Crack Initiation Model Research Articles

A Review of Subsurface Crack Initiation Models in High-Cycle Fatigue for Titanium Alloys

The characterization of subsurface fatigue crack initiate sites of near α and α-β types titanium alloys and their cracking models proposed were reviewed. The crack initiation sites consisted of facets mostly on near basal plane of α grain, although the crystallographic orientation and surface topography of the facets presented a subtle difference. The crack initiation mechanisms were a quasi-cleavage accompanying high normal stress on the plane, a combination of basal slip and normal stress across the basal plane, and a pure slip on facet plane inclined near 45 degree to loading axis.

Stability analysis of the phase-field method for fracture with a general degradation function and plasticity induced crack generation

The phase-field method is a popular technique for modeling crack initiation, bifurcation and coalescence without the need to explicitly track the crack surfaces. In this framework, the governing equations are derived from thermodynamic principles and cracks are modeled as continuous entities, whose width is defined by a small process zone parameter.Propagation of cracks is governed by the partition of strain energy that contributes to fracture and may be stable, in which case additional energy is required to form cracks, or unstable, where cracks advance with no additional input energy.In this work we propose a stability framework, based on a linear perturbation analysis, to determine the onset of unstable crack growth. The derivations lead to an analytical, energy based criterion for the phase field method in linear elastic and visco-plastic materials. The stability criterion is valid for a general degradation function and accounts for fracture induced by cold-work.Numerical results on linear elastic materials show that the proposed criterion not only recovers the critical stress value reported in the literature but also provides a stability criterion for visco-plastic materials with a general degradation function. The criterion is tested on one dimensional problems and a two dimensions homogeneous example, successfully predicting the instability point.

A cyclic slip irreversibility based model for fatigue crack initiation of nickel base alloys

The opportunity to define a microscopic law of fatigue crack initiation using Manson-Coffin law formulated in terms of cyclic slip irreversibility deduced from AFM measurements is discussed for a polycrystalline superalloy with different grain sizes and precipitate sizes. The results show that the modified Manson-Coffin law, relating cyclic slip irreversibility parameter to fatigue crack initiation life, is sustained through a two-parameter power law: εf′ and c. The analysis suggests that the exponent c-value can be related to the degree of plastic strain incompatibility between grains, and the cumulative irreversible cyclic plastic strain to crack initiation is a relevant damage indicator for crack initiation. Consequently, our approach allows giving a physical base of engineering law.

Application of hysteresis energy criterion in a microstructure-based model for fatigue crack initiation and evolution in austenitic stainless steel

The Sistaninia-Niffenegger Fatigue (SNF) model, a mesoscale hysteresis energy-based model of fatigue crack initiation, is calibrated and validated both by experiments and numerical modeling. The simulations are able to reproduce the fatigue life curves for the AISI 316L austenitic stainless steel of different grain sizes. In addition, it’s shown that the model captures the crack initiation site and the subsequent propagation through the anisotropic microstructure in a real multi-notched sample subjected to high cycle fatigue (HCF) loading. The microstructure of the polycrystal is determined by electron back scattering diffraction (EBSD), whereas the material properties of the polycrystal and the parameters of the model are obtained by inverse analysis using the Levenberg-Marquardt algorithm, based on the tensile stress-strain curves and the HCF test results, respectively. The model can be applied to different microstructures under HCF loading and evaluate crack initiation and its evolution with precision within the intrinsic scattering of HCF tests.

Bayesian uncertainty quantification and propagation for validation of a microstructure sensitive model for prediction of fatigue crack initiation

A microstructure and deformation mechanism based fatigue crack initiation and life prediction model, which links microstructure variability of a polycrystalline material to the scatter in fatigue life, is validated using an uncertainty quantification and propagation framework. First, global sensitivity analysis (GSA) is used to identify the set of most influential parameters in the fatigue life prediction model. Following GSA, the posterior distributions of all influential parameters are calculated using a Bayesian inference framework, which is built based on a Markov chain Monte Carlo (MCMC) algorithm. The quantified uncertainties thus obtained, are propagated through the model using Monte Carlo sampling technique to make robust predictions of fatigue life. The model is validated by comparing the predictions to experimental fatigue life data.

The role of extrusions and intrusions in fatigue crack initiation

The profiles of persistent slip markings produced by uniaxial and biaxial cyclic straining in four different polycrystalline materials with f.c.c. structure were investigated using focused ion beam (FIB) cutting and TEM observation of oriented surface foils. Typical shapes of persistent slip markings are extrusions accompanied by parallel intrusions. In some cases only extrusions were developed and intrusions were produced later in fatigue life. In polycrystalline copper extrusions and intrusions appear on the surface of the grain where persistent slip band characterized by ladder-like dislocation structure egress on the surface. Similar features were observed in fatigued austenitic 316L and Sanicro 25 steels but the extrusion and intrusion shapes were more complicated. Crack-like intrusion shapes produce high stress and strain concentration and primary stage I crack starts to grow from the tip of intrusions. The experimental observations were compared with the predictions of the existing crack initiation models.

Modelling of overload effects on fatigue crack initiation in case of carbon steel

AbstractThis paper deals with the modelling of short crack initiation within a microstructure of medium carbon steel under fatigue loading, as well as with the influence of overload on the crack initiation period. Studies on the long crack growth show that the overload introduces first an increase in the crack growth rate that is then followed with a decrease, a so‐called retardation. A micro‐model containing the microstructure of the material is analysed using the finite element method in combination with a model for crack development – the assessment of number of cycles needed for crack initiation was based on the Tanaka–Mura equation. The analysis brings in a correlation between the crack growth rate and the crack length together with the effects of the overload on the crack growth rate. The overload is found to accelerate the short crack growth; however, the following retardation could not be captured due to the inability of the model to produce residual stresses, which are considered to be the main cause of the retardation effect.

Profiles of persistent slip markings and internal structure of underlying persistent slip bands

AbstractFocused ion beam sections and lamellae for transmission electron microscopy were prepared from fatigued specimens of polycrystalline copper and austenitic Sanicro 25 steel. The profiles of persistent slip markings developed on the surface were observed and documented simultaneously with the underlying dislocation structure. In copper fatigued at room temperature and close to liquid nitrogen temperature, persistent slip markings consisting of pronounced extrusions and parallel intrusions appeared at locations where persistent slip bands having the ladder‐like dislocation structure egress on the surface. Stage I cracks initiated from the tip of the intrusions. In Sanicro 25 steel, more planar character of the dislocation structure led to thin extrusions and intrusions and several stage I cracks running parallel to the primary slip plane. Exceptionally, ladder‐like structure and generally alternating dislocation‐rich and dislocation‐poor volumes were observed in the PSBs. Dislocations bands of secondary slip systems in the matrix disappeared on intersections with PSBs. Experimental findings were compared with predictions of recent physically based models of fatigue crack initiation.

A Bayesian analysis of component life expectancy and its implications on the inspection schedule

A model of crack initiation and residual component life is fitted to the inspection history, inclusive of two in-service failures, of a set of gas circulator impellers at two UK power stations. The model is then used to estimate the probability of future in-service failure of each item in scenarios in which the next opportunity for inspection (i.e. detection of a developing crack) is exploited or forgone.The study takes into account in exact manner both variability and uncertainty. A novel Approximate Bayesian Computation (ABC) methodology is introduced for the quantification of uncertainty, i.e. the sampling of the posterior distribution of the parameters of the model. At the price of the discretization of this distribution, the methodology represents a quickly implemented option in problems where standard ABC rejection sampling is unacceptably inefficient.

Effects of Cracking Test Conditions on Estimation Uncertainty for Weibull Parameters Considering Time-Dependent Censoring Interval.

It is extremely difficult to predict the initiation time of cracking due to a large time spread in most cracking experiments. Thus, probabilistic models, such as the Weibull distribution, are usually employed to model the initiation time of cracking. Therefore, the parameters of the Weibull distribution are estimated from data collected from a cracking test. However, although the development of a reliable cracking model under ideal experimental conditions (e.g., a large number of specimens and narrow censoring intervals) could be achieved in principle, it is not straightforward to quantitatively assess the effects of the ideal experimental conditions on model estimation uncertainty. The present study investigated the effects of key experimental conditions, including the time-dependent effect of the censoring interval length, on the estimation uncertainties of the Weibull parameters through Monte Carlo simulations. The simulation results provided quantified estimation uncertainties of Weibull parameters in various cracking test conditions. Hence, it is expected that the results of this study can offer some insight for experimenters developing a probabilistic crack initiation model by performing experiments.

Surface Relief Formation in Relation to the Underlying Dislocation Arrangement

Two fatigued materials with f.c.c. lattice, i.e. pure polycrystalline copper and austenitic Sanicro 25 stainless steel, were subjected to the study of the persistent slip markings (PSMs) developed on the surface of the suitably oriented grains. They were observed using scanning electron microscopy (SEM) and thin surface FIB lamellae were prepared and studied by transmission electron microscopy (TEM). The aim was to correlate the specimen surface profile with the underlying internal dislocation structure. The localization of the intensive cyclic slip into persistent slip bands (PSBs) of the material was observed and associated with the PSMs on the specimen surface. Extrusions, intrusions and the dislocation structure appertaining to them were analysed, documented and discussed in relation to the models of fatigue crack initiation.

XFEM-based model for simulating zigzag delamination growth in laminated composites under mode I loading

Interfaces adjacent to a 90° ply in laminated composites show a typical zigzag path during the mode I delamination propagation process, which is considered to be closely related to high propagation values of fracture toughness. DCB (double cantilever beam) tests of specimens with a starter crack inserted into two 90° mid-layers were carried out, during which the zigzag delamination growth and pronounced R-curve behavior were obtained. To simulate the zigzag delamination propagation path, four XFEM-based delamination growth models were proposed which were comprised of a crack initiation model and a crack propagation model, respectively. In the framework of the delamination growth model, a new crack initiation model was developed, which took a quadratic criterion as the crack initiation criterion and the direction orthogonal to the maximum principal stress as the crack growth direction. Based on the mechanism of the delamination resistance, four crack propagation models considering whether the delamination follows a pure or mixed mode damage evolution law and whether a constant or varying critical fracture toughness dominates the damage evolution were introduced. By comparing the predictions from the four delamination growth models and the experimental results, the mode I delamination mechanism with a zigzag path was investigated. The delamination growth model that adopted a critical fracture toughness function and the mixed mode damage evolution law showed the best agreement with the experimental results and was recommended.

Probabilistic prediction models for crack initiation and progression of spray sealed pavements

ABSTRACTCracking is one of the primary distress modes in spray (chip)-sealed pavement surface performance and its prediction is a major concern for pavement engineers. In order to identify, manage and asses effectively and efficiently cracked pavement at a network level, a probabilistic modelling approach is utilised to develop cracking initiation and progression models. This study aims to predict the probability of pavement cracks occurring using a binary logistic model and cracks progression over time using an ordinal logistic regression model. These models have been developed to take into account the effect of variations among observations, among sections and among highways. Readily available historical time series data (from 2004 to 2011) from 40 highway segments have been collected and prepared for modelling. These time series include surface cracking as a performance parameter and traffic loading, expansion potential of subgrade soil, climate condition, condition of drainage system and pavement strength as predictor parameters. Cracking data include all types of cracking: transverse, longitudinal and crocodile cracking and is reported as a percent of the affected area. The study estimates the probability of crack initiation at a certain time and predicts the probability of a pavement maintaining its current level of cracking. It is found that with the 50% estimated probability, about 82% of the observations are correctly predicted by the crack initiation model and 65% of the observations are correctly predicted by the crack progression model. The study has concluded that the effect of time is stronger than the other variables on crack initiation and progression. Also, the effect of traffic loading is stronger than the effect of initial pavement strength in crack initiation phase. However, the effect of pavement strength at any time is stronger than the effect of traffic loading in crack progression phase. The predicted probabilities have been successfully validated using another data-set from the same network and the results indicate that the developed probability models are well estimating the crack conditions and have the ability to predict future conditions accurately.

A coupled stress and energy failure model for crack initiation in arbitrarily shaped adhesive lap joints

AbstractIn this work, crack initiation in adhesive lap joints of arbitrary joint configuration is studied by means of a finite fracture mechanics approach. The analysis is based on a general stress solution for adhesive joints combined with a coupled stress and energy criterion. The instantaneous formation of a crack of finite size is predicted if a stress and energy criterion are satisfied simultaneously. The closed‐form analytical solution of the stress field allows for an efficient evaluation of the crack initiation load and corresponding finite crack length. A comparison to experimental results from literature and to numerical results obtained with a cohesive zone model approach shows a good agreement. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Comparative Study on Crack Initiation and Propagation of Glass under Thermal Loading

This paper explores the fracture process based on finite element simulation. Both probabilistic and deterministic methods are employed to model crack initiation, and several commonly used criteria are utilized to predict crack growth. It is concluded that the criteria of maximum tensile stress, maximum normal stress, and maximum Mises stress, as well as the Coulomb-Mohr criterion are able to predict the initiation of the first crack. The mixed-mode criteria based on the stress intensity factor (SIF), energy release rate, and the maximum principal stress, as well as the SIF-based maximum circumferential stress criterion are suitable to predict the crack propagation.

Simulation of Environmentally-Assisted Material Degradation by a Thermodynamically Consistent Phase-Field Model

Environmentally-assisted material degradation involves mass transport and mechanical processes interacting in the material. A well-known example is hydrogen-induced stress-corrosion cracking. One major challenge within this scope is the quantification of the coupling mechanisms in question. The computational modeling of environmentally-assisted cracks is the key objective ofthis investigation and realised within the theory of gradient-extended dissipative continua with length-scales. The modeling of sharp crack discontinuities is replaced by a diffusive crack model based onthe introduction of a crack phase-field to maintain the evolution of complex crack topologies. Withina thermodynamical framework allowing for mechanical and mass transport processes the crack phase-field is capable to model crack initiation and propagation bythe finite element method. As complexcrack situations such as crack initiation, curvilinear crack patterns and crack branching are usuallyhard to realise with sharp crack models, they can be assessedwithout the requirement of a predefinedcrack path within this method. The numerical modeling of a showcase demonstrates a crack initiationas well as a crack propagation situation with respect to the determination of stress-intensity factors; acrack deviation situation with a curvilinear crack path is modeled by the introduction of a geometricalperturbation and a locally enhanced species concentration

Uncertainty Evaluation of Weibull Estimators through Monte Carlo Simulation: Applications for Crack Initiation Testing.

The typical experimental procedure for testing stress corrosion cracking initiation involves an interval-censored reliability test. Based on these test results, the parameters of a Weibull distribution, which is a widely accepted crack initiation model, can be estimated using maximum likelihood estimation or median rank regression. However, it is difficult to determine the appropriate number of test specimens and censoring intervals required to obtain sufficiently accurate Weibull estimators. In this study, we compare maximum likelihood estimation and median rank regression using a Monte Carlo simulation to examine the effects of the total number of specimens, test duration, censoring interval, and shape parameters of the true Weibull distribution on the estimator uncertainty. Finally, we provide the quantitative uncertainties of both Weibull estimators, compare them with the true Weibull parameters, and suggest proper experimental conditions for developing a probabilistic crack initiation model through crack initiation tests.

An all-in-one numerical methodology for fretting wear and fatigue life assessment

Many mechanical components such as, bearing housings, flexible couplings and spines or orthopedic devices are simultaneously subjected to a fretting wear and fatigue damage. For this reason, the combined study on a single model of wear, crack initiation and propagation is of great interest. This paper presents an all-in-one 2D cylinder on flat numerical model for life assessment on coupled fretting wear and fatigue phenomena. In the literature, two stages are usually distinguished: crack nucleation and its subsequent growth. The method combines the Archard wear model, a critical-plane implementation of the Smith-Watson- Topper (SWT) multiaxial fatigue criterion coupled with the Miner-Palmgren accumulation damage rule for crack initiation prediction. Then, the Linear Elastic Fracture Mechanics (LEFM) via eXtended Finite Element Method (X-FEM) embedded into the commercial finite element code Abaqus FEA has been employed to determine the crack propagation stage. Therefore, the sum of the two stages gives a total life prediction. Finally, the numerical model was validated with experimental data reported in the literature and a good agreement was obtained.

Macromodeling of Crack Damage in Steel Beams Subjected to Nonstationary Low Cycle Fatigue

This study proposes a model of crack initiation and propagation in steel beams subjected to ultralow cycle fatigue. The model can be included in the general framework of lumped damage mechanics. A state variable called damage is introduced for each plastic hinge and can be related to the extension of the crack in the real structural component. The damage evolution law is based on the Manson–Coffin law, the Palmgren–Miner rule and two new concepts: the instantaneous plastic amplitude and a crack-driving variable. The model also describes crack closure effects using the unilateral damage assumption. It was validated by the numerical simulation of tests of steel beam-column connections subjected to cyclic loadings with constant and variable amplitudes, as reported in the literature. Advantages and limitations of the model are discussed for wider applications on the damage simulation of steel frame systems subjected to mechanical overloads, typically earthquake loading.

An improved ductile fracture model for structural steels considering effect of high stress triaxiality

This study presents results of experimental investigation and ductile fracture model for ductile crack initiation, propagation and final failure in structural steels subjected to high stress triaxiality. To this end, uniaxial tension tests on smooth flat bars, U-notched specimens and V-notched specimens are conducted. Nonlinear finite element analysis of the notched specimens is carried out to obtain the stress triaxiality distributions and histories of notch tip and center of specimens. Based on the previous three-stage and two-parameter ductile fracture model proposed by the authors, the equivalent plastic displacement at element failure during simulations is obtained by notched specimen tests, and an improved ductile fracture model is presented considering the effect of high stress triaxiality during both the plastic stage and the softening stage. The relationship between the equivalent plastic displacement at element failure and nonuniform ratio (nonuniform ratio is the ratio of the average value of stress triaxiality of notch tip and center) is determined by a series of tests and analyses. Detailed finite element analyses that employ the improved ductile fracture model are shown to predict ductile fracture behavior under high stress triaxiality with good accuracy across the mesh sizes, notch radii, and notch degree in terms of ductile crack initiation point, ultimate load point and load-displacement curve.