Crack Growth Model Research Articles

Peridynamic modeling of elastic-plastic ductile fracture

A peridynamics-based framework is established for the elastic-plastic ductile fracture analysis. In this frame, a new state-based peridynamic elastic-plastic model is presented using the novel bond extension state forms of yield function and plastic flow rule. The nonlinear energy release rate is computed by the extended peridynamic finite crack extension (PFCE) method, and an energy dissipation rate-based bond failure criterion is proposed for ductile crack growth modeling. Numerical methods for plastic states update and yield function solution are also given. Then, examples of plates with a center hole or a center crack, and compact tension (CT) tests are analyzed by the proposed models, and compared to those from theoretical and FEM solutions. The results demonstrate that the proposed peridynamic models can well capture the characteristics of elastic-plastic deformation and ductile fracture, including the plastic shape and size, energy distributions, nonlinear energy release rate, load-displacement and resistance curves, etc.

Modelling of Crack Formation and Growth using FEM for Selected Structural Materials at Static Loading

The purpose of this paper is to show the results of a study focused on the occurrence of damage heterogeneous materials, especially on the issue of modelling crack formation and propagation. In the beginning the attention is paid to the direct application of the finite element method to different types of materials in order to find critical parameters determining behaviour of materials at damage process. The applications of damage mechanics and possible approaches to model the origin of a crack propagation through modifications in FEM systems are presented and some practical applications are tested. Main effort is devoted to cement fibre composites and the search for new methods for their more accurate modelling, especially close to the field stress concentrator, respectively ahead of the crack tip. Modified XFEM method has been used as a suitable tool for numerical modelling.

Phase field modeling of thermal fatigue crack growth in elastoplastic solids and experimental verification

It is challenging to simulate thermal fatigue crack growth in elastoplastic solids, meanwhile, the phase field model is very attractive for simulating complex cracking problems. A thermal-elastoplastic phase field model for thermal fatigue was developed, and its accuracy and availability were verified by typical examples. Then a verified thermal fatigue experiment of the V-notch specimen was carried out and the crack growth was simulated based on the phase field model. The results indicate that the process of thermal fatigue crack in elastoplastic solids from initiation to propagation is effectively simulated by the proposed phase field model. As the regularization length increases, the simulated crack has a longer length and stronger diffusivity. The appropriate regularization length needs to be determined based on experimental results.

Crack propagation and mechanical properties simulation of G/(HfNbTaTiZr)C–Al2O3 gradient composites

The rapid development of computer simulation technology has provided theoretical and technical support for the performance prediction of ceramic materials. A two-dimensional simulation model was established to investigate the effect of the graphene (G) and gradient structure on the mechanical properties of (HfNbTaTiZr)C. Voronoi mosaics were applied in Abaqus to characterize the particle distribution of high entropy ceramics (HECs). The G/(HfNbTaTiZr)C–Al2O3 gradient ceramics were characterized through the formation of cohesive elements within grain boundaries and grains of each element using Python language. The fracture toughness, flexural strength and hardness of G/(HfNbTaTiZr)C–Al2O3 gradient ceramics were investigated through simulation model. The toughening mechanisms of G/(HfNbTaTiZr)C–Al2O3 gradient composites were investigated by establishing crack growth model. The simulation consequences are consistent with the experimental results in the literature, which verifies the accuracy of the simulation consequences. The toughening mechanism is validated through crack propagation experiments and its correctness is testified. Therefore, the simulation consequences are conducive to improving the design efficiency of HECs.

Mechanistic modeling of fatigue crack growth in asphalt fine aggregate matrix under torsional shear cyclic load

Fatigue crack growth in asphalt pavements under vehicle load may primarily occur within the asphalt fine aggregate matrix (FAM) phase of the mixture. This study aims to predict fatigue crack growth in FAM by developing a mechanistic-based fatigue crack characterization model and fatigue crack growth model under torsional shear cyclic load. Initially, a fatigue crack characterization indicator, fatigue damage density, was derived using principles of torque and dissipated strain energy equivalence. Afterwards, a fatigue crack growth model was established based on the pseudo J-integral Paris’ law. Finally, the viscoelastic damage constitutive model was further constructed by coupling the fatigue crack growth model with a viscoelastic model, which was subsequently implemented in COMSOL Multiphysics. The results show that the fatigue damage density can be determined by the initial shear modulus and phase angle, as well as shear modulus and phase angle under fatigue conditions. Additionally, a logarithmic-linear correlation exists between the fatigue crack growth rate and the dissipated pseudo strain energy rate. The parameters of the fatigue crack growth model exhibit minimal variation across different shear strain levels and temperatures. Overall, the proposed numerical model can effectively simulate damaged torsional shear cyclic tests of FAM.

High cycle fatigue life assessment of notched components with induced compressive residual stress

A method for predicting the high cycle fatigue life of cyclically loaded components with induced residual stress based on standard S–N curve data, a fracture mechanics crack growth model, and Finite Element Analysis using the ANSYS SMART crack growth modelling tool is proposed. The method is appropriate to high cycle fatigue analysis of components in which the working stress cycle is linear elastic and the conditions required by LEFM and the SMART FEA method are satisfied. The total fatigue life of the component is calculated as the sum of the crack initiation life and crack propagation life. Crack initiation life is evaluated for an assumed initiation crack length by reference to an S-Ni curve relating stress amplitude to number of cycles to crack initiation, generated from standard S–N data and application of SMART FEA to determine the crack growth component of total test specimen life. Crack propagation life is evaluated by superposition of the individual applied load and residual stress fields, where variation in stress intensity factor with increasing crack length is obtained in the form of polynomial equations. Numerical and experimental investigation of double-notch 316L stainless steel tensile specimens show that the proposed method gives an improved estimate of fatigue life when compared to standard stress-life fatigue assessment for specimens both with and without induced compressive residual stress.

Prediction model of S-N curve without fatigue test or with a minimum number of fatigue tests

A prediction method of S-N curve without fatigue tests is proposed based on the small crack growth model expressed as dadN=C∗σσw-1m∗an∗, where a: crack size in terms of area, σ: applied stress amplitude, σw: fatigue limit which decreases cycle by cycle with crack growth. The constants C*, m* and n* were identified to be C* = 10–4, m* = 2.0 and n* = 1 for various steels, cast irons and alloys. S-N curves for various materials were predicted by the proposed model and were compared with experimental data. The predicted S-N curves are in good agreement with the experimental results for conservative predictions.

Cohesive crack growth in polyethylene considering Schapery equation using XFEM

A nonlinear rate-dependent cohesive rule based on a novel incorporation by Schapery nonlinear coefficients is suggested to model crack growth in the case of polyethylene which is well-defined through the Schapery nonlinear constitutive equation. As the matter between the crack faces in a polymeric medium like polyethylene may tolerate large strain ranges during crazing and before complete separation, it may involve stress-dependent factors as same as bulk material. A useful damage-creeping cohesive rule is selected and its creeping part is extended in a way to incorporate the nonlinear Shapery parameters. The augmented relation is fitted to both high and low constraint results and applied to an experimented medium using Extended Finite Element Method (XFEM) to evaluate its ability to properly predict cohesive crack propagation. The results are in tight agreement with the existing experimental outputs. The suggested framework may illuminate a way of expressing the damage zone in polymers using nonlinear specifications of the bulk material.

Crack‐like effectiveness of some discontinuities in AA2024

AbstractMaintaining aircraft airworthiness to ensure the fleet's safe operation and maintain its readiness is critically dependent on accurate modelling and reliable predictions of fatigue crack growth. In this process, a knowledge of the representative initial discontinuity sizes that cause fatigue crack nucleation and early growth in aircraft is essential. Here the effective pre‐crack size of aluminum alloy 2024, from samples of aircraft production material and tested under aircraft spectra, are considered.

Multiphysics modeling of subcritical crack growth in glass

Subcritical crack growth starting from flaws on glass surfaces/edges causes slow degradation in glass strength. This phenomenon involves multiple physics and is very challenging to predict. In this work, we introduce a novel multiphysics model for subcritical crack growth in glass. This model considers water-assisted stress relaxation, stress-dependent chemical reaction between water and glass, diffusion of water to the crack tip, and reaction-driven slow crack growth. Stress relaxation is achieved by using a Prony series in the bond-based peridynamic viscoelastic model, and a new bond breakage criterion based on the concentration of reaction product is introduced. A displacement-loaded double beam with a pre-crack is used to obtain the crack velocity vs. stress intensity factor (v-K) curve. With proper simplifications and assumptions, v-K curves obtained from the model successfully reproduced their typical patterns in experiments. This model will help us better understand fundamental mechanisms and make predictions for subcritical crack growth in glass.

Variability Estimation in a Nonlinear Crack Growth Simulation Model With Controlled Parameters Using Designed Experiments Testing

Abstract Variability in multiple independent input parameters makes it difficult to estimate the resultant variability in a system's overall response. The propagation of errors (PE) and Monte Carlo (MC) techniques are two major methods to predict the variability of a system. However, the formalism of PE can lead to an inaccurate estimate for systems that have parameters varying over a wide range. For the latter, the results give a direct estimate of the variance of the response, but for complex systems with many parameters, the number of trials necessary to yield an accurate estimate can be sizeable to the point the technique becomes impractical. The effectiveness of a designed experiment (orthogonal array) methodology, as employed in Taguchi tolerance design (TD) method to estimate variability in complex systems is studied. We use a linear elastic three-point bending beam model and a nonlinear extended finite elements crack growth model to test and compare the PE and MC methods with the TD method. Our focus is on assessing their effectiveness under those specific circumstances. Results from an MC estimate, using 10,000 trials, serve as a referent to evaluate the result in both cases. We find that the PE method works suboptimal for a coefficient of variation above 5% in the input variables. In addition, we find that the TD method works very well with moderately sized trials of designed experiments for both models. Our results demonstrate how the variability estimation methods perform in the deterministic domain of numerical simulations and can assist in designing physical tests by providing a guideline performance measure.

Application of machine learning approaches for modelling crack growth rates

AbstractThe scientific community has widely accepted the use of machine learning techniques to tackle complex engineering problems. Among the most intriguing problems is finding the correlation between alloy steel properties and cyclic fatigue and crack growth rate. Employing machine‐learning models can provide more robust and accurate predictive models to address such challenges. This paper presents the application of four machine learning models, namely decision trees (DT), random forest (RF), adoptive boosting (AdaBoost), and gradient boosting regression tree (GBRT) to predict the crack growth rate of steel/alloys. The study utilizes a large database gathered from literature to construct the predictive models and compares the results using various statistical metrics and graphical representation. The study's findings demonstrate the effectiveness and suitability of machine learning techniques to handle complex databases related to fatigue problems.

Fatigue crack growth in mooring chain steel at different mean load levels

The fatigue crack growth rates of R4 mooring chain steel at different R-ratios are investigated. Crack growth experiments are performed at three different R-ratios, 0.1, 0.3 and 0.7, utilizing compact tension specimens in air environment. Huang and Moan's driving force parameter ΔKE, which relates the growth rates at different R-ratios to those obtained at R=0, is explored and adapted for R4 steel.A full-scale fatigue experiment involving a chain assembly with an identified crack is presented, where the observed crack growth was successfully modelled by the proposed crack growth model.Case studies with different mean loads are explored where the crack growth model is utilized to predict the fatigue life of D = 145 mm chain links with a crack at the crown location. The crack growth simulations are compared and discussed against published S–N curves for chain links with varying mean load. The S–N curves may give very inaccurate results when extrapolated outside of the underlying test data. The crack growth model predicts longer lives at low stress ranges and low mean loads compared to the S–N curves, indicating that current guidelines may be overly conservative in these conditions.

Crack growth-based life prediction for additively manufactured metallic materials considering surface roughness

Additively Manufactured (AM) components are prone to fatigue damage due to defects accompanied by the manufacturing process, such as surface roughness, internal porosity, and anisotropy due to differences in build directions. This is especially true for as-built components with significant surface roughness, where the surface polishing and treatments are not possible due to resource or space limitations. This paper proposes a crack growth-based methodology for the fatigue life assessment of AM components subjected to uniaxial and multiaxial, constant and variable loading conditions. The work is based on a previously developed subcycle fatigue crack growth model. The developed FCG model is extended with the stress concentration factor due to surface roughness and an asymptotic stress intensity factor (SIF) interpolation method for notched specimens. The proposed model approximates the surface roughness as an equivalent notch having the same stress concentration as that posed by the irregularities on the surface. Fatigue life assessment is performed based on the concept of equivalent initial flaw size (EIFS) and FCG analysis. The proposed methodology is validated against in-house as well as experimental data from the available literature.

Effect of sustained load on fatigue crack growth behavior of FGH96 at elevated temperature

Accurate prediction of fatigue crack growth behavior is crucial to damage tolerance assessment of turbine disk. Powder nickel-based superalloy is a kind of preferred material of turbine disk. For the purpose of better understanding the characteristics of its crack growth behavior under dwell fatigue conditions at elevated temperature, dwell fatigue crack growth tests of powder nickel-based superalloy FGH96 were conducted with compliance method at three temperatures (600℃, 650℃, 700℃) and multiple dwell time conditions (from 0 s to 60 s). The results show that sustained load can accelerate fatigue crack growth rate of FGH96 significantly at high temperature, and it is more pronounced with higher temperature and prolonged dwell time. At higher ΔK level, the acceleration effect brought by sustained load seems to diminish, this is ascribed to rapid crack growth rate which leads to insufficient time for time-dependent damage occurring at crack tip zone. The effect of temperature on dwell fatigue crack growth rate is more remarkable from 650℃ to 700℃, compared with that from 600℃ to 650℃. The fatigue crack growth resistance of FGH96 is sensitive to sustained load at 700℃, just 1 s dwell loading can produce remarkable acceleration effect on fatigue crack growth rate. The time-dependent crack extension in a loading cycle increases with dwell time in a decelerated manner. Finally, A phenomenological-based crack growth model considering time-dependent damage was proposed, the comparation between the proposed model and the experiment data confirms that it works well for a wide range of temperature and dwell time.

Spectral fatigue analysis of ship structures based on a stochastic crack growth state model

Fatigue life estimation in ship structures is a very complex problem, because of the stochasticity in the wave loading experienced by the hull and the inherent variability in the material and geometric parameters. On an effort to quantify such aleatoric uncertainties, this work integrates in a novel setting the spectral approach to loading description into a probabilistic fatigue crack growth model. The proposed framework effectively models both the randomness in the experienced sea states and the corresponding random sequence of the sea states that are encountered by the ship and contribute to the fatigue accumulation. The spectral approach eventually allows for the construction of potential crack growth path instances from a single realization of an effective random stress range that is applied for a corresponding realization of number of cycles. The obtained bundle of stochastic crack paths is further used in order to perform reliability estimations in the entire life cycle. Initially the proposed method is presented formally and algorithmically and its application is demonstrated through a numerical case study of a cracked plate where we are interested in estimating its remaining useful life along with the time distribution of the probability of failure.

Dynamic Crack Growth in Viscoelastic Materials with Memory

AbstractIn this paper we introduce a model of dynamic crack growth in viscoelastic materials, where the damping term depends on the history of the deformation. The model is based on a dynamic energy dissipation balance and on a maximal dissipation condition. Our main result is an existence theorem in dimension two under some a priori regularity constraints on the cracks.

Microstructure relevant fatigue short crack propagation behavior of Al0.3CoCrFeNi high entropy alloy: in-situ SEM study

The microstructure effects on fatigue short crack propagation behavior of Al0.3CoCrFeNi high entropy alloys (HEAs) were studied by in-situ fatigue testing under scanning electron microscope (SEM). The experimental results indicated that fine grain (FG) specimens had better fatigue crack propagation resistance and higher fatigue life compared with coarse-grain (CG) specimens. Fatigue short crack propagation followed transgranular mode, associated with octahedral slip. The fatigue small crack growth is primarily microstructurally sensitive, showing evident fluctuations related to the blocking effects of grain boundaries and twin boundaries. Furthermore, a modified fatigue crack growth model has been proposed, which can successfully evaluate the crack growth rates of HEAs with different grain microstructures under different fatigue stresses.

Modelling Crack Growth in Additively Manufactured Inconel 718 and Inconel 625

This paper first examines crack growth in a range of tests on additively manufactured (AM) and conventionally manufactured Inconel 718. It is shown that whereas when the crack growth rate (da/dN) is plotted as a function of the range of the stress intensity factor (ΔK), the crack growth curves exhibit considerable scatter/variability, when da/dN is expressed in terms of the Schwalbe crack driving force (Δκ), then each of the 33 different curves essentially collapse onto a single curve. This relationship appears to hold over approximately six orders of magnitude in da/dN. The same phenomenon also appears to hold for 20 room temperature tests on both conventionally and additively manufactured Inconel 625. Given that the 53 studies examined in this paper were taken from a wide cross section of research studies it would appear that the variability in the da/dN and ΔK curves can (to a first approximation) be accounted for by allowing for the variability in the fatigue threshold and the cyclic fracture toughness terms in the Schwalbe crack driving force. As such, the materials science community is challenged to address the fundamental science underpinning this observation.

Short crack growth model for the evaluation of the fatigue strength of WAAM Ti-6Al-4V alloy containing pore-type defects

The role of defects in the fatigue strength of Wire Arc Additively Manufactured (WAAMed) Ti-6Al-4V is analysed by means of the IBESS model, a fracture mechanics short crack growth approach based on the cyclic R-curve. Pores and crack-like defects are analysed. Estimations of the role of pore shape and size agree well with published fatigue data of WAAM Ti-6Al-4V with pores. The model is also used to explain the effect of fabrication defects on the scatter of experimental data. This demonstrates that short crack growth models represent a suitable engineering tool for the fatigue assessment of defective AM materials.