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

Fatigue crack growth behavior of in-plane gusset welded joints is studied using the strain energy density factor approach. Fatigue tests were performed in order to estimate fatigue strength under tension. Fatigue crack growth analysis was carried out to show the effects of the initial crack shape, the initial crack length, and the stress ratio on the crack types of in-plane gusset welded joints. The assumed crack types were edge crack, semi-elliptical crack, and corner crack. Fatigue crack growth parameters were obtained from crack growth curves assuming constant crack shapes for the given crack types. The results of analysis for the assumed crack types agreed well with the experimental data. The fatigue life did not change as initial crack shape varied for a given initial crack length.     

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 weld size on fatigue crack growth behaviour of cruciform joints by strain energy density factor approach

The effect of weld size on fatigue crack growth behaviour of cruciform joints containing lack of penetration defect has been analysed by using the strain energy density factor concept. Load carrying cruciform joints were fabricated from ASTM 517‘F' grade steel. Fatigue crack growth experiments were carried out in a mechanical resonance vertical pulsator (SCHENCK 200 kN capacity) with a frequency of 30 Hz under constant amplitude loading (R=0). It was found that the crack growth rates were relatively lower in the larger welds fabricated by multipass welding technique than the smaller welds fabricated by the single pass welding technique.     

Kinetics of microcrack blunting ahead of macrocrack approaching shear wave speed

The fracturing of glass and tearing of rubber both involve the separation of material but their crack growth behavior can be quite different, particularly with reference to the distance of separation of the adjacent planes of material and the speed at which they separate. Relatively speaking, the former and the latter are recognized, respectively, to be fast and slow under normal conditions. Moreover, the crack tip radius of curvature in glass can be very sharp while that in the rubber can be very blunt. These changes in the geometric features of the crack or defect, however, have not been incorporated into the modeling of running cracks because the mathematical treatment makes use of the Galilean transformation where the crack opening distance or the change in the radius of curvature of the crack does not enter into the solution. Change in crack speed is accounted for only via the modulus of elasticity and mass density. For this simple reason, many of the dynamic features of the running crack have remained unexplained although speculations are not lacking. To begin with, the process of energy dissipation due to separation is affected by the microstructure of the material that distinguishes polycrystalline from amorphous form. Energy extracted from macroscopic reaches of a solid will travel to the atomic or smaller regions at different speeds at a given instance. It is not clear how many of the succeeding size scales should be included within a given time interval for an accurate prediction of the macroscopic dynamic crack characteristics. The minimum requirement would therefore necessitate the simultaneous treatment of two scales at the same time. This means that the analysis should capture the change in the macroscopic and microscopic features of a defect as it propagates. The discussion for a dual scale model has been invoked only very recently for a stationary crack. The objective of this work is to extend this effort to a crack running at constant speed beyond that of Rayleigh wave. Developed is a dual scale moving crack model containing microscopic damage ahead of a macroscopic crack with a gradual transition. This transitory region is referred to as the mesoscopic zone where the tractions prevail on the damaged portion of the material ahead of the original crack known as the restraining stresses, the magnitude of which depends on the geometry, material and loading. This damaged or restraining zone is not assumed arbitrarily nor assumed to be intrinsically a constant in the cohesive stress approach; it is determined for each step of crack advancement. For the range of micronotch bluntness with 0 < β < 30° and 0.2 σ_∞/σ₀ 0.5, there prevails a nearly constant restraining zone size as the crack approaches the shear wave speed. Note that β is the half micronotch angle and the applied stress ratio is σ_∞/σ₀ with σ₀ being the maximum of the restraining stress. For σ_∞/σ₀ equal to or less than 0.5, the macrocrack opening displacement COD is nearly constant and starts to decrease more quickly as the crack approaches the shear wave speed. For the present dual scale model where the normalized crack speed v/c_s increases with decreasing with the one-half microcrack tip angle β. There prevails a limit of crack tip bluntness that corresponds to β 36° and v/c_s 0.15. That is a crack cannot be maintained at a constant speed if the bluntness is increased beyond this limiting value. Such a feature is manifestation of the dependency of the restraining stress on crack velocity and the applied stress or the energy pumped into the system to maintain the crack at a constant velocity. More specifically, the transitory character from macro to micro is being determined as part of the unknown solution. Using the energy density function dW/dV as the indicator, plots are made in terms of the macrodistance ahead of the original crack while the microdefect bluntness can vary depending on the tip geometry. Such a generality has not been considered previously. The macro-dW/dV behavior with distance remains as the inverse r relation yielding a perfect hyperbola for the homogeneous material. This behavior is the same as the stationary crack. The micro-dW/dV relations are expressed in terms of a single undetermined parameter. Its evaluation is beyond the scope of this investigation although the qualitative behavior is expected to be similar to that for the stationary crack. To reiterate, what has been achieved as an objective is a model that accounts for the thickness of a running crack since the surface of separation representing damage at the macroscopic and microscopic scale is different. The transitory behavior from micro to macro is described by the state of affairs in the mesoscopic zone.     

Local weight functions for semi-elliptical surface cracks in finite thickness plates

Weight functions for any local point, 0 < Φ < π/2 along a semi-elliptical surface crack in finite thickness plates were derived from an assumed approximate general weight function and two reference stress intensity factors. The resulting weight functions were verified using available finite element results for two nonlinear stress fields and good agreement was achieved. When used together with weight functions for Φ = 0 and Φ = π/2 the weight functions are suitable for the calculation of stress intensity factors anywhere along the crack front for semi-elliptical surface cracks in complex stress fields with aspect ratios in the range 0 ≤ a/c ≤ 1 and relative depths 0 ≤ a/t ≤ 0.8.     

Limitation on crack speed for a strip-craze model applied to PMMA

A strip-craze model is proposed to study crack propagation in polymers. A nonlinear differential equation is derived to govern the dynamic process of crack propagation. The viscous feature of the material in the craze zone is taken into account by means of an experimentally determined relationship between the craze stress and crack speed. By fitting experimental data of PMMA into the model, some parameters including the strip-craze length are deduced. A non-singular stress is introduced to control the crack propagation with a strip craze at its tip. Variations of the crack length and the crack speed with time are computed and their dependence on the non-singular stress is investigated. For PMMA, three stages of crack propagation are identified in terms of initial non-singular stress σ_ns0. When σ_ns0<60 MPa, the crack speed mm/s and the crack is basically stationary; when 60 <σ_ns0<95 MPa, then mm/s the crack is in slow propagation; when σ_ns0>95 MPa, then mm/s and the crack is in rapid propagation. The proposed model is applicable only in slow crack propagation.     

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.     

Fatigue crack opening stress based on the strip-yield model

The modified strip-yield model based on the Dugdale model and two-dimensional approximate weight function method were utilized to evaluate the effect of in-plane constraint, transverse stress, on the fatigue crack closure. The plastic zone sizes and the crack opening stresses considering transverse stress were calculated for four specimens: single edge-notched tension (SENT) specimen, single edge-notched bend (SENB) specimen, center-cracked tension (CCT) specimen, double edge-notched tension (DENT) specimen under uniaxial loading. And the crack opening behavior of the center-cracked specimen under biaxial loading was also evaluated. Normalized crack opening stresses σ_op/σ_max for four specimens were successfully described by the normalized plastic zone parameter Δω^′_rev/ω^′ considering transverse stress, where Δω^′_rev and ω^′ are the size of the reversed plastic zone at the moment of first crack tip closure and the size of the forward plastic zone for maximum stress, respectively. The normalized plastic zone parameter with transverse stress also was satisfactorily correlated with the behavior of crack closure for CCT specimen under biaxial loading.     

Bifurcation of a running crack in antiplane strain

An elastodynamic explanation of running crack bifurcation is explored. The geometry is a semi-infinite body in a state of antiplane strain, which contains a two-dimensional edge crack. It is assumed that a quasi-static increase of the external loads gives rise to rapid crack propagation at time t = 0, with an arbitrary and time-varying speed, but in the plane of the crack. A short time later the crack is assumed to bifurcate at angles −κπ and +gkπ, and with velocities v. The elastodynamic intensity factors are computed, and the balance of rates of energies is employed to discuss the conditions for bifurcation.     

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.     

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90° and 180° is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress σ^∞ and electric field E^∞ or (σ^∞,E^∞) is replaced by strain ε^∞ and electric displacement D^∞ or (ε^∞,D^∞). Mixed conditions (σ^∞,D^∞) and (ε^∞,E^∞) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E_y^∞,σ_y^∞) for negative E_y^∞ and (D_y^∞,ε_y^∞) for positive D_y^∞ while the mechanical conditions σ_y^∞ or ε_y^∞ are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth.     

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.     

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.     

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.     

Fatigue life prediction of welded cruciform joints using strain energy density factor approach

The influences of two welding processes, namely, shielded metal arc welding (SMAW) and flux cored arc welding (FCAW), on fatigue life of cruciform joints containing lack of penetration (LOP) defects have been analyzed by using the strain energy density factor (SEDF) approach. Load carrying cruciform joints were fabricated from ASTM 517 ‘F’ grade steel. Fatigue crack growth experiments were carried out in a mechanical resonance vertical pulsator (SCHENCK 200 kN capacity) with a frequency of 30 Hz under constant amplitude loading (R=0). It was found that the fatigue lives of the cruciform joints fabricated by SMAW process were relatively higher than the FCAW counterpart. Moreover, fracture mechanics equations have been developed to predict the fatigue life of the cruciform joints fabricated by the above-mentioned two processes.     

Fractal geometry concerned with stable and dynamic fracture mechanics

Fractal modeling of the rugged crack geometry is considered for the stable and dynamic fracture mechanics characterizing the morphology of a fracture surface and the influence of its growth. It is shown that the fractal dimension has a strong influence on the rising of the R-curve in brittle materials. For the unstable Griffith–Mott’s approach or dynamical crack growth the fractal dimension has a strong influence on the velocity limit of the crack growth. It is also shown that the limit of crack velocity lowers with increasing surface ruggedness (higher fractal dimension D = 2 − H) explaining the intangibility of the Rayleigh wave velocity by the cracks.     

Cohesive properties of nickel-alumina interfaces determined via simulation of ductile bridging experiments

A combined experimental and computational study is carried out to characterize a nickel-alumina interface in terms of the two parameter (σ̂, Γ₀) computational cohesive zone (CCZ) model of Tvergaard and Hutchinson. Experiments were performed using a sandwich specimen consisting of a thin nickel foil bonded between two pre-cracked alumina plates. The specimen was loaded in tension with the nickel foil bridging the cracks in the ceramic. Numerical simulations of the experiments were used to extract the parameters for the CCZ model.Effects of various parameters of the CCZ model are investigated and it is found that the most dominant parameter is the interface strength, σ̂. Effects of the residual thermal stresses are also investigated and it is shown that these stresses can enhance the specimen fracture toughness by almost 16%. The parameters for the nickel-alumina interface are found to be σ̂ = 148 MPa and Γ₀ = 11 J m⁻². It is observed that for the foil thicknesses tested, the work of rupture does not vary linearly with the thickness as predicted by many theoretical models. We found that interfaces which are neither too strong nor too weak contribute most to the overall fracture toughness of such a composite. Although the macroscopic loading at the nickel-alumina interface is shear, the failure is primarily tensile due to the thinning that occurs in the metal as it is stretched.     

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.     

Variation of crack-opening stresses in three-dimensions: finite thickness plate

Crack growth and closure behavior of a center cracked finite thickness plate subjected to constant amplitude cyclic load is investigated by means of a three-dimensional elastic-plastic finite-element analysis. Results are obtained for initial half crack length c_i to half plate thickness t ratios of c_i/t = 3.891 and 1.465 which shall be referred to, respectively, as thin and thick plate. A constant amplitude load with R = S_min/S_max = 0.1 and S_max/σ₀ = 0.25 is applied, where S stands for the stress amplitude and σ₀ the effective yield stress. Crack closure for the thinner plate is found to be largest at and near the free plate surface and to decrease toward the interior during the unloading portion of cyclic loading. The closure pattern stabilizes at the interior and exterior regions, respectively, for c_i/t = 3.981 at 0.34S_max and 0.56S_max and for c_i/t = 1.465 at 0.26S_max and 0.46S_max.A load-reduced displacement technique was used to determine crack-opening stresses at specified locations in the plate from the displacements calculated after 7th cycle (using unloading and reloading portions of cyclic loading). All locations were on the plate exterior surface and were located behind the crack tip and at the centerline of the crack. The opening stresses at the specified points as certain percentage of the maximum stress amplitude were obtained.