Monotonic Plastic Zone Size Research Articles

The effect of microstructure on the fatigue crack growth behavior of Ni-Cr-Mo-V steel weld metal

Fatigue crack growth (FCG) rate, which could significantly affect fatigue lifetime of thick wall components, has been studied extensively in forgings with homogeneous microstructure. However, there were few studies on the effect of inhomogeneous microstructure on FCG rate in weld metal. In this work, the effect of microstructure on FCG behavior of Ni-Cr-Mo-V weld metal was investigated. The FCG rate in the Paris regime was similar to that reported in the literature. However, in the near-threshold regime, the FCG rate decreased rapidly at first with the decrease of stress intensity factor range (ΔK) and then increased slightly. Finally, the FCG rate slowly decreased with the decrease of ΔK. It was found that when the monotonic plastic zone size around the crack tip was equivalent to the ferrite grain size in reheated grain zone at a certain ΔK, the crack propagated along the ferrite grain boundaries. The occurrence of intergranular fracture increased the fracture surface roughness, and enhanced the roughness-induced crack closure effect, which increased the FCG resistance and reduced the FCG rate drastically at the early stage. At a lower ΔK level, frequent deflection and crack branching were observed and the mechanisms were investigated by crystallographic analysis.

Plane-strain fracture toughness of AISI 4140 steel austempered below MS

Ultrahigh-strength low alloy steels transformed below the martensite start temperature (MS) with a mixed microstructure consisting of lath martensite, lower bainite, and minor amounts of retained austenite are of interest in a variety of potential commercial applications as they exhibit good combinations of strength, ductility, and toughness. However, their use requires a knowledge of the resistance to crack propagation. Analysis of the microstructure and fractography show that it is possible to distinguish the fracture behavior of steels austempered below MS from those quenched and tempered. The sharp-notch plane-strain fracture toughness KIC has been determined by the notched tensile testing and modeled with different expressions from literature. Based on pioneer works of Irwin (1962) [20] and Naylor (1979) [22], KIC associated with austempering below MS has been modeled with the aspect ratio of the microstructural subunits and monotonic plastic zone size ahead of the crack tip. A comparison between existing expressions and the new one is conducted. It is found that modeling with the new expression delivers the best agreement with the experimental values.

Fatigue Crack Tip Plasticity for Inclined Cracks

The evaluation of the crack tip deformation is essential to the estimation of crack growth under either static or cyclic loading. A 3-D elastic–plastic finite element analysis was developed to simulate the crack tip deformation along mixed mode inclined edge cracks in a steel plate subjected to either monotonic or cyclic loading at selected R-ratios. In this paper, two types of crack configurations were investigated: inclined cracks with equal inclined lengths (EICL) and inclined cracks with equal horizontal projection length (ECHP). The development of the monotonic (Δm) and cyclic (Δc) crack tip plastically zones and the monotonic (CTOD) and cyclic (ΔCTOD) crack tip opening displacements were traced to find the effect of the crack inclination angle, which significantly affected the size and shape of the crack tip plastic zone. The finite element results compared well with the analytical results based on modified Dugdale’s model. It was observed that Mode II has a significant effect on the plastic zone in the case of equal inclined crack length (EICL), i.e., Mode II increases as the crack angle decreases. Also, it is interesting to note that for the EICL case, the magnitude of Δc is delayed to appear with decreasing the inclination angle, for example, for θ = 90° the cyclic plastic zone appeared at Δσ = 103.32 MPa, while for θ = 45° the cyclic plastic zone appeared at Δσ = 132.84 MPa. Whereas, the variation of monotonic and cyclic plastic zone size in the equal crack horizontal projection (ECHP) case is not affected by the crack inclination angle. Furthermore, it was observed that the static crack tip opening displacement (CTOD) and the cyclic (ΔCTOD) are independent of the crack inclination angle in case of ECHP, due to such cracks take into consideration the effect of inclination angle through its length.

Effect of single tensile overload on fatigue crack growth behavior in DP780 dual phase steel

The purpose of this study was to analyze the effect of single tensile overload on fatigue crack growth (FCG) behavior in DP780 dual phase steel. The compact tension samples were tested under constant amplitude load and overload condition. The results showed that all the material conditions responded favorably to the single tensile overloads; the magnitude and extent of crack retardation was amplified due to an increase in overload ratio (OLR) and a longer crack length at overload application. The error between the overload affected crack growth increment and the magnitude of overload monotonic plastic zone size decreased about 30% after introducing the factor (n−1)/(n+1) into Irwin model. A plastic zone size factor was used to modify the Wheeler model to calculate the FCG rate during retardation period after an overload, the predicted results were in good agreement with the experimental data. During the application of an overload, a crescent moon shaped damage zone was formed ahead of the crack tip characterized by cleavage surfaces, tearing ridges, dimples and voids. The fracture morphology after crack front reformation was severely damaged due to the premature contact of the crack flanks. Crack branching was not significant interaction effect for the crack growth retardation under overload.

Material property controlling non-propagating fatigue crack length of mechanically and physically short-crack based on Dugdale-model analysis

Non-propagating fatigue crack lengths were analytically calculated under stress control conditions using plasticity-induced crack closure analysis with the Dugdale model. In addition, a non-dimensionalization method was applied in terms of the Burgers vector and a monotonic plastic zone size under small-scale yielding conditions, which was validated for various initial crack lengths and material properties. When the yield strength was increased, the non-propagating fatigue crack lengths were found to increase for a short crack and decrease for a long crack. The non-dimensionalization enabled the analytical derivation of a generalized non-propagating fatigue crack length, which can be utilized for fatigue designs. The material property controlling the threshold stress intensity factor range of mechanically and physically short-crack was discussed.

Study of fatigue crack propagation behaviour for dual-phase X80 pipeline steel

ABSTRACTLoad-controlled fatigue tests were conducted on dual-phase X80 pipeline steel to investigate the effects of stress ratio (R-ratio) on the fatigue crack growth behaviour. Dual-phase X80 pipeline steel showed a non-linear relationship between fatigue crack growth rate (da/dN) and the stress intensity factor range (ΔK) at each R-ratio. Fatigue crack propagation curves of X80 pipeline steel were evaluated using the conventional Paris equation and a new exponential equation named αβ model. In addition, the electron back-scattered diffraction technique was used to study the effects of stress ratio on the fatigue crack growth behaviour. The results indicated that the corresponding ΔK of the transition point decreased with the increase of R-ratio. That was attributed to the variation of the crack path and the fracture mode because of the changes in the size of monotonic plastic zone and cyclic plastic zone at crack tip. Compared to the overall fitting, piecewise fitting by Paris equation and αβ model, piecewise fitting was the most accurate method, and αβ model is more convenient and efficient than the conventional Paris-based equations.

Numerical models of plastic zones and associated deformations for elliptical inclusions in remote elastic loading–unloading with different R-ratios

Plastic zones and associated deformations ahead of a fatigue crack are well established nowadays. In-depth plane strain elasto-plastic finite element analysis is conducted in this investigation to understand the nature of cyclic plastic deformation and damage around soft and hard elliptical inclusions. Similar to fatigue crack tip, cyclic/reverse plastic zone and monotonic plastic zone are visible for soft elliptical inclusion. In the cyclic plastic zone, low cycle fatigue is the dominant cyclic deformation mode during symmetric load cycling, while ratcheting is dominant during asymmetric load cycling. The size of cyclic plastic zone depends upon the amplitude of remote stress while, the size of monotonic plastic zone depends upon the maximum remote stress. The size of monotonic plastic zone is equal to cyclic plastic zone during symmetric load cycling. The shape and size of plastic zones also depend upon the orientation of the soft inclusion. Cyclic plastic damage progression in the cyclic plastic zone for soft (MnS) inclusion is significant, while no cyclic plastic zone is visible for hard inclusion (Al2O3).

Numerical models of plastic zones and associated deformations for a stationary crack in a C(T) specimen loaded at different R-ratios

To understand the nature of cyclic plastic deformation and damage on a fatigue crack tip, in-depth plane strain elasto-plastic finite element analysis was conducted on a compact tension specimen. In the cyclic plastic zone, low cycle fatigue is the dominant cyclic deformation mode during symmetric load cycling, while ratcheting is dominant during asymmetric load cycling. The size of cyclic plastic zone depends upon the amplitude of stress intensity factor while, the size of monotonic plastic zone depends upon the maximum stress intensity factor. The size of monotonic plastic zone is equal to cyclic plastic zone during symmetric load cycling.

Effects of dissolved oxygen on corrosion fatigue cracking of Alloy 690(TT) in pressurized water reactor environments

Alloy 690(TT) is widely used for steam generator tubes in pressurized water reactor (PWRs), where it is susceptible to corrosion fatigue. In this study, the effects of dissolved oxygen on the corrosion fatigue cracking behavior of Alloy 690(TT) in simulated PWR environments were investigated under small scale yielding conditions. Dissolved oxygen, combined with the monotonic plastic zone size (rp), had a significant influence on out-of-plane cracking of corrosion fatigue crack and environment factor (Fen).

Dislocation processes that affect kineticsof fatigue crack growth

Fatigue damage involves an irreversible plastic flow, and requires two load parameters for its unique description. We have examined the dislocation processes at the crack tip due to cyclic loads and showed that the two-parameter requirement naturally follows from the analysis. Hence, there are two fatigue thresholds, K max,th and ΔK th, instead of just ΔK th, as is normally assumed. Examination of dislocation behaviour reveals that the K max threshold can be related to the stress necessary to nucleate additional slip needed for crack growth. Similarly, ΔK th can be related to the stress to overcome reversible slip. The value of K max,th is always greater than or equal to ΔK th. The two-parameter requirement can be related to the presence of monotonic and cyclic plastic zones characteristic of a fatigue crack. The size of monotonic plastic zone is always larger than that of the cyclic plastic zone. The former moves the crack tip forward while the latter re-sharpens it. The analysis also shows that the effect of crack wake plasticity on the crack tip driving force is limited and becomes increasingly negligible with increasing crack length. Dislocation concepts and continuum concepts are brought together to analyse the two-parameter requirement of fatigue crack growth.

709 特異な異方性を有する純アルミニウム板における疲労き裂進展経路に及ぼす板厚の影響

Fatigue crack of pure aluminum plates with unique anisotropy propagated to rolling direction that made 30° to loading direction. The crack propagated as a mixed mode I+II crack. Effects of plate thickness to fatigue crack were observed by conducting fatigue test on CCT specimens with thickness of 0.8mm, 1.5mm and 2.5mm. The stress intensity factor of the crack was analyzed with Finite Element Method (FEM) using the displacement extrapolation method. As the result, the crack starts to grow to rolling direction as △K_<*>=5&acd;8MPa・m^<1/2>. It is also confirmed that the thicker plates cause the smaller monotonic plastic zone size r_p on the crack tip. It leads to near plane-strain condition on the crack tip and the crack grows easier to rolling direction.

An alternative method of decreasing ΔK FCGR testing

The conventional technique of decreasing ΔK FCGR testing often presents experimental difficulties in terms of the length of crack that must be accommodated and the time required to reach low values of ΔK. Addressing these issues, an alternative method of conducting such tests has been proposed. A relation according to which ΔK must be decreased has been derived assuming that the monotonic plastic zone size can be decreased at a constant rate with increase in crack length without adversely affecting the integrity of the FCGR data. Through experimental assessment of the alternative method and examination of crack closure effects, such an asumption has been vindicated. It has been shown that this method is particularly suitable for high strength materials and that it provides great advantages when conducting FCGR tests at low frequencies. The employment of the method for obtaining threshold regime corrosion fatigue crack growth data has been demonstrated for HSLA steels.

X‐ray diffraction studies on fatigue crack plastic zones developed under plane strain state conditions

ABSTRACTAn overview of the X‐ray fractography technique, as performed on fatigue crack surfaces of several steels and Al‐alloys under different loading conditions, is presented. The plastic zone sizes of fatigue cracks, for plane strain conditions, are measured from the in‐depth distribution of residual stresses and X‐ray diffraction peak broadening. In addition to the usual monotonic plastic zone size determination methodology, a model for the estimation of the reverse plastic zone size was established in the case of fatigue softening materials. Monotonic and cyclic plastic zone sizes are related to the stress intensity by, respectively, rpm = α (Kmax /σys )2 and rpc = α (ΔK/2σ′ys )2. The α‐value, in the monotonic plastic zone size equation, increases as the yield strength of the material increases, following the relationship α = 0.196 [σys /(129 + 0.928σys )]2. The α‐value versus σys evolution has been understood through the influence of the hardening rate of materials on the plastic zone size. X‐ray fractography has been applied to actual failure analyses to predict some aspects of the actual loadings.

A STUDY ON THE CHANGE OF FATIGUE FRACTURE MODE IN TWO TITANIUM ALLOYS

The appearance of the fatigue fracture surface and crack growth curve have been examined for a Ti–2.5Cu alloy with different microstructures (two equiaxed and two lamellar microstructures), and for TIMETAL 1100 with a lamellar microstructure. With increasing ΔK, a slope change in the crack growth curve correlates with a transition in the fracture surface appearance (induced by a fracture mode transition); this being found in each microstructure. The microstructure size that controls the fatigue fracture is found to be the grain size for equiaxed microstructures and the lamella width for lamellar microstructures. The transitional behaviour can be interpreted in terms of a monotonic plastic zone size model in microstructures having a coarse microstructure size and in terms of a cyclic plastic zone size model for microstructures having a fine microstructure size.

A finite-element analysis of the residual stress distribution in the vicinity of a fatigue fractured surface

An analytical study by the elastic–plastic finite element method was made of the residual stress and equivalent plastic strain distributions near the fatigue crack surface. Emphasis was on finding the correlation between the residual stress on the fracture surface and the applied stress intensity factor range ΔK. Special attention was given to the effects of applied stress ratio and the work-hardening rate. A characteristic behavior was found: the residual stress on the fracture surface increases with the increase of ΔK, reaches a maximum at a certain value of ΔK, and then decreases. The decrease of the residual stress on the crack surface was correlated with the growth of an instability into the distributions of residual stresses and equivalent plastic strain under the fracture surface. It was also found that both the residual stress and equivalent plastic strain distributions under the fracture surface were useful for the estimation of the monotonic plastic zone size or Kmax and the cyclic plastic zone size or ΔK.

Fatigue life enhancement of specimens with stress concentrators using a thermo-mechanical technique

Experimental work by Lam and Griffiths (1) has shown that the crack growth rate in single edge notched fatigue test specimens made from C-Mn steel can be retarded by the application of a load-heat (or thermo-mechanical) cycle. The thermo-mechanical treatment consisted of applying a tensile stress while simultaneously heating the region around the crack tip. The increase in temperature reduced the yield stress of the steel, creating a larger monotonic crack tip plastic zone size than would have been created had heating not been applied. Upon cooling to room temperature, and then unloading, a reversed (compressive) crack tip plastic zone was created which was larger than if the thermo-mechanical treatment had not been carried out. It was concluded that these larger monotonic and reversed plastic zone sizes retarded fatigue crack growth.

Delta-K correlation of fatigue crack growth rates under general monotonic yielding

Linear Elastic Fracture Mechanics, LEFM, principles are successfully used to characterize the behavior of flawed structures and components under monotonic loading. Crack length increment, da, correlates with maximum stress intensity factor, K, when the monotonic plastic zone size is small. Cracks can grow under cyclic loading even at stress levels lower than that required for crack extension under static loading. Paris et al. established the correlation between crack growth rate, da/dN, and stress intensity factor range, delta-K, of the load cycle. Aplication of LEFM principles to crack extension under monotonic cyclic loading can be seen.

Fatigue fracture surface analysis in C45 steel specimens using X-Ray fractography

X-Ray fractography is a useful technique to analyse the mechanisms operating in fracture and involves an examination of the fracture surface. In the present investigation, this technique has been employed to study the fatigue fracture behaviour of a medium carbon steel of C45 grade in different heat treated conditions. The different trends observed in the residual stress (σ r) and diffraction profile full width at half maximum intensity ( B) relationships with the maximum stress intensity factor ( K max ) on the fracture surface have been correlated to the differences in flow characteristics of these materials. The root mean square value of microstrain ϵ, and the coherent domain (particle) size, D, were determined through single line diffraction profile (Voigt's) analysis. It has been observed that contribution of microstrain to profile broadening is more significant than that due to domain size. However, at higher K max values an influence of D was found on line broadening, to a small extent. Results of sub-surface stress measurements were compared in two conditions. A good correlation was noticed between the depths below the fracture surface, designated as y max , at which the measured σ r , reaches the base material value and the corresponding monotonic plastic zone size ( r p ) obtained by calculation. The observed depths below the fracture surface ( y peak ) at which an increase in σ r or a decrease in B was noticed, appear to be related to the conditions of the near-tip regions where the material has undergone severe fatigue damage and cyclic softening.

Fatigue crack growth transitions in Ti-6Al-4V alloy

There are 2 transitions during fatigue crack growth in Ti-6Al-4V alloy, caused by cyclic and monotonic plastic zones when their resp. sizes become equal to the $\alpha$ lath size. The transition due to cyclic plastic zone size is a combined action of environment and the stage where cyclic plastic zone size becomes equal to lath size. Crack closure levels exhibited a transition. The crack path exhibited multiple crack branching at this transition. The cyclic plastic zone size is uniquely related with $\delta$Keff (closure-free stress intensity range) as against $\delta$K at large crack closure. A transition occurred when the monotonic plastic zone size was equal to the $\alpha$ lath size, and this is attributed to the change from continuum to single crystal behavior at the crack tip. Both the transitions were induced by $\alpha$ laths because of thick interplatelet $\beta$ layer in the microstructure.

Fatigue Crack Propagation Threshold

Abstract Service-type fatigue loading conditions are critically analyzed with respect to their relevance for a fatigue crack growth threshold. It was found that a threshold should be experimentally determined as a function of the monotonic-plastic zone size (i.e., as a function of Kmax). For each Kmax the cyclic-plastic zone size depends on the applied ΔK and threshold testing should cover the range ΔK ≈ ΔKth and ΔK (R = 0) for tension fatigue. For a given plastic zone, Kmax and ΔK fixed, the threshold ΔKth could occur anywhere between Kmax and Kmin. This study presents experimental procedures and furnishes results for Inconel 617 and a Ti-6A1-4V alloy which allow one to analyze the influence of the three parameters cited above. It demonstrates the following: • The threshold decreases “linearly” with increasing monotonic-plastic zone size; this confirms existing data. • The cyclic-plastic zone has minimal influence on the fatigue threshold with Ti-6A1-4V, while this influence is substantial in the case of Inconel 617. • A shift of threshold between Kmax and Kmin does not alter the magnitude of the threshold.