Crack Growth Rate Equation Research Articles

Thermally Activated Crack Growth and Fracture Toughness Evaluation of Pipeline Steels Using Acoustic Emission

The article presents an approach to assessing the fracture toughness of structural alloys based on thermally activated crack growth and recording acoustic emission signals. The kinetic and structural features of the stable growth of the initiated crack are estimated using a multilevel acoustic emission model based on the time dependence of the logarithm of the cumulative acoustic emission count. The article provides an evaluation of the stable kinetic constants included in the equation of the thermal fluctuation steps of a crack according to literature sources and using the acoustic emission method. It is shown that parameters such as activation energy, activation area before the crack tip, and the rate of non-activation crack growth are stable and show a satisfactory correspondence between the reference literature and real experiments. The approach does not require a set of laboratory experiments to determine the empirical constants of traditional crack growth rate equations, and it also differs in that it takes into account the unique features of the destruction of a particular specimen or technological equipment and allows for a non-destructive assessment of fracture toughness. The values obtained are conservative. The concentration criterion of destruction requires further investigation.

Experimental and probabilistic study of fatigue crack growth behavior of steel Q345qC under different stress ratios

The stress ratio effects and the scatter of the fatigue test results are the key issues in the design of steel fatigue performance. This paper reports an experimental and probabilistic investigation of the fatigue crack growth (FCG) behavior of steel Q345qC. Firstly, the microstructural characteristics and mechanical properties of steel Q345qC were examined via an optical microscope and tensile tests. Next, the FCG behavior of steel Q345qC was investigated under different stress ratios. The fatigue crack growth rate (FCGR) equations incorporating survival probabilities were proposed based on Paris and Walker laws. Finally, the theoretical FCG life under different survival probabilities in the crack stable growth region is calculated based on the integral formulas of Paris and Walker law and compared with the tested FCG life. The experimental results demonstrate that the larger the stress ratio, the shorter the length of stress intensity factor (SIF) amplitude experienced in the stable growth region and the smaller the SIF at the end of this region. Both probabilistic Paris and Walker equations can be used for FCGR calculations when the survival probability is set as 50%. The FCG life is calculated using the integral formula based on the Walker law with a high safety tolerance and a wide application interval of stress ratio when the survival probability is set as 90%.

Theoretical assessment of fatigue life of metal materials at constant cycle stress range

A computational model is proposed for theoretical evaluation of fatigue life of samples made of metallic materials at a constant applied cycle stress range. The total fatigue life is divided into two stages: the stage of crack nucleation, i.e., the number of loading cycles before its initiation (stage 1) and the stage of crack growth (stage 2). Different approaches are used to estimate the duration of each stage. For stage 1, the power law fatigue life equation is obtained from the condition that the accumulated strain energy is equal to the specific cracking energy, and for stage 2, the number of cycles is obtained by integrating the crack growth rate equation, where the effective range of the stress intensity factor (SIF), defined as the difference between the applied "external" range of the SIF and the "internal" range of the SIF, which characterizes the material's resistance to crack growth, is taken as its driving force. The initial data for the calculation, in addition to the loading parameters, are the characteristics of the static strength and microstructure of the initial material. Calculations based on the proposed fatigue life model for steel 0.45%C specimens show good agreement with experimental results.

On the strain energy release rate and fatigue crack growth rate in metallic alloys

The field of fracture mechanics started with Griffith’s energy concept for brittle fracture in 1920. In 1963, Paris et al. used a fracture mechanics’ parameter to introduce an equation for the fatigue crack growth rate in ductile materials and this equation is now commonly known as the ‘Paris law’. However, the Paris law and the semi-empirical models that followed ever since do not fully account for the main intrinsic and extrinsic properties involved with fatigue crack growth in metallic alloys. In contrast, here a dimensionally correct fatigue crack growth rate equation is introduced that is based on the original crack driving force as introduced by Griffith and the presence of plasticity in a metal to withstand crack propagation. In particular it is shown that the fatigue crack growth rate shows a power law relationship with the cyclic strain energy release rate over the maximum stress intensity factor. The new description corrects for the ratio between the minimum and maximum stress in a cycle during constant amplitude loading and for crack growth retardation under variable amplitude loading. The method has been successfully applied to variable amplitude crack growth with spectra that are representative of different fatigue dominated aircraft locations. As such, it allows for accurate predictions of variable amplitude fatigue crack growth life in aerospace structures.

A robust probabilistic fatigue crack growth model based on walker’s crack growth rate equation for metallic materials

The fatigue crack growth data inherits statistical variation despite carefully controlled test procedures. The available probabilistic models rely extensively on fatigue crack growth test data of the coupon material under replicate loading conditions. In view of the often unavailability of such a database, this work proposes a new probabilistic model based on Walker’s crack growth rate equation and considers the variability in both the stress intensity factor range, ΔK and stress ratio, R. The optimum estimates of the model parameters are established using the maximum likelihood estimation (MLE) method. The model is examined using selected sets of measured fatigue crack growth curves of 7075-T6 and 2024-351 aluminum alloys. It demonstrates acceptable predictions for fatigue crack growth data on replicate and variable R-ratio loadings with failure probabilities in the range of 0.10 ≤pF≤ 0.90. The error on the observed fatigue crack growth rate data is normally distributed. The criterion of the minimum number of replicate tests for a valid probabilistic assessment of the fatigue crack growth data is established. Based on the mean squared error (MSE) parameter, the model provides a better representation of the mean fatigue crack growth rate behavior of the material for fatigue loading with variable R-ratios.

Stress ratio effect on crack growth behavior of dissimilar friction stir welded butt joint between AA6061 and AA7075 alloys

Many engineering components are subjected to random nature of loading during their life period. In this work, the fatigue crack growth in friction stir welded dissimilar AA6061 and AA7075 was investigated under different stress ratio. AA6061 was kept on the advancing side due to having a higher solidus temperature and softer than AA7075 for smooth material flow. The microstructure characterization, tensile and crack growth behavior was studied. It was observed that the joint material exhibited lower strength and ductility as compared to the base material. About 41%, 34%, and 66% reduction in tensile strength, yield strength, and percentage of elongation as compared to AA6061 (base material) were observed. About 27% higher hardness in the HAZ of retreating side than the advancing side was noticed. The crack deflection and tortuosity features were observed in the fatigue fractured specimens. In this paper, a comparative study using different crack growth models has been studied and a simple crack growth rate equation has been proposed considering the crack closure effect.

Three-Dimensional Numerical Simulation of Creep Crack Growth Behavior for 316H Steel Using a Stress-Dependent Model

Based on detailed three-dimensional numerical simulation, creep crack growth behavior of C(T) specimen with different thicknesses of 316H steel was predicted using a stress-dependent creep ductility and strain rate model. Three regions were observed in the relation of creep crack growth rate versus fracture parameter C ∗ . The C(T) specimen with higher thickness exhibits higher CCG rate. The turning point 1 location from low C ∗ region to transition C ∗ region increases with increasing thickness, while that of turning point 2 seems to be independent of specimen thickness. Based on the finite element results, constraint-dependent turning point 1 location and creep crack growth rate equations were fitted. More accurate and realistic life assessment may be made when the stress-dependent model and the constraint effect were considered for creep life assessments of high-temperature components subjecting to a low applied load.

Fatigue crack propagation of planar three-dimensional cracks

In this paper the Fourier series is used to evaluate mode I Stress Intensity Factors (SIF) in three-dimensional planar flaws based on a distortion transformation of a reference disc. Under the hypothesis of an isolated crack, the SIF at each point of the crack border is calculated to assess the crack shape after propagation according to the crack growth rate equation of Paris and Erdogan. The contour is moved along the outward normal to the crack shape. Many examples are proposed with the aim of predicting the final shape of different types of embedded planar flaws.

Exploiting fractal features to determine fatigue crack growth rates of metallic materials

An alternative approach to the classical fracture mechanics equation to quantify the fatigue crack growth rate is proposed and examined. The method exploits the fractal features of the propagating fatigue crack. The reference crack growth response of AISI 410 martensitic stainless steel is established using compact tension C(T) specimens. Fractal analysis of microscopic images along the edge length of the crack establishes the fractal dimensions, dF of the fatigue crack. The box-counting algorithm is developed for the fractal analysis based on optical images of the crack at 100X magnification and the resolution of 1090 pixels/mm. Results show that the crack initially exhibits a Euclidean nature (dF ≈ 1). The fractal dimension increases steadily with increasing crack length in the Paris crack growth rate region with 1.05 < dF < 1.24. The corresponding stress intensity factor range varies between 18 ≤ ΔKI ≤ 40 MPa√m. The fractal dimension, dF correlates linearly with the normalized stress intensity factor range, ΔKKIC within the Paris crack growth region. This enables the multifractal fatigue crack growth rate equation to be established in terms of the fractal dimension, Paris coefficient and exponent, and fatigue fracture properties of the material. The fatigue crack growth rate of the material could then be determined using the multifractal fatigue crack growth rate model without requiring the geometry factor of the crack.

Three-dimensional fatigue crack propagation by means of first order SIF approximation

In this paper we make use of a closed-form solution for mode I Stress Intensity Factors (SIF) in three-dimensional planar flaws based on homotopy transformations of a disc. The utilised equations are very accurate when the flaw is a small deviation from a circle. Under the hypothesis of an isolated crack, the SIF at each point of the crack border is calculated to assess the crack shape after propagation. The solution is proposed in terms of the Fourier series and the crack growth rate equation is taken according to Paris’ low. Many examples are proposed with the aim of predicting the final shape of different types of embedded planar flaws in butt welded joints under fatigue tensile loading.

Investigation on fatigue crack propagation law of the crack perpendicular to interface for Zr/Ti/steel composite plate

In this paper, the effects of load ratio, elastic mismatch and plastic mismatch on the fatigue crack growth behavior of zirconium-titanium-steel composite plate are discussed in detail. Firstly, considering the crack closure effect caused by load ratio, different effective driving force models of crack tip are studied. The results show that Daniel's two parameter driving force model has the best normalization effect. Then, based on the material inhomogeneity theory, the equation of actual stress intensity factor at crack tip is obtained, and the crack growth rate equation considering elastic mismatch is obtained. Furthermore, the influence of plastic mismatch is studied. Finally, by dividing the influence area of the elastic-plastic mismatch and combining the respective crack growth criteria, the crack growth rate equation considering the load ratio and elastic-plastic mismatch is obtained.

Fatigue Crack Growth Prediction under Spectrum Load in an Aluminium Alloy using Crack Driving Force K*eff Approach

Fatigue Crack Growth (FCG) behaviour in a Single-Edge-Notched Tension (SENT) specimen of 2024-T3 aluminium alloy under a standard mini-FALSTAFF spectrum load sequence was experimentally determined. Further, the FCG behaviour was predicted using cycle-by-cycle method and compared with experimental results. Prediction procedure involved are rain-flow counting of fatigue load cycles, estimation of crack driving force for each of the counted cycle and prediction of crack extension per cycle from constant amplitude crack growth rate equation. In the present work, a new crack driving force (CDF) K*eff involving Kujawski’s crack driving force K* in conjunction with Elber’s crack closure concept was used to account for load interaction effects. FCG prediction was also made using conventional CDF ΔKeff (Elber’s) approach. A good correlation was observed between experimental and predicted FCG behaviour under spectrum loads by the proposed K*eff approach. Also, this prediction was observed to be better than that predicted by conventional ΔKeff approach.

Laser shock peening-induced surface gradient stress distribution and extension mechanism in corrosion fatigue life of AISI 420 stainless steel

Surface gradient stress distribution was prepared on AISI 420 martensitic stainless steel (MSS) by massive laser shock peening treatment (MLSPT) with different pulse energies, and effects of MLSPT on residual stress and corrosion fatigue properties in NaCl solutions with different pH values were investigated by microstructural observation, residual stress measurement, corrosion fatigue test, and fractural morphology. Results showed that the coupling effect of MLSPT-induced surface microstructural evolution and gradient stress distribution effectively contributed to an extension in corrosion fatigue properties. Furthermore, the corrosion fatigue crack growth rate equation considering both gradient compressive residual stress and pH value was developed.

Crack growth rate and lifetime prediction for aviation gas turbine engine compressor disk based on nonlinear fracture mechanics parameters

In this study, the fatigue crack growth and life-time prediction of aviation gas turbine engine compressor disks under operating conditions are analyzed. Different combinations of rotational speed, temperature, surface flaw forms and sizes, as well as elastic–plastic titanium alloy BT3-1 properties are considered. A crack growth rate equation, which included the fracture process zone size and nonlinear stress intensity factor, is derived. The assessments of the structural integrity of the rotating disk are compared for elastic and elastic-plastic solutions. It is indicated that the traditional elastic crack growth models overestimate the residual fatigue lifetime with respect to the nonlinear fracture mechanics approach.

Creep–fatigue crack growth rate prediction based on fracture damage zone models

Based on a new fracture damage zone formulation and nonlinear elastic–plastic and creep crack tip fields, the prediction of creep–fatigue crack growth rate is studied. A unified crack growth rate equation is derived using the equivalent nonlinear stress intensity factor, monotonic low-cycle fatigue, and creep material properties at an elevated temperature. The crack growth rate model includes the size of the fracture process zone and damage parameters. The predicted creep–fatigue crack growth rates are compared with the experimental data of the 12Cr1MoV power plant steel and good agreement is observed.

Life-time prediction for aviation GTE compressor disk based on mixed-mode and multi-axial fracture resistance parameters

This study is concerned with analysis of fatigue crack growth and life-time prediction for aviation GTE compressor disk under operation conditions. For consideration were different combinations of rotational speed, temperature, surface flaw form and sizes as well as elastic-plastic titanium alloy BT3-1 properties are employed. A crack growth rate equation is derived involving the fracture process zone size and nonlinear stress intensity factor. The assessments of the structural integrity of the rotating disk are compared for elastic and elastic-plastic solutions. It is stated that the traditional elastic crack growth models overestimate the residual fatigue lifetime with respect to the nonlinear fracture mechanics approach.

Fatigue crack growth of G20Mn5QT cast steel based on a two-parameter driving force model

This paper performs a research on fatigue crack growth in G20Mn5QT cast steel using the experimental method and a semi-empirical fatigue crack growth model. The model combines the two-parameter driving force and fatigue damage accumulation. It would take into account the effects of mean stress and load history, and the fatigue crack growth rate curve would only be influenced by the sort of material. Comparing to the experimental results, the proposed model has good simulation results. A unified fatigue crack growth rate equation for G20Mn5QT cast steel has been given out, which is more convenient for engineering applications.

Microstructure-sensitive estimation of small fatigue crack growth in bridge steel welds

A probabilistic finite element model is implemented to estimate microstructurally small fatigue crack growth in bridge steel welds. Simulations are based on a microstructure-sensitive crystal plasticity model to quantify fatigue indicator parameters (FIPs) at the slip system level and a fatigue model that relates FIPs to fatigue lives of individual grains. Microstructures from three weld zones, namely, fusion zone (FZ), heat affected zone (HAZ), and base metal (BM), are constructed based on their microstructural attributes such as grain morphology, size, and orientation. Statistical volume elements (SVEs) are generated and meshed independently for the three welding zones. Each grain within the SVEs is divided into several slip bands parallel to crystallographic planes. During the loading process, cracks nucleate at the slip bands (SBs) with the largest FIP next to the free surface. The crack extension path is assumed to be transgranular along SBs and the number of cycles required to crack the neighbor grain is calculated by the corresponding FIP-based crack growth rate equation. The simulation process is carried out using ABAQUS with a user defined subroutine UMAT for crystal plasticity. After the calibration of the constitutive model and irreversibility parameters, numerical simulations for small crack growth in three zones are presented. The crack length vs. the predicted fatigue resistance shows significant differences in the mean values and variability among the three weld zones.

Crack Initiation and Growth from Pre-corroded Pits in Aluminum 7075-T6 Under Laboratory Air and Salt Water Environments

Small crack growth behavior, including the pit-to-crack transition, of pre-corroded aluminum alloy 7075-T6 was investigated under ambient air and saltwater environments. Through pit and corner crack pits were created prior to constant stress amplitude fatigue testing. The small crack growth life (SCGL) and crack initiation life (CIL) under salt water condition were about 5-8 times less when compared to those under ambient air. The ratio of SCGL to CIL was significantly smaller with large uncertainty (variation) under salt water environment. The small crack growth rates under salt water were 2-12 times larger than corresponding rates under laboratory air at identical stress amplitude and crack length. The crack lengths required to attain Paris region growth rates (Paris region threshold crack lengths) were about 1-3 mm for stress amplitudes less than 45 MPa. Sub-millimeter cracks attained 10−4 mm/cycle fatigue crack growth rates (FCGR) for stress amplitudes greater than 45 MPa. The crack growth rates of 0.25-mm-long cracks were about 2 times higher for salt water environment when compared to identical stress conditions in ambient air. Empirical crack growth rate versus stress intensity factor range equations similar to Paris law were developed for small crack growth and crack initiation under ambient air and salt water condition, for fatigue crack prognostics applications. For the design applications, a modified Kitagawa-Takahashi (K-T) diagram for corrosion-pitted aluminum 7075-T6 is presented.

High Cycle Fatigue Property of Carburized 20Cr Gear Steel under Axial Loading

The high cycle fatigue property of carburized 20Cr gear steel was experimentally investigated under axial loading with a stress ratio of zero. The test results show that this steel exhibits gradually decreasing S-N characteristics, and the fatigue strength corresponding to 109 cycles is about 455 MPa. Based on the observation of fracture surfaces, the interior inclusion fisheye-induced fracture is the predominant fracture mode in the life regime beyond 105 cycles. The fine granular area (FGA) cannot be found clearly around the inclusion. Based on the evaluation of stress intensity factor ranges (ΔK) at the front of inclusion and fisheye, the interior crack growth rate (da/dN) equation can be characterized by da/dN = 2.39 × 10−21(ΔK)12.32. Corresponding to the tested specimen, the predicted maximum inclusion size is about 52.02 μm. The predicted fatigue strength corresponding to 109 cycles by using Wang’s model is slightly higher than the experimental result, but that by using Murakami’s model is relatively conservative.