Crack Initiation Model Research Articles

Special Issue on Tribology of Additive Manufacturing

Special Issue on Tribology of Additive Manufacturing

Numerical and experimental investigations on fretting fatigue properties of GH4169 superalloy at the elevated temperature

Fretting fatigue is a detrimental phenomenon in aeronautic industry, where the appropriate methods for crack location prediction and total life prediction are vital. In the present paper, both experimental and numerical approaches were developed for GH4169 superalloy with different interference magnitudes at 650 °C. Three fretting crack initiation models were compared for crack location prediction, among which the SWT model was extended to describe the initiation face in the three-dimensional model considering the subsurface stresses. Moreover, three propagation models were conducted for crack growth rate calculation. One of the methods was the combination of the linear superposition model with the Harter-T method, which emphasized the compression load effect on the driving force of crack propagation rates and the negative stress ratio variation impact. Finally, the life prediction approach was proposed using the averaged SWT parameters combined with the composite propagation model. The obtained total life estimations were found to agree well with the experimental results.

Prediction of Tensile Strain Capacity for X52 Steel Pipeline Materials Using the Extended Finite Element Method

Strain-based design (SBD) plays an important role in pipeline design and assessment of pipelines subjected to geo-hazards. Under such hazards, a pipe can be subjected to substantial plastic strains, leading to tensile failure at locations of girth weld flaws. For SBD, the finite element method (FEM) can be a reliable tool to calculate the tensile strain capacity (TSC) for better design in pipelines. This study aims to investigate the ductile fracture properties for specific vintage pipeline steel (API 5L grade of X52) using the extended finite element method (XFEM). Eight full-scale tests were simulated using the commercial finite element analysis software ABAQUS Version 6.17. Maximum principal strain is used to assess the damage initiation using the cohesive zone model (CZM) when the crack evolution is evaluated by fracture energy release. A proper set of damage parameters for the X52 materials was calibrated based on the ability of the model to reproduce the experimental results. These experimental results included the tensile strain, applied load, endplate rotation, and crack mouth opening displacement (CMOD). This study describes a methodology for validation of the XFEM and the proper damage parameters required to model crack initiation and propagation in X52 grades of pipeline.

Hybrid finite‑discrete element simulator based on GPGPU‑parallelized computation for modelling crack initiation and coalescence in sandy mudstone with prefabricated cross-flaws under uniaxial compression

Discrete element method or extended finite element method is often adopted to simulate crack initiation, propagation, and coalescence. However, the transition of rock from continuous medium to the discontinuous medium cannot be simulated. Moreover, previous studies on propagation and coalescence of prefabricated flaws often focus on single or multiple parallel prefabricated flaws. In reality, the fractures in rock mass usually exist in the form of cross flaws. To solve the inconsistency, the uniaxial compression of rock samples with prefabricated cross-flaws is modelled in this study through the GPGPU-parallelized Y-HFDEM IDE, and the modelling results are compared with those from laboratory experiments. The effects of four geometric parameters of the prefabricated cross-flaws on the crack initiation, propagation, and coalescence process are explored: (1) the joint continuity parameter k, (2) the angle α between the axial load direction and the dip direction of the primary flaw, (3) the angle β between the direction of the rock bridge and the dip direction of the primary flaw, and (4) the angle γ between primary and secondary flaws. It is found that numerical simulation results are in good agreement with those of laboratory experiments in terms of not only the qualitative crack initiation, propagation, and coalescence processes but also the quantitative crack initiation locations and stress, crack propagation mechanism, and coalescence locations. It is concluded that the presence of the prefabricated cross flaws promotes the rock samples fracture more seriously during uniaxial loading. Moreover, two new crack coalescence mechanisms that have not been reported in previous studies are observed through numerical simulations and laboratory experiments. Thus, compared with laboratory experiments, the GPGPU-parallelized Y-HFDEM IDE provides another cheaper but more flexible and robust tool for the study on the crack initiation, propagation, and coalescence process in rocks with prefabricated flaws.

Prediction of Rolling Contact Fatigue Behavior in Rails Using Crack Initiation and Growth Models along with Multibody Simulations

Rolling contact fatigue (RCF) is a common cause of rail failure due to repeated stresses at the wheel-rail contact. This phenomenon is a real problem that greatly affects the safety of train operation. Preventive and corrective maintenance tasks have a big impact on the Life Cycle Cost (LCC) of railway assets, and therefore cutting-edge strategies based on predictive functionalities are needed to reduce it. A methodology based on physical models is proposed to predict the degradation of railway tracks due to RCF. This work merges a crack initiation and a crack growth model along with a fully nonlinear multibody model. From a multibody assessment of the vehicle-track interaction, an energy dissipation method is used to identify points where cracks are expected to appear. At these points, crack propagation is calculated considering the contact conditions as a function of crack depth. The proposed methodology has been validated with field measurements, conducted using Eddy Currents provided by the infrastructure manager Network Rail. Validation results show that RCF behavior can be predicted for track sections with different characteristics without the necessity of previous on-track measurements.

Development of probabilistic primary water stress corrosion cracking initiation model for alloy 182 welds considering thermal aging and cold work effects

We experimentally investigated the effects of thermal aging and cold work on the microstructure, mechanical properties, and primary water stress corrosion cracking (PWSCC) initiation time for Alloy 182 welds. The effects of thermal aging and cold work on the PWSCC initiation time of Alloy 182 were modeled based on the plastic energy concept and the PWSCC initiation data of this study and previous reports by considering censored data. Based on the results, it is estimated that the PWSCC resistance of the Alloy 182 weld firstly increases and then decreases with thermal aging time when the applied stress is kept constant.

A phase field numerical manifold method for crack propagation in quasi-brittle materials

In the present work, a phase field numerical manifold method (PFNMM) is proposed for crack growth in brittle materials. The advantages of the phase field method (PFM) in modeling crack initiation and crack branching, and those of the numerical manifold method (NMM) in discretizing the computational model are integrated together in the proposed numerical model. The proposed numerical model is very suitable for simulating multiple crack propagation problems. The implementation details of the proposed numerical model are well presented. Several benchmark examples are adopted to validate the proposed numerical approach. The results indicate that the crack propagation topologies and force-displacement curves obtained by the proposed numerical model are in good agreement with others, e.g. Miehe et al. (2010) and Molnar and Gravouil (2017) [3]. The convergence of numerical solution from the proposed numerical model is also investigated. The PFNMM deserves a further investigation.

Phase-field modeling of crack propagation in polycrystalline materials

A phase-field model based on a modified form of the regularized formulation of Griffith’s fracture theory is presented to investigate intergranular and transgranular crack propagations in polycrystalline brittle materials. Grains and grain boundaries are incorporated in the crack initiation and propagation model based on a phase-field model for grain growth, in which the elastic anisotropy varies based on the grain orientation angle, and the grain boundary energy is related to the misorientation angle of the adjacent grains. Correction parameters are utilized in the total free energy functional and mechanical equilibrium equations to consider the effect of material strength on crack nucleation and propagation independent of the regularization parameter. This allows controlling the strength and crack surface energy along the grain boundaries as a function of the misorientation angle in order to mediate intergranular and/or transgranular crack propagation. To demonstrate the capability of the proposed model, intergranular and transgranular crack propagation in ZrB2 bicrystal systems under tensile loading are studied in detail. The effects of grain boundary misorientation angle, grain boundary inclination with respect to initial crack direction, and grain boundary strength (and/or crack surface energy) on the crack propagation path are investigated. Intergranular crack propagation can be promoted by specific combinations of grain boundary strength and crack surface energy, which can contribute to the fracture toughness of polycrystalline materials.

Model of Crack Initiation in a Brake Drum

In this paper, we perform a theoretical analysis to determine the quantitative relationship between abrasive wear and crack initiation in a brake drum when a wheeled vehicle is braking. Using the model of a rough friction surface, a closed system of algebraic equations that allows one to study cracking in the brake drum depending on the abrasive wear of the friction surface is constructed. The developed model is shown to allow calculating the effect of wear on crack initiation in the brake drum in the design stage.

Microstructural analysis and fatigue crack initiation modelling of additively manufactured 316L after different heat treatments

This study investigates the fatigue behaviour of 316L stainless steel manufactured by laser powder bed fusion. More specifically, the influence of the microstructure on fatigue is analysed for four different material conditions: as-built, stress relieved, fully annealed and hot isostatic pressed. Fully reversed tension-compression fatigue results on miniaturised vertically built and machined samples indicate that as-built and stress relieved specimens exhibit superior fatigue behaviour compared to fully annealed and hot isostatic pressed ones. Fine sub-grained cellular microstructure in as-built and stress relieved samples resulted in high fatigue performance, which was decreased with microstructure coarsening from the high temperature heat treatments. Secondly, a microstructure-based fatigue crack initiation model is adapted for additively manufactured 316L and verified for different material states. The results show that the analytical model depicts a conservative prediction for crack initiation life when compared with experimental results for full fracture. This validation offers the potential to expand the model for other material and process conditions.

Experimental and numerical evaluations on the effects of adhesive fillet, overlap length and unbonded area in adhesive‐bonded joints

AbstractTo realize robust structural design, the effects of the adhesive fillet, overlap length and unbonded area in adhesive‐bonded joints need to be fully understood and incorporated into a fatigue life estimation method. In the present work, both static and fatigue experiments are performed on six types of adhesive‐bonded joints to illuminate these effects systematically. A straightforward total fatigue life evaluation method is proposed to address these effects. A statistical crack initiation model is established based on the fatigue data of bulk adhesive specimens. Growth life is calculated using the interfacial crack model and mixed mode crack growth method. Good correlation is observed between the calculated and experimental fatigue lives. Furthermore, the effects of the adhesive fillet, overlap length and unbonded area are analysed based on both calculated and experimental results. Results indicate that adhesive fillet postpones crack initiation by reducing local strain level, both overlap length and unbonded area change the growth life by length. Besides, overlap length promotes the fraction of mode II strain energy release rate in total, reducing crack growth rates and extending growth life.

Micromechanics based modelling of fatigue crack initiation of high strength steel

The cyclic behaviour and fatigue crack initiation in low cycle regime of dual phase (DP) steel grade 590 were characterized. Experimental strain-controlled tension–compression tests and corresponding simulations using representative volume elements were carried out. The Chaboche kinematic hardening parameters were determined for each individual phases. The damage model based on accumulated inelastic hysteresis energy was incorporated for describing crack onset mechanism in the microstructure. Damage parameters were calibrated with experimental strain-life curves for crack initiation state. Effects of pre-strain on crack occurrence of steel were studied. Observed crack initiation and its life were well predicted by the proposed modelling scheme.

Low cycle fatigue damage model and sensitivity analysis of fatigue crack initiation by finite element approach

To meet the design requirements, different types of defects are often machined on the surface of fatigue components. Local stress concentration formed at the notch accelerate the initiation of fatigue crack, therefore greatly shorten the service lives of such components. Based on the theory of continuous damage mechanics and the principle of irreversible thermodynamics, the damage evolution model of low cycle fatigue is investigated. By programming the damage evolution model as UMAT subroutine and coupling it to ABAQUS, the fatigue damage and crack initiation life of notched P92 steel samples under specific loads are simulated, and the crack initiation location is determined. Furthermore, the damage evolution and crack initiation sensitivity of notch morphology are considered. The results show that the crack initiation occurs easily in the notch root where the damage is greatest and the plastic strain accumulates fastest under cyclic loading. The fatigue damage accumulates slowly at the initial stage, but the damage accumulates rapidly after the cumulative damage reaches a critical value. The fatigue damage evolution and fatigue initiation life are very sensitive to the notch morphology parameters. The notch morphology need to be carefully analyzed, to improve the fatigue life of the notched samples.

Crystal plasticity finite‐element modelling of cyclic deformation and crack initiation in a nickel‐based single‐crystal superalloy under low‐cycle fatigue

AbstractNickel‐based single‐crystal superalloys are predominantly used for turbine blades in aircraft engines and land‐based gas turbines. Understanding and predicting the fatigue failure of Ni‐based single‐crystal superalloys are critical to ensure the safety of these components during operation. In this paper, low‐cycle fatigue experiments were carried out to investigate cyclic deformation of a nickel‐based single‐crystal superalloy MD2, recently developed by GE Power, with different crystallographic orientations. Specialty in situ scanning electron microscope (SEM) tests were also conducted to study the slip‐controlled initiation of short cracks under low‐cycle fatigue. In particular, the stress–strain response for both [001] and [111] orientations was used to calibrate a crystal plasticity model, which allowed us to simulate the activation of crystallographic slip systems and predict the initiation of short fatigue crack. Using the accumulated shear strain as a criterion, the simulations confirmed that the slip system with the maximum accumulated shear strain appeared to control the crack initiation. The location and direction of slip traces and short cracks, captured by the crystal plasticity finite‐element simulations, agreed with the in situ SEM observations. The modelling tool will be valuable for assessing the structural integrity of critical gas turbine blades.

A Methodology for Incorporating the Effect of Grain Size on the Energy Efficiency Coefficient for Fatigue Crack Initiation Estimation in Polycrystalline Metal

Estimating fatigue crack initiation of applied loading is challenging due to the large number of individual entities within a microstructure that could affect the accumulation of dislocations. In order to improve the prediction accuracy of fatigue crack initiation models, it is essential to accurately compute the energy dissipated into the microstructure per fatigue loading cycle. The extent of the energy dissipated within the microstructure as a fraction of the overall energy imparted by loading has previously been defined as the ‘energy efficiency coefficient’. This work studied the energy efficiency coefficient as a factor in the measurement of accumulated plastic strain energy stored at the crack initiation site during cyclic loading. In particular, the crystal plasticity constitutive formulation was known as ’length scale independent’ previously. As a result, a semi-empirical approach was presented whereby the potential effect of grain size can be accounted for without the use of a strain gradient plasticity approach. The randomized representative volume elements were created based on the experimental analysis of grain size distribution. The work was aimed at capturing some of the effects of grain size and utilizing them to complete a semi-empirical estimation of crack initiation in polycrystalline materials. The computational methodology ensured the representative of microstructural properties, including the elastic constant and critical resolved shear stress via appreciable fit achieved with the empirical tensile test results. Crystal plasticity finite element modeling was incorporated into a finite element code to estimate the potential for crack initiation. The energy efficiency coefficient was computed for a class of material with grain size to C11000 electrolytic tough pitch (ETP) copper. This methodology can improve fatigue crack initiation life estimation and advance the fundamental study of energy efficiency coefficient during fatigue crack initiation.

Investigation on solidification cracks in pulsed laser spot welding of an AZ31 magnesium alloy

A direction-dependent model of solidification crack initiation and propagation is established to analyze the influence of the melt pool shape on the distribution of solidification cracks in pulsed laser spot welding. The formation direction of the initial crack is related to the variation of the solidification parameters. When the aspect ratio of the spot welds with a default Rectangular pulse is greater than 0.3 and less than 0.8, an initial crack is formed in the 45° direction of the mushy zone, and then the crack propagates along the grain boundary. That is, the solidification cracks are distributed in the direction of 45° on both sides of the surface center of the welding cross-section. When the aspect ratio of the spot welds is less than 0.3 or greater than 0.8, an initial crack is formed in the 90° direction of the mushy zone, and then the solidification crack is vertically distributed at the center of the welding cross-section. The Step-Down-10ms-0.3P pulse can significantly reduce the solidification rate of the melt pool interface, preventing the formation of initial cracks in the sensitive directions of the spot welds with an aspect ratio less than 0.8, thereby eliminating solidification cracks.

A 2D peridynamic model for fatigue crack initiation of railheads

Due to the use of PDEs (Partial Differential Equations), classical continuum mechanics is difficult to solve the problems of discontinuous deformation. Using integral equations, peridynamic theory can overcome this difficulty. A 2D method for predicting fatigue crack initiation of railheads was presented based on the peridynamic theory. First, the reasonable values of the model parameters were analyzed. Second, the accuracy of the method was verified through comparisons with the results of classical continuum mechanics and existing conclusions in the literature. Finally, the effects of wheel-rail rolling-sliding status, friction coefficient, and wheel load on fatigue crack initiation were analyzed and discussed.

Thermal-conductivity degradation across cracks in coupled thermo-mechanical systems modeled by the phase-field fracture method

Dynamic loading of polycrystalline metallic materials can result in brittle or ductile fracture depending on the loading rates, geometry and material type. At high strain rates, mechanical energy due to plastic deformation may lead to significant temperature rise and shear localization due to thermal softening. These shear bands reduce the stress bearing capacity of the material and act as a precursor to ductile fracture (e.g. cracks that develop rapidly on top of a shear band).Understanding the heat transfer physics in thermo-mechanical problems when cracks are developed, is a fundamental science that has not been rigorously addressed. In particular, reliable damage models, that degrade the thermal-conductivity in continuum crack descriptions, are necessary to capture the correct heat transfer physics across fracture surfaces but are currently absent.In this paper, a novel set of isotropic thermal-conductivity degradation functions is derived based on a micro-mechanics void extension model of Laplace’s equation. The key idea is to employ an analytical homogenization process to find the effective thermal-conductivity of an equivalent sphere with expanding spherical void. The closed form solution is obtained by minimization of the flux differences at the outer surfaces of the two problems, which can be achieved using the analytical solution of Laplace’s equations, so called spherical-harmonics.A unified model, which has been developed in McAuliffe and Waisman (2015) to account for the simultaneous formation of shear bands and cracks is used herein as a numerical tool to investigate the behavior of the aforementioned thermal-conductivity model. In this unified model, the phase-field method is used to model crack initiation and propagation and is coupled to a temperature dependent visco-plastic model that captures shear bands. Two benchmark problems are presented to show the necessity of such physics-based degradation function in dynamic fracture problems.

Accelerating crack growth simulations through adaptive model order reduction

SummaryAccurate numerical modeling of fracture in solids is a challenging undertaking that often involves the use of computationally demanding modeling frameworks. Model order reduction techniques can be used to alleviate the computational effort associated with these models. However, the traditional offline‐online reduction approach is unsuitable for complex fracture phenomena due to their excessively large parameter spaces. In this work, we present a reduction framework for fracture simulations that leaves out the offline training phase and instead adaptively constructs reduced solutions spaces online. We apply the framework to the thick level set (TLS) method, a novel approach for modeling fracture able to model crack initiation, propagation, branching, and merging. The analysis starts with a fully‐solved load step, after which two consecutive reduction operations—the proper orthogonal decomposition and the empirical cubature method—are performed. Numerical features specific to the TLS method are used to define an adaptive domain decomposition scheme that allows for three levels of model reduction coexisting on the same finite element mesh. Special solutions are proposed that allow the framework to deal with enriched nodes and a dynamic number of integration points. We demonstrate and assess the performance of the framework with a number of numerical examples.

Crack Initiation Behaviors of Granite Specimens Containing Crossing‐Double‐Flaws with Different Lengths under Uniaxial Loading

Crack initiation is an important stage in the failure process of rock masses. In this paper, crack initiation behaviors (crack initiation model, crack initiation location, crack initiation angle, and crack initiation stress) of granite specimens containing crossing‐double‐flaws with different lengths were investigated using PFC2D software. Crack initiation models were all tensile wing cracks, which did not exactly initiate from the main flaw with a length of 30 mm. They can initiate from the secondary flaw with a length 20 mm at α of 30° (included angle between main flaw and horizontal direction) and β of 90° (included angle between main and secondary flaws) and from main and secondary flaws at α of 30° and β of 60°. These were mainly induced by the superposition of stress fields around the main and secondary flaws as β varied from 0° to 90°, especially the tensile force concentration zones superposition. The tensile forces concentration zone around flaw shrank towards flaw tips with the increase of flaw’s inclinations measured horizontally. Under stress field superposition effects, the crack initiation stress decreased firstly and then increased with β at α of 30° and 45°. Crack initiation locations were close to flaw tips but not restricted to them. The distances between crack initiation locations and flaw tips, and the crack initiation angles depended on the flaw where first macrocracks initiated from. Microdisplacement field distributions of granite specimens to reveal the mesomechanism of crack initiation behaviors were discussed.