Mixed mode fatigue crack growth with a sudden change in loading direction

With a sudden change in the maximum load level, there will be a corresponding change in the crack driving force regardless of whether the load is applied monotonically or cyclically. The effective strain energy density factor range ΔS_p,eff has been used to correlate mixed mode fatigue crack propagation where the crack growth direction is not known as an a priori. Examined in this work is a sudden change of load direction on fatigue crack growth while the load level remains unchanged. Yielding is assumed to be localized near the crack tip such that the crack growth behavior can be described adequately by the elastic stress field. Under the conditions investigated, minimal change on crack growth rates is observed. No firm conclusion could be drawn on deviation of crack path for the case considered.     

Evaluation of crack initiation angle under mixed mode loading at diverse strain rates

Crack initiation angle, under mixed mode loading at several strain rates, is analysed using an experimental–numerical approach. The physical phenomenon for the problem at hand is influenced by the local and global conditions. One of such factors is the strain rate at the crack tip. For this purpose, PMMA plates with centred angled cracks under mixed mode loading were tested. The strain rate at the neighbourhood of the crack tip before crack propagation was evaluated. Considering that this material is strain rate sensitive, the numerical models were calibrated with the modulus of elasticity measured in tension tests at the observed strain rates. Numerical evaluations were performed with the finite element method in conjunction with the volume energy density criterion. An improvement in the evaluation of the crack propagation angle was observed. In order to complete the analysis, the crack initiation angle was also evaluated with the strain energy density factor S, considering the mechanical properties of PMMA, as evaluated at the observed strain rates, and the stress intensity factors k₁ and k₂. Results are in agreement with those observed experimentally.     

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.     

Stress intensity factor range and propagation mode of surface cracks under rolling–sliding contact

Finite element analyses were conducted in order to evaluate the mode I and mode II stress intensity factors for inclined edge cracks under cyclic contact load under rolling and rolling–sliding condition. The SIF range depends on crack orientation, crack length to Hertzian contact zone half-width ratio, friction between the crack faces and friction on the contact surface. The results were combined in two compact functions that determine the ΔK_I and ΔK_II values. The crack propagation mode and direction were investigated using both the maximum stress criterion and the minimum strain energy density criterion. The results are displayed in graph form, which allows a fast evaluation of the crack growth condition.     

Influence of load amplitude and uniaxial tensile properties on fatigue crack growth

The rate at which energy is accumulated within a unit volume of material in fatigue is assumed to depend not only on load-time history but also on the specimen size and geometry in addition to material type. A threshold level for the hysteresis strain energy density function accumulated in the material is used for predicting macrocrack growth. This is accomplished by application of the incremental theory of plasticity for each increment of crack growth. The accumulated hysteresis strain energy density factor ΔS to crack growth increment Δa ratio is found to be constant for fixed specimen size and loading, i.e., . Results are obtained for the cylindrical bar specimens with a penny-shaped defect at the center subjected to a constant amplitude and frequency loading. The resistance curves in the ΔS versus Δa plot are parallel lines as specimen size is altered. This information provides a rational means for predicting the influence of specimen size on fatigue lifetime.The results are also compared with those found for geometrically similar plate specimens with line cracks. Cylinder bar specimens of the same material are found to sustain more load cycles prior to catastrophic failure.     

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.     

Damage accumulation and crack growth in bilinear materials with softening: Application of strain energy density theory

A pseudo-elastic damage-accumulation model is developed by application of the strain energy density theory. The three-point bending specimen is analyzed to illustrate the crack growth characteristics according to a linear elastic softening constitutive law that is typical of concrete materials. Damage accumulation is accounted for by the decrease of elastic modulus and fracture toughness. Both of these effects are assessed by means of the strain energy density functions in the elements around a slowly moving crack. The rate of change of the strain energy density factor S with crack growth as expressed by the relation dS/da = constant is shown to describe the failure behavior of concrete. Results are obtained for different loading steps that yield different slopes of lines in an S versus a (crack length) plot. The lines rotate about the common intersect in an anti-clockwise direction as the load steps are increased. The intersect shifts upward according to increase in the specimen size. In this way, the combined interaction of material properties, load steps and specimen geometry and size are easily analyzed in terms of the failure mode or behavior that can change from the very brittle to the ductile involving stable crack growth. An upper limit on specimen or structural size is established beyond which stable crack growth ceases to occur and failure corresponds to unstable crack propagation or catastrophic fracture. The parameters that control the failure mode are the threshold values of the strain energy density function (dW/dV)_c and the strain energy density factor S_c.     

Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials

In this paper, an investigation of fatigue crack propagation in rectangular plates containing an inclined surface crack is presented. A criterion for the three-dimensional stress state is proposed to predict fatigue crack initiation angles. It is assumed that the direction of crack initiation coincides with the direction of the minimum radius of the plastic zone defined by the von Mises yield criterion. The maximum energy release rate criterion, i.e., G_max criterion, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the consideration of the plastic strain energy. Subsequently, this concept is applied to predict crack growth due to fatigue loads. Experiments for checking the theoretical predictions from the proposed criterion have been conducted. The results obtained are compared with those obtained using the commonly employed fracture criteria and the test data.     

Influence of indenter geometry on half-plane with edge crack subjected to fretting condition

An edge crack is analyzed to study fretting failure. A flat punch with rounded corners and a half-plane are regarded as an indenter and a substrate, respectively. Plane strain condition is considered. Contact shear traction in the case of partial slip is evaluated numerically. It is assumed that an initial crack is extended to the point of minimum strain energy density in the half-plane from the trailing edge of contact. Dislocation density function method is used to evaluate K_I and K_II. The variations of K_I and K_II during crack growth are examined in the case of indentation by a punch with different ratio of the flat region (l) to the punch width (L). Sih's minimum strain energy density theory [1] is also applied to predict the propagation direction of the initial crack. The direction evaluated is similar to that found in the experiment. Stress intensity factor ranges (ΔK_I and ΔK_II) are examined during cyclic shear on the contact. For the design of contacting bodies, a suggestible geometry of punch for alleviating cracking failure is studied.     

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.     

Strain energy density prediction of crack initiation and direction in cracked T-beams and pipes

In this paper, the S-theory is applied to determine crack initiation and direction for cracked T-beams and circumferentially cracked pipes. It makes use of a parameter called strain energy density factor, S, which is a function of the stress intensity factors. The strain energy density theory provides a more general treatment of fracture mechanics problems by virtue of its ability in describing the multiscale feature of material damage and in dealing with mixed mode crack propagation problem. A simple method for obtaining approximate stress intensity factors is also applied. It takes into account the elastic crack tip stress singularity while using the elementary beam theory. Some basic loading conditions in beams and pipes are studied.     

Effect of humidity and R-ratio on the near threshold fatigue crack growth of two granular bainitic microstructures

The present report has shown that in ferrite-martensite microstructures, the relative humidity of an air environment can affect both the near threshold fatigue crack growth behaviour and the intermediate Stage II fatigue characteristics. The magnitude of the threshold stress intensity, ΔK_th, was not affected by relative humidity and the significant effect of R-ratio on ΔK_th was suitably demonstrated.The relative humidity affected the nature of both the subcritical static failure mode and the final stage III static failure mode. A direct relationship between the degree of fatigue crack growth enhancement and the extent of transgranular cleavage was evidenced.     

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.     

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.     

Fatigue crack growth studies in rail steels and associated weld metal

Fatigue crack growth studies in rail steels and associated weld metal have shown that (a) deformed rail steel exhibited fatigue crack growth rates that are slightly faster than undeformed rail steel and (b) weld metal growth data are appreciably faster than rail steel growth results and exhibit growth rate plateaux that reside above the upper bound reported for rail steel fatigue crack growth.In rail steel microstructures at low ΔK levels fatigue crack extension occurred by a ductile striated growth mechanism. However at K_max values approaching 40 MPa √m transgranular cleavage facets initially formed and their incidence increased with K_max until final fast fracture. The average cleavage facet size agreed well with pearlite nodule dimensions of 60–100 μm.The weld metal microstructure was much coarser than the rail steel and contained highly directional columnar grain growth. At all ΔK levels the dominant fracture mode was transgranular cleavage containing small isolated regions of ductile striated fatigue crack growth. The cleavage facet size varied from 150 to 600 μm; such a large variation was explained by the fact that in general crack extension tended to occur in association with the proeutectoid ferrite phase.     

Arrest characteristics of an impacted crack dissipating plastic energy

When a structural member is accidentally struck, an initial defect may grow and then arrest. An estimate of its size increase is made by considering the geometry of a centrally cracked panel subjected to a step function load in time. Two load amplitudes differing by a factor of five are considered. Under impact, the crack accelerates and then decelerates prior to arrest. The dynamic characteristics depend on the interaction of the elastic-plastic stress waves intervening with the physical boundaries. This effect is assessed quantitatively by computing for the energy stored in a unit volume of material and by incorporating sliding nodes in the finite element method. The energy dissipated by plastic deformation must be accounted for as it is no longer available for creating new macrocrack surface. Obtained are the near tip normal stresses that are found to change from compression to tension. Their magnitude is considerably larger than the corresponding static values. Increase in crack length changes from 0.87% to 20.6% when the magnitude of the impact load is raised five times. The rate of change of the strain energy density factor ΔS with crack growth Δa is found to be governed by the condition ΔS/Δa = const. during loading while dynamic relaxation corresponded to a nonlinear behavior. The physical implication of this remains to be clarified in view of the fact that plasticity theory may not adequately explain the near tip crack behavior.     

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.     

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.     

Fatigue life prediction of out-of-plane gusset welded joints using strain energy density factor approach

Fatigue growth behavior of out-of-plane gusset welded joints is studied using the strain energy density factor approach. Fatigue tests on two types of specimens with curvatures of ρ = 0 and ρ = 30 were performed in order to estimate fatigue strength under tension. Fatigue crack growth analysis is carried out to show the effects of initial crack shape, initial crack length and stress ratio. Fatigue crack growth parameters were obtained from crack growth curves assuming constant crack shapes. The results of analysis for the assumed crack shapes agreed well with the experimental data. Fatigue propagation life of the ρ = 30 specimen was larger than that of the ρ = 0 specimen.