On fatigue lifetimes and fatigue crack growth behavior of bone cement

Bone cement is used to develop a mechanical bond between an artificial joint and the adjacent bone tissue, and any degradation of this bond is of serious concern since it can lead to loosening and eventually malfunction of the artificial joint. In the present study, the fatigue lives and fatigue crack propagation behavior of two bone cements, CMW Type 3 and Zimmer, were investigated, and it was found that the size and distribution of pores played a major role in influencing both the fatigue crack initiation and propagation processes. The fatigue lifetimes of CMW exceeded those of Zimmer because of a lesser density of large pores. When the fatigue lifetimes were plotted as a function of K _limax, the maximum initial stress intensity factor based upon the initiating pore size, the difference in fatigue lifetimes between CMW and Zimmer bone cements was greatly reduced. The fatigue crack growth behavior of both bone cements were similar. This is a further indication that the noted differences in fatigue lifetimes were related to the size of the pore at the crack initiating site.     

Transient effects in fatigue crack propagation

The transient fatigue crack propagation resulting from the sudden change of the stress intensity factor amplitude or from the change of the stress cycle asymmetry or from the application of the single overload cycle was measured on carbon steel specimens. To simplify the conditions and to increase the accuracy the shape of the specimens was chosen in such a way, that the stress intensity factor was independent of the crack length. It was shown that the transient effects can be qualitatively understood and quantitatively in the first approximation described solely on the basis of the steady state fatigue crack propagation data, provided that the threshold conditions of non-propagation are taken into account.     

Energy considerations in fatigue crack propagation

The concept of Griffith fracture theory was extended to fatigue crack propagation problems by defining the Gibbs free energy of solids under cyclic loading.As a result, the rate of fatigue crack propagation, dc/dN, was obtained as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbqfgBHr% xAU9gimLMBVrxEWvgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvA% Tv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9% vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea% 0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabe% aadaabauaaaOqaamaalaaabaGaciizaiaadogaaeaaciGGKbGaamOt% aaaacqGH9aqpcaGGOaGaaGOmaiaac6cacaaIZaGaciiEaiaaigdaca% aIWaWaaWbaaSqabeaacaGGTaGaaGOmaaaakiaacMcadaWcaaqaaiab% eQ7aRjaacIcacqGHuoarcaWGlbGaaiykamaaCaaaleqabaGaaGinaa% aaaOqaaiabeY7aTjabeo8aZnaaCaaaleqabaGaaGOmaaaaiqGakiaa% -vfaaaaaaa!547A!\[\frac{{\operatorname{d} c}}{{\operatorname{d} N}} = (2.3\operatorname{x} 10^{ - 2} )\frac{{\kappa (\Delta K)^4 }}{{\mu \sigma ^2 U}}\] where is a proportionality constant (01), K is the stress intensity amplitude, is the shear modulus, is an appropriate strength parameter for fatigue failure of the alloy and U is the energy to make a unit fatigue surface.

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Résumé Le concept de la théorie de rupture de Griffith a été étendu aux problèmes de propagation des fissures de fatigue en définissant l'énergie libre de Gibbs pour les solides soumis à sollicitations cyclique.Le résultat de cette approche est la détermination de la vitesse de propagation d'une fissure de fatigue dc/dN par la formule suivante: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbqfgBHr% xAU9gimLMBVrxEWvgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqefqvA% Tv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0dXdh9% vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea% 0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabe% aadaabauaaaOqaamaalaaabaGaciizaiaadogaaeaaciGGKbGaamOt% aaaacqGH9aqpcaGGOaGaaGOmaiaac6cacaaIZaGaciiEaiaaigdaca% aIWaWaaWbaaSqabeaacaGGTaGaaGOmaaaakiaacMcadaWcaaqaaiab% eQ7aRjaacIcacqGHuoarcaWGlbGaaiykamaaCaaaleqabaGaaGinaa% aaaOqaaiabeY7aTjabeo8aZnaaCaaaleqabaGaaGOmaaaaiqGakiaa% -vfaaaaaaa!547A!\[\frac{{\operatorname{d} c}}{{\operatorname{d} N}} = (2.3\operatorname{x} 10^{ - 2} )\frac{{\kappa (\Delta K)^4 }}{{\mu \sigma ^2 U}}\] où est une constante de proportionnalité, K est l'amplitude de l'intensité de contrainte, est le module de cisaillement, est un paramètre de résistance approprié à la rupture par fatigue de l'alliage considéré, et U est l'énergie nécessaire à la création d'une surface de fatigue unitaire.

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This research was supported by the Air Force Office of Scientific Research, Grant No. AF-AFOSR-76-2892A, and partially supported under the NSF-MRL program through the Materials Research Center of Northwestern University (Grant DMR 76-80847).     

First-passage solutions in fatigue crack propagation

The statistical characteristics of the time required by the crack size to reach a specified length are sought. This time is treated as the random variable time-to-failure and the analysis is cast into a first-passage time problem. The fatigue crack propagation growth equation is randomized by employing the pulse train stochastic process model. The resulting equation is stochastically averaged so that the crack size can be approximately modelled as Markov process. Choosing the appropriate transition density function for this process and setting the proper initial and boundary conditions it becomes possible to solve the associated forward Kolmogorov equation expressing the solution in the form of an infinite series. Next, the survival probability of a component, the cumulative distribution function and the probability density function of the first-passage time are determined in a series form as well. Corresponding expressions are also derived for its mean and mean square. Verification of the theoretical results is attempted through comparisons with actual experimental data and numerical simulation studies.     

A fatigue crack propagation model

A model for fatigue crack propagation has been developed which incorporates mechanical, cyclic and fatigue properties as well as a length parameter. The latter can be associated with the microstructure of the material. The fatigue failure criterion is based on a measure of the dissipated plastic strain energy. This model predicts crack propagation at low and intermediate ΔK values, i.e. stage I crack growth rate as well as that of the stage II. A number of crack growth rate models proposed earlier, are shown to be particular cases of the one developed herein. Predictions of the model are in good agreement with the experimental data. The required data for predicting the crack growth rate, can be found in standard material handbooks where fatigue properties are listed.     

Resonance controlled fatigue crack propagation

Fatigue crack growth in resonating structural members is studied. The crack propagation rate is related to the stress intensity factor range by way of the well known power law. The depth of the crack determines the local flexibility due to crack which in turn influences the dynamic response of the system under an external force with constant amplitude and frequency. The propagating crack introduces additional flexibility to the system which results in gradual shift away from the resonance with smaller loading of the cracked section. This slows down the crack growth rate.It was shown that this mechanism can guide the system to a value of the crack growth rate below a conventional threshold rate which can be interpreted as dynamic crack arrest. It was found that material damping is the decisive factor determining the crack growth rate in a resonant system where the material damping is the dominant damping mechanism of the system.     

Fracture toughness and fatigue crack propagation behavior of 8090 Al-Li alloy

We present results of fatigue tests of high-strength 8090 Al-Li alloy and data on its fatigue crack growth resistance. High strength combined with fairly high crack growth resistance and endurance limit results in much better service characteristics compared to other high-strength aluminum alloys. We discuss results of tensile and impact tests of Charpy specimens and the critical values of theJ-integral andK _1c for 10-mm-thick specimens in the T-L and L-T orientations subjected to complete and partial aging. The experimental results are compared with published data for 8090 and other high-strength aluminum alloys. We suggest a numerical method for the evaluation of fatigue strength according toda/dN-K diagrams.Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 1, pp. 45–58, January – February, 1995.     

微观组织对贝氏体钢疲劳裂纹扩展行为的影响

为了研究组织对疲劳裂纹扩展行为的影响,对3种不同贝氏体组织钢进行了疲劳裂纹扩展实验,并采用SEM和EBSD等方法对裂纹进行了分析.结果表明,板条贝氏体组织在近门槛区和稳定扩展区阻碍裂纹扩展的能力最强,具有最小的裂纹扩展速率.板条贝氏体组织中的大角度晶界使裂纹更容易发生偏折,导致断口表面粗糙度增加,裂纹扩展受到较强的粗糙度诱导裂纹闭合效应的作用.随着ΔK的增大,塑性诱导裂纹闭合效应取代粗糙度诱导裂纹闭合效应开始占据主导作用,是板条贝氏体组织中裂纹扩展速率对ΔK的变化较敏感的原因.     

A low-cycle fatigue approach to fatigue crack propagation

The damage accumulation hypothesis is used to derive a fatigue crack growth rate equation. The fatigue life of a volume element inside the plastic zone is evaluated by using low-cycle fatigue concepts. Crack growth rate is expressed as a function of cyclic material parameters and plastic zone characteristics. For a given material, crack growth increment, is predicted to be a fraction of the plastic zone size which can be expressed in terms of fracture mechanics parameters,K andJ. Hence, the proposed growth rate equation has a predictive capacity and is not limited to linear elastic conditions.     

Quantifying the parameters in fatigue crack propagation

Fatigue crack growth data in the region of stage II(a) and stage II(b) have been attempted. It has been observed that the stage II(a) and the stage II(b) crack growth rate vs ΔK relations have their own pivot points. The dependence of the threshold stress intensity factor on the stress ratio and temperature has been obtained in terms of the pivot point co-ordinates. The predicted values of the threshold ΔK compare well with the experimental data.     

Modelling fatigue crack propagation in CT specimens

Although there are a great number of numerical studies focused on the numerical simulation of crack shape evolution, a deeper understanding is required concerning the numerical parameters and the mathematical modelling. Therefore, the objectives of the paper are the study of the influence of numerical parameters, particularly the radial size of crack front elements and the magnitude of individual crack extensions, the mathematical modelling of crack propagation regimes, and the linking of crack shape changes with K distribution. A relatively simple through-crack geometry, the CT specimen, was studied and the numerical model was validated with experimental results with a good agreement. The K distribution along crack front was found to be the driving force for shape variations. Shape variations were found to be one order of magnitude lower than K variations.     

Early stage crack propagation in fretting fatigue

A stress model of the fretting fatigue damage mechanism is developed on the basis of microscopic observations of the fatigue failure process in fretting. According to the model the state of stress in the element in the region of fretting pads defines the fatigue strength of the fretting assembly. Areas where the first fatigue crack initiates and the direction of its early stage propagation can be well explained by the elastic strain energy in the specimen near the fretting pads. The main fatigue crack initiates in the cyclically loaded member from the edge of the fretting pad, grows at the beginning and then stops, becoming a non-propagating crack, when the member is loaded below the fretting fatigue limit.     

A model for fatigue crack propagation

A model for fatigue crack propagation is presented which incorporates low cycle fatigue, mechanical properties and a microstructurally-associated process zone. Comparison of the model to published date for 4340 (hard and soft), a series of TRIP steels, Ti-6A1-4V, 2024-T6 and 300 grade maraging steel shows good agreement.     

Mechanisms for corrosion fatigue crack propagation

ABSTRACT The corrosion fatigue crack growth (FCG) behaviour, the effect of applied potential on corrosion FCG rates, and the fracture surfaces were studied for high‐strength low‐alloy steels, titanium alloys, and magnesium alloys. During investigation of the effect of applied potential on corrosion FCG rates, polarization was switched on for a time period in which it was possible to register the change in the crack growth rate corresponding to the open‐circuit potential and to measure the crack growth rate under polarization. Due to the higher resolution of the crack extension measurement technique, the time rarely exceeded 300 s. This approach made possible the observation of a non‐single mode effect of cathodic polarization on corrosion FCG rates. Cathodic polarization accelerated crack growth when the maximum stress intensity (K_max) exceeded a certain well‐defined critical value characteristic for a given material‐solution combination. When K_max was lower than the critical value, the same cathodic polarization, with all other conditions (specimen, solution, pH, loading frequency, stress ratio, temperature, etc.) being equal, retarded or had no influence on crack growth. The results and fractographic observations suggested that the acceleration in crack growth under cathodic polarization was due to hydrogen‐induced cracking (HIC). Therefore, critical values of K_max, as well as the stress intensity range (ΔK) were regarded as corresponding to the onset of corrosion FCG according to the HIC mechanism and designated as K_HIC and ΔK_HIC. HIC was the main mechanism of corrosion FCG at K_max > K_HIC (ΔK > ΔK_HIC). For most of the material‐solution combinations investigated, stress‐assisted dissolution played a dominant role in the corrosion fatigue crack propagation at K_max < K_HIC (ΔK < ΔK_HIC).     

U75V重轨钢弯曲疲劳裂纹扩展行为EI北大核心

为明确珠光体钢轨的疲劳裂纹扩展行为,测定U75V重轨钢轧态和热处理态两种条件下的三点弯曲疲劳裂纹扩展速率,采用光学显微镜、扫描电镜、EBSD对钢轨的微观组织、片层、断口形貌及裂纹扩展轨迹进行观察。结果表明:轧态和热处理态钢轨的疲劳辉纹平均间距分别为253,215 nm,轧态钢轨的疲劳断口呈现解理台阶与河流花样形貌,且河流花样趋于合并,而热处理态钢轨的疲劳断口呈现大量的解理台阶及较多的微裂纹和撕裂棱,河流花样以支流为主;热处理态钢轨的疲劳裂纹扩展速率远低于轧态,到达裂纹失稳阶段也较滞后;轧态和热处理态钢轨的疲劳裂纹扩展都是以穿晶断裂为主的穿晶断裂和沿晶断裂混合扩展方式进行,轧态和热处理态钢轨的珠光体片层间距分别为272,148 nm,其中热处理态钢轨的珠光体片层细密且方向多样,存在显著的珠光体团簇,裂纹扩展轨迹中出现较多的分支裂纹和裂纹桥接现象,对扩展起到阻碍作用,是热处理态钢轨抗疲劳裂纹扩展能力优于轧态的重要原因。     

A theory for fatigue crack propagation

A new continuum mechanics model is developed for predicting fatigue crack propagation rates using a fracture mechanics approach. The model demonstrates the critical dependence of fatigue crack growth on the fatigue ductility exponent, the fatigue ductility coefficient, the elastic modulus and the fracture toughness; it is related to the stress intensity range, implying that fatigue crack growth is critically dependent upon the condition at the tip of the crack.Four materials are studied, namely a creep resistant stainless steels, FV535; a $\text{2}\text{1}\text{2}$ per cent nickel-chromium-molybdenum direct hardening steel, 2S96D; a nickel base heat resisting alloy INCO 901; and a ferrous alloy containing titanium carbide in a medium alloy tool steel matrix, known as Ferrotic C.The developed model provides a means of predicting crack propagation rates based on mechanical properties, and the simplified model provides a fundamental basis for a more general form of the Paris relationship.     

Some aspects of fatigue crack propagation

The models of fatigue crack propagation proposed by Forman et al. and Roberts and Erdogan were studied in this paper. By applying these models to existing data in the literature for thin 2024-T3 and 7075-T6 aluminum plates subjected to fluctuating tensile loads, it was found that both models gave comparable results when one considered just a gross correlation of the experimental data. By modifying Forman's model to incorporate the ideas of Roberts and Erdogan, a model was produced which appeared to be a more rational basis for studying the problem of fatigue crack propagation in thin plates and shells subjected to tensile loads, bending loads, or a combination of both. This fact was demonstrated for the case of thin plates subjected to fluctuating bending loads and for the case of thin cylindrical shells subjected to fluctuating internal pressure.