Crack Front Shape Research Articles

Evaluation of Fatigue Crack Front Shape for a Specimen with Finite Thickness

Two-dimensional elastic or elasto-plastic models dominate the current fatigue crack growth assessment and life prediction procedures for plate components with through-the-thickness cracks. However, as demonstrated in many theoretical and experimental papers, the stress field near the crack tip is always three-dimensional and the fatigue crack front is not straight. In this paper, we develop a simplified approach for the evaluation of the front shapes of through-the-thickness fatigue cracks. We validate this approach against experimental results available from published papers.

Calibration of the potential drop method for monitoring small crack growth from surface anomalies – Crack front marking technique and finite element simulations

The Direct Current Potential Drop method is one of the possibilities to measure the crack growth during fatigue tests without optical access to the sample. The accuracy of this technique applied to short cracks mainly depends on the calibration curve. In the present work experimental and numerical approaches are proposed to calibrate the potential drop measurement. An optimization of the calibration procedure is supported by finite element calculations. The crack front shape and the location of the potential probes are found to be of great influence. An extensive study is conducted to identify all the mechanisms controlling the potential drop measurement. Plastic deformation remains the last parameter which is not directly considered in this study; therefore a calibration strategy is suggested to take into account this effect and achieve a calibration curve with high accuracy. This strategy shows a very good agreement between the obtained calibration curve and the experimental calibration.

A simplified method for the evaluation of fatigue crack front shapes under mode I loading

Two-dimensional elastic or elasto-plastic models dominate the current fatigue crack growth assessment and life prediction procedures for plate components with through-the-thickness cracks. However, as demonstrated in many theoretical and experimental papers, the stress field near the crack tip is always three-dimensional and, as a result, the fatigue crack front is not straight. It is normally curved towards the plate faces. Over the past few years there were a number of very careful numerical studies focusing on the evaluation of fatigue crack front shapes. However, the application of the direct numerical techniques to fatigue phenomena is a very tedious and time consuming process and, sometimes, it is quite ambiguous. In the current paper we develop a simplified method for the evaluation of the front shapes of through-the-thickness fatigue cracks. Further, we validate the developed method against experimental results, investigate the influence of various parameters on the crack front shapes at stable (steady-state) propagation and analyse the differences in the results of fatigue crack growth evaluation obtained with two- and three-dimensional approaches.

A theoretical model of semi-elliptic surface crack growth

A theoretical model of semi-elliptic surface crack growth based on the low cycle strain damage accumulation near the crack tip along the cracking direction and the Newman–Raju formula is developed. The crack is regarded as a sharp notch with a small curvature radius and the process zone is assumed to be the size of cyclic plastic zone. The modified Hutchinson, Rice and Rosengren (HRR) formulations are used in the presented study. Assuming that the shape of surface crack front is controlled by two critical points: the deepest point and the surface point. The theoretical model is applied to semi-elliptic surface cracked Al 7075-T6 alloy plate under cyclic loading, and five different initial crack shapes are discussed in present study. Good agreement between experimental and theoretical results is obtained.

3D Numerical Study on how the Local Effective Stress Intensity Factor Range Can Explain the Fatigue Crack Front Shape

The plasticity-induced crack closure of through-thickness cracks, artificially obtained from short cracks grown in CT specimens of 304L austenitic stainless steel, is numerically simulated using finite elements. Crack advance is incremented step by step, by applying constant ΔK amplitude so as to limit the loading history influence to that of crack length and crack wake. The calculation of the effective stress intensity factor range, ΔKeff, along curved shaped crack fronts simulating real crack fronts, are compared to calculation previously performed for through-thickness straight cracks. The results for the curved crack fronts support that the front curvature is associated to constant ΔKeff amplitude, thus assumed to be the propagation driving force of the crack all along its front.

A new modeling method for natural PWSCC cracking simulation in a dissimilar metal weld

Cracks found in a nuclear power plant reactor coolant system (RCS), such as primary water stress corrosion cracking (PWSCC) and intergranular stress corrosion cracking (IGSCC), usually have natural crack front shapes that can be very different from the idealized semi-elliptical or rectangular shapes considered in engineering handbooks and other analytical solutions based on limited shapes. Simplifications towards semi-elliptical shape or rectangular shape may potentially introduce unnecessary conservatism when the simplified shape has to contain the actual crack shape. On the other hand, it is very time-consuming to create a three-dimensional (3D) finite element (FE) model to simulate crack propagation in a natural shape using existing public-domain software like ABAQUS or ANSYS.In this study, a local deformation-based mesh-mapping (LDMM) method is proposed to model cracks with a natural front shape in any 3D structures. This methodology is first applied to model circumferential surface cracks with a natural crack front shape in the cross-sectional plane of a cylinder. The proposed new method can be applied to simulate both shallow and deep cracks. Also discussed in this paper is a direct method to reproduce welding residual stresses in the crack model using temperature fields combined with other sustained loads to predict crack propagations.With this novel LDMM method, natural crack fronts and non-planar crack faces can be easily modeled. The proposed new method can be used to generate a high-quality finite element model that can be used for both linear-elastic fracture mechanics (LEFM) and elastic–plastic fracture mechanics (EPFM) analyses. The study case illustrates that the proposed LDMM method is easy to implement and more efficient than the existing commercial software.

Crack Front Shapes and Stress Intensity Factors in Plates under a Pure Bending Loading that Induces Partial Closure of the Crack Faces

This paper investigates, both experimentally and numerically, stress intensity factors and evolving geometry of through edge cracks in plates loaded under pure transverse bending; the loading induces partial closure of the crack faces. After performing experiments on steel specimens, it was found that a kink in the crack front forms as the crack grows, changing the initial straight front into an L-shape. To understand the distribution of stress intensity factors along such crack fronts, the observed crack shapes were reproduced in a three-dimensional fracture code (FRANC3D) coupled with a finite element analysis program (ABAQUS). With this coupled system, linear elastic stress analyses were performed considering the nonlinear effects caused by the crack face contact in the compressed region. The proposed methodology computes stress intensity factors along the crack front based on observed crack front shapes obtained from the experimental tests. A method is proposed to treat numerical noise around the crack front kink and at crack front end. In addition, normalized empirical expressions for stress intensity factors are proposed.

Simulation of crack paths at three-dimensional corners of laminated structures

A fracture mechanics-based approach focused on modelling the shape of such interface cracks and calculating the critical stress for steady-state propagation has been developed. The crack propagation is investigated by estimating the fracture mechanics parameters including the energy release rate and the three-dimensional mode-mixity along the crack front allowing determining the shape of the crack front profiles. A numerical approach is applied for coupling the far field solutions utilising the capability of the finite element method to the near field solutions at the crack front based on the J-integral. The developed two-dimensional numerical approach for the calculation of fracture mechanical properties has been validated with three-dimensional models for varying crack front shapes. A quantitative approach was formulated based on the finite element method with iterative adjustment of the crack front to estimate the critical delamination stress as a function of the fracture criterion and corner angles. The implication of the results on the delamination is discussed in terms of crack front profiles and the critical stresses.

Fatigue Crack Propagation in Steels for Railway Axles

The paper deals with the influence of order of cycles in the loading block on the fatigue crack growth rate in railway axle. The railway axle can include some cracks from manufacturing process or initiated fatigue cracks from previous operation. It is advantageous to know how the crack will behave during further service of the train to ensure its safe operation. The most common approaches describing the fatigue crack growth do not take into account the effects of overload cycles, which enlarge the plastic zone ahead of the crack tip. The enlarged plastic zone generates residual compressive stresses, which cause a retardation of the fatigue crack growth. Finite element numerical calculations were used together with the generalized Willenborg model to determine influence of overload cycles on the increment of fatigue crack growing in railway axles. Real geometry of the axle, the crack front shape and typical loading spectrum were taken into account.

Estimation of Apparent Fracture Toughness of Alumina Based Ceramic Laminate

The main aim of this contribution is the fracture behavior of layered ceramic composite with residual stresses. The influence of laminate composition on crack propagation (influence of material interfaces on crack shielding, effect of residual stresses, etc.) was investigated. The crack behavior was described by procedures based on linear elastic fracture mechanics (LEFM) and generalized LEFM. Computations were performed in 2D geometry under plain strain assumptions. For determination of the real crack front shape during the crack propagation the three dimensional FEM models were developed. Both (2D/3D) approaches were compared and differences were closely discussed. The influence of laminate composition with residual stresses on critical values for crack propagation through laminate interfaces was also determined. The results obtained can be used for a design of new layered composites with improved resistance against propagation of cracks.

Influence of Crack Front Shape on 3D Numerical Modelling of Plasticity-Induced Closure of Short and Long Fatigue Cracks

The simultaneous effect of crack length and crack front shape on plasticity-induced crack closure (PICC) for a 304L austenitic stainless steel is simulated through 3D numerical modelling using finite element software Abaqus for through-thickness cracks with different curved crack fronts in CT specimens in comparison with bidimensional through crack with a straight front. The influence of possible loading history effect is avoided by applying constant K amplitude. The local stress intensity factor range for crack opening Kop is evaluated from the simulation of the loss of the last local contact between the crack lips near the crack tip. The pertinence of the different crack front shapes is discussed in term of the effective stress intensity factor range Keff and in comparison with the experimental crack front observations.

Fatigue Crack Propagation Analysis of Repaired Pipes With Composite Patch Under Cyclic Pressure

The pipes in offshore and marine structures are mainly made of low-strength structural steels such as A537 steel and are subjected to the effects of both corrosive medium and cyclic loading caused by many factors. Reinforcement and repair of components using composite patches can be used for piping to reduce the stress intensity factors at the crack-front of a corrosion fatigue crack. In this paper 3D finite element analyses in general mixed-mode fracture condition are performed to study the crack growth behavior of repaired pipes subjected to internal cyclic pressure. The required formulations, crack growth modeling, and remeshing are automatically handled by developing an ANSYS parametric design language (APDL) program. For this purpose an offshore pipe made of low-strength steel containing an initial fatigue corrosion crack repaired by glass/epoxy composite patch is considered. A parametric study will be performed to find the effects of patch thickness on fatigue crack growth life extension and crack-front shape of the repaired pipes.

Steady-state propagation of interface corner crack

Steady-state propagation of interface cracks in thin surface layers or thin films close to three-dimensional corners has been analyzed. Attention was focused on modeling the shape of the interface crack front and calculating the critical stress for steady-state propagation of the crack. The crack propagation was investigated by estimating the fracture mechanics parameters that includes the strain energy release rate, crack front profiles and the three-dimensional mode-mixity along the interface crack front. A numerical approach was then applied for coupling the far field solutions based on the Finite Element Method to the near field (crack tip) solutions based on the J-integral. The adopted two-dimensional numerical approach for the calculation of fracture mechanical properties was compared with three-dimensional models for quarter-circular and straight sided crack front shapes. A quantitative approach was formulated based on the finite element method with iterative adjustment of the shape of the crack front to estimate the critical delamination stresses as a function of the fracture criterion and corner angles. The implication of the results on the delamination is discussed in terms of crack front profiles and the critical stresses for propagation and the angle of intersection of the crack front with the free edge.

Effects of curing thermal residual stresses on fatigue crack propagation of aluminum plates repaired by FML patches

One of the main disadvantages of using composite patches in repair of metallic panels is development of thermal residual stresses due to the curing cycles of the bonded repairs. Fiber Metal Laminates (FMLs) have the overall larger thermal expansion coefficients when compared with the fully composite patches. In this study, the thermal residual stresses that occur due to the thermal expansion coefficient mismatch between the FML patch and underlying cracked aluminum panel are investigated using both numerical and experimental studies. The fatigue crack growth behaviors of centrally cracked aluminum panels in mode-І condition with single-side repairs of FML patches that are made by alternating layers of aluminum and glass fiber-epoxy are carried out. Sensitivity of the curing temperature on fatigue crack-growth life extension and crack-front shape of the repaired panels is also investigated. It is shown that implementing of various curing temperatures do not significantly affect the thermal residual stresses, crack-growth lives and crack-front shapes of the repaired panels by FML patches.

Probabilistic Prediction of Fatigue Life of Cracked Parts: Linear Elastic Fracture Mechanics based Approach

In the context of regular inspections of structures, the presence of cracks can sometimes be revealed. It is therefore interesting to know whether the structure can still be used or if a degraded mode of operation should be considered. It is of concern to assess the scatter of the remaining life of such cracked parts due to the uncertainties on the parameters of the prediction model. Thus for the purpose of the present study, a special attention has been given to the quantification of the uncertainty of each collected data (e.g., material properties, crack measurements) to be integrated in the crack propagation model. Three families of uncertainties have been studied, namely, material properties, geometrical and loading uncertainties. A linear elastic fracture mechanics (LEFM) based approach has been used to predict crack propagation in a widely used pressure vessel steel. The model uses classical Paris’ law where all the controlling parameters have been replaced by statistical distributions obtained from experiment, namely, crack growth tests, hardness tests, tensile tests and Charpy tests. Crack growth tests have also been carried out on thick notched specimen submitted to uniaxial cyclic load to obtain two dimensional cracks that can be representative of those to be found in industrial structures. During these tests, crack lengths have been measured simultaneously by time of flight diffraction (TOFD) ultrasonic method, digital image correlation (DIC) and some markings have been performed to estimate the crack length and crack front shape after the specimen failure. The comparison of data obtained from different observation techniques allowed for the quantification of the crack measurement uncertainty of the industrial TOFD technique. A sensitivity analysis has been carried out on the parameters of the model to evaluate and classify the influence of all sources of uncertainty on the residual life prediction. Last, results from crack growth tests on notched specimen have been used to assess the accuracy of the model prediction.

Experimental investigation of the effect of residual stresses on rapid crack propagation in polyethylene (PE100) pipes

AbstractPipe extruded from polyethylene of strength class PE100 was tested using the ISO 13477 Small Scale Steady State “S4” method, to investigate the effect of frozen‐in stress on rapid crack propagation (RCP). It was found that the lower the residual stress, the lower the S4 critical temperature TcS4 for RCP. Different experimental thermal treatments were used to independently modify residual stresses and crystallinity, to study the separate effects on RCP. It was found that the effect of crystallinity was less significant than that of residual stresses. It has previously been suggested that the residual stress influence on TcS4 is determined by the balance of two mechanisms: additional stored strain energy prior to fracture helps to drive the crack, while the closing moment after fracture helps to close the flaring pipe wall. Tests on annealed specimens suggested that the first effect dominates, especially soon after crack initiation. However, the observed effect seems too large to be explained by this mechanism, and we suggest that the observed benefit from annealing may be better explained by a change in crack front shape. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers

Modeling Delamination of Interfacial Corner Cracks in Multilayered Structures

Multilayered electronic components, typically of heterogeneous materials, delaminate under thermal and mechanical loading. A phenomenological model focused on modeling the shape of such interface cracks close to corners in layered interconnect structures for calculating the critical stress for steady-state propagation has been developed. The crack propagation is investigated by estimating the fracture mechanics parameters that include the strain energy release rate, crack front profiles and the three-dimensional mode-mixity along the crack front. The developed numerical approach for the calculation of fracture mechanical properties has been validated with three-dimensional models for varying crack front shapes. A custom quantitative approach was formulated based on the finite element method with iterative adjustment of the crack front to estimate the critical delamination stress as a function of the fracture criterion and corner angles.

On the crack front curvature in bonded joints

Standard tests of adhesively bonded specimens are likely to produce heterogeneous stress distribution along the crack front and its vicinity. High separation rate mode I dominated fracture test is performed. Observation of post mortem fractured surfaces with an optical microscope reveals characteristic features of mixed mode I/III fracture near the sides of the specimen but not in the middle. At first, finite elements calculations are presented to highlight that the adhesive layer is not loaded in pure mode I. We focus on the effect of mode III contribution near the side of the test pieces. To accommodate the anticlastic curvature of the adherends and the stress heterogeneity in the bondline, the crack front is curved during propagation. The anticlastic curvature of the adherend is evidenced with interferometric profilometry. These experimental observations are compared with finite element calculations in case of straight and curved crack front. Mode mixity along the crack front, local strain energy density and global energy release rate are evaluated. Difference between local and global approaches are discussed. It is found that the local strain energy density criterion suffices to allow for predicting the crack front shape.

Experimental Study on Fatigue Crack Propagation of through-Thickness Crack under Out-of-Plane Bending

In Japan, fatigue through-thickness cracks have been reported in steel bridges. Some of the cracks are originated by out-of-plane bending. For performing more efficient maintenance against the fatigue damages, it is essential to identify the crack propagation behavior of the through-thickness crack under out-of-plane bending. As an important factor to assess the crack propagation behavior, generally, stress intensity factor for through-thickness crack under bending was determined by some assumptions that crack front shape is straight in thickness direction. However, the actual crack front is curved under out-of-plane bending. In this paper, in order to identify the propagation behavior of through-thickness crack under out-of-plane bending, the fatigue test on through-thickness cracked plate was carried out. Moreover, through finite element analysis on the test specimen, the stress intensity factor along curved crack front was investigated.

On the Distinction Between Plasticity- and Roughness-Induced Fatigue Crack Closure

A series of experiments has been carried out to determine why some alloys display plasticity-induced fatigue crack closure (PIFCC), whereas other alloys display roughness-induced crack closure (RIFCC). Two alloys were studied, the aluminum alloy 6061-T6 (PIFCC) and a steel of comparable yield strength, S25C (RIFCC). The experiments included the determination of the crack-opening levels as a function of ΔK, da/dN as a function of ΔK eff – ΔK effth, removal of the specimen surface layers, removal of the crack wake, the determination of crack front shapes, crack surface roughness profiles, and the degree of lateral contraction in the plastic zone at a crack tip. Based on crack tip opening displacement (CTOD) considerations, it is concluded that PIFCC is favored in alloys of low modulus and relatively low yield strength. In addition, a low strain-hardening rate such as for the 6061 alloy will favor PIFCC. Steels with a higher modulus and a higher strain-hardening rate than 6061 will, in general, exhibit RIFCC, even at comparable yield strength levels. In ferritic steels, the fracture surface roughness and consequently the crack-opening level will increase as the coarseness of the microstructure increases.