Crack Closure Model Research Articles

Numerical modelling of three-dimensional fatigue crack closure: Plastic wake simulation

Finite element method has been broadly used to study fatigue crack closure. The simulated plastic wake length is one of the key modelling parameters involved. This paper presents a complete analysis in fatigue crack closure 3-D models.It is aimed at two aspects: the influence on the calculation of opening and closure values, and the effect on other main results. Conclusion indicates a 0.6 times Dugdale’s plastic size length to stabilise results as plastic zone or contact area, but a reduced length could be acceptable in terms of crack closure results. This suggests some independence among this parameter and fatigue crack closure.

Fatigue Failure Characteristics of Single-Crystal Fe-3%Al Alloy

To obtain a better understanding of the mechanical properties and failure characteristics of the single-crystal Fe-3%Al alloy (SC), tensile and fatigue properties of the SC and polycrystalline Fe-3%Al alloy (PC) have been investigated. The tensile strength and fracture strain for the SC samples were different depending on the loading direction, i.e., 〈111〉, 〈110〉 and 〈100〉, which could be explained by the Schmid factor. Fatigue strength for the SC samples was basically correlated with their tensile strength. Different fatigue properties were obtained for the PC sample, e.g., the high fatigue strength was obtained in the early fatigue stage, and significant reduction in the fatigue strength was appeared in the later fatigue stage, e.g., low endurance limit at 107 cycles. The reason for this was caused by the material brittleness due to the accumulated dislocation at the grain boundaries. Because the high ductile SC samples made severe plastic deformation ahead of the crack tip, the crack growth rate did not enhance even if the high stress intensity factor range was applied in Region II (da/dN versus ΔK). The crack growth rate dropped just before the final fracture. Effective stress intensity factor range was estimated using the crack closure model, but the crack growth rate is found to be affected strongly by the slip system of SC sample.

Crack Closure Effect and Energy Dissipation Model for Rocks under Uniaxial Compression

Through the uniaxial compression tests of sandstone, the crack closure effect and the relationship between the crack parameters and the height to diameter ratio (H/D) were analyzed. Then, a nonlinear model for characterizing energy dissipation based on the crack closure effect was established. The results show that the peak strength and peak axial strain of sandstone decrease gradually with the increase of H/D, but the elastic modulus has a small change. The maximum crack axial closure strain and crack axial closure stress of sandstone increase with the H/D. While the peak crack axial strain and axial crack initiation stress decrease. The dissipative energy firstly increases with the axial stress, and the increase rate decreases gradually. Then, the dissipative energy nearly remains as a constant. The axial crack closure model was established to describe the crack closure effect of sandstone, and the equivalent elastic modulus of crack closure of sandstone calculated by axial crack closure model decreases nonlinearly with the H/D. A rock energy dissipation model based on crack closure under uniaxial compression was established. The experimental results agree well with the theoretical values, which indicates that the proposed model can describe the energy dissipation of rocks under uniaxial compression. The research conclusion provides a theoretical reference for the stability evaluation of underground rock masses with different sizes.

Two new models of fatigue crack growth rate based on driving force parameter and crack closure method at negative load ratios

The fatigue crack growth rate (FCGR) is strongly dependent on the load ratio R and most FCGR models are established on the basis of R. At present, there are more FCGR models with positive load ratio. In this paper, fatigue crack growth (FCG) behavior of commercial pure titanium at negative load ratios is studied. The FCGRs at various load ratios are fitted by driving force parameter model and crack closure model. The advantages and disadvantages of different models are analyzed by calculating the dispersion of FCGR curves which are condensed by each model. Improved two-parameter driving force model and proposed crack closure model are proposed by two FCGR modeling methods, respectively. One is to modify the FCGR by improving the stress intensity factor (SIF) K with the two-parameter driving force method. Another is established by correlating the crack closure ratio U and load ratio R, positive SIF range ΔK+, maximum SIF Kmax based on the variation of crack closure level in stable crack growth stage. It is found that proposed crack closure model is superior to the former in both the condensation effect and the physical significance. Under different loading conditions, proposed crack closure model can reliably and accurately condense the FCGR curves and reflect the variation of crack closure level in the whole stable crack growth stage. The integrity and validity of proposed crack closure model is also further verified by FCGR data of other researchers.

A new method for analysis of part-elliptical surface cracks in structures subjected to fatigue loading

This paper presents a new analytical method for the analysis of fatigue growth of surface cracks in various structural components. The method is based on a governing equation describing the front evolution of surface cracks of elliptical and part-elliptical shapes. This method avoids the need for various numerical schemes for the calculation of the incremental crack front advance, which were used in all previous studies. Plasticity-induced crack closure models can also be incorporated into the method or these models can be deducted from a correlation of experimental data and the method predictions. When the plastic constraint conditions change significantly along the crack front, the implementation of the plasticity induced crack closure models can significantly improve the accuracy of fatigue life predictions. The method is validated against previous theoretical and experimental studies.

Quantitative dependence of oxide-induced crack closure on air humidity for railway axle steel

The paper analyses fatigue crack closure in the near-threshold regime of the EA4T railway axle steel. The dependence of fatigue crack growth threshold on air humidity was experimentally obtained. Varying air humidity led to changes of fatigue threshold values Kmax,th in the range from 4 to 7 MPa m0.5, which was explained by the effect of oxide-induced crack closure (OICC). Such a wide range of threshold values results in significant changes of residual fatigue lifetime of railway axles (by one or two orders of magnitude) operated under various humidity conditions. The Newman's model of plasticity-induced crack closure is not sufficient to explain high portions of crack closure near threshold and their variation, since roughness-induced crack closure (RICC) and OICC has also be taken into account. Detailed explanations and interpretations of the parameters quantifying crack closure are presented. A quantitative model for separation of the crack closure components was applied to threshold data from literature for dry and humid atmosphere as well as for new experimental data of the EA4T steel tested at various levels of humidity. The levels of OICC determined from threshold values were compared to those calculated from thicknesses of oxide debris measured on fracture surfaces. The oxide layers were measured after the experiments in scanning electron microscope using focused-ion-beam cuts. The results were plotted as dependences on absolute air humidity and were in a good agreement. Very low threshold values measured in dry air can occur in operation when the temperature is around 0 °C which is not exceptional in many countries.

A novel driving force parameter [formula omitted] for fatigue crack propagation in prestressed-CFRP-repaired steel structure

A study was numerically and experimentally conducted to investigate the crack driving mechanism of steel structures strengthened with non- and prestressed CFRP (Carbon Fiber-reinforced Polymer) plates. A novel and simple crack driving force model using both ΔKeff and Kmax was established to account for the interplay of cyclic and monotonic damage by introducing a correlation factor to define their contribution. The extensive crack growth curves of tensile fatigue testing under constant amplitude loading were referred to in the literature, and finite element method (FEM) modeling was performed to calculated the stress intensity factors (SIF) of the specimens. The relationship between the correlation factor and stress ratio (R-ratio) was determined by the reverse-reasoning method through the remaining life in the experimental data. Then the fatigue tests of different steel elements, including tensile plate, I-section and RHS beam, were used to verify the prediction accuracy. These results validated the proposed method that provides much higher accurate estimation of the remaining fatigue life at a wide range of R-ratios comparing to the traditional methods, such as crack closure model and two crack driving force model.

Fatigue-crack growth in two aluminum alloys and crack-closure analyses under constant-amplitude and spectrum loading

Fatigue-crack-growth tests were conducted on compact, C(T), and middle-crack tension, M(T), specimens made of 7075-T6 and 7249-T76511 aluminum alloys. The 7075 tests were conducted on thin-sheet (2-mm thick) material; whereas, the 7249 tests were conducted on three thicknesses (2, 3.2 and 6.35-mm). The thin-sheet 7075 alloy did not have residual stresses, but the 7249 alloy (B = 2 mm) had low-level (<10 MPa) residual stresses from measurements. However, the other two 7249 alloy thicknesses were residual-stress free based on measurements. These tests were conducted to generate fatigue-crack-growth-rate data from threshold to near fracture at two load ratios (R = 0.1 and 0.7). Two methods were used to generate near threshold data on C(T) specimens: (1) compression pre-cracking constant-amplitude (CPCA) and (2) compression pre-cracking load-reduction (CPLR). Constant-amplitude tests were conducted on the M(T) specimens at the same two load ratios. Crack-closure measurements using a compliance method were made on some of the low R tests and a crack-closure model were used to develop an effective stress-intensity factor range against rate relation using a constant constraint factor (α = 1.85). The constraint factor accounts for three-dimensional stress-state effects on plastic yielding at crack tips and crack-closure behavior.Simulated aircraft wing spectrum tests were conducted on the M(T) specimens using two modified full-scale-fatigue-test (FSFT) spectra used on the P-3C aircraft. Tensile pre-cracking was used on all of the M(T) specimens, except one 3.2-mm thick 7249 specimen, before the spectra were applied. The same spectrum sequence was applied, but one had tension-compression loads, whereas, the other only tension-tension loads. The spectrum tests were used to calibrate the constraint-loss regime (plane-strain to plane-stress; α = 1.85–1.0) behavior for the FASTRAN strip-yield model. Comparisons were made between the spectrum tests and calculations made with the FASTRAN life-prediction code; and the calculated crack-growth lives were generally within ±20% of the test results.

Effect of loading sequences on fatigue crack growth and crack closure in API X65 steel

This paper presents a predictive model for fatigue crack growth under loading sequences. Several parameters had been quantified mainly under variable amplitude loading due to its peculiarities. The applicability of the crack closure model was studied to predict the fatigue life span resulting from the continuous effect of loading blocks. The API grade X65 steel, which is widely used in the crude oil and gas industries, was used in this study. Spectrum loading with a two-level block sequences, designated as high-to-low and low-to-high, were designed to correspond to variable amplitude loading. A stress ratio of 0.1 and 0.7 was retained at each block sequences. The effect of block transition from high-to-low caused a delay in crack growth due to the residual plastic wake left behind the crack tip. The crack growth under low-to-high loading blocks were faster than that under high-to-low loading blocks. A modified Walker was established and demonstrated to be capable of describing the features of crack arrest and crack growth acceleration under continuous loading sequences. The normalised root-mean-square error of the predictive model ranged from 0.05 to 0.22 at both load ratios. The integrated crack closure into Walker can reasonably predict the influence of loading sequences on the fatigue crack growth in the API X65 steel.

Modeling R-dependence of near-threshold fatigue crack growth by combining crack closure and exponential mean stress model

A previously proposed equivalent driving force model was modified to account for crack closure for modeling stress ratio, R, dependence of fatigue crack growth in near-threshold regime. A new fatigue crack growth driving force model was established in the form of ΔK⋅f(R), where the f(R) includes both crack closure and mean stress contributions, and well informs the shift from dominance of stress intensity factor range ΔK to maximum stress intensity factor Kmax with increasing R. The model was validated widely with sound agreement between modeling results and experimental data.

Crack Closure in the Near-threshold Region in Metallic Materials

Resistance to fatigue crack propagation is divided into the intrinsic (effective) component and the extrinsic component, represented by crack closure, which is very significant in the near-threshold regime. Crack growth rate measurements were done on the compact tension specimens made of the ferritic-pearlitic steel for automotive at the stress ratio R = 0.1 and R = 0.8. Crack closure was quantified from the experimentally measured data using the effective crack growth rate curve da/dN-ΔKeff and a new expression of the crack closure ratio Rcl = Kcl/Kmax depending on plasticity-induced crack closure, roughness-induced crack closure, oxide-induced crack closure and the exponent of the Paris power law. The presented methodology helps to analyse the crack closure mechanisms and to calibrate parameters used in the crack closure models.

Influence of crack closure and local near-tip stress on crack growth life estimation

Currently, among other models for crack growth prediction, crack closure models that consider the decrease in stress intensity factor (SIF) range associated with cyclic loading asymmetry are more popular. One of drawbacks of these models is impossibility of considering the loading history sequence.The theory related threshold SIF range and ΔKth and local near-tip stresses, induced by overloads, and postulated that the overload effect in the near-threshold region of growth rates is caused by residual local stresses. The proposed model applies the local stress and strain approach to estimate stress σ* in the stress concentration region for fatigue analysis. This region is characterized by local near-tip stress σ*, whose amplitude is determined by cyclic inelastic reaction at crack tip. Further development of the model is due to varying nature of the threshold SIF range ΔKth.As a basis, the Forman-Mettu formula was adopted, which describes the fatigue crack growth curve in all three regions of fatigue crack growth rate. The range ΔK was determined by the peak load ΔP of the load history. The crack closure was considered by the Schijve equation, considering the asymmetry of the half-cycle U = f(R), and effective SIF was estimated by ΔKeff = ΔK*U. Given known SIF range ΔK, the value of the local stress σ* at distance from the crack tip r* was determined for each half cycle by Neuber and Ramberg-Osgood equations, and threshold SIF was estimated from the analytical formula of Кth=f(σ). Thus, known loading history made it possible to determine ΔKeff, Kmax, and Kth on each cycle for fatigue life estimation.Mathematical modeling of fatigue crack growth life, especially in near-threshold region of its growth, according to the Sunder’s scheme, showed that investigated aluminum alloy 2024-T3 exhibited crack growth sensitivity to various types of force action, including various types of random loading.

An applied method for fatigue life assessment of engineering components using rigid-insert crack closure model

The purpose of this paper is to provide a new method for analyzing and evaluating the fatigue crack closure load and estimating the life of engineering components using RICC (Rigid-Insert Crack Closure Model), non-destructive replica technique, and a new sample. For this purpose, first, the method of solving the RICC model has been changed from linear approximation to nonlinear state and therefore, a significant improvement in the accuracy of the model results has been achieved. Then, using the model, a new formulation for the influence line in the points of sample is obtained, which has a significant accuracy. The formulation of the RICC model results in a set of equations that can help to determine the closure load and the characteristics of the load-displacement diagram using the residual crack mouth opening displacement in zero load (residual CMOD), which is the only empirical input parameter of Model. The new formulation method has been applied to a standard sample that has the same conditions as a real instance. The amount of residual crack openness in zero load (crack residual displacement) was measured using the replica technique and COD-gage simultaneously on a standard sample and were investigated using the obtained relationships and the accuracy of the outcomes. To prove the reliability, model results have been investigated through doing the experimental tests on aluminum alloys. Finally, the results obtained from the proposed relationship for the analysis and evaluation of the crack closure load and fatigue life were compared with the experimental results, which showed acceptable results.

Fatigue crack tip strain evolution and crack growth prediction under single overload in laser melting deposited Ti-6.5Al-3.5Mo-1.5Zr-0.3Si titanium alloy

This paper focuses on the fatigue crack tip strain evolution in laser melting deposited Ti-6.5Al-3.5Mo-1.5Zr-0.3Si titanium alloy under constant amplitude loading plus single overload (OL). The digital image correlation (DIC) technique was used to capture and evaluate the crack tip strain fields and crack closure variation; the results showed that the strains near the crack tip become larger and the crack opening load increases after the application of the OL. The size of the retardation distance is consistent with the analysis results of the crack tip strain fields. The crack closure model based on the DIC analysis results can provide good predictions of the crack growth life for both the low and high overload ratios.

Development of an Optimization Tool for Calibrating Crack Growth Material Models

Abstract Crack growth models are typically calibrated using experimental data prior to conducting damage tolerance analyses of aircraft structures. This process can be trivial for crack growth models that only have a few fitting parameters. However, other models, such as the FASTRAN crack growth equation with the analytical crack-closure model, include several model parameters that make calibration challenging. To simplify the calibration process and improve the accuracy of crack growth simulations, an automated crack growth model optimization tool was developed. This tool also aims at improving the robustness of crack growth models by reducing their dependency on loading spectra and specimen geometries. To achieve this, numerical optimization is used to minimize the discrepancy between experimental data and analytical crack growth. To demonstrate this approach, material model parameters were calibrated for P-3/CP-140 aircraft applications using the FASTRAN crack growth equation with the analytical crack-closure model. The optimization tool was found to be very effective at fitting crack growth simulation results to experimental data by changing the values of selected parameters. It was, however, observed that the automated calibration process could find multiple sets of FASTRAN parameter values that provide equivalent correlations with experimental data. In an attempt to develop a more robust material model, multiple test configurations with different geometries and loading spectra were used to determine an optimal trade-off model that maximizes the correlation for multiple test configurations. The conducted tests demonstrated that this approach is viable and could be used to improve the robustness of crack growth simulations.

Numerical modelling of three-dimensional fatigue crack closure: Mesh refinement

Fatigue crack closure has been studied by means of the finite element method for a long time. Most work has been performed considering bi-dimensional models where the numerical methodology has been developed. A great number of bi-dimensional studies analyses different numerical parameters and optimise them.Three-dimensional models have extended lately. Nevertheless, the methodology employed was taken from the one developed for bi-dimensional cases. The current computational capabilities allow a comprehensive three-dimensional study of the influence of the different modelling parameters in a similar way to those studies carried out with bi-dimensional models.In particular, one of the key issues is related to the element size, which has a huge influence on crack opening and closure values. In the present work, a CT aluminium specimen has been modelled three-dimensionally and several calculations have been made in order to evaluate the influence of the mesh size around the crack front. The numerical accuracy is analysed in terms of crack closure and opening values. Classical bi-dimensional recommendations are updated. A similar linear relationship has been identified and a minimum mesh recommendation of 60 divisions of the Dugdale’s plastic zone size is made.

Understanding of fatigue crack growth behavior in welded joint of a new generation Ni-Cr-Mo-V high strength steel

This study was mainly concerned with the long fatigue crack growth rate (FCGR) of a new generation Ni-Cr-Mo-V high strength steel and its welded joints used in modern marine environment. Several major factors, including stress ratio, microstructure, welding residual stresses (WRSs) and specimen thickness were investigated. Results showed that the weld metal (WM) possessed better resistance to crack propagation relative to the base material (BM) under each stress ratio owing to the interlocking acicular ferrite microstructure and the resultant higher crack closure level. WRSs partly retained in the extracted fracture mechanics samples and noticeably affected FCGR of the WM. Post-welding heat treatment could never eliminate the WRSs and might generate new residual stress distribution. Both the crack closure model and the two-parameter model yielded fairly good consolidation for the R-ratio effect of the BM whereas they failed to correlate the data for the WM because of the retained WRSs. Accelerated FCGR with increased specimen thickness was measured for both the BM and the WM. The fracture mechanism was scrutinized by means of fractography and fatigue trajectory map. The results obtained in the present work are helpful in shedding light on the damage tolerance design of the Ni-Cr-Mo-V high strength steel welded joints employed in modern marine structures.

Small Fatigue Crack Initiation and Growth behavior of Low Carbon Steel with Simulated HAZ Heat Treatment

Naturally initiated small fatigue crack and its growth behavior of several simulated HAZ microstructures were successively observed using automatic microscope system. Simulated HAZ microstructure specimen were prepared by heat treatment with controlling maximum temperature and cooling rate. In addition, crack initiation and early stage crack opening-closing behaviors were evaluated by Digital Image Correlation (DIC) technique. As a results, fatigue life of coarse grained microstructure was shorter than that of finer grained one due to the difference from not crack initiation life but crack growth life. Since initiated crack size, depending on microstructural unit size, of the coarse grained specimen was larger than the other, remained fatigue crack growth life became shorter. In addition, early stage crack opening stress of naturally initiated small fatigue crack were successfully measured by combination of automatic microscope system and DIC technique. This result showed that small fatigue crack just after initiation opens near the minimum load, under the compressive stress, and it was increased depending on crack length. However, crack opening stress of coarse grained specimen increased more slowly than that of finer grained specimen. This behavior also affected to fatigue crack growth life. Furthermore, early stage small crack growth life became comparable to long crack data by using effective J-integral range evaluated from measured crack opening point. Therefore, it was indicated that initial crack size and early stage crack closure model depending on microstructure are needed to calculate fatigue life.

An Integral Formulation of Two‐Parameter Fatigue Crack Growth Model

A two‐parameter fatigue crack growth algorithm in integral form is proposed, which can describe the continuous crack growth process over the time period. In this model, the fatigue crack propagation behavior is governed by the temporal crack‐tip state including the current applied load and the physical condition due to the previous load sequence. The plasticity‐induced crack closure, left by the historical loading sequence, controls the following fatigue crack growth behavior and typically leads to the interaction effects. In the proposed method, a modified crack closure model deriving from the local plastic deformation is employed to account for this load memory effect. In general, this model can simulate the fatigue crack growth under variable amplitude loading. Additionally, this model is established on the physical state of crack tip in the small spatial and temporal scale, and it is used to evaluate the macroscopic crack propagation and fatigue life under irregular tension‐tension loading. A special superimposed loading case is discussed to demonstrate the advantage of the proposed model, while the traditional two‐parameter approach is not proper functional. Moreover, the typical various load spectra are also employed to validate the method. Good agreements are observed.

Fatigue and crack-growth behavior in a titanium alloy under constant-amplitude and spectrum loading

A titanium alloy (Ti-6Al-4V STOA) plate material was provided by the University of Dayton Research Institute from a previous U.S. Air Force high-cycle fatigue study. Fatigue-crack-growth tests on compact, C(T), specimens have been previously performed at Mississippi State University on the same material over a wide range in rates from threshold to near fracture for several load ratios (R = Pmin/Pmax). These tests used the compression pre-cracking method to generate fatigue-crack-growth-rate data in the near-threshold regime. Current load-reduction procedures were found to give elevated thresholds compared to compression pre-cracking methods. A crack-closure model was then used to determine crack-front constraint and a plasticity-corrected effective stress-intensity-factor-range relation over a wide range in rates and load ratios. Some engineering estimates were made for extremely slow rates (small-crack behavior), below the commonly defined threshold rate. Newly-developed single-edge-notch-bend, SEN(B), fatigue specimens were machined from titanium alloy plates. These specimens were fatigue tested at two constant-amplitude load ratios (R = 0.1 and 0.5) and a modified Cold-Turbistan engine spectrum. All of the tests were conducted under laboratory air and room temperature conditions. Calculated fatigue lives from FASTRAN, a fatigue-life-prediction code, using small-crack theory with an equivalent-initial-flaw-size (semi-circular surface flaw) of 9-μm in radius at the center of the semi-circular edge notch fit the constant-amplitude test data fairly well, but under predicted the spectrum loading results by about a factor of 2–3. The reasons for the large under prediction were discussed. Life predictions made with linear-cumulative damage (LCD) calculations agreed fairly well with the spectrum tests.