Monotonic Plastic Zone Research Articles

Finite‐element analysis of fatigue crack closure under plane strain conditions: stabilization behaviour and mesh size effect

ABSTRACTAn elastic–plastic finite‐element analysis of fatigue crack closure is performed for plane strain conditions. The stabilization behaviour of crack opening level and the effect of mesh size on the crack opening stress are investigated. It has been well reported that the crack opening level under plane stress conditions becomes stable after the crack advances beyond the initial monotonic plastic zone. In order to obtain a stabilized crack opening level for plane strain conditions, the crack must be advanced through approximately four times the initial monotonic plastic zone. The crack opening load tends to increase with the decrease of mesh size. The mesh size nearly equal to the theoretical plane strain cyclic plastic zone size may provide reasonable numerical results comparable with experimental crack opening data. The crack opening behaviour is influenced by the crack growth increment and discontinuous opening behaviour is observed.

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.

Numerical analysis for prediction of fatigue crack opening level

Finite element analysis (FEA) is the most popular numerical method to simulate plasticity-induced fatigue crack closure and can predict fatigue crack closure behavior. Finite element analysis under plane stress state using 4-node isoparametric elements is performed to investigate the detailed closure behavior of fatigue cracks and the numerical results are compared with experimental results. The mesh of constant size elements on the crack surface can not correctly predict the opening level for fatigue crack as shown in the previous works. The crack opening behavior for the size mesh with a linear change shows almost flat stress level after a crack tip has passed by the monotonic plastic zone. The prediction of crack opening level presents a good agreement with published experimental data regardless of stress ratios, which are using the mesh of the elements that are in proportion to the reversed plastic zone size considering the opening stress intensity factors. Numerical interpolation results of finite element analysis can precisely predict the crack opening level. This method shows a good agreement with the experimental data regardless of the stress ratios and kinds of materials.

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.

424 構造部材の完全圧縮疲労負荷時のき裂進展

Fatigue crack growth behaviors in weld components under compressive cyclic loading were studied. The crack growth rate not only under tensile cyclic loading but also under compressive one can be described quantitatively by the reverse plastic zone size at the crack tip. The reverse plastic zone size was calculated by finite element method taking initial weld residual stress and crack closure into account. Crack growth rate was reduced with its length in a logarithm function because of crack closure. However, the crack tip location finally progressed near the boundary position of monotonic plastic zone.

Role of crack tip plasticity in fatigue crack growth

Abstract The effect of plasticity ahead of the crack tip as well as behind the crack tip (crack wake plasticity) on the crack tip driving force is examined using a dislocation model. The plastic zone is approximated by a superdislocation, and linear elasticity is assumed. Dislocation effects are computed using the Lin–Thomson equations. The error involved in the superdislocation approximation is shown to be small. Results indicate that the plasticity ahead of the crack tip induces a large retarding force which a crack must overcome for it to grow. The existence of a threshold in K max for fatigue crack growth as illustrated by the unified two-parameter approach can be related to this crack growth resistance. The plasticity behind the crack tip. however, has a negligible effect on the crack tip driving force and therefore has no effect on the K max threshold. Overload effects, underload effects and fatigue crack growth resistance with increasing K are all relatable to the internal stresses arising from the dislocations in the plastic zone. The two thresholds K max, th and ΔK th in the unified approach can be related to the effects of monotonic and cyclic plastic zones. Since the effects of plasticity in the wake are negligible, plasticity-induced closure due to crack wake plasticity is also negligible from the dislocation point of view. A three-zone approximation for the plastic enclave around crack tip is shown to be adequate for the description of the role of plasticity in the crack tip driving force.

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.

A study on the determination of closing level for finite element analysis of fatigue crack closure

An elastic-plastic finite element analysis is performed to investigate detailed closure behavior of fatigue cracks and the numerical results are compared with experimental results. The finite element analysis performed under plane stress using 4-node isoparametric elements can predict fatigue crack closure behavior. The mesh of constant element size along crack surface can not predict the opening level of fatigue crack. The crack opening level for the constant mesh size increases linearly from initial crack growth. The crack opening level for variable mesh size, is almost flat after crack tip has passed the monotonic plastic zone. The prediction of crack opening level using the variable mesh size proportioning the reversed plastic zone size with the opening stress intensity factors presents a good agreement with the experimental data regardless of stress ratios.

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.

Ｘ線材料強度 高マンガンオーステナイト鋼の疲労破面におけるＸ線フラクトグラフィ

Fatigue tests were carried out under constant stress amplitude, using a non-magnetic high manganese Mn-Cr steel. X-ray fractography was applied on the fatigue fractured surface to investigate the relationship between stress intensity factor and residual stress or half-value breadth of the X-ray diffraction profile. The fatigue crack propagation rate of this non-magnetic Mn-Cr steel had the same tendency as in the ordinary structural ferritic steels. The relationship between stress intensity factor and the residual stress or half-value breadth of the steel was almost the same as that of the ferritic cyclic work hardening steels. No stress induced transformation was observed on the fracture surface, but the residual stress on the fractured surface was compressive in the high stress intensity factors range, which is typical in the cyclic work hardening steels. The half-value breadth on the fractured surface increased with increasing effective stress intensity factor range. The relationship between the half-value breadth and stress intensity factor range was represented by a linear line regardless of the stress ratio. Therefore, the acting stress intensity factor range at the time of fracture can be estimated from the half-value breadth. The depth of monotonic plastic zone was estimated from the distribution of half-value breadth beneath the fractured surface. The relationship between the maximum stress intensity factor and half-value breadth was expressed by the equation ωm=α(Kmax/σy)2, where the value of α was 0.025. This is about one sixth of the value for ferritic steels, and the fact shows the severe work hardening occuring in the plastic zone in this manganese steel.

ｘ線材料強度 初期引張残留応力場をき裂が進展した疲労破面におけるｘ線フラクトグラフィ

Fatigue tests were performed using CCT specimens having initial tensile residual stress caused by welding. The residual stress distribution on the fatigue fracture surface was measured by X-ray diffraction method. The monotonic plastic zone depth corresponds to the Kmax, true which is the sum of the Kmax related to the applied maximum stress and the Kres caused by the initial residual stress. So, if the initial residual stress distribution is known, the Kmax or the applied maximum stress can be estimated from the monotonic plastic zone depth. The residual stress on the fatigue fracture surface corresponds to the sum of the tensile residual stress related to the Kmax, true and the compressive residual stress related to the ΔKeff. So, even if the initial residual stress distribution is unknown, the ΔKeff or the stress amplitude can be estimated from the residual stress on the fatigue fracture surface and the monotonic plastic zone depth.

Elastoplastic analysis of thermal cycling: layered materials with compositional gradients

Elastopllastic analyses are presented for the cyclic thermal response in multi-layered materials which comprise layers of fixed compositions of a metal and a ceramic, and a compositionally graded interface. Analytical solutions for the characteristic temperature at which the onset of thermally induced plastic deformation occurs are derived for the layered composite. Solutions for the evolution of curvature and thermal strains, and for the initiation of plastic yielding are also obtained for different combinations of the geometry, physical properties and compositional gradation for both thermoelastic and thermoplastic deformation. Finite-element formulations incorporating continuous and smooth spatial variations in the composition and properties of the graded layer are used to simulate the evolution of thermal stresses, the accumulation of plastic strains, and the development of monotonic and cyclic plastic zones at the interfaces, edges and free surfaces of different layers during thermal cycling. Engineering diagrams detailing the effects of compositional gradients are also presented for optimizing thermal residual stresses, layer geometry, and plastic strain accumulation.

Acoustic emission behaviour during stage II fatigue crack growth in an AISI type 316 austenitic stainless steel

Acoustic emission (AE) behaviour during fatigue crack growth (FCG) in a ductile AISI type 316 austenitic stainless steel is reported. The two substages in the stage II Paris regime of FCG could be distinguished by a change in the rate of acoustic activity with increase in crack growth rate. The transition point in the cumulative ringdown count plot coincides with that in the da/dn plot. The AE activity increases with increase in ΔK during stage IIa and decreases during stage IIb. The major source of AE during stage IIa is found to be the plastic deformation within the cyclic plastic zone (CPZ) as compared to the phenomena such as monotonic plastic zone (MPZ) expansion, ductile crack growth, crack closure, etc. The increase in AE activity with increase in ΔK during stage IIa is attributed to the increase in the size of the CPZ which is generated and developed only under plane strain conditions. The decrease in AE activity during stage IIb is attributed to the decrease in the size of the CPZ under plane stress condition. The high acoustic activity during the substage IIa is attributed to irreversible cyclic plasticity with extensive multiplication and rearrangement of dislocations taking place within the CPZ. The AE activity is found to strongly depend on the optimum combination of the volume of the CPZ, average plastic strain range and the number of cycles before each crack extension. Based on this, an empirical relationship between the cumulative RDC and ΔK has been proposed and is found to agree well with experimentally observed values.

Elastoplastic analysis of thermal cycling: Layered materials with sharp interfaces

We present analllyses of the elastoplastic deformation in a layered bimaterial with a sharp interface which is subjected to cyclic variations in temperature. Closed-form solutions are derived, as functions of the thermomechanical properties and the geometry of the layers, for different critical temperatures at which distinct transitions occur in the deformation due to thermal fluctuations. Finite-element simulations are also used to examine the stress-strain hysteresis and the evolution of monotonic and cyclic plastic zones along interfaces and sharp edges in the layered material during thermal cycling. The influence of variations in physical and mechanical properties of the constituent phases with temperature on thermally-induced deformation is investigated. Analytical results arc also compared with the predictions of the finite-element models for a layered Ni-A1 2O 3 model bimaterial system. Furthermore, the analytical predictions are found to be in good agreement with experimental measurements of curvature during thermal cycling of a layered material comprising an Al film on a Si substrate.

A Fatigue Crack Growth Model for Single Overload Tests

Crack growth rate experiments are conducted by applying an intermediate single overload cycle in constant amplitude load (CAL) tests. For a particular overload ratio, three to four tests are conducted by applying the overload cycle at different crack lengths. The loads are selected in such a way that for a given overload ratio, the size of the overload and CAL monotonic plastic zones are the same at each crack length. A functional form for the crack growth during the retardation was developed that accurately describes all the tests. For comparison, the corresponding CA-load tests are also conducted separately. Finally, a crack growth rate model is developed.

Cyclic near-tip fields for fatigue cracks along metal-metal and metal-ceramic interfaces

Finite element analyses were conducted with the objective of determining the cyclic near-tip fields ahead of a stationary tensile fatigue crack lying along the interface between two dissimilar solids. The model systems analyzed are (i) a metal-metal bimaterial whose components have the same elastic properties but different plastic deformation characteristics, and (ii) a metal-ceramic bimaterial. In both cases, monotonic loading to the peak tensile load results in a predominantly mode I field ahead of the crack. However, unloading in one or both components of the bimaterial with prior plastic deformation generates mixed-mode conditions at the crack tip. The mode mixity persists during a significant portion of the next loading phase and is gradually removed upon reloading to the peak stress. The cyclic plastic zone size directly ahead of the fatigue crack is approximately one-fifth the size of the monotonic plastic zone. The residual compressive stresses within the cyclic plastic zone are computed. The implications of reversed yielding and mixed-mode near-tip fields to constant-amplitude and variable-amplitude fatigue fracture are discussed.

Intrinsic thresholds in polycrystalline Udimet 720

The long crack threshold behaviour of polycrystalline Udimet 720 has been investigated. Faceted crack growth is seen near threshold when the monotonic crack tip plastic zone is contained within the coarsest grain size. At very high load ratios R (=P min/P max) it is possiblefor the monotonic crack tip plastic zone to exceed the coarsest grain size throughout the entire crack growth regime and non1aceted structure insensitive crack growth is then seen down to threshold. Intrinsic threshold values were obtained for non1aceted and faceted crack growth using a constant K max, increasing K min, computer controlled load shedding technique (K is stress intensity factor). Very high R values are obtained at threshold using this technique (0.75-0.95), eliminating closure effects, so the intrinsic resistance of the material to crack propagation is reflected in these values. The intrinsic non1aceted threshold value ΔK th is lower (2.3 MN m -3/2) than the intrinsicfaceted ΔK th value (4.8 MN m -3/2). This is thought to reflect not only the effect of crack branching and deflection (in the faceted case) on the crack driving force, but also the inherent difference in resistance of the material to the two different crack propagation micromechanisms. © 1993 The Institute of Materials.

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.