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.     

Cyclic fatigue of a silicon nitride: influence of frequency and fatigue mechanism

An investigation has been carried out on the slow crack growth behaviour of an advanced Si₃N₄ ceramic material at room temperature at different loading frequencies. The results clearly show a detrimental effect of cyclic loading on crack growth rate in terms of time and a reduced crack growth resistance with increasing cyclic frequency. Crack growth rates can be described by the Paris power-law expression for both static and cyclic loading, but the exponent n increases with decreasing loading frequency. Further support for the existence of mechanical fatigue in this material is provided from experiments involving alternate cyclic and static fatigue using the same specimen, which show substantial differences in crack growth rate in terms of time. Removal of crack wakes resulted in an unchanged crack growth rate under sustained load, which suggests that the crack wake does not play a key role in enhanced crack growth under cyclic loading. The likely crack growth mechanism is discussed.     

A model for fatigue crack growth with a variable stress intensity factor

A model for fatigue crack growth, similar to that of Majumdar and Morrow, is proposed where the crack growth rate is determined from the low cycle fatigue and cyclic stress-strain response of the material. The model is for a constant stress range at infinity, but does allow for a variable stress intensity factor due to the changing crack length. The study also includes an analysis of the strain range in the neighborhood of the crack tip. Further it is shown that the model predicts the critical stress intensity factor. A prediction of the crack growth rate is made for 2024-T351 aluminium, copper and CU-6.3 AL alloy and is compared to the experimental observations.     

Bifurcation and propagation of a mixed-mode crack in a ductile material

The bifurcation and the propagation of a 2-D mixed-mode crack in a ductile material under static and cyclic loading were investigated in this work. A general methodology to study the crack bifurcation and the crack propagation was established. First, for a mixed-mode crack under static loading, a procedure was developed in order to evaluate the fracture type, the beginning of the crack growth, the crack growth angle and the crack growth path. This procedure was established on the basis of a set of criteria developed in the recent studies carried out by the authors [Li J, Zhang XB, Recho N. J-M^p based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading. Engng Fract Mech 2004;71:329-43; Recho N, Ma S, Zhang XB, Pirodi A, Dalle Donne C. Criteria for mixed-mode fracture prediction in ductile material. In: 15th European conference on fracture, Stockholm, Sweden, August 2004]. A new criterion, by combining experimentation and numerical calculation, was developed in this work in order to predict the beginning of the crack growth. Second, in the case of cyclic loading, the crack growth path and crack grow rate are studied. A series of mixed-mode experiments on aluminium and steel specimens were carried out to analyse the effect of the mixed mode on the crack growth angle and the crack growth rate. On the basis of these experimental results, a fatigue crack growth model was proposed. The effect of the mixed mode on the crack growth rate is considered in this model. The numerical results of this model are in good agreement with the experimental results.     

Observations and modeling of the small fatigue crack behavior of an extruded AZ61 magnesium alloy

The objective of this paper is to quantify the microstructurally small fatigue crack growth of an extruded AZ61 magnesium alloy. Fully reversed and interrupted load-controlled tests were conducted on notched specimens that were taken from the material in the longitudinal and transverse orientations with respect to the extrusion direction. In order to measure crack growth, replicas of the notch surface were made using a dual-step silicon-rubber compound at periodic cyclic intervals. By using microscopic analysis of the replica surfaces, crack initiation sites from numerous locations and crack growth rates were determined. A marked acceleration/deceleration was observed to occur in cracks of smaller length scales due to local microheterogeneities consistent with prior observations of small fatigue crack interaction with the native microstructure and texture. Finally, a microstructure-sensitive multistage fatigue model was employed to estimate the observed crack growth behavior and fatigue life with respect to the microstructure with the most notable item being the grain orientation. The crack growth rate and fatigue life estimates are shown to compare well to published findings for pure magnesium single crystal atomistic simulations.     

Effects of welding residual stresses on fatigue crack growth behaviour in butt welds of a pipeline steel

In the present test the fatigue crack growth rate in the parent plate, weld and cross-bond regions was measured and the results were correlated with the stress intensity range ΔK and the effective stress intensity range ΔK_eff. It is indicated that the welding residual stresses strongly affect the crack growth rate. For the weld metal and cross-bond compact tension specimens in which crack growth is along the weld line the fatigue crack growth rate increases as the crack grows. However, for the T compact tension specimen in which crack growth is perpendicular to the weld line at a constant value of applied ΔK the crack growth rate initially decreases as the crack grows. Particularly, at a low constant value of applied ΔK the crack growth rate obviously decreases and the crack fails to grow after short crack growth. When the crack grows to intersect the welded zone, the fatigue crack growth rate gradually increases as the crack grows further. It is clear that the effect of welding residual stresses on the crack growth rate is related to the position of the crack and its orientation with respect to the weld line. Finally, the models of welding residual stress redistribution in the compact tension specimens with the growing crack and its influence on the fatigue crack closure are discussed. It appears that for a butt-welded joint one of the crack closure mechanisms may be considered by the bend or rotation deformation of crack faces due to the welding residual stress redistribution as the fatigue crack grows in the welded joint.     

Fatigue crack initiation and growth of 16MnR steel with stress ratio effects

The effects of stress ratio on the fatigue crack initiation and growth were investigated by a newly developed unified model, which is based on the cyclic plasticity property of material and a multiaxial fatigue damage criterion in incremental form. The cyclic elastic-plastic stress-strain field was analyzed using the general-purpose finite element software (ABAQUS) with the implementation of a robust cyclic plasticity theory. The fatigue damage was determined by applying the calculated stress-strain responses to the incremental fatigue criterion. The fatigue crack growth rates were then obtained by the unified model. Six compact specimens with a thickness less than 3.8 mm were used for the fatigue crack initiation and growth testing under various stress ratios (−1.0, 0.05, 0.1, 0.2, 0.3 and 0.5). Finite element results indicated that crack closure occurred for the specimen whose stress ratio was less than 0.3. The combined effects of accumulated fatigue damage induced by cyclic plastic deformation and possible contact of cracked surfaces were responsible for the fatigue crack initiation and growth. The predicted results agreed with the benchmark mode I fatigue crack growth experiments very well.     

Effect of frequency on ambient temperature fatigue crack growth in a silicon carbide reinforced silicon nitride composite

A detailed study on a silicon nitride reinforced with silicon carbide whiskers has been undertaken on room temperature fatigue during static and dynamic loading at constant ΔK. It is shown that sub-critical crack growth rates are lower when the material experiences sustained far field loading than during cyclic far field loading. The increased crack growth rate during cyclic loading is attributed to a wedging effect within the crack wake causing an increase in the tensile stress and resultant increased micro-cracking ahead of the crack tip. This additional micro-structural damage leads to enhanced sub-critical crack growth rates during cyclic loading. The asperities that are responsible for the wedging effect are attributed to the isolation of small portions of material due to branching of small cracks and by degradation of the bridging SiC whiskers and Si₃N₄ grains within the crack wake.     

复合材料裂纹敏感性的评定──(Ⅱ)HTA/6376和T300/M10的Ⅱ型分层扩展行为

应用ENF试验研究了HTA/6376和T300/M10两种碳/环氧复合材料的静态与疲劳层间断裂行为。在静态载荷下,两种材料均呈现脆性不稳定和稳定的裂纹扩展特性。在R=0.1且△G_I大幅度变化的疲劳加载过程中,两种材料呈现稳定的裂纹扩展。采用位移控制方法,确定了裂纹扩展速率与循环应变能释放率的关系和应变能释放率门槛值。与T300/914C相比,HTA/6376和T300/M10具有较高的抗裂纹扩展能力。     

ELEVATED TEMPERATURE FATIGUE CRACK GROWTH BEHAVIOR OF Ti-1100

Abstract— The fatigue crack growth behavior of Ti-1100 is analyzed at elevated temperatures to evaluate the effects of mechanical and environmental variables. Experiments conducted over a wide range of frequencies from 0.01 Hz to 200 Hz indicate a strong dependence of the growth rate upon cyclic loading frequency. Superposition of hold time at maximum and minimum loads over a baseline 1.0 Hz cyclic loading frequency produces an insignificant variation in crack growth rate, which may be attributed to the combined effects of enhanced environmental degradation, crack-tip blunting and increased asperity-induced closure level in this material. It is deduced that a hold time at maximum load results in an interaction of the environmental effects with a retardation effect due to crack tip blunting as a consequence of creep under maximum applied load, whereas for hold at minimum loads, extensive crack-branching and micro-cracking appear to enhance crack closure loads resulting in lower crack growth rates. A linear superposition model is employed to account for the complex interactions due to fatigue, creep and environmental degradation.     

Crack growth in ferroelectric ceramics under electric loading

Summary A crack with growth in ferroelectric ceramics under purely electric loading is analyzed. The crack tip stress intensity factor for the growing crack under small scale conditions is evaluated by employing the model of nonlinear domain switching. The electrical fracture toughness is obtained from the result of the stress intensity factor. It is shown that the ferroelectric material can be either toughened or weakened as the crack grows. Fatigue crack growth in a ferroelectric material under cyclic electric loading is also examined. The incremental fatigue crack growth under cyclic electric loading is obtained numerically. The fatigue crack growth rate is affected strongly by the electrical nonlinear behavior. It is found that the curve of fatigue crack growth rate versus electric field intensity factor is linear on the log-log plot at intermediate values of the electric field intensity factor.     

Fatigue crack growth for a surface crack in a round bar under multi-axial loading condition

In this paper, the fatigue life, surface crack extension direction and crack growth rate in an elastic bar with a circular cross section are determined through experiments under cyclic torsion with axial static and cyclic tension/compression loading. The effects of the loading type, loading value and stress ratio on the crack growth behaviour are discussed. The results show that, under pure fatigue torsion loading, the crack extension direction is almost the same whatever the value of torsion loading. Under fatigue torsion with cyclic tension loading, it is found that the crack extension direction is mainly determined by the alternating parts of the stresses and is almost independent of the average parts of the stresses, whereas the fatigue life is obviously dependent on the average stress.     

The effects of loading waveform and microstructure on the fatigue response of titanium aero-engine compressor disk alloys

Microstructural variations produced from manufacturing processes and their influence on fatigue crack growth in titanium disks were investigated. Charpy‐tests on titanium disk material were performed and materials with fracture energy values in the range of 3.8–19.1 J/cm² were selected for tests under cyclic loads. Results of Charpy‐tests were compared with fractographic features related to fatigue crack growth in Ti?6Al?3Mo?0.4Si and Ti?6Al?3Mo?2Cr alloys with a two‐phase (α + β) lamellar structure under various cyclic waveforms using specimens made from compressor disks. The material sensitivity to cyclic load waveform can be seen for in‐service disks using a criteria based on fracture energy values determined in Charpy‐tests. A difference in fatigue crack growth periods of 2.5 times was discovered for specimens made from the disk with a filament type microstructure and the mainly globular two‐phase structure of the Ti?6Al?3Mo?0.4Si alloy. The shorter crack growth period correlated with the mainly facetted pattern formation with local zones of fatigue striations when fatigue crack growth is along the planes of the filaments. Fatigue striations are the major fracture surface relief when crack growth occurs in the perpendicular direction to the plane of the filaments. A quantitative fractographic method for estimating the crack growth period for in‐service failed disks was performed for the case of crack development along planes of such microstructural filaments created during the manufacturing process. Specimen tests involving a hold‐time in the cyclic loads are recommended for in‐service accepted titanium disks using a criteria based on the fracture energy value. Selection of disks based on these criteria can indicate a material sensitivity to cyclic load waveforms.     

复合材料裂纹敏感性的评定──（Ⅱ）HTA／6376和T300／M10的Ⅱ型分层扩展行为

应用ＥＮＦ试验研究了ＨＴＡ／６３７６和Ｔ３００／Ｍ１０两种碳／环氧复合材料的静态与疲劳层间断裂行为。在静态载荷下，两种材料均呈现脆性不稳定和稳定的裂纹扩展特性。在Ｒ＝０．１且△Ｇ＿Ｉ大幅度变化的疲劳加载过程中，两种材料呈现稳定的裂纹扩展。采用位移控制方法，确定了裂纹扩展速率与循环应变能释放率的关系和应变能释放率门槛值。与Ｔ３００／９１４Ｃ相比，ＨＴＡ／６３７６和Ｔ３００／Ｍ１０具有较高的抗裂纹扩展能力。     

Crack initiation and crack propagation under thermal cyclic loading

Theoretical and experimental investigations of crack initiation and crack propagation under thermal cyclic loading are presented. For the experimental investigation a special thermal fatigue test rig has been constructed in which a small circular cylindrical specimen is heated up to a homogeneous temperature and cyclically cooled down under well defined thermal and mechanical boundary conditions by a jet of cold water. At the end of the cooling phase the specimen is reheated to the initial temperature and the following cycle begins. The experiments are performed with uncracked and mechanically precracked specimens of the German austenitic stainless steel X6CrNi 1811.

In the crack initiation part of the investigation the number of load cycles to initiate cracks under thermal cyclic load is compared to the number of load cycles to initiate cracks under uniaxial mechanical fatigue loading at the same strain range as in the cyclic thermal experiment. The development of initiated cracks under thermal cyclic load is compared with the development of cracks under uniaxial mechanical cyclic load.

In the crack propagation part of the investigation crack growth rates of semi-elliptical surface cracks under thermal cyclic loading are determined and compared to suitable mechanical fatigue tests made on compact-tension and four-point bending specimens with semi-elliptical surface cracks. The effect of environment, frequency, load shape and temperature on the crack growth rate is determined for the material in mechanical fatigue tests.

The theoretical investigations are based on the temperature distribution in the specimen, which is calculated using finite element programs and compared to experimental results. From the temperature distribution, elastic and elastic-plastic stress distributions are determined taking into account the temperature dependence of the material properties. The prediction of crack propagation relies on linear-elastic fracture mechanics. Stress intensity factors are calculated with the weight function method and crack propagation is determined using the Paris relation.

To demonstrate the quality of the crack growth analysis the experimental results are compared to the prediction of crack propagation under thermal cyclic load.     

FATIGUE CRACK INITIATION LIFE PREDICTION FOR WELDED JOINTS BY LOW CYCLE FATIGUE APPROACH

Abstract— Analytical procedures based on low cycle fatigue theory are used to estimate the fatigue crack initiation life (N_i) for a cruciform welded joint in mild steel under constant amplitude tensile cyclic loading; the fatigue crack initiating at the weld toe. Effects due to welding such as residual stresses, geometrical variability and changes in material properties are handled. It is shown that for high mean stresses the discrepancies observed between the N _i estimates provided by commonly used analytical procedures exceed an order of magnitude. For the base metal (BM) the discrepancies become negligible if cyclic relaxation of notch mean stress is taken into consideration. The differences betwen the N _i estimates for heat affected zone (HAZ) material (where fatigue cracks at the weld toe usually initiate) and for BM are quantified. The applicability of HAZ material properties, estimated from hardness, to N _i prediction is evaluated.     

Damage tolerance reliability analysis of automotive spot-welded joints

This paper develops a damage tolerance reliability analysis methodology for automotive spot-welded joints under multi-axial and variable amplitude loading history. The total fatigue life of a spot weld is divided into two parts, crack initiation and crack propagation. The multi-axial loading history is obtained from transient response finite element analysis of a vehicle model. A three-dimensional finite element model of a simplified joint with four spot welds is developed for static stress/strain analysis. A probabilistic Miner's rule is combined with a randomized strain-life curve family and the stress/strain analysis result to develop a strain-based probabilistic fatigue crack initiation life prediction for spot welds. Afterwards, the fatigue crack inside the base material sheet is modeled as a surface crack. Then a probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction for spot welds. Both methods are implemented with MSC/NASTRAN and MSC/FATIGUE software, and are useful for reliability assessment of automotive spot-welded joints against fatigue and fracture.     

CRACK FACE INTERACTIONS AND NEAR-THRESHOLD FATIGUE CRACK GROWTH

Rough fracture surfaces usually influence substantially the fatigue growth properties of materials in the regime of low growth rates. Friction, abrasion, interlocking of fracture surface asperites and fretting debris reduce the applied load amplitude to a smaller effective value at the crack tip (“sliding crack closure”, or “crack surface interaction” or “crack surface interference”). The influence of these phenomena on the fatigue crack growth properties of structural steel is discussed and compared for the two kinds of mixed mode loading employed in this work. Mixed mode loading was performed by (A): cyclic mode III + superimposed static mode I and (B): cyclic mode I + superimposed static mode III loading. Such loading cases frequently occur in rotating load-transmission devices. Several differences are typical for these two mixed-mode loading cases. A superimposed static mode I load increases the crack propagation rate under cyclic mode III loading whereas cyclic mode I fatigue crack propagation is retarded when a static mode III load is superimposed. Increase of the R -ratio (of the cyclic mode III load) leads to an insignificant increase of fracture surface interaction and subsequently to a small decrease of the crack growth rate for cyclic mode III loading, whereas higher R -values during cyclic mode I+ superimposed static mode III loading lead to a significant reduction of the crack growth rates.     

Kurzrisswachstum bei mehrachsig nichtproportionaler Beanspruchung

Short fatigue crack growth under multiaxial nonproportional loading Initiation and short fatigue crack growth have been investigated under nonproportional cyclic loading. A critical plane approach based on fracture mechanics is used for modelling the fatigue process. A Paris‐type crack growth law, formulated using the effective cyclic J‐integral as crack driving force parameter, is integrated to give crack growth curves. Crack opening stresses and strains are calculated with approximation equations. Jiang's plasticity model is used to predict the stress‐strain path. The good agreement between model and real damage evolution is shown comparing experimentally determined crack growth curves, crack orientations, and life curves.     

Fracture toughness and fatigue crack growth in Ti‐6Al‐4V friction stir welds

Friction stir welding of titanium holds the promise for producing joints with microstructures and mechanical properties that are more comparable to wrought material than traditional fusion welding processes. Extensive data exist on the microstructure and static mechanical properties of titanium friction stir welds, but very little are available on the durability (fatigue) and even less on the damage tolerance (fracture toughness and fatigue crack growth). This paper presents the results of an investigation into the damage tolerance of friction stir welds made in 6 mm thick Ti‐6Al‐4V after a post‐weld heat treatment. It was found that the apparent fracture toughness was lower than the wrought base material, 7–25% depending on the crack orientation relative to the weld, but the crack growth performance (ΔK vs. da/dN) of the weld in the absence of weld‐induced residual stresses was identical to the base material.