mode of loading. Phenomena such as crack propagation, twinning and emission of edge and screw dislocations are observed.

Effects of water chemistry and loading conditions on stress corrosion cracking of cold-rolled 316NG stainless steel in high temperature water

The effects of electrode potential, stress intensity factor and loading history on stress corrosion cracking growth of a cold-rolled 316NG stainless steel in 288 °C pure water were investigated. Crack branching and intergranular stress corrosion cracking along random grain boundaries were observed by electron-back scattering diffraction. A strong dependence of crack growth rate on stress intensity factor is observed. A single-cycle overloading produced a retarded transient cracking growth period. The mild inhibiting effect of decreasing electrode potential on crack growth of cold-rolled 316NG SS is analyzed based on the interaction between crack tip mechanics and crack tip oxidation kinetics.

Mesomechanics of energy and mass interaction for dissipative systems

Small and large specimen data cannot be connected because the respective theories are developed independently by different physical laws. The disparities are becoming more and more transparent as nanospecimen data cannot be brought up to the macroscopic scale. The inability to address quantum and gravitational field mechanics in a unified manner adds to the diversification. One of the apparent deficiencies is not being able to treat small (atomic) and large (galaxial) bodies by a common multiscale model for addressing nonequilibrium and nonhomogeneous conditions. The time of arrow must also be reflected to invoke finiteness of the life sustaining energy. The synergis-tic thought leads to a pulsating mass manifested by matter activated by energy absorption and dissipation. The near simultaneity of energy intake and outlet of physical systems resembles the pulsation arising from contraction and expansion. The pulses, caused by the fatigue of metals, are within the range of micropulsations of geomagnetic energy fluctuations. The dualism of energy absorption and dissipation provides a common dialogue for establishing multiscale shifting laws. Mass pulsation, coupled with the equivalence of motion and energy, gives a unique mass-matter relation, bypassing the diversities of current concepts and theories in physics and mechanics. The scheme of scaling by segments such as pico, nano, micro and macro creates gaps among the scale ranges that requires cementation. Mesomechanics serves this purpose for developing scale shifting laws for connecting the gaps. Determination of energy density from velocity of physical systems was shown to be possible from the application of crack tip mechanics and ideomechanics. Four fundamental parameters l, v, M and Ware used. They stand, respectively, for the length, velocity, mass density and energy density. Their combinations can be formulated into unique mathematical groups. The three scale ranges: pico-nano, nano-micro and micro-macro are selected for demonstration. The objective is to explain real accelerated test data without making idealized assumptions for determining the life distributed over the three scale ranges. In short, a nonclassical approach will be adopted to derive scale shifting laws consisting of the transitional functions RjJ+1 which stand for the mass ratios of the absorption energies WjJ+1 and dissipation energies DjJ+1The notations J and J+1 stand for two successive scales: pico-nano, nano-micro and micro-macro. Hence, the mass ratios Rpina, Rnami and Rmima can be referred to as the transitional inhomogeneity coefficients. They make up the multiscale shifting laws WjJ+1 = RjJ+1DjJ+1 Validation of the method involves connecting the accelerated test data at the different scales, say from pico to nano to micro to macro. A key step in this development is the use of an energy density dissipation function, the definition of which is scale invariant. Referred to the contraction and expansion of a control volume, energy is said to be absorbed and dissipated, respectively. The respective mass densities M↓ and M↓ may then be regarded to pulsate by contraction and expansion. Real fatigue data for the precracked 2024-T3 aluminum panels are used to derive energy loss by dissipation. Equivalency of mass and energy also enables numerical evaluation of mass loss.

Synergistic action of fatigue and corrosion during crack growth in the 2024 aluminium alloy

This study was undertaken with the aim of identifying the domains where synergistic interactions between mechanical, environmental and microstructural parameters may occur during corrosion fatigue crack growth in the aluminum alloy 2024, as well as the rate controlling factors. Corrosion fatigue crack propagation tests have been carried out at different frequencies and/or waveforms, grain orientations and tempers, in air, distilled water and 3.5% NaCl solution at free potential. In saline solution in the S-L orientation, crack growth rates are shown to decrease with decreasing frequency. In addition, at high frequencies, these growth rates are substantially higher than in air and in distilled water. This enhancement is accompanied by a typical change in the shape of the dadN curve. It is demonstrated that this enhancement, that is only observed in metallurgical conditions of high sensitivity to stress corrosion cracking, is controlled by the loading rate, and not by the duration of exposure to the corrosive medium. The behaviour is discussed on the basis of a competition between passivation and anodic dissolution and/or hydrogen embrittlement. It is finally proposed that the fatigue crack growth enhancement observed is related to a crack-tip embrittlement mechanism by hydrogen produced by anodic dissolution in relation with film rupture periodicity.

Formulating stress corrosion cracking growth rates by combination of crack tip mechanics and crack tip oxidation kinetics

A theoretical equation for stress corrosion crack growth rate of austenitic alloys in high temperature water is reformulated based on crack tip asymptotic fields and crack tip transient oxidation kinetics. A general oxidation kinetic law is introduced, emphasizing the role of mass transport through solid oxide film at the crack tip. The effects of several parameters on crack growth rate are evaluated. The results are compared with available experimental data and other equations. A good prediction of the effect of K on stress corrosion cracking growth rate of typical austenitic alloys in simulated light water reactor environments has been achieved.

Crack tip mechanics based on progressive damage of arrow: Hierarchy of singularities and multiscale segments

Crack tip mechanics based on progressive damage of arrow: Hierarchy of singularities and multiscale segments