Inertial effects on fatigue crack growth

In this paper, a cohesive zone model is used to study the influence of inertial effects on crack growth considering cyclic loading in homogenous rate‐independent materials. Quasi‐static and dynamic solutions are compared in order to establish the conditions in which the inertial effects become important in the analysis. It is discussed how speed and frequency of the loading and specimen sizes modify crack growth characteristics. In general, an increase in the loading frequency leads to a higher propagation velocity. Very high loading frequencies may lead to the formation of microcracks ahead of the crack tip and may change the failure mode of the cracked structure from crack propagation to uniform debonding. This work shows that inertial effects are specially noticeable for frequencies in the kHz range. However, applied frequencies close to natural frequencies of the cracked specimen can give rise to strong inertial effects and then a substantial reduction of fatigue life for much lower frequencies. This work also shows that critical frequencies depend on the specimen size.     

The sensitivity of surface crack initiation to surface roughness in low-cycle fatigue at high temperature

Low-cycle fatigue tests have been carried out on AISI 304L stainless steel and Cr---Mo---V steel specimens with two different modes of surface roughness at 823 K. In the case of Cr---Mo---V steel, grain boundary cavities were not formed during the test. Transgranular cracks were formed and then propagated. The number of cycles required for the crack initiation was observed to be a very large fraction of the toral fatigue life. In the case of AISI 304L stainless steel, grain boundary cavities formed and intergranular crack initiation and propagation was also observed to occur. The number of cycles required for crack initiation was negligible in comparison with the total low-cycle fatigue life.     

Fatigue crack growth with overloads/underloads: Interaction effects and surface roughness

The generalization of damage tolerance to variable amplitude fatigue is of prime importance in order to maintain the reliability of structures and mechanical components subjected to severe loading conditions. Engineering spectra usually contain overloads and underloads which distribution may not be random. However for predicting the life of a structure, a simplified spectrum is usually determined from the real one, in order to reduce testing periods on prototypes. Therefore it is thus important to know which cycles can contribute to crack growth and which can be neglected. This paper presents an analysis of fatigue crack growth on M (T) specimens made of a medium carbon steel DIN Ck45. The specimens are subjected to repeated blocks of cycles made up of one or several (1, 2, 6 or 10) overloads (or underloads) separated by a variable number (10, 1000 or 10 000) of baseline cycles. The main objective of this study is to better understand the mechanisms at the origin of interactions effects due to the presence of overloads (or underloads) at different locations of each block loading. Under constant amplitude loading, single variables ΔK and K_max are required in crack growth relationships. The transferability of fatigue laws, obtained under constant amplitude loading to variable amplitude fatigue, requires at least an additional variable, whose evolution with crack length accounts for the interactions effects between cycles of different types. Results have shown that the interaction effects in fatigue crack growth are closely related to the mechanisms of crack growth: cyclic plastic behaviour of the material and fracture surface roughness. Measurements of roughness of the surface fracture were carried out in both constant amplitude and variable amplitude tests. The roughness characterization helped to determine the importance of the mechanisms on variable amplitude fatigue crack growth and determine the influence of overloads/underloads on fatigue crack growth.     

The effects of crack surface friction and roughness on crack tip stress fields

A model is presented which can be used to incorporate the effects of friction and tortuosity along crack surfaces through a constitutive law applied to the interface between opposing crack surfaces. The problem of a crack with a saw-tooth surface in an infinite medium subjected to a far-field shear stress is solved and the ratios of mode I stress intensity to mode II stress intensity are calculated for various coefficients of friction and material properties. The results show that tortuosity and friction lead to an increase in fracture loads and alter the direction of crack propagation.

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Résumé On présente un modèle utilisable pour tenir compte des effets de friction et de la rugosité sur les surfaces d'une fissure, en appliquant une loi constitutive à l'interface entre les surfaces opposées d'une fissure. On résoud le problème d'une fissure présentant une surface en dents de scie, dans un milieu infini soumis à un champ de contrainte de cisaillement appliqué à une certaine distance. On calcule les rapports de l'intensité de contraintes relative au mode I sur celle relative au mode II, pour divers coefficients de friction et diverses propriétés de matériau. Les résultats montrent que la rugosité et la friction conduisent à un accroissement de la charge correspondant à la rupture, et à une altération de la direction de propagation de la fissure.

     

考虑裂纹表面摩擦阻尼的振动疲劳裂纹扩展分析

以含表面裂纹悬臂梁为研究对象,研究了裂纹面摩擦效应对裂纹疲劳扩展的影响。分析时,用双线性弹簧描述裂纹呼吸行为,用Galerkin方法把呼吸裂纹梁简化为单自由度系统,基于Coulomb摩擦模型和能量耗散理论推导了摩擦阻尼损耗因子,运用广义的Forman方程模拟疲劳裂纹扩展,通过振动分析与裂纹扩展计算同步进行的方法考虑振动与疲劳的耦合效应,探讨了摩擦阻尼对裂纹梁疲劳裂纹扩展寿命的影响。结论表明,摩擦阻尼损耗因子随裂纹扩展呈单调递增趋势,摩擦阻尼对振动疲劳裂纹扩展的影响不容忽视     

Fatigue crack growth in TRIP steel under positive R-ratios

Load-controlled fatigue tests are conducted for four positive R values on a low-alloy TRIP steel for two different heat treatments: an optimal treatment leading to a multiphase microstructure containing retained austenite, ferrite, bainite and martensite, and a non-optimal treatment leading to a ferritic–martensitic dual-phase microstructure. A significantly increased resistance to fatigue crack growth is found for the optimal case with respect to the non-optimal case. The amount of crack closure is found to be larger in case of the non-optimally treated (ferritic–martensitic) steel. Close to the crack tip, an increased hardness suggests martensite formation. An EBSD technique is used to quantify the volume of retained austenite ahead of the crack tip, within the plastic zone. It is found that martensite formation only occurs within the monotonic plastic zone during fatigue. By evaluation of the retained austenite fraction during straining in static tensile tests, the plastic strain levels within the plastic zone are assessed. Additionally, the effect of martensite formation on fracture toughness is estimated.     

A fatigue crack initiation model incorporating discrete dislocation plasticity and surface roughness

Although a thorough understanding of fatigue crack initiation is lacking, experiments have shown that the evolution of distinct dislocation distributions and surface roughness are key ingredients. In the present study we introduce a computational framework that ties together dislocation dynamics, the fields due to crystallographic surface steps and cohesive surfaces to model near-atomic separation leading to fracture. Cyclic tension–compression simulations are carried out where a single plastically deforming grain at a free surface is surrounded by elastic material. While initially, the cycle-by-cycle maximum cohesive opening increases slowly, the growth rate at some instant increases rapidly, leading to fatigue crack initiation at the free surface and subsequent growth into the crystal. This study also sheds light on random local microstructural events which lead to premature fatigue crack initiation.     

Strength level effects on fatigue crack growth and retardation

Constant amplitude and spectrum loading fatigue crack growth rate tests were performed on HP-9Ni-4Co-30C steel heat treated to three strength levels. It was concluded that the constant amplitude crack growth rate is dependent on the strength level of the material and independent of the toughness of the material. It is also shown that the fatigue crack growth retardation is greater for a material with low strength and high toughness. These findings are discussed in light of the Elber closure model and it is shown that the model predicts that both the constant amplitude fatigue crack growth data and the retardation data are controlled by the yield strength.     

Temperature effects on fatigue crack growth in polycarbonate

The fatigue behaviour of a high strength thermoplastic, polycarbonate, has been investigated as a function of temperature. Fatigue crack growth properties were measured in the temperature range of 100 to 373 K and were analysed using a fracture mechanics approach. Fatigue behaviour was found to be related to the fracture toughness of the material. This correlation with fracture toughness was used to develop an empirical model based on the toughness for describing the effect of temperature on fatigue crack growth, and to consider fatigue in terms of the secondary losses of the polymer.     

Residual stress effects in fatigue crack growth

The paper describes the influence of residual stresses on the propagation of fatigue cracks in low-alloy steels used in the construction of North Sea Oil platforms. The results show faster crack growth in thicker plates and the development of secondary fatigue cracks in the residual stress field. Characteristics of fatigue crack growth are discussed.     

Shape change of surface crack during fatigue growth

Approximate analytical solutions of the differential equation controlling the shape change of a semielliptical surface crack during tension and bending fatigue growth are presented. These solutions reduce the prediction of the shape change of a surface crack to the calculation of elementary functions and reduce the prediction of fatigue life to the calculation of a definite integral. The solutions are compared with more than 680 pairs of experimental data for 22 different metallic materials published in the literature and the agreements are excellent. A multipoint analysis procedure combining the Paris relation and the requirement that the surface crack remain semielliptical during fatigue growth has been developed.     

Temperature and frequency effects on fatigue crack growth of uPVC

Temperature and frequency effects on fatigue crack growth rate have been modelled. The stress intensity factor- biased Arrhenius equation and a result from the two-stage zone model have been incorporated into the present model. Subsequently, temperature and frequency effects on fatigue crack growth in unplasticized polyvinyl chloride (uPVC) were studied over a temperature range 15–55 °C and a frequency range 0.01–10 Hz. Data for PVC taken from the literature were also included for analysis. It was found that the predicted values from the proposed model are in good agreement with experimental results.     

Evaluation of overload effects on fatigue crack growth and closure

Fatigue crack propagation tests with single tensile peak overloads have been performed in 6082-T6 aluminium alloy at several baseline ΔK levels and stress ratios of 0.05 and 0.25. The tests were carried out at constant ΔK conditions. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. The observed transient post-overload behaviour is discussed in terms of overload ratio, baseline ΔK level and stress ratio. The crack closure parameter U was obtained and compared with the crack growth transients. Experimental support is given for the hypothesis that plasticity-induced closure is the main cause of overload retardation for plane stress conditions. Predictions based on crack closure measurements show good correlation with the observed crack growth rates for all the post-overload transients when discontinuous closure is properly taken into account.     

Internal stress effects on fatigue crack initiation at notches

In this paper the effects of the internal stresses on crack initiation at notches is investigated. Internal stresses are induced by applying two pre-loading cycles at a given load ratio, R = S_MIN/S_MAX, to the ‘virgin’ notched specimen. After pre-loading, blocks of 10⁶ cycles with a constant nominal stress range, ΔS, slightly larger than the nominal threshold stress range, ΔS_th, are applied with increasing minimum stress, S_MIN, in each subsequent block until a crack initiates. The lowest S_MIN above which a crack initiates is recorded as S_IN. The process is repeated for a wide range of positive and negative load ratios in order to obtain S_IN/S_MAX vs. load ratio curve. This curve for positive load ratios surprisingly resembles the K_PR/K_MAX plot reported in the literature for a cracked specimen. The results are explained in terms of compressive internal stress and the associated local clamping action at the notch cyclic plastic zone. Both the analytical and finite element calculations show a fairly good agreement with the experimental results.     

The effect of microstructure and environment on fatigue crack growth in 7049 aluminium alloy at negative stress ratios

The influence of environment and microstructure on fatigue crack growth has been investigated on a high strength 7049 aluminium alloy. This aluminium alloy was artificially aged to underaged (UA) and overaged (OA) microstructures. The heat treatment procedure was performed in order to obtain an UA and OA microstructure having the same yield strength properties, but differing in the mode of slip deformation: the UA alloy deforms by planar slip and that of the OA alloy by wavy slip. The crack growth measurements were performed in MT specimens at constant load ratios for R=0, −1, −2, −3 near-threshold and Paris regime in ambient air and vacuum conditions. Crack closure loads were measured in order to determine the P_open for each R ratio. Micromechanisms of near-threshold crack growth are briefly discussed for several concurrent processes involving environmentally assisted cracking with intrinsic microstructural effects. The results showed that the presence of humid air leads to a larger reduction in ΔK_th for both the ageing conditions, but the UA specimens were superior probably because of crack branching. The role of environmental effect and microstructures near-threshold regime seems to be more significant than any mechanical contributions to the crack closure, such as plasticity, roughness, oxide, etc.     

The measurement and analysis of semi-elliptical surface fatigue crack growth

Fatigue tests in which the development of crack shape was studied with the a.c. field measurement technique have been conducted on semi-elliptical cracks growing in flat plate specimens under tension and bending stresses. The a.c. field measurement technique, which was used to measure the cracks, exploits the fact that high frequency alternating current tends to flow in a thin skin along the metal surface and the crack depths can be interpreted from the changes in the voltage distribution produced by the presence of a crack. In order to interpret the measured voltages so as to provide accurate estimates of the crack length and depth, a theoretical analysis of the a.c. field around a semi-elliptical crack is required. This analysis was used to interpret the measured voltages in terms of the changes in the crack shape. Finally the interpreted data on the changes in crack shape were then used to test the accuracy of various stress intensity factor solutions.     

The effects of overloads in fatigue crack growth

Several theories have been proposed to explain the transient fatigue crack growth decelerations and accelerations which follow overloads. The mechanisms that have been proposed to explain retardation after a tensile overload, for example, include residual stress, crack deflection, crack closure, strain hardening, and plastic blunting/resharpening. These mechanisms are reviewed in the light of recent experimental results, and implications with regard to their applicability are examined. It is suggested that no single mechanism can be expected to represent observed effects over the entire range of da/dN versus ΔK; eg, behaviour ranging from the near threshold region to the Paris region.     

Fatigue crack growth thresholds-the influence of Young''s modulus and fracture surface roughness

In the present investigation it is shown that the effective fatigue threshold is uniquely correlated to the Young's modulus for a wide range of metallic and composite materials (ΔK_th,eff=1.64·10⁻²·E). It is also demonstrated that the crack closure level K_cl increases with increased roughness of the fracture surface . K_cl and are quantitatively related via the equation for steels with widely different mechanical properties and grain sizes (120 MPa<R_p<1100 MPa, 1 μm<λ<100 μm). This relation can be extended to materials other than steels (e.g. aluminium and WC-Co alloys) by normalising against Young's modulus. The roughness value represents the standard deviation of height of the fracture surface and is shown to be simply related to the length and angle distributions of the linear length elements constituting the fracture profile.     

Effects of frequency on fatigue crack growth at elevated temperature

The effects of frequency on fatigue crack growth behaviour have been studied in a prealloyed powder material, Udimet 720Li, at 650 °C. Fracture mode and fatigue crack growth behaviour were studied at frequencies ranging from 0.001 to 5 Hz using a balanced triangular waveform. Tests were carried out under constant Δ K control, with load ratio and temperature being held constant. A mechanism map was constructed where predominantly time, mixed and cycle-dependent crack growth behaviour were identified. The results were verified by SEM analyses. Cycle-dependent crack growth data were obtained at room temperature, while fully time-dependent crack growth data were generated under sustained loads at 650 °C.
It was found that mixed time/cycle-dependent behaviour is of most significance for this material at the temperature and frequencies studied. Data for other nickel-based superalloys from various sources in the literature were compiled and compared with those of U720Li alloy at a given stress intensity and temperature in the mixed regime. An analysis was developed to rationalize the observed effect of frequency on fatigue crack growth rate.