Cyclic Stress Intensity Factor Research Articles

Fatigue life assessment of notched laminated composites: Experiments and modelling by Finite Fracture Mechanics

In this paper, the coupled Finite Fracture Mechanics criterion is extended to assess the finite fatigue life of orthotropic notched laminated composites. The approach is validated through a comprehensive experimental program conducted on laminated composites under tension-tension cyclic loading conditions with two distinct lay-ups. For a given loading ratio, fatigue tests on plain and cracked specimens are first performed to provide the model inputs, the critical cyclic stress and stress intensity factor amplitudes. Fatigue tests on samples weakened by circular holes of two different radii are then used for blind predictions. Accurate predictions of the number of cycles to failure are achieved without the need for inverse calibration of material properties or deviation from standard testing procedures. Finally, a parametric study is performed to investigate the hole radius effect. It is worth mentioning that the proposed approach is general and can be applied to any notched geometry.

A path‐independent domain integral to characterize fatigue crack propagation by cyclic material forces

AbstractA lot of structures undergoing cyclic loading fail at load values smaller than their ultimate design loads. In the framework of fracture mechanics, the crack propagation process can be separated into three different stages. In the first stage, micro‐cracks propagate and form together a macro‐crack. The macro‐crack propagates stably in the second stage, which is also known as the PARIS' regime. In the third stage, the crack propagates unstably leading to the failure of the structure. The pioneering law characterizing the stable crack growth is PARIS' law. The aforementioned law correlates the crack growth rate to the cyclic stress intensity factor. Unfortunately, the cyclic stress intensity factor is limited to cases where the theory of linear elastic fracture mechanics is applicable. To overcome the limitations of the cyclic stress intensity factor, domain‐integrals evaluated by configurational forces or material forces are used as a fatigue crack growth criterion. However, the aforementioned domain‐integrals are path‐dependent. The aim of the study at hand is to derive a path‐independent domain integral to characterize fatigue crack propagation in elastic‐plastic and linear viscoelastic solids at small strains. First of all, the cyclic material forces are derived using the cyclic free energy. Furthermore, the path‐independence of the cyclic material forces approach is illustrated by numerical examples. Finally, the cyclic material force approach is validated by comparing it to experimental results.

Uniform fatigue damage tolerance assessment for additively manufactured and cast Al-Si alloys: An elastic-plastic fracture mechanical approach

• Influence of additively manufacturing and casting on microstructure and porosity characteristics as well as quasi-static and cyclic stress-strain behavior of Al-Si alloys. • Evaluation of Murakami-Noguchi approach and Shiozawa approach for fatigue limit and lifetime estimation, however, both approaches are not sufficient for AM Al-Si alloys. • Linking J integral (elastic-plastic fracture mechanics) including cyclic stress-strain curve by means of morrow parameter (K’, n’), defect size and position, stress amplitude and stress ratio. • New approach enables a uniform fatigue damage tolerance assessment of fatigue lifetime and limit for additively manufactured alsi10mg alloy as well as die-cast and sand-cast alsi7mg alloy. Lightweight Al-Si alloys are used in the automotive and railway industry due to their excellent strength-to-weight ratio and near-net-shape manufacturing. In additive manufacturing and casting, the near-net-shape manufacturing results in a non-homogenous solidification and cooling of the parts, leading to significant local gradient in microstructural and defect features as well as deformation behavior. In this paper, a uniform damage tolerance assessment was developed based on fracture mechanical approaches of Murakami (√area) and Shiozawa for a reliable defect-based mechanical design of fatigue-loaded structures. The linear-elastic fracture mechanical (LEFM) approaches of Murakami and Shiozawa were used to calculate defect-based lifetime curves, where the cyclic stress intensity factor (ΔK) at the failure-initiating defect (√area) was used to describe the local stress concentration conditions, called K-N curves, instead of nominal stress-based S-N curves. The LEFM-based K-N curves did not allow to describe the fatigue behavior in terms of a unified fatigue design of AM and casting material. Therefore, the cyclic stress-strain (CSS) behavior was used for a plasticity-modification of the LEFM approach by calculating the effective cyclic J integral (ΔJ eff ) to plot J-based K-N curves, called Kj-N curves. This elastic-plastic fracture mechanical (EPFM) approach allowed a uniform fatigue damage tolerance (FDT) assessment of AM and cast Al-Si alloys for the HCF regime by FDT law and fatigue limit by FDT limit. Exemplarily, the FDT limit could be used to predict synthetic Haigh diagrams for specific AM and cast batches and derive process- and service-relevant knowledge on the effect of tensile or compressive mean stress.

Uniform fatigue damage tolerance assessment for additively manufactured and cast Al-Si alloys: size and mean stress effects

• Influence of additively manufacturing and casting on microstructure and porosity characteristics as well as quasi-static and cyclic stress-strain behavior of Al-Si alloys • Linear-elastic (LEFM: Murakami, Murakami-Schijve) and elastic-plastic fracture mechanics (EPFM: Fischer) were used for determination of stress intensity factor at failure-initiating defect and plotted in Shiozawa diagrams • LEFM and EPFM enables to consider the size effect within fatigue damage tolerance assessment • Benchmark of Woehler, Murakami, Murakami-Schijve and Fischer approaches for fatigue damage tolerance assessment regarding size effect and mean stress effect, whereby only Fischer approach enables a uniform fatigue damage tolerance assessment The near-net-shape manufacturing in additive manufactured and cast of Al-Si alloys results in a heterogeneous solidification and cooling of the parts, leading to significant gradients in microstructural and defect features as well as deformation behavior. In this paper, an elastic-plastic fracture mechanical model for uniform fatigue damage tolerance assessment of Al-Si alloys was further qualified and extended for a uniform view of different testing volumes as well as various stress ratios between R = -2…0.5 based on the fracture mechanical approaches of Murakami (√area) and Shiozawa for a reliable main crack defect-based mechanical design of fatigue-loaded structures. The linear-elastic fracture mechanical (LEFM) approaches of Murakami, Murakami-Schijve and Shiozawa were used to calculate defect-based lifetime curves, where the cyclic stress intensity factor (ΔK) at the failure-initiating defect (√area) was used to describe the local stress concentration conditions (so-called K-N curves) instead of nominal stress-based S-N curves. The LEFM-based K-N curves did not allow a unified assessment of fatigue behavior. Therefore, the cyclic stress-strain (CSS) behavior (K’, n’) was used for a plasticity-modification of the LEFM approach based on the elastic-plastic fracture mechanical (EPFM) approach of Fischer by calculating the effective cyclic J integral (ΔJ eff ) to plot J-based K-N curves, called Kj-N curves. This EPFM approach could be qualified for a uniform and reliable fatigue damage tolerance assessment of AM and sand cast Al-Si alloys for the HCF regime.

Enhanced fatigue performance of auxetic honeycomb/substrate structures under thermal cycling

This paper studies the fatigue behavior of auxetic honeycomb layer/substrate structures due to interfacial delamination damage. First, the interfacial thermal stress and cyclic interfacial thermal stress intensity factor (ITSIF) at the free ends of the structure are determined in terms of the thermal shock time, relative density, aspect ratio, and internal cell angle of the honeycomb. Then, a theoretical model for the service life analysis of the structures is established based on Paris's law. The results show that the auxetic structures have a lower ITSIF level and a longer service life compared with those of the non-auxetic structures. Another interesting finding is that a reduction in the relative density of the honeycomb layer will increase the service life of the structures. This confirms the significance of applying auxetic materials in re-usable structures for thermal protection purposes. This research is the first attempt to evaluate the service life of the auxetic honeycomb layer/substrate structures under thermal cycling.

A numerical study of the effects of overload on fatigue crack growth in plastically compressible hardening and hardening-softening-hardening solids

Variation of cyclic loading effect on fatigue crack growth is investigated under plane strain and small scale yielding (SSY) conditions. The material is characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The influence of cyclic stress intensity factor range (), load ratio (R), number of cycles (N), plastic compressibility ( overload and material softening on near tip deformation was studied in detail. For comparison purpose, a few results pertaining to plastically incompressible solids are also considered. The crack tip opening displacement (CTOD), plastic crack growth, deformed crack tip shape, plastic zone shape and size near the crack tip appear to depend significantly on R, N, overload and material softening. The overload produces strong plastic deformation ahead of the crack tip and decreases the fatigue crack growth substantially. Highlights Variation of cyclic loading effect on fatigue crack growth is investigated for materials characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Both plastically compressible and incompressible solids are considered. The influence of cyclic stress intensity factor range (), load ratio (R), number of cycles (N), plastic compressibility ( overload and material softening on near tip deformation was studied in detail. The crack tip opening displacement, plastic crack growth, plastic zone shape and size near the crack tip appear to depend significantly on R, N, overload and material softening. The combination of softening or softening-hardening material response and plastic compressibility leads to major deviations in crack tip blunting and fatigue crack growth from those that prevail for a hardening material.

J-integral analysis: An EDXD and DIC comparative study for a fatigue crack

Synchrotron Energy Dispersive X-ray Diffraction (EDXD) and Digital Image Correlation (DIC) have been applied to map simultaneously the 2D elastic strain and displacement fields of a propagating fatigue crack in the HAZ of a welded Cr2Ni4MoV bainitic steel. The position of the crack tip was tracked via a phase congruency analysis of the displacement field, and also by detection of its cyclic plastic zone. Both types of full field data provided independent inputs to finite element/J-integral analyses that directly quantified the elastic cyclic stress intensity factor range applied to the crack. No knowledge was required of the specimen geometry, crack length or applied loads. The agreement between the two analyses in this controlled study shows that strain mapping by synchrotron EDXD can provide a reliable method to study the crack fields in more complex problems, such as interactions between crack closure, residual stresses and applied loading.

Improvement of sub-critical fatigue crack growth life by nano-structuring of pearlite

Nano-structured pearlitic steels with interlamellar spacing between 60–160 nm have been developed in bulk by austenitizing and subsequent austempering at different temperatures. Their response to subcritical fatigue crack propagation has been studied using a compact-tension specimen while varying interlamellar spacing and maintaining similar prior austenite grain size. Pearlite with the finest lamellae spacing shows the best resistance to fatigue crack propagation sustaining the highest number of cycles and the largest cyclic stress intensity factor (ΔK) before failure. For low ΔK, the crack propagation behaviour was invariant with microstructural features and the crack propagated along softer ferrite phase contained in a single colony of pearlite. At higher cyclic stress intensity factor the finest lamellae pearlite with better strain accommodation ability, smaller CTOD and smaller reversed plastic zone size offered the best resistance to crack growth. Hence, for pearlitic steels, it is possible to enhance the strength as well as fatigue crack growth tolerance by decreasing the inter-lamellar spacing.

On fatigue crack growth in plastically compressible hardening and hardening–softening–hardening solids using crack-tip blunting

In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening–softening–hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range ( $$\Delta \hbox {K})$$ , load ratio (R), number of cycles (N), plastic compressibility ( $${\upalpha })$$ and material softening on near tip deformation, stress–strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on $$\Delta \hbox {K}$$ , R, N, $${\upalpha }$$ and material softening. For both hardening and hardening–softening–hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress–strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study.

A method to numerically predict the loading ratio dependency of long crack propagation rates under cyclic loading

The investigation of cyclic crack propagation rates (CPR) for different loading ratios is very elaborate. A multiscale numerical approach to predict high cycle fatigue (HCF) strength for a ferritic-pearlitic steel has been modified to be applicable for the numerical calculation of its cyclic CPR. The original approach involves a series of numerical and mechanism-based analytical models. Microstructural features of the material are statistically characterized for the generation of synthetically representative volume element (RVE) models of the microstructure. A combined isotropic and kinematic hardening model for crystal plasticity is used to include the microdeformation behavior under cyclic loading in the model. The simulation of cyclic loading with numerous of these statistically equivalent RVEs results in fatigue indicator parameter (FIP) fields which differ from one RVE to the other. With regard to the weakest link theory, only the highest FIP in each RVE is extracted for further fatigue calculations. Theses FIPs are distributed by an extreme value distribution function which can be uniquely described by two parameters. These parameters are used to determine the crack propagation rate. For the comparison of results from experiment and simulations, a concept is proposed which links the globally applied stress amplitude on the RVEs to the cyclic stress intensity factor. The model needs to be calibrated by cyclic CPR results conducted with arbitrarily chosen loading ratios. The validation of the calibrated model is achieved by the prediction and comparison of cyclic CPR at a different loading ratio. The obtained numerical values are in good agreement with the experimental results.

Static mode fatigue crack propagation and generalized stress intensity correlation for fatigue–brittle polymers

Stable fatigue crack propagation is predominantly described by the Paris power law correlation of the crack growth rate with the amplitude cyclic stress intensity. The Paris relationship works well for most ductile materials but does not capture the response for fatigue–brittle materials lacking a cyclic damage mechanism, including ceramics and many polymers. Instead, crack growth rate of fatigue–brittle materials correlates to the peak cyclic stress intensity factor, $$\hbox {K}_{\mathrm{max}}$$ . This work shows that $$\hbox {K}_{\mathrm{max}}$$ correlation of fatigue crack growth is derived directly from static mode crack tip behavior with constant correlation coefficients, and that $$\Delta \hbox {K}$$ correlations are not generally applicable for static mode crack propagation in fatigue–brittle polymers. This derivation predicts load ratio, frequency, and waveform effects, which are included in a general static mode fatigue crack propagation law. Fatigue crack propagation data of a known fatigue–brittle polymer are presented to demonstrate static mode crack propagation behavior correlation with $$\hbox {K}_{\mathrm{max}}$$ with constant parameters.

On the question of predicting the service life of lattice steel structural elements

Present paper deals with the evaluation of fatigue strength at crack initiation stage in the double angle elements of lattice steel structures. The current construction norms for steel structures do not include check for fatigue strength at crack initiation stage, and the calculation of elements endurance limit does not account actual stress-strain state in stress concentration zones, material deformation characteristics in these areas, and strength properties of steel. Experimental study of the stress-strain state kinetics in the areas of gusset plate breakage of double angle welded joints was carried out by strain gauge method. Results were obtained regarding the stress state stabilization under cyclic loading and stress intensity factor. During cyclic tests, maximum load level varied depending on the yield stress. The formation of fatigue cracks was detected in the zone of gusset plate breakage. The curve at fatigue cracks initiation stage, by deformational fracture criteria at 'stiff' loading, was described by the equations presented in the 'Standards of strength calculation of equipment and pipelines of nuclear power plants'. Calculation analysis of results for number of cycles before fatigue crack initiation has been made and good agreement with test results has been obtained.

A crack tip driving force model for mode I crack propagation along linear strength gradient: comparison with the sharp strength gradient case

In the present work, based on the Dugdale criterion, a closed-form theoretical crack tip driving force model of simple expressions was proposed for static and fatigue crack propagation along a linear yield strength gradient (YSG). Qualitative and quantitative analyses of the YSG effect on the crack tip driving force are given. The crack tip driving force depends on the yield strength at the crack tip, the YSG within the plastic zone and the applied load. A positive (or negative) YSG has a shielding (or amplifying) effect on the crack tip driving force. A difference of material-toughening mechanisms between smooth and sharp strength gradient was revealed both theoretically and numerically. In the linear YSG case, when a fatigue crack propagates along the YSG at a constant applied cyclic crack tip stress intensity factor, the cyclic crack tip opening displacement decreases (or increases) when the crack propagates towards a higher (or lower)-strength region; however, the cyclic crack tip stress intensity factor increases, no matter when the crack propagates towards a higher- or lower-strength region. This abnormal phenomenon causes theoretical and experimental challenges for characterizing the smooth strength gradient effect on the crack tip driving force.

Survival-rate analysis of surface treated dental zirconia (Y-TZP) ceramics.

The role of surface preparation, hydrothermal ageing exposure and subsequent cyclic fatigue testing on the biaxial strength of a dental Y-TZP material are investigated. The initial strength and survival rate of a dental Y-TZP ceramic material to fatigue testing was found to be highly dependent upon surface preparation more so than exposure to various hydrothermal exposure conditions. The results suggest that the monoclinic phase generated by either surface damage (especially sandblasting) and to a lesser extent hydrothermal exposure does appear to mitigate strength and fatigue degradation. The results are discussed in terms of the size of defects generated following various surface treatments and the role of cyclic fatigue induced crack growth. A critical ratio is established between the monotonic strength and fatigue stress survival. From the specimens that failed and exhibited reduced strength after cycling a plot of averaged crack growth rate versus max cyclic stress intensity factor was established which closely matched existing results for Y-TZP ceramics.

Influence of Process-Related Defects on the Fatigue Behaviour of Welded Aluminium Joints at Very High Cycles

The influence of geometrical notch and weld defects (pores and incomplete fusions) on the fatigue behaviour at very high numbers of loading cycles is shown for welded samples made of the base material EN AW-5083 and EN AW-6082 and the filler material S Al 5183. High frequency fatigue tests with specimens highest stressed cross-sections representing different welding zones show no endurance limit up to 2·109 load cycles. The weakest link of the weld seams are the geometrical notch and (if present) pores and incomplete fusions in the seam interior and at the surface. Considering weld defects in the filler material as fatigue crack initiating notches, a threshold value for the cyclic stress intensity factor (ΔKmin) of 0.9 MPam was found. Using ΔKmin the fatigue life of the samples is discussed on the basis of stress amplitude, the projected area of the defect and its position. X-ray examinations revealed a good correlation between the failure-relevant defect areas and the overall fatigue life of welded samples.

A two-parameter fracture mechanics model for fatigue crack growth in brittle materials

Nonstandard samples were used to conduct fatigue experiments on brittle material (PMMA) to study the effect of local state of stress at crack tip on fatigue crack propagation rate (FCPR). Results indicated that FCPR cannot be generally characterized by cyclic stress intensity factor range alone and that a second parameter representing the influence of K-dominance zone size and nonsingular stress field is needed. New phenomenological model based on the two-parameter fracture mechanics is proposed for FCPR prediction. Model allows accurate transferability of laboratory data to life prediction in service situations of defects in engineering components under fatigue conditions.

Crack growth behavior of 9Cr−1Mo (P91) steel under creep–fatigue conditions

Several components operated at high temperature are also subjected to cyclic loading making crack growth behavior under creep–fatigue conditions a significant concern during design and during service. This is especially the case for components designed for long term service. Creep–fatigue crack growth tests were conducted on a modified 9Cr–1Mo (P91) steel at 625°C under constant load amplitude conditions with various hold times using compact type specimens. The crack growth rates per cycle increased significantly with increase in hold time when crack growth data were plotted with the cyclic stress intensity factor, ΔK. It is shown that the creep–fatigue interactions during crack growth for various hold times are represented better by the (Ct)avg parameter implying that the P91 steel behaves in a creep-ductile manner. The test results are also used for assessing the newly developed American Society for Testing and Materials (ASTM) test standard, E2760-10 for creep–fatigue testing.

Transient and Steady State Regimes of Fatigue Crack Growth in High Strength Steel

This paper analyzes the propagation of fatigue cracks in pearlitic steel in two forms, hot rolled bar and cold drawn wire. The experimental procedure consisted of fatigue tests on bars under tensile loading, using steps with decreasing amplitude of stress and constant stress range during each step. The curves plotting cyclic crack growth rate versus stress intensity factor range show a main steady-state regime preceded by transient paths. The steady-state regime is associated with the curves of the Paris regime. The cold drawing process improves the fatigue behaviour of steel by retarding the cyclic crack growth rate, and the propagation rate is not dependent on theR-ratio. The transient branches allow one to calculate the plastic zone size, considering that they are a consequence of the overload retardation effect at each step change, and a unique expression is fitted as a function ofKmaxΔKproduct and of the conventional mechanical properties.

Fatigue crack growth assessments in welded components including crack closure effects: Experiments and 3-D numerical modeling

This work provides a numerical and experimental investigation of fatigue crack growth behavior in steel weldments including crack closure effects and their coupled interaction with weld strength mismatch. A central objective of this study is to extend previously developed frameworks for evaluation of crack closure effects on FCGR to steel weldments while, at the same time, gaining additional understanding of commonly adopted criteria for crack closure loads and their influence on fatigue life of structural welds. Very detailed non-linear finite element analyses using 3-D models of compact tension C(T) fracture specimens with center cracked, square groove welds provide the evolution of crack growth with cyclic stress intensity factor which is required for the estimation of the closure loads. Fatigue crack growth tests conducted on plane-sided, shallow-cracked C(T) specimens provide the necessary data against which crack closure effects on fatigue crack growth behavior can be assessed. Overall, the present investigation provides additional support for estimation procedures of plasticity-induced crack closure loads in fatigue analyses of structural steels and their weldments.

Stress and Stress Intensity Factor Near Notches in Thick Cylinders

This work investigates the impact of semi-elliptical notches (erosion grooves) at the bore of pressurized and autofrettaged thick cylinders. It provides a robust yet rapid method to determine the rapidly varying stress in the near-notch region prior to crack development and crack tip stress intensity factor after a crack develops at the notch root. The procedure involves a sequence of asymptotic solutions and adjustments. A superposition is presented for the stress concentration factor (SCF) of a small edge notch in a pressurized cylinder with bore pressure infiltrating and acting upon the notch surface. A procedure for adjusting this SCF to account for a varying pre-existing stress field is described. This provides accurate predictions for notch depths of up to 15% of wall thickness. Stress variation beyond the notch root is determined by scaling analytic solutions. Solution accuracy appears to be approximately 5%. Stress profiles were used to calculate stress intensity factor (SIF) for cracks emanating from the notch root and deep into the wall. There are notable differences between SIF behavior in the pressurized tube and in the autofrettaged tube. The main reason for this difference is that compressive reyielding near the notch disrupts the residual compressive stress profile over an extended distance. This leads to the conclusion that a crack originating from a notch in an autofrettaged tube exhibits a much higher cyclic SIF range during pressurization than the same length crack originating from the bore. This will cause higher fatigue crack growth rates and shorter fatigue lifetimes.