Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.     

Finite element analyses of deformation around holes near a crack tip and their implications to the J-resistance curve

The initiation phase of ductile crack growth is investigated in a detailed finite element analysis. The process is modelled by the growth and coalescence of a series of holes in front of a blunted crack tip, representing the growth of holes separated from large inclusions. The reductions of each ligament between neighbouring holes due to hole growth are calculated as well as crack-tip opening displacements (CTOD). All the ligaments except the first and last show similar behaviour of reduction, with the reduction curves separated in an equal CTOD increment. The CTOD increment as a function of effective crack extension due to hole growth defines crack-tip opening angle, a measure of crack-growth resistance for a given condition. As the CTOD increment changes substantially due to crack extension in small-scale yielding, crack initiation is defined at the point of deviation from the linear increment of CTOD against J for a stationary crack. The effective crack tip is defined at each hole with the ligament reduction of crack initiation. Therefore, the J -resistance curve may be derived from the hole growth model, and hence the effects of specimen geometry, crack length and specimen size on the R-curve are discussed. The calculations for a hole spacing 10 times of the initial hole diameter are in agreement with the experimental R-curve of 2024-T351 aluminium alloy.     

A new approach to determination of CTOD and axis of rotation in small scale yielding situation

A theoretical model for predicting crack tip opening displacement (CTOD) in small scale yielding situation has been developed by combining the elastic solution of Muskhelishvili with Irwin's idea of notional crack. The model is used to calculate the CTOD from the displacement at the mouth of the crack, without the use of rotational factor, r. An attempt has also been made to relate the rotational factor, r with the yield strength of the material.

The above model has been used to compute CTOD values in a low alloy steel with yield strength ranging from 400–2100 MPa and the results have been compared with Wells' as well as Xiao's CTOD values. The significance of the factor m' in the K-CTOD relationship has been investigated in the light of the results observed in the present investigation.     

The fatigue crack growth rate and crack opening displacement in 18G2A-steel under tension

In the paper, the results of crack tip opening displacement (CTOD) and crack opening displacement (COD) in place of crack initiation as well as the fatigue crack growth rate in higher strength steel are presented. The investigation were carried out on flat specimens with central notch under constant amplitude tensile fatigue loading at stress ratio R = 0.2 and different value of the stress σ_max. The test results showed that with growth of crack length l grew values of the CTOD and COD. In the work, it was proposed calculation of the CTOD value on basis various dependence of plastic zone radius on crack tip.     

Plastic CTOD as fatigue crack growth characterising parameter in 2024‐T3 and 7050‐T6 aluminium alloys using DIC

The plastic range of crack tip opening displacement (CTOD) has been used for the experimental characterisation of fatigue crack growth for 2024‐T3 and 7050‐T6 aluminium alloys using digital image correlation (DIC). Analysis of a complete loading cycle allowed resolving the CTOD into elastic and plastic components. Fatigue tests were conducted on compact tension specimens with a thickness of 1 mm and a width of 20 mm at stress ratios of 0.1, 0.3 and 0.5. The range of plastic CTOD could be related linearly to da/dN independent of stress ratio for both alloys. To facilitate accurate measurements of CTOD, a method was developed for correctly locating the crack tip and a sensitivity analysis was performed to explore the effect of measurement position behind the crack tip on the CTOD. The plastic range of CTOD was demonstrated to be a suitable alternate parameter to the stress intensity factor range for characterising fatigue crack propagation. A particularly innovative aspect of the work is that the paper describes a DIC‐based technique that the authors believe gives a reliable way to determine the appropriate position to measure CTOD.     

THE EFFECTS OF CRACK DEPTH ON THE J-INTEGRAL AND CTOD FRACTURE TOUGHNESS FOR WELDED BEND SPECIMENS

This work deals with the influence of crack depth on the fracture toughness at initiation of crack growth and the constraint factor in relationship between the J-integral and the crack tip opening displacement (CTOD). A series of tests were performed on high strength low alloyed HT80 steel welds, and the critical J-integral and CTOD were determined using the load versus load point displacement record from three-point bend specimens with 0.05 < a/W < 0.5. It was found that the fracture toughness for shallow cracks at the onset of crack growth was larger than that for deep cracks for the steel welds tested, but it is felt that there is no fixed relationship between these values in the welds tested. The constraint factor is also a function of crack depth, and values of the factor increase from 0.5 to 1.5 when a/W increases from about 0.05 to 0.5. The factors are not very sensitive to the crack tip materials (HAZ or weld metal) in the welds tested.     

Determination of critical CTOD using crack flank opening angle method in general yield regime

The crack tip opening displacement (CTOD) evaluation from CMOD values using compact tension (CT) specimen geometry and plastic hinge model (PHM) is well standardized in the literature. However, the model is found to be conservative for the general yielding situation. Moreover, the knowledge of the location of apparent axis of rotation which in turn depends on plastic rotational factor, r_pl, is essential for the conversion from CMOD to CTOD. In the present investigation, the ‘crack flank opening angle’ (CFOA) method has been suggested for the evaluation of plastic CTOD. This approach has facilitated the exact determination of apparent axis of rotation. The effect of the specimen thickness and notch root radius on CTOD has been investigated using the PHM and CFOA method. These results have been compared with finite element analysis results. Results achieved point out that the CTOD obtained from the traditional PHM are underestimated for the general yield situation.     

EFFECT OF ELASTIC MISMATCH ON THE GROWTH OF A CRACK INITIALLY TERMINATED AT AN INTERFACE IN ELASTIC PLASTIC BIMATERIALS

Abstract A crack perpendicular to, and initially with the tip on, a bimaterial interface is studied. An asymptotic analysis is performed and crack growth proceeds straight ahead at constant remote load. Mode I conditions and plane strain are assumed. The materials on both sides of the interface are elastic perfectly-plastic with different elastic properties and the same yield stress. A finite element analysis is made and crack growth is simulated by an element relaxation technique. Because of the interface, the crack-tip driving force is not constant, which is reflected in the near-tip state. The development of the plastic zone and the crack opening displacements is presented for different elastic mismatches. Small scale yielding like results are obtained after a crack extension of about the plastic zone size from the interface, i.e. long before a square-root singular stress field may be expected to embed the plastic zone. An important observation is that the development of the crack opening displacement at the initial stage of growth is reversed when plasticity is introduced, as compared to the prediction by an elastic model. A region of stable crack growth is identified at the initial phase of growth into a stiffer material, solely due to elastic mismatch.     

CTOD WITH SLOW STABLE CRACK GROWTH: ANALYSIS OF THE ELASTIC COMPONENT

Abstract— The errors made during calculations for the "elastic" component of CTOD, δ_e, under slow stable crack growth conditions are analyzed and a model that considers this situation is proposed. Some examples are shown in which important errors occur in the CTOD value as a consequence of not having considered slow stable crack growth. This analysis complements previous work where an adaptation of the Plastic Hinge Model was made in order to consider corrections in the plastic component of CTOD due to rotation and stable crack growth.
The errors in Schwalbe's CTOD term, δ₅, which relate to a lack of alignment to the average crack front are also studied. Since the absolute value of this inexactitude is not known, bounds are set to this error.     

Finite deformation cohesive polygonal finite elements for modeling pervasive fracture

In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening–softening–hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range (\(\Delta \hbox {K})\), load ratio (R), number of cycles (N), plastic compressibility (\({\upalpha })\) and material softening on near tip deformation, stress–strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on \(\Delta \hbox {K}\), R, N, \({\upalpha }\) and material softening. For both hardening and hardening–softening–hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress–strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study.     

Plastic zone correction on a Zener–Stroh crack interacting with a circular inclusion in ductile materials

Elastic–plastic stress analysis on a matrix Zener–Stroh crack interacting with a circular inclusion (fibre) in fibre‐reinforced composites has been carried out. The Zener–Stroh crack is initiated near the fibre in the pure matrix. Plastic zone correction is introduced the first time for such a crack–inclusion interaction problem so that the fracture behaviour can be analysed more accurately. To determine the plastic zone sizes, a generalized Irwin model is proposed for the mixed‐mode problem where the Von Mises stress yielding criterion is employed. Different to a Griffith crack, a Zener–Stroh crack propagation always occurs from the sharp tip whose relative position to the inclusion has great effect on the elastic–plastic fracture behaviour of the crack. In our study, the plastic zone size (PZS), crack tip opening displacement (CTOD) and effective stress intensity factor (SIF) are evaluated by solving the formulated singular integral equations. Through the numerical examples, the influence of the inclusion (fibre) shear modulus, crack–inclusion distance and the crack sharp tip position on the fracture behaviour of the crack is discussed. It is found that the shear modulus ratio and the crack–inclusion distance have great effect on the normalized values of PZS and CTOD, but the effects highly depend on the crack sharp tip position.     

Statistical analysis of fatigue crack growth behavior for grade B cast steel

Tests for fatigue crack growth rate (FCGR) and crack-tip opening displacement (CTOD) were performed to clarify the fatigue crack growth behavior of a railway grade B cast steel. The threshold values of this steel with specific survival probabilities are evaluated, in which the mean value is 8.3516 MPa m^1/2, very similar to the experimental value, about 8.7279 MPa m^1/2. Under the conditions of plane strain and small-scale yielding, the values of fracture toughness for this steel with specific survival probabilities are converted from the corresponding critical CTOD values, in which the mean value is about 138.4256 MPa m^1/2. In consideration of the inherent variability of crack growth rates, six statistical models are proposed to represent the probabilistic FCGR curves of this steel in entire crack propagation region from the viewpoints of statistical evaluation on the number of cycles at a given crack size and the crack growth rate at a given stress intensity factor range, stochastic characteristic of crack growth as well as statistical analysis of coefficient and exponent in FCGR power law equation. Based on the model adequacy checking, result shows that all models are basically in good agreement with test data. Although the probabilistic damage-tolerant design based on some models may involve a certain amount of risk in stable crack propagation region, they just accord with the fact that the dispersion degree of test data in this region is relatively smaller.     

Experimental evaluation of hinge phenomenon in notched three point bend bars using laser speckle metrology

In elastic-plastic fracture, material behavior is often characterized by the J-integral or crack tip opening displacement (CTOD) parameters. In order to evaluate these parameters accurately, the location of the plastic hinge point, and subsequently the value of the plastic rotational factor, r_p, must be determined. Traditionally, hinge point location and r_p have been inferred through crack opening displacement (COD) measurements. However, this work indicates that laser speckle metrology can be used to analyse directly the hinging phenomenon. Using notched three point bend bars fabricated from a high stretch low alloy steel, a full-field map of in-plane displacements was generated over the course of each test. The results indicate the existance of a hinge region, rather than an explicit hinge point. The hinge region appears to contain the computed hinge point location using the range of cited r_p values. This indicates that it may be appropriate to use the centroid of the hinge region in subsequent CTOD and J-integral calculations.     

A continuously distributed dislocation model for fatigue cracks in anisotropic crystalline materials

An elastic-plastic crack model is developed for anisotropic crystalline materials exhibiting elastic-perfect plastic behavior, using the continuously distributed dislocation theory (CDDT). The crack and its associated plastic zone are represented by an inverted pile-up of dislocations. The plastic zone size, the crack-tip opening displacement (CTOD) and the energy release rate of the crack are obtained in closed forms, in a fashion similar to the Bilby–Cottrell–Swinden–Dugdale model for isotropic materials, but in terms of material constants that are orientation dependent. Application of the model to the case of small-scale yielding, e.g., long fatigue cracks in Ni-base single crystal superalloys, is discussed.     

Fatigue crack propagation in a ductile superalloy at room temperature and extensive cyclic plastic flow

Fatigue crack propagation experiments under both force and displacement control have been performed on the wrought superalloy Haynes 230 at room temperature, using a single edge notched specimen. The force controlled tests are nominally elastic, and the displacement controlled tests have nominally large plastic hysteresis at the beginning of the tests, but saturates towards linear elastic conditions as the crack grows. As some tests are in the large scale yielding regime, a non-linear fracture mechanics approach is used to correlate crack growth rates versus the fracture parameter $\mathrm{\Delta }$J. It is shown that crack closure must be accounted for, to correctly model the crack growth seen in all the tests in a unified manner. For the force controlled small scale yielding tests the Newman crack closure model was used. The Newman equation is however not valid for large nominal cyclic plasticity, instead the crack closure in the displacement controlled tests is extracted from the test data. A good agreement between all tests is shown, when closure is accounted for and effective values of $\mathrm{\Delta }$J are used.     

Effect of thickness on fracture criterion in general yielding fracture mechanics

In this research work, the effect of thickness on fracture criterion is studied for extra deep drawn (EDD) steel sheets. Experimental results are generated on fracture toughness of EDD steel sheets using compact tension specimens and a ‘maximum load’ as a fracture criterion. Critical crack tip opening displacement (CTOD) is found with the help of three methods: plastic hinge model (PHM), crack flank opening angle (CFOA) and finite element model (FEM). The fracture toughness is found to increase with increase in thickness of specimens. The fracture behaviour exhibited characteristics of general yielding fracture mechanics.     

A review of the CTOA/CTOD fracture criterion

The crack-tip-opening angle or displacement (CTOA/CTOD) fracture criterion is one of the oldest fracture criteria applied to fracture of metallic materials with cracks. During the past two decades, the use of elastic–plastic finite-element analyses to simulate fracture of laboratory specimens and structural components using the CTOA criterion has expanded rapidly. But the early applications were restricted to two-dimensional analyses, assuming either plane-stress or plane-strain behavior, which lead to generally non-constant values of CTOA, especially in the early stages of crack extension. Later, the non-constant CTOA values were traced to inappropriate state-of-stress (or constraint) assumptions in the crack-front region and severe crack tunneling in thin-sheet materials. More recently, the CTOA fracture criterion has been used with three-dimensional analyses to study constraint effects, crack tunneling, and the fracture process. The constant CTOA criterion (from crack initiation to failure) has been successfully applied to numerous structural applications, such as aircraft fuselages and pipelines. But why does the “constant CTOA” fracture criterion work so well? This paper reviews the results from several studies, discusses the issues of why CTOA works, and discusses its limitations.     

FATIGUE CRACK GROWTH LAWS FOR BRITTLE AND DUCTILE MATERIALS INCLUDING THE EFFECTS OF STATIC MODES AND ELASTIC-PLASTIC DEFORMATION

A fatigue crack growth damage accumulation model is used to derive laws for the fatigue crack growth rates of brittle and ductile materials. The damage accumulated during cyclic loading is assumed to be proportional to the cyclic change in the plastic displacement in the crack tip yielded zone. The static mode contribution to the fatigue damage is assumed to be proportional to some power of the crack tip displacement. The laws are applicable in either the small or large scale yielding regimes provided that the stress ratio remains positive. Static modes are assumed to be controlled by the fracture toughness value in brittle materials, and by the gradient of the crack growth resistance curve in ductile materials. In the analysis of ductile materials it is assumed that the crack growth resistance of the material is not significantly altered by fatigue crack growth.
The growth rate equations are expressed in terms of the near field value of the J -integral, i.e. the value which would be calculated from assuming the material deformed in a non-linear elastic manner during the increasing load part of the fatigue cycle. Examples are given of the predictions of the growth law for ductile materials. It is predicted that after the initiation of stable tearing the crack growth rate, when expressed in terms of the cyclic change in the stress intensity factor, depends on both the structural geometry and the degree of crack tip plastic deformation. In both brittle and ductile materials the fatigue crack growth rate is predicted to accelerate as the failure criteria relevant to static crack instability are approached.     

Effects of non-singular stresses on crack-tip fields for pressure-sensitive materials,Part 1: Plane strain case

Mode I near-tip stress fields for elastic perfectly plastic pressure-sensitive materials under plane strain and small-scale yielding conditions are presented. A Coulomb-type yield criterion described by a linear combination of the effective stress and the hydrostatic stress is adopted in the analysis. The finite element computational results sampled at the distance of a few crack opening displacements from the tip show that, as the pressure sensitivity increases, the magnitudes of the normalized radial and hoop stress ahead of the tip decrease, the total angular span of the singular plastic sectors decreases, and the angular span of the elastic sectors bordering the crack surfaces increases. When non-singular T stresses are considered along the boundary layer of the small-scale yielding model, the near-tip stresses decrease as the T stress decreases. The plastic zone shifts toward the crack surfaces as the T stress increases. When the discontinuities of the radial stress and the out-of-plane normal stress along the border between the plastic sector and the elastic sector are allowed, the angular variations of the asymptotic crack-tip fields agree well with those of the finite element computations. Variation of the Q stresses for pressure-sensitive materials can be found from the asymptotic solutions when the plastic zone size ahead of the tip is relatively larger than the crack opening displacement. In addition the T stress is shown to have strong effects on the plastic zone sizes and shapes which could affect the toughening of pressure-sensitive materials.     

A crack propagation criterion based on ΔCTOD measured with 2D‐digital image correlation technique

The fatigue cracks growth rate of a forged HSLA steel (AISI 4130) was investigated using thin single edge notch tensile specimen to simulate the crack development on a diesel train crankshafts. The effect of load ratio, R, was investigated at room temperature. Fatigue fracture surfaces were examined by scanning electron microscopy. An approach based on the crack tip opening displacement range (ΔCTOD) was proposed as fatigue crack propagation criterion. ΔCTOD measurements were carried out using 2D‐digital image correlation techniques. J‐integral values were estimated using ΔCTOD. Under test conditions investigated, it was found that the use of ΔCTOD as a fatigue crack growth driving force parameter is relevant and could describe the crack propagation behaviour, under different load ratio R.