Stress Intensity Factor Amplitude Research Articles

Influence of contour processing parameters on porosity, surface roughness, and fatigue life in laser powder bed Al-10Si-0.4Mg

Additive manufacturing (AM) enables fabrication of net-shape components with high geometric complexity, however mechanical properties of parts with as-fabricated surfaces are limited by surface roughness and subsurface porosity that may initiate fatigue cracks. This study aims to improve the utility of parts with as-fabricated surfaces by quantifying processing-surface condition-fatigue performance relationships, optimizing surface contour parameters for fatigue performance, and investigating the application of surface profilometry as a non-destructive quality control method. Eleven contour parameter sets of varying energy densities were produced in three classifications: no contour passes, single contour passes, and contours with secondary healing passes. Surface roughness was evaluated using line scan profilometry and subsurface porosity by optical microscopy. Contouring reduced the average surface roughness from Ra ≅ 25 μm to Ra ≅ 5 μm, and the layer of subsurface porosity introduced by this process could be partially eliminated by a secondary healing pass. One set of processing conditions from each contour class was selected for fatigue studies (R = -1), and their results were compared with the fatigue data from machined and polished specimens to evaluate the relative influence of surface condition. Relative to machined and polished specimens, fatigue lives are approximately five times lower for contoured specimens (with and without a healing pass) and twenty times lower for non-contoured specimens at equivalent stress levels up to 107 cycles to failure. Fractographic measurements of initial defect √area of all specimens reveal that fatigue behavior is well characterized by stress intensity factor amplitude across all surface conditions. An extreme value statistical method is developed using profilometry data to predict S-N curves, and it is concluded that non-destructive surface roughness measurements may be suitable for estimating the fatigue lives of components with as-fabricated surfaces as a rapid method for quality control.

Fatigue performance and parameter optimization of CFRP-reinforced steel plate considering elevated temperature

This article aims to investigate the effect of elevated temperature on the fatigue performance of CFRP-reinforced cracked steel plates and optimize the design parameters for their reinforcement. Based on the self-developed adhesive GY34, a finite element model of the CFRP-reinforced central cracked steel plate is established by the ABAQUS software. Parametric analysis is carried out on different bonding methods of CFRP plates and different thicknesses of adhesive layers for CFRP-reinforced cracked steel plates. The effect of elevated temperature on the reinforcement is also studied to verify the excellent performance of GY34 adhesive. Furthermore, the enhancement of fatigue life for cracked steel plates reinforced with CFRP plates at different temperatures is investigated using the Paris model and modified Newman model. The results show that double-sided reinforcement with CFRP is more effective than single-sided reinforcement. All of the different bonding methods could reduce effectively the stress intensity factor of cracked steel plates and improve significantly the bearing capacity of the steel plates. Among them, increasing the number of CFRP layers and their elastic modulus yield the most significant improvement on the reinforcing effect. Elevated temperatures effect greatly on the mechanical properties of adhesively bonded CFRP-reinforced steel plates. The effective bonding length and the stress intensity factor amplitude at the crack tip of the steel plate increases with temperature rises, which may accelerate the growth rate of fatigue crack and reduce the reinforcing effect on fatigue life.

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.

Combined loading effect on high cycle fatigue fracture behaviors of a stainless steel welded structure of elbow and socket

In welded structures with complicated geometries and combined loading state, it is crucial to establish the criteria for fatigue failure. High cycle fatigue tests under combined loading states were performed using stainless steel sheets and welded specimens of elbow pipe and socket in this work. The cyclic stress–strain curve of the parent sheet were applied to the characteristics analysis of the welded specimens. Mode I or Mode I + III fatigue fracture occurred at the stress concentration part of the weld, and the crack starting point was different depending on the loading mode. The applied load was divided into bending and torsion for analysis, and the crack initiation was found on the side with the higher equivalent stress converted according to the Gough-Pollard failure criterion. The crack grew almost perpendicularly to the surface of the elbow pipe, and exhibited the appearance of a transgranular fracture. The fatigue limit based on the stress intensity factor (SIF) amplitude calculated by the proposed method using the strain energy release rate remained nearly constant even though the measured surface strain differed greatly. It is possible to predict the fatigue limit and life of similar structures by simplified models.

Experimental and probabilistic study of fatigue crack growth behavior of steel Q345qC under different stress ratios

The stress ratio effects and the scatter of the fatigue test results are the key issues in the design of steel fatigue performance. This paper reports an experimental and probabilistic investigation of the fatigue crack growth (FCG) behavior of steel Q345qC. Firstly, the microstructural characteristics and mechanical properties of steel Q345qC were examined via an optical microscope and tensile tests. Next, the FCG behavior of steel Q345qC was investigated under different stress ratios. The fatigue crack growth rate (FCGR) equations incorporating survival probabilities were proposed based on Paris and Walker laws. Finally, the theoretical FCG life under different survival probabilities in the crack stable growth region is calculated based on the integral formulas of Paris and Walker law and compared with the tested FCG life. The experimental results demonstrate that the larger the stress ratio, the shorter the length of stress intensity factor (SIF) amplitude experienced in the stable growth region and the smaller the SIF at the end of this region. Both probabilistic Paris and Walker equations can be used for FCGR calculations when the survival probability is set as 50%. The FCG life is calculated using the integral formula based on the Walker law with a high safety tolerance and a wide application interval of stress ratio when the survival probability is set as 90%.

Fatigue Life Evaluation of Orthotropic Steel Deck of Steel Bridges Using Experimental and Numerical Methods

Orthotropic steel deck (OSD) structures are widely used in the bridge deck system of rail transit bridges. Reducing the amplitude of the stress intensity factor is the most effective method to improve the fatigue life of OSD structures. In order to explore the fatigue crack propagation of the OSD structure and the factors affecting the amplitude of the structural stress intensity factor, linear elastic fracture mechanics and Paris’ law is used for theoretical support in this paper. Firstly, a cable-stayed bridge of urban rail transit is taken as the research object, a full-scale segment model of the OSD structure is designed and static and fatigue tests are carried out. Based on the test data, the fatigue life of the structure is simulated and predicted. Finally, ABAQUS and Franc3D are used to analyze the influence of parameters, such as U-rib thickness, roof thickness and diaphragm thickness, of the OSD structure on the amplitude of the stress intensity factor. The test and FEM analysis results show that the thickness of diaphragm and the height of the U-rib have little effect on the fatigue life of the OSD structure, appropriately increasing the thickness of the top plate and U-rib has a positive significance for prolonging the fatigue life of the structure. In addition, it is also of reference value to the application of sustainability and the science of sustainable development.

Fatigue Performance of CFRP-Strengthened Rib-to-Diaphragm Welded Details of Orthotropic Steel Decks: Experimental and Numerical Evaluation

Rib-to-diaphragm welded details of orthotropic steel decks (OSDs) are susceptible to fatigue cracking. To deal with such cracking problem, a strengthening method using externally bonded carbon fiber-reinforced polymer (CFRP) plates was investigated by fatigue experiment and numerical evaluation. A full-scale OSD specimen with two ribs and two diaphragms was tested to evaluate fatigue cracking behavior, as well as the stress before and after strengthening. An experimentally validated numerical model was established to confirm the optimal opportunity for CFRP strengthening. The influence of different CFRP strengthening measures were then discussed on the stress intensity factors at crack tips. It was shown that bonding of CFRP plates can significantly reduce stress of rib-to-diaphragm welded details. The best opportunity for CFRP strengthening is selected as the length of crack reaches at 25.00 mm where the amplitude of stress intensity factor is the smallest. The attachment of CFRP plates by bonding on the surface of cracked plates can reduce stress response at cracked region by more than 30%. The length of crack is of no flat growth until the total number of loading cycle after strengthening arrived at 0.8 million. Results of SIFs calculated by numerical model dropes after strengthening with reduction rate more than 35% and 18% at two crack tips and crack midpoint, respectively. Compared to the geometric dimensions of CFRP, the elastic modulus of CFRP and glue layer shows more significant influence on the fatigue performance of Rib-to-diaphragm welded details due to their stronger restraint to the propagation of crack peaks. This study provided a technical reference to the design and actual application of CFRP in the strengthening of welded details in OSDs.

Research of optimization for crack propagation method

At present, extensive works have been done to predict the shape evolution of fatigue crack based on conventional numerical analysis method. However, few efforts have been made in the majorization of propagation points and increment for the accuracy of simulation. In this paper, a new error calculation method is proposed to quantify the simulation results and experimental results. Based on this, the influence of distribution and quantity of propagation points on the simulation results of crack propagation has been studied and optimized. And a kind of equivalent stress intensity factor amplitude expression based on the assumption that the stress intensity factor changes exponentially with crack depth is derived to achieve the larger crack growth increment by using calculus method. The validity is verified by comparing simulation results with existing expressions of stress intensity factor.

Fatigue strength estimation of single self-piercing riveted joints of steel and aluminium plates under different loading modes

Self-piercing riveting (SPR) has recently been adopted to join automotive body components because this method can reduce manufacturing costs via product automation while also providing a simpler process. In this study, fatigue tests were conducted using cross-tension and coach-peel specimens with aluminium alloy (A5052) and cold-rolled steel (SPCC) plates to evaluate the fatigue strength of SPR joints. For the combination of a top steel plate and a bottom aluminium alloy plate, designated here as T.S-B.A, the applied load amplitudes corresponding to the fatigue limit in the cross-tension and the coach-peel specimens are approximately 13% and 15% of the monotonic strength, respectively. The fatigue strength of SPR joints of aluminium and steel plates under various types loading conditions can be adequately predicted by the equivalent stress intensity factor amplitude.

Analysis of Damage Tolerance of the Stiffened Structure Based on XFEM

A calculation method of damage tolerance of stiffened structure based on extended finite element method (XFEM) is proposed.The crack propagation process is divided into small intervals to calculate the amplitude of stress intensity factor of the structure under different crack lengths. Each small interval is integrated to calculate the crack growth life. The accuracy of the method is verified by calculating the stress intensity factor, the load at both ends and crack growth life. The flat slab structure model with different numbers of stiffeners is established. The above calculation method shows that the stiffeners can share the load for the structure, reduce the amplitude of stress intensity factor, increase the fatigue life.The more the number of stiffeners, the more obvious the improvement effect. The equivalent treatment of the stiffened structure was conducted, and the equal area widening model, unfolding model and thickening model were established. The calculation results show that the calculation results of expansion model is very close to the stiffened structure. It shows that the stiffeners share the load for the structure by increasing the local thickness of the area, reduce the amplitude of stress intensity factor and improve the fatigue intensity.

Study on the shape change of crack growth rate curve under different forms of additional stress field

In this paper, FRANC3D is used to simulate the fatigue crack growth process under different additional stress fields to explore the key mechanical parameters influencing the fatigue crack growth curve. For finite large plate model with penetrating crack, the crack growth rate is calculated under different forms and different values of applied load and additional stress coupling, the fatigue life curves, as well as crack growth rate curves and Pairs formulas under different applied loads are obtained. Through the analysis, the relationship between the additional stress field and the parameters in Pairs formula of crack growth rate is obtained. Because of the existence of the additional stress field, the stress intensity factor amplitude of crack tip changes, which is the root cause of the change of crack growth rate curve shape.

Creep–fatigue interaction behavior of nickel-based single crystal superalloy at high temperature by in-situ SEM observation

Creep-fatigue interaction behavior of nickel-based single crystal superalloy was studied in an in-situ SEM platform at 900 °C. Dwell times of 15, 30, 60, 90, 120 s were introduced at the tensile peak stress of each cycle. Experimental results showed that the life cycles firstly decreased rapidly then slightly increased with the increasing dwell time, which was explained by the accumulated inelastic strain. Dislocation microstructure and inelastic strain were correlated for different dwell time by TEM analysis. Crack propagation mode transition was analyzed. Comparing with the stress intensity factor amplitude, crack tip opening displacement was more suitable for characterizing the creep-fatigue small crack growth rate.

Fatigue Crack Growth Behavior of TA29 Titanium Alloy at Different Temperatures

TA29 titanium alloy forging was heated by duplex annealing. The fatigue crack growth behaviour of the alloy at room temperature, 400 °C, 500 °C and 600 °C was studied. The relationship between the fatigue crack growth rate (Da/dN) and the stress intensity factor amplitude (△K) of TA29 alloy at different temperatures was revealed by Paris formula. The fatigue fracture morphology of fatigue crack growth specimens was analysed by scanning electron microscopy (SEM). The results showed that the TA29 titanium exhibited good crack growth resistance at room temperature. With the increase of test temperature, the C value of the Paris formula increased, the m value decreased, and the fatigue crack growth rate increased. From the fatigue fracture morphology of the specimens, it was found that the fractures of fatigue crack growth specimens at different temperatures exhibited typical pre-splitting zone, steady-state expansion zone and rapid expansion zone. As the temperature increased, the range of the pre-cracking zone was larger, the range of the steady-state extension zone and the rapid expansion zone were smaller. At room temperature, there was no obvious fatigue strips in the steady-state expansion zone, and the transient fracture zone exhibited the characteristics of cleavage fracture, while the steady-state expansion zone at high temperature showed obvious fatigue strips and secondary cracks, and the transient fracture zone was a typical ductile fracture mechanism.

Investigation on the fatigue crack behavior of Zr702/TA2/Q345R composite plate with a crack normal to interface

AbstractIn this paper, the effects of maximum load, load ratio, and average load on fatigue crack propagation of Zr702/TA2/Q345R composite plate with a crack normal to the interface are studied by experiment and finite element method. When crack propagates to the interface from the compliant material side, the crack growth rate decreases to the minimum at first. After crack penetrates through the interface, the fatigue crack growth rate accelerates continuously. When crack propagates to the interface from the stiff material side, the fatigue crack growth rate generally increases with the crack length. Regardless of the direction of crack growth, the increase of load ratio will weaken the difference of crack growth rate near the interface caused by material property mismatch. Finite element results show that elastic modulus mismatch significantly changes the variation of the stress intensity factor amplitude. All results demonstrate that crack growth rate is dependent on the competition of the stress intensity factor amplitude, the fatigue crack growth rate in the corresponding material, and the interface strength.

Understanding the effect of crack tip deformation on fatigue crack growth behavior in 300-series austenitic stainless steel

Fatigue crack growth rates (FCGRs) of Type 304/304L stainless steel at stress ratios above 0.7 in elevated temperature (250–320 °C), high purity water are observed to be accelerated by 10× to 100× (relative to comparable tests in air) during testing at low frequencies (0.167–0.000167 Hz). These effects are most prominent for fatigue tests with applied stress intensity factor amplitudes (ΔK) less than ∼10 MPa√m and has been attributed to a hydrogen-based mechanism. This work evaluates that hypothesis, at ambient temperature, through a combination of fatigue testing (using deuterium pre-charged and uncharged specimens) and materials characterization. Over a range of ΔK values (∼6 to 12 MPa√m), the FCGRs of pre-charged specimens are found to be marginally higher (at most 20–30%) relative to comparable tests of uncharged specimens. However, while the FCGRs between pre-charged and uncharged specimens are comparable, the morphology of the fracture surface of the pre-charged specimens is predominately faceted while the morphology of the fracture surface of the uncharged specimen is quasi-cleavage with some poorly defined faceted regions. Planar slip (and few cell structures) is predominate ahead of the crack tips in which the faceted fracture surface morphology is observed. In contrast, quasi-cleavage and poorly defined faceted fracture surfaces are associated with a cellular structure embedded within a planar slip region ahead of crack tips. These differences in deformation suggest the fracture surface morphology may form by either cracking along slip planes in the case of deuterium pre-charged specimens or by cracking along cell walls in the case of uncharged specimens. The fracture mechanism that operates is controlled by differences in the number of cycles required to evolve the deformation structures ahead of the fatigue crack tip, the grain orientation, and local hydrogen concentration.

ON THE MATHEMATICAL GENERALIZATION OF S. YA YAREMA FORMULA

The goal of the article is a mathematical generalization of S. Ya Yarema formula derived for approximation of the experimental diagrams of the fatigue fracture and subsequent analysis of the capabilities of the formula. The analysis is performed on the basis of the operator for smooth transition from one mathematical function to another. Formula of S. Ya Yarema is shown to be a special case of this mathematical operator when a smooth differentiable transition occurs from one constant level of the amplitude of stress intensity factor to another constant level. The obtained mathematical expressions can be interpreted as the cumulative probability and the probability density of random values of the fatigue crack rate. This allowed us to give a statistical interpretation of the fatigue fracture diagrams. On this basis we developed a methodology for estimation of the residual resource of a structural part containing a fatigue crack.

Near‐threshold fatigue crack growth properties of wrought magnesium alloy AZ61 in ambient air, dry air, and vacuum

AbstractEnvironmental influences on near‐threshold fatigue crack growth in wrought magnesium alloy AZ61 were investigated. Fatigue tests were performed in ambient (humid) air, dry air, vacuum, and dry nitrogen gas at 19 kHz cycling frequency and load ratio R = −1. Threshold stress intensity factor amplitudes, Kth, determined for limiting growth rates below 5 × 10−13 m/cycle were 1.1 MPam1/2 in ambient air and 1.2 MPam1/2 in dry air. A much higher Kth of 1.9 MPam1/2 was measured in vacuum and dry nitrogen gas. This suggests oxygen to be the most detrimental constituent of ambient air that increases near‐threshold crack propagation rates and decreases Kth. The deleterious effect of humidity is comparatively small. Corrosive influences are effective at ultrasonic cycling frequency for growth rates below approximately 3 × 10−9 m/cycle. The crack propagation curves in ambient and dry air show a plateau‐like regime where the fracture mode changes from purely ductile to a mixed ductile and brittle mode. In vacuum and dry nitrogen gas, a ductile crack path is found for all investigated crack growth rates.

Research on the fatigue whole life of asphalt mixture based on the nonlinear damage theory

The analytical solution of the fatigue crack forming life based on the nonlinear cumulative damage model was deduced by using the simply supported beam with mid-span loads as the study model. Then the fatigue whole life model by the Paris formula with the crack length factor was established. Flexural-tensile strength test and fatigue test were made by using the trabecular specimen at different temperatures. By the contrast of the asphalt mixture fatigue life at different temperatures and stress ratios, it was found that as increasing of temperature, the fatigue life of the trabecular specimen will reduce. When it is at the same temperature, the fatigue life will reduce as the stress ratio increasing. The fatigue developing life of the asphalt pavement will occupy a higher ratio of the whole fatigue life when the temperature is higher. The fatigue developing life is shorter when the temperature is lower. The values of the fatigue damage parameter a∗ and p were obtained by the regression of the test data. The expressions of the functional relation between a∗ and p with temperature T were deduced. The change law between the crack developing speed and the stress intensity factor amplitude was studied to determine the parameters A and n in the formula Paris under different stress ratio. The established model in this paper was verified effectively by contrast of the calculation values of the fatigue whole life model and the test values.

Experimental measurement of out-of-plane displacement in crack propagation under gaseous hydrogen

A huge enhancement of fatigue crack growth rates was observed on a 15-5PH martensitic stainless steel under gaseous hydrogen. The observation of fracture surfaces showed a change in fracture mechanisms depending on hydrogen pressure and loading condition, namely the stress intensity factor amplitude and the loading frequency. The present study was undertaken in order to analyze the effect of gaseous hydrogen on the out-of-plane displacement at the crack tip plasticity by means of out-of-plane displacement measurements. An interferometric microscope was used to obtain high resolution measurements of out-of-plane displacement. These measurements showed an increase in out-of-plane displacement in presence of gaseous hydrogen compared to an inert or slightly aggressive environment, depending on the hydrogen pressure and the maximum stress intensity factor applied during static or cyclic loading.

Corrosion Fatigue Crack Growth Behavior of Alloy 690 in High-Temperature Pressurized Water

Corrosion fatigue crack growth behavior of Alloy 690 was investigated in air and high-temperature pressurized water environments. The stress intensity factor amplitude threshold (ΔKth) was obtained, and the effects of stress intensity factor (ΔK), cyclic frequency (f), loading ratio (R), and material orientation on the corrosion fatigue crack growth rates were studied. The observed environmental acceleration on corrosion fatigue crack growth was quantitatively analyzed, and an empirical formula and the Ford-Andresen model were utilized to describe and explain the corrosion fatigue behavior of Alloy 690.