Effect of grain size on slow fatigue crack propagation and plastic deformation near crack tip

Fatigue crack growth and its threshold are investigated at a stress ratio of 0.5 for the three-point bend specimen made of Austenitic stainless steel. The effect of grain size on the crack tip plastic deformation is investigated. The results show that the threshold value Δk_th increases linearly with the square root of grain size d and the growth rate is slower for materials with larger grain size. The plastic zone size and ratio for different grain sizes are different at the threshold. The maximum stress intensity factor is k_max and σ_ys is the yield strength. At the same time, the characteristics of the plastic deformation development is discontinuous and anti-symmetric as the growth rate is increased from 2·10^—8 to 10⁻⁷ mm/cycle.A dimensionless relation of the form for collating fatigue crack starting growth data is proposed in which Δk_th represents the stress intensity factor range at the threshold. Based on experimental results, this relation attains the value of 0.6 for a fatigue crack to start growth in the Austenitic stainless steel investigated in this work. Metallurgical examinations were also carried out to show a transgranular shear mode of cyclic cleavage and plastic shear.     

Effect of stress ratio and specimen thickness on fatigue crack growth of CK45 steel

Presented are the effect of stress ratio and thickness on the fatigue crack growth rate of CK45 steel according to DIN 17200. Test results are obtained for constant amplitude load in tension with three stress ratios of R=0, 0.2 and 0.4 and three specimen thicknesses of B=6, 12 and 24 mm. Microgauge crack opening values were used to calculate ΔK_eff values from which the da/dN − ΔK_eff curves are obtained. Crack closure can be applied to explain the influence of mean stress and specimen thickness on the fatigue crack growth rate in the second regime of the two-parameter crack growth rate relation. An empirical model is chosen for calculating the normalized load ratio parameter U as a function of R, B and ΔK and, for correlating the test data.     

Micro/macro-crack growth due to creep–fatigue dependency on time–temperature material behavior

The implicit character of micro-structural degradation is determined by specifying the time history of crack growth caused by creep–fatigue interaction at high temperature. A dual scale micro/macro-equivalent crack growth model is used to illustrate the underlying principle of multiscaling which can be applied equally well to nano/micro. A series of dual scale models can be connected to formulate triple or quadruple scale models. Temperature and time-dependent thermo-mechanical material properties are developed to dictate the design time history of creep–fatigue cracking that can serve as the master curve for health monitoring.In contrast to the conventional procedure of problem/solution approach by specifying the time- and temperature-dependent material properties as a priori, the desired solution is then defined for a class of anticipated loadings. A scheme for matching the loading history with the damage evolution is then obtained. The results depend on the initial crack size and the extent of creep in proportion to fatigue damage. The path dependent nature of damage is demonstrated by showing the range of the pertinent parameters that control the final destruction of the material. A possible scenario of 20 yr of life span for the 38Cr2Mo2VA ultra-high strength steel is used to develop the evolution of the micro-structural degradation. Three micro/macro-parameters μ^*, d^* and σ^* are used to exhibit the time-dependent variation of the material, geometry and load effects. They are necessary to reflect the scale transitory behavior of creep–fatigue damage. Once the algorithm is developed, the material can be tailor made to match the behavior. That is a different life span of the same material would alter the time behavior of μ^*, d^* and σ^* and hence the micro-structural degradation history. The one-to-one correspondence of the material micro-structure degradation history with that of damage by cracking is the essence of path dependency. Numerical results and graphs are obtained to demonstrate how the inherently implicit material micro-structure parameters can be evaluated from the uniaxial bulk material properties at the macroscopic scale.The combined behavior of creep and fatigue can be exhibited by specifying the parameter ξ with reference to the initial defect size a₀. Large ξ (0.90 and 0.85) gives critical crack size a_cr = 11–14 mm (at t < 20 yr) for a₀ about 1.3 mm. For small ξ (0.05 and 0.15), there results critical a_cr = 6–7 mm (at t < 20 yr) for a₀ about 0.7–0.8 mm. The initial crack is estimated to increase its length by an order of magnitude before triggering global to the instability. This also applies ξ ≈ 0.5 where creep interacts severely with fatigue. Fine tuning of a_cr and a₀ can be made to meet the condition oft = 20 yr.Trade off among load, material and geometric parameters are quantified such that the optimum conditions can be determined for the desired life qualified by the initial–final defect sizes. The scenario assumed in this work is indicative of the capability of the methodology. The initial–final defect sizes can be varied by re-designing the time–temperature material specifications. To reiterate, the uniqueness of solution requires the end result to match with the initial conditions for a given problem. This basic requirement has been accomplished by the dual scale micro/macro-crack growth model for creep and fatigue.     

Fatigue crack growth rate in ferrite-martensite dual-phase steel

An empirical study is made on the fatigue crack growth rate in ferrite-martensite dual-phase (FMDP) steel. Particular attention is given to the effect of ferrite content in the range of 24.2% to 41.5% where good fatigue resistance was found at 33.8%. Variations in ferrite content did not affect the crack growth rate da/dN when plotted against the effective stress intensity factor range ΔK_eff which was assumed to follow a linear relation with the crack tip stress intensity factor range ΔK. A high ΔK_eff corresponds to uniformly distributed small size ferrite and martensite. No other appreciable correlation could be ralated to the microstructure morphology of the FMDP steel. The closure stress intensity factor K_cl, however, is affected by the ferrite content with K_cl/Kmax reaching a maximum value of 0.7. In general, crack growth followed the interphase between the martensite and ferrite.Dividing the fatigue crack growth process into Stage I and II where the former would be highly sensitive to changes in ΔK and the latter would increase with ΔK depending on the R = σ_min/σ_max ratio. The same data when correlated with the strain energy density factor range ΔS showed negligible dependence on mean stress or R ratio for Stage I crack growth. A parameter α involving the ratio of ultimate stress to yield stress, percent reduction of area and R is introduced for Stage II crack growth so that the da/dN data for different R would collapse onto a single curve with a narrow scatter band when plotted against αΔS.     

Piezomagnetic and piezoelectric poling effects on mode I and II crack initiation behavior of magnetoelectroelastic materials

The ferrite and ferroelectric phase of magnetoelectroelastic (MEE) material can be selected and processed to control the macroscopic behavior of electron devices using continuum mechanics models. Once macro- and/or microdefects appear, the highly intensified magnetic and electric energy localization could alter the response significantly to change the design performance. Alignment of poling directions of piezomagnetic and piezoelectric materials can add to the complexity of the MEE material behavior to which this study will be concerned with.Appropriate balance of distortional and dilatational energy density is no longer obvious when a material possesses anisotropy and/or nonhomogeneity. An excess of the former could result in unwanted geometric change while the latter may lead to unexpected fracture initiation. Such information can be evaluated quantitatively from the stationary values of the energy density function dW/dV. The maxima and minima have been known to coincide, respectively, with possible locations of permanent shape change and crack initiation regardless of material and loading type. The direction of poling with respect to a line crack and the material microstructure described by the constitutive coefficients will be specified explicitly with reference to the applied magnetic field, electric field and mechanical stress, both normal and shear. The crack initiation load and direction could be predicted by finding the direction for which the volume change is the largest. In contrast to intuition, change in poling directions can influence the cracking behavior of MEE dramatically. This will be demonstrated by the numerical results for the BaTiO₃–CoFe₂O₄ composite having different volume fractions where BaTiO₃ and CoFe₂O₄ are, respectively, the inclusion and matrix.To be emphasized is that mode I and II crack behavior will not have the same definition as that in classical fracture mechanics where load and crack extension symmetry would coincide. A striking result is found for a mode II crack. By keeping the magnetic poling fixed, a reversal of electric poling changed the crack initiation angle from θ₀=+80° to θ₀=−80° using the line extending ahead of the crack as the reference. This effect is also sensitive to the distance from the crack tip. Displayed and discussed are results for r/a=10⁻⁴ and 10⁻¹. Because the theory of magnetoelectroelasticity used in the analysis is based on the assumption of equilibrium where the influence of material microstructure is homogenized, the local space and temporal effects must be interpreted accordingly. Among them are the maximum values of (dW/dV)_max and (dW/dV)_min which refer to as possible sites of yielding and fracture. Since time and size are homogenized, it is implicitly understood that there is more time for yielding as compared to fracture being a more sudden process. This renders a higher dW/dV in contrast to that for fracture. Put it differently, a lower dW/dV with a shorter time for release could be more detrimental.     

Crack repair using an elastic filler

The effect of repairing a crack in an elastic body using an elastic filler is examined in terms of the stress intensity levels generated at the crack tip. The effect of the filler is to change the stress field singularity from order 1/r^1/2 to 1/r^(1-λ) where r is the distance from the crack tip, and λ is the solution to a simple transcendental equation. The singularity power (1-λ) varies from (the unfilled crack limit) to 1 (the fully repaired crack), depending primarily on the scaled shear modulus ratio γ_r defined by G₂/G₁=γ_rε, where 2πε is the (small) crack angle, and the indices (1, 2) refer to base and filler material properties, respectively. The fully repaired limit is effectively reached for γ_r≈10, so that fillers with surprisingly small shear modulus ratios can be effectively used to repair cracks. This fits in with observations in the mining industry, where materials with G₂/G₁ of the order of 10^-3 have been found to be effective for stabilizing the walls of tunnels. The results are also relevant for the repair of cracks in thin elastic sheets.     

Influence of mean stress on the fatigue crack growth characreristics of CrlMo steel tube at elevated temperature

The fatigue crack growth characteristics of CrlMo steel have been investigated at 861 K over the R-ratio range 0.1–0.7 utilising a dwell time of 10 min. at maximum load. All tests were conducted under load control in a laboratory air environment. It was established that the R-ratio significantly affected the fatigue crack extension behaviour inasmuch that with increasing R-ratio, the critical ΔK level for the onset of creep fatigue interactive growth, ΔK^IG, decreased from 20 to 7 MPa√m and the threshold stress intensity, ΔK_th, decreased from 9 to about 3 MPa√m. At intermediate ΔK levels, i.e. between ΔK_th and ΔK^IG, the fatigue crack extension rates, for all R-ratio values, resided on or slightly below the CTOD line, which represents the upper bound for contrnuum controlled fatigue crack growth. Creep fatigue interactive growth was typified by crack extension rates that reside above the CTOD line with a ΔK^IG dependence; the attainment of some critical creep condition or crack linkage condition which causes the abrupt change in crack extension behaviour at ΔK^IG; and crack extension occurs almost exclusively in an intergranular manner. The R-ratio and ΔK^IG followed a linear relation. A literature review concerning the effect of temperature on the threshold fatigue crack growth characteristics of low alloy ferritic steels demonstrated powerful effects of temperature; the magnitude of these effects, however, were dependent upon the testing temperature regime and R-ratio level. The effect of R-ratio on ΔK_th was greatest at temperatures >400°C, significant at ambient temperatures and least in the temperature range 90°C to <300°C. The relationship between temperature and ΔK_th, at a given R-ratio, exhibited a through and a minimum ΔK_th value was observed in the temperature range 200–250°C. The magnitude of the temperature effects on ΔK_th decreased with increasing R-ratio. Such effects of temperature and R-ratio on ΔK_th was reasonably explained in terms of crack closure effects. Finally, the present elevated temperature fatigue crack growth data exhibited massive crack extension enhancement values when compared to ambient near-threshold fatigue crack growth data for CrlMo steel. Such large enhancement values were the combined effects of temperature (environment) and frequency.     

The effect of contact stress intensity factors on fatigue crack propagation

Using the technique of Dimensional Analysis the phenomenon of crack closure is modelled using the concept of a contact stress intensity factor Kc. For constant amplitude loading, a simple expression, Kc_max = g(R) ΔK, is obtained without making idealized assumptions concerning crack tip behaviour. Further, by assuming that crack closure arises from the interaction of residual plasticity in the wake of the crack and crack tip compressive stresses, the function g(R) is shown to be constant for non-workhardening materials. This implies that any dependency of Kc_max on R must be attributed to the workhardening characteristic of the material. With Kc known, an “effective” stress intensity factor Ke may be calculated and incorporated into a crack growth law of the form da/dn = f(ΔKe). From analysis, it can be deduced that for a workhardening material, Kc_max will decrease as R increases and the effective stress intensity factor will increase. This means that the fatigue crack propagation rate will increase with R, in accordance with experimental observations.     

Grain boundary oxidation and fatigue crack growth at elevated temperatures

Fatigue crack growth rate at elevated temperatures can be accelerated by grain boundary oxidation. Grain boundary oxidation kinetics and statistical distribution of grain boundary oxide penetration depth were studied.At a constant ΔK-level and at a constant test temperature, fatigue crack growth rate, da/dN, is a function of cyclic frequency, ν. A fatigue crack growth model of intermittent micro-ruptures of grain boundary oxide is constructed. The model is consustent with the experimental observations that, in the low frequency region, da/dN is inversely proportional to ν, and fatigue crack growth is intergranular.     

Prediction of mixed-mode fracture based on an elasto–plastic energy balance criterion

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. This fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, however, the G _max criterion has been modified in order to accommodate the consideration of plastic strain energy. This modified criterion is extended to study the fatigue crack growth characteristics of mixed-mode cracks. To predict crack propagation due to fatigue loads, a new elasto–plastic energy model is presented. This new model includes the effects of material properties such as strain hardening exponent n, yield strength σ _y , and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

Isoparametric shear spring element applied to crack patching and instability

In this work the isoparametric shear spring element is applied to the stress and energy analysis of a center-crack panel reinforced by a rectangular patch. In this model, only transverse shears are assumed to prevail in the adhesive layer. The stresses and crack-tip stress intensity factors are obtained for reinforcement on both sides and one side of the panel, and are found to be in agreement with those obtained by previous authors using the triangular shear spring element.Crack stability that tends to vary with patch thickness is determined from the local and global maximum of the minimum strain energy density function denoted, respectively, as [(dW/dV)_min^max]_L at point L and [(dW/dV)_min^max]_G at point G. The distance l between L and G gives the prospective path of subcritical crack growth and its magnitude provides a measure of the degree of crack stability. A patched panel with small l tends to be more stable than that with large l. By increasing the patch thickness beyond a certain value, l can be contained within the patch such that failure, if initiated, will be highly localized. Such a behavior is exhibited. Numerical results are provided to support the foregoing conclusion.     

Dislocation pile-up model of fatigue thresholds for 2024- and 7075-alike aluminium alloys

Two parameters, K_max^* and δK_th^*, are presented to describe fatigue threshold behaviour and damage under any load ratio without invoking crack closure. Modelled are two fatigue thresholds that are coherently related to fatigue limit δσ_FL; they predict the fundamental threshold curves for aluminium alloys. By using a continuous configuration of dislocations in pile-up, fatigue limit behaviour is simulated as pile-up of dislocations against grain boundaries. A fatigue limit is determined in terms of a critical condition at which a fictitious microcrack associated with the pile-up corresponds to the onset of propagation. These two fatigue thresholds are attainable as the local stresses at the crack front approaching the fatigue limit. Microstructure is incorporated in the model to account for the effect on threshold behaviour. As a result, two fatigue threshold criteria are required. Quantitative assessment of the two criteria requires only knowledge of the conventional material properties in conjunction with microstructure. The micromechanical modelling exhibits a strong dependence of fatigue thresholds upon local microstructure.     

Fatigue crack growth of cable steel wires in a suspension bridge: Multiscaling and mesoscopic fracture mechanics

Intrinsically, fatigue failure problem is a typical multiscale problem because a fatigue failure process deals with the fatigue crack growth from microscale to macroscale that passes two different scales. Both the microscopic and macroscopic effects in geometry and material property would affect the fatigue behaviors of structural components. Classical continuum mechanics has inability to treat such a multiscale problem since it excludes the scale effect from the beginning by introducing the continuity and homogeneity assumptions which blot out the discontinuity and inhomogeneity of materials at the microscopic scale. The main obstacle here is the link between the microscopic and macroscopic scale. It has to divide a continuous fatigue process into two parts which are analyzed respectively by different approaches. The first is so called as the fatigue crack initiation period and the second as the fatigue crack propagation period. Now the problem can be solved by application of the mesoscopic fracture mechanics theories developed in the recent years which focus on the link between different scales such as nano-, micro- and macro-scale.On the physical background of the problem, a restraining stress zone that can describe the material damaging process from micro to macro is then introduced and a macro/micro dual scale edge crack model is thus established. The expression of the macro/micro dual scale strain energy density factor is obtained which serves as a governing quantity for the fatigue crack growth. A multiscaling formulation for the fatigue crack growth is systematically developed. This is a main contribution to the fundamental theories for fatigue problem in this work. There prevail three basic parameters μ^∗, σ^∗ and d^∗ in the proposed approach. They can take both the microscopic and macroscopic factors in geometry and material property into account. Note that μ^∗, σ^∗ and d^∗ stand respectively for the ratio of microscopic to macroscopic shear modulus, the ratio of restraining stress to applied stress and the ratio of microvoid size ahead of crack tip to the characteristic length of material microstructure.To illustrate the proposed multiscale approach, Hangzhou Jiangdong Bridge is selected to perform the numerical computations. The bridge locates at Hangzhou, the capital of Zhejiang Province of China. It is a self-anchored suspension bridge on the Qiantang River. The cables are made of 109 parallel steel wires in the diameter of 7 mm. Cable forces are calculated by finite element method in the service period with and without traffic load. Two parameters α and β are introduced to account for the additional tightening and loosening effects of cables in two different ways. The fatigue crack growth rate coefficient C₀ is determined from the fatigue experimental result. It can be concluded from numerical results that the size of initial microscopic defects is a dominant factor for the fatigue life of steel wires. In general, the tightening effect of cables would decrease the fatigue life while the loosening effect would impede the fatigue crack growth. However, the result can be reversed in some particular conditions. Moreover, the different evolution modes of three basic parameters μ^∗, σ^∗ and d^∗ actually have the different influences on the fatigue crack growth behavior of steel wires. Finally the methodology developed in this work can apply to all cracking-induced failure problems of polycrystal materials, not only fatigue, but also creep rupture and cracking under both static and dynamic load and so on.     

Reverse temper embrittlement — environmentally assisted cracking interactions in ferritic low alloy steels

Assessed in this study are the relationships that were recorded between the magnitude of the environmental assisted crack (EAC), growth contribution and the fatigue fractographic details observed in steels under ambient conditions. Four discrete static failure modes were observed on the fatigue surfaces; they are primarily transgranular cleavage and intergranular decohesion with a few instances of fan-shaped growth and macrofacet formation. All static failure modes could be explained by Beacham's model for hydrogen assisted cracking. It was established that the extent of EAC growth was uniquely related to the amount of static failure mode and that the relationship agreed well with the predictions of Congleton's model for EAC growth expressed in terms of the ratio of crack growth rate (da/dN)^* in environments of humid air and saline solution to da/dN in dry air for a given stress intensity factor range ΔK.     

Crack size and speed interaction characteristics at micro-, meso- and macro-scale

The motivation to examine physical events at even smaller size scale arises from the development of use-specific materials where information transfer from one micro- or macro-element to another could be pre-assigned. There is the growing belief that the cumulated macroscopic experiences could be related to those at the lower size scales. Otherwise, there serves little purpose to examine material behavior at the different scale levels. Size scale, however, is intimately associated with time, not to mention temperature. As the size and time scales are shifted, different physical events may be identified. Dislocations with the movements of atoms, shear and rotation of clusters of molecules with inhomogeneity of polycrystals; and yielding/fracture with bulk properties of continuum specimens. Piecemeal results at the different scale levels are vulnerable to the possibility that they may be incompatible. The attention should therefore be focused on a single formulation that has the characteristics of multiscaling in size and time. The fact that the task may be overwhelmingly difficult cannot be used as an excuse for ignoring the fundamental aspects of the problem.Local nonlinearity is smeared into a small zone ahead of the crack. A “restrain stress” is introduced to also account for cracking at the meso-scale.The major emphasis is placed on developing a model that could exhibit the evolution characteristics of change in cracking behavior due to size and speed. Material inhomogeneity is assumed to favor self-similar crack growth although this may not always be the case. For relatively high restrain stress, the possible nucleation of micro-, meso- and macro-crack can be distinguished near the crack tip region. This distinction quickly disappears after a small distance after which scaling is no longer possible. This character prevails for Mode I and II cracking at different speeds. Special efforts are made to confine discussions within the framework of assumed conditions. To be kept in mind are the words of Isaac Newton in the Fourth Regula Philosophandi:

“Men are often led into error by the love of simplicity which disposes us to reduce things to few principles, and to conceive a greater simplicity in nature than there really is … We may learn something of the way in which nature operates from fact and observation; but if we conclude that it operates in such a manner, only because to our understanding that operates to be the best and simplest manner, we shall always go wrong.”––Isaac Newton

Fatigue crack extension behaviour in porous plasma spray 80%Ni---20%Cr material: The influence of R-ratio

This paper attempts to describe the fatigue crack growth response of a plasma spray 80%---20%Cr material, utilised in the corrosion protection of engineering components, whose microstructure consisted of (i) an austenitic matrix, (ii) a secondary dispersion of a chromite non-metallic inclusion phase and (iii) regions of closed and connected porosity.It was demonstrated that little or no effect of R-ratio was observed on the threshold stress intensity range ΔK_th, which was attributed to both the materials fine to intermediate grain size and probable plain stress testing conditions which significantly decrease crack closure effects. At intermediate fatigue crack growth rates high ratio results were an order of magnitude faster than the low R-ratio data. This was the result of the high R-ratio case seeking out more regions of porosity which then increased the local ΔK on the remaining ligaments leading to accelerated crack growth rates.Porosity was shown to significantly decrease the value of ΔK_th and the extent of porosity observed on fatigue fracture surfaces increased with ΔK level and was well in excess of that of 5% recorded by metallography. Hence the growing fatigue crack preferentially sought out regions of porosity as they represented locations of low fracture energy.     

Analytical and experimental evaluations of the influence of fracture surface roughness,its sliding actions and the associated plasticity on fatigue crack propagation

An investigation of fatigue crack propagation in rectangular AM60B magnesium alloy plates containing an inclined through crack is presented in this paper. The behavior of fatigue crack growth in the alloy is influenced by the fracture surface roughness. Therefore, in the present investigation, a new model is developed for estimating the magnitude of the frictional stress intensity factor, k_f, arising from the mismatch of fracture surface roughness during in-plane shear. Based on the concept of k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, the proposed model is applied to predict crack growth due to fatigue loads. Experiments for verifying the theoretical predictions were also conducted. The results obtained are compared with those predicted using other employed mixed mode fracture criteria and the experimental data.     

Experimental analysis of an arbitrarily inclined semiinfinite crack terminated at the bimaterial interface

In this paper, the digital photoelastic technique was employed to investigate the effect of different material combinations and different crack inclination angles on the stress-intensity factors (SIFs). To produce a true bimaterial plate, the two component materials were naturally adhered together by a special casting procedure. The experimental results show that dimensionless combined SIF increases with increasingG ₁/G ₂ (or crack inclination angles) for different crack inclination angles (orG ₁/G ₂'s).     

Ultrasonic evaluation of fatigue crack growth of high strength steel at ambient temperature and below

By means of an ultrasonic testing device, the crack length in compact tension specimens is monitored. Four ultrasonic probes are used to cover the region of crack extension by transmission waves. The echo of the crack is amplified during fatigue crack propagation. By a knowledge of the initial crack length after precracking and the critical crack length, the alteration of the ultrasonic echo provides the information for determining the intermediate crack length which can be used to calculate the stress intensity range ΔK with respect to the elapsed cycles and the crack growth rate, da/dN.