Crack Front Profile Research Articles

Enhanced real-time crack monitoring and updating in welded structural components with limited measurement data

This paper presents an enhanced neural network-bootstrap particle filtering algorithm to construct the complex relationship between the normalized strain relaxation indicators and the crack front profiles based on numerical simulation and experimental validation. The metamodel of normalized strain relaxation indicators and the crack front profile in welded plate joints under bending cyclic loadings is built based on the optimal regression neural network and finite element analysis. To overcome the uncertainties caused by the limited strain measurement, crack measurement, and different non-destructive techniques, this study further proposes new crack-related weight functions and combines a bootstrap particle filtering approach with an interpolation method to finely tune the metamodel and the crack prediction algorithm. As validated by the experimental results, the intelligent crack sizing approach demonstrates a potential solution for crack size monitoring through affordable strain gauges in the broad framework of digitally twinning the next-generation infrastructure.

An adaptive learning approach to determine and update crack sizes from strain relaxation data for welded plate joints

This paper proposes the framework to determine and update the crack-front profile at the toe of welded plate joints based on the strain relaxation data. This study determines the crack depth by classifying the nodes in the thickness direction as open nodes on the crack surface and closed nodes on the intact ligament. To update the crack size during the loading history, this research employs the modified bootstrap particle filtering approach, which entails enhanced adjustment capabilities by imposing additional uncertainty distributions. This approach improves the crack size prediction by absorbing limited measurement data on the strain values or crack sizes.

Fatigue crack propagation behaviors in Ti-5Al-3Mo-3V-2Zr-2Cr-1Nb-1Fe alloy with STA and BASCA heat treatments

Fatigue crack propagation behaviors of a novel high strength Ti-5Al-3Mo-3V-2Zr-2Cr-1Nb-1Fe alloy with equiaxed and lamellar microstructures were systematically investigated. Fatigue crack propagation tests at both increasing and decreasing stress intensity factor range values were carried out with a frequency of 15 HZ and stress radio R of 0.1 by using compact tension samples. The sample with lamellar microstructure displayed the faster fatigue crack propagation rates in near-threshold regime compared to the sample with equiaxed microstructure. The fatigue threshold (ΔKth) was 2.7 MPa·m1/2 for lamellar microstructure, and 3.2 MPa·m1/2 for equiaxed microstructure. The steady state crack growth rate in lamellar microstructure was slightly slower than that in equiaxed microstructure in the Paris regime, while much faster in the rapid growth regime. The interactions between crack path and microstructures as well as the microscopic fracture surface morphology in both microstructures were detected and analyzed by scanning electron microscope (SEM), revealing the different crack propagation behaviors in three regimes. The results showed that the crack propagation behaviors were a result of two contributing factors: interface obstacles and crack front profile. The increased fatigue crack propagation resistance of equiaxed microstructure in near-threshold regime can be attributed to the interface obstacles which dominated over the rougher crack front profile. While the higher fatigue crack growth resistance for lamellar microstructure in Paris regime was attributed to the more positive effect of rougher crack front profile. In the rapid growth regime, the crack in lamellar microstructure was found to be extended along the grain boundary α, which was regarded as a low energy crack path and led to the faster crack propagation rate.

Modeling ductile fracture using critical strain locus and softening law for a typical pressure vessel steel

This work describes the framework to model ductile damage based on phenomenological stress-modified critical strain criterion (SMCS) coupled with a softening law to predict the onset of ductile initiation and ductile propagation in typical fracture specimens, extracted from a flat plate made of ASTM A285 Gr. C steel. A very detailed and well-illustrated methodology has been developed for the identification of material parameters. Laboratory testing of cylindrical tensile bars and SE(B) specimens, at room temperature, provides necessary and sufficient information to calibrate the numerical parameters in the proposed model. For either geometry, the applied loading is measured by a continuous record of the load (P) and displacement (Δ). After the model parameters have been set, verification studies are carried out for SE(B) specimens having shallow cracks with and without side-grooves. Consequently, parameter transferability, outside small-scale yielding condition between specimens having different crack tip conditions, can be addressed and the constraint influence on the driving force better understood. An additional check is performed by comparing the final crack front profile measured on the fracture surface of the SE(B) specimens with the numerical calculated in the finite element analyses. The phenomenological model adopted herein can reproduce and predict reasonably well the experimental data obtained for specimens with different levels of stress triaxiality (constraint). Overall, it is shown that the SMCS criterion combined with a softening law can be used to study and to predict the influence of stress state on ductile failure initiation and ductile crack growth by identifying nine model parameters through testing notched round bar geometries and SE(B) specimens. The proposed methodology shows great potential as an engineering tool for assessing the integrity of complex structures such as welded pipelines and pressure vessels.

A finite element study of fatigue crack propagation in single lap bonded joint with process-induced disbond

This paper presents a method for predicting fatigue crack propagation in adhesive bonded composite joints with an initial full-width disbond using finite element analysis and numerical integration of the material's fatigue crack growth rate law. Fatigue tests were conducted on single lap joints. Crack lengths were monitored from four runout corners. In-situ crack growth measurements were performed by ink injection to identify the crack front profile during fatigue loading. The crack growth was modelled using a fracture mechanics criterion considering two different crack propagation patterns. The material's fatigue crack growth rate law was determined experimentally using the standard double cantilever beam and end notch flexure specimens. Using the total strain energy release rate and the two crack scenarios, the numerical model predicted the lower and upper bounds of the measured fatigue crack growth rates of the lap joint.

An experimental-finite element method based on beach marks to determine fatigue crack growth rate in thick plates with varying stress states

The relation between the fatigue crack growth rate and stress state is significant for fatigue life estimation, especially for thick-welded structures with complex stress states. This paper proposes a hybrid Experimental-Finite Element Method aimed to obtain the fatigue crack growth rate corresponding to plane stress and plane strain states. A static load marking method is proposed to mark a series of crack fronts in a single edge notched bending specimen at known numbers of cycles, which is analysed by nonlinear finite element method to evaluate the stress state by a local constraint factor. Stress intensity factor at the center of the thickness and the surface position where plane strain and plane stress states approximately exist and remain unchanged with crack propagation, is calculated by the 1/4-node displacement method with consideration of non-orthogonal mesh influence. The J-integral method and the virtual crack closure technique are also applied to check the performance of the methods in dealing with the actual cracked body problem. Crack length increments are determined based on the crack front profiles. The da/dN-ΔK curves of plane strain and plane stress states are determined and compared with the results from normal fatigue crack growth rate tests according to Chinese standard: GB/T 6398-2000. The fatigue crack growth behavior of a semi-elliptical surface crack located at the weld toe of a T-plate welded joint subjected to cyclic tension loading is assessed based on the curves and the analytical results are compared with the experimental results. The asymptotic crack shape observed in experiments is successfully predicted by using the curves determined by the hybrid method.

High cycle fatigue behavior of Ti–5Al–5Mo–5V–3Cr–1Zr titanium alloy with bimodal microstructure

In this study, high–cycle fatigue (HCF) damage behavior of Ti–55531 alloy with bimodal microstructure (BM) was studied at room temperature. Fatigue crack initiation and propagation mechanisms of the alloy were thoroughly investigated by studying fracture morphology, crack front profiles, polished microstructure and dislocation structures beneath fatigue main–crack initiation sites of HCF samples. The results indicate that this alloy presents an excellent HCF strength (107cycles, R = −1) as equal to 656 MPa. Dislocation analyses exhibit that typical dislocation structures include straight prismatic slip lines, curved dislocation lines, dislocation tangles and {1¯011}α type twins in fatigued specimens. Primary αp particles and secondary αs lamellae accommodate more cyclic deformation than retained βr laths. Furthermore, the dislocation free zone can be observed in the αp/βtrans (β transformed microstructure) boundary. As a result, microcracks primarily nucleate at the αp/βtrans interface or at αp particles. Moreover, a few microcracks initiate at the αs/βr interface or at αs plates of βtrans microstructure. These fatigue crack initiation behaviors promote the fracture of Ti–55531 alloy.

Effect of microstructure on high cycle fatigue behavior of Ti–5Al–5Mo–5V–3Cr–1Zr titanium alloy

High-cycle fatigue (HCF) behavior of Ti–5Al–5Mo–5V–3Cr–1Zr (Ti-55531) alloy with both lamellar microstructure (LM) and bimodal microstructure (BM) was studied at room temperature. The results indicate that BM presents much higher strength, lower ductility and slightly higher HCF strength (107cycles, R=−1) than those of LM. Typical dislocation structures including straight prismatic slip lines, curved dislocation lines, dislocation tangles and twins can be discovered in fatigued specimens with two different microstructures. Primary α (αp) particles and secondary α (αs) lamellae accommodate more cyclic deformation than retained β (βr) laths. Grain boundary (GB) α layers have more effect on promoting crack initiation in LM than that in BM. As a result, fatigue microcracks mainly initiate at the interface between GB α films and prior β grains or at the αs/βr interphase for LM. However, microcracks primarily nucleate at the αp/βtrans (β transformed microstructure) interface or at αp particles in BM. The combination of transgranular and intergranular crack propagation could be observed in the two microstructures. Crack front profile of macrocrack in LM is rougher than that of BM during the stable propagation region.

Failure mode analysis of two diesel engine crankshafts

A failure analysis of two damaged crankshafts are presented: one obtained from a diesel engine of a mini backhoe, and another one from an automobile vehicle. The diesel motor suffered a serious mechanical damage after 3 years and 5000 hours in service: the connecting rod n° 3 broke and, in consequence, the crankcase and motor block suffered damage. The motor was repaired by a non-authorized workshop, but maintaining the same crankshaft without being properly inspected. After 1100 hours working the crankshaft failed on the 3rd crankpin. The second crankshaft failed after 105 000 km in service. In both crankshafts a crack grew from the crankpin-web fillet, and their symmetric semi-elliptical crack front profiles confirms the effect of a pure mode I (reversed bending). Fractographic analyses show the semi-elliptical beach marks and results indicate that fatigue fracture was the dominant failure mechanism of these two crankshafts.

A stress-concentration-formula generating equation for arbitrary shallow surfaces

Analytical understanding of how stress concentrates is invaluable. An equation that generates stress concentration formulas is derived and shown to apply very well to a number of shallow irregularities on surfaces, for the plane stress conditions and to a first-order approximation. Under shallow conditions, for any first-order Hölder-continuous surface function f(x), the derived equation is: kt(x)=1-2Hf′(x), where H is the Hilbert transform and f′(x) is the spatial derivative of f with respect to the independent variable. It is shown that using this generating equation, well-known traditional results can be easily derived. Also, a number of other stress concentration formulas for various cases are generated. Furthermore, a second-order approximation is introduced, which shows the dependence of kt on not only the slope but also on the concavity of the surface. The approach used herein can be extended to finding closed-form solutions to other integral equations possessing similar kernels for applications such as the variation of the stress intensity factor due to an arbitrary crack front profile (work in progress).

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 performance of tubular X-joints with PJP+ welds: II — Numerical investigation

This paper summarizes the numerical investigation on the fatigue crack propagation in CHS X-joints under constant amplitude brace in-plane bending, in parallel with the experimental investigation reported in the companion paper. The finite element procedure examines the effects of the crack propagation angle, the crack-front profile and the interaction between adjacent fatigue cracks on the fatigue driving force, measured by the stress-intensity factors. The Paris type estimation provides a close prediction on the propagation life of weld toe cracks observed in the experiment. The initiation of the root crack, based on the Paris prediction, occurs much later than that of the toe crack.

Finite element prediction of fatigue crack growth in Super CMV hollow shafts with transverse holes under combined torsional and axial loading

Fatigue crack growth tests have been carried out on two types of pre-cracked, hollow, Super CMV shaft specimens with transverse holes, under combined torsional and axial loading, from which crack growth patterns and crack growth data have been obtained. Experimental results show that the cracks were found to initially propagate under the Mode I condition on the planes of maximum tensile stress, and these then veered toward the planes of maximum shear stress and propagated under a mixture of Modes II and III patterns. A finite element approach is used to predict the fatigue crack growth, under the Mode I condition, in the shaft specimens tested at relatively low magnitudes of torque. A series of incremental finite element analyses, in conjunction with the use of Paris’ law, with different crack lengths and crack front profiles, are used to simulate the progressive fatigue crack growth process. The finite element predicted crack growth data are compared with the corresponding experimental data. Good agreement is obtained between the finite element predictions and the experimental results for relatively “short” crack growths, for crack lengths of up to about 1.25 mm. For the crack lengths greater than 1.25 mm, the finite element approach underpredicts the fatigue crack growth rates and overpredicts the fatigue lives. The possible reasons for the difference between the predicted and tested results are also discussed.

Implementation of a plastically dissipated energy criterion for three dimensional modeling of fatigue crack growth

Fatigue crack growth is simulated using three dimensional elastic–plastic finite element analysis. The crack extension per load cycle, da/dN, as well as crack front profile changes (crack tunneling) under cyclic loading is not specified as an input but evaluated based on a condition that relates plastically dissipated energy to a critical value. Simulation of cyclic crack propagation in a middle-crack tension M(T) specimen using this implementation captures the well established, experimentally obtained crack growth rate reduction accompanying a single overload event. The analysis predicts that the single overload also affects the crack front profile, where a tunneling crack propagates with a flatter crack front in the overload affected zone.

A compliance-based approach to measure fracture resistance curve for surface cracked steel plates

This paper proposes a compliance-based approach to determine the fracture resistance $$J$$ – $$R$$ curve for surface cracks in high-strength steel (S690) plate specimens in a four-point-bend set up. This study extends the $$\eta $$ -approach used in the fracture test for the typical specimens with a through-thickness crack, to the surface cracks in plate specimens in calculating the energy release rate from the area below the measured moment versus the crack-plane rotation. The energy release rate, computed from the detailed finite element models using the domain integral approach, confirms a constant $$\eta $$ value for surface cracked steel plates. Coupled with the post-test sectioning, the unloading compliance method quantifies the extended crack-front profiles ahead of the fatigue pre-cracked surface notch, using the crack-size versus the compliance relationship derived from linear-elastic finite element analyses. The fracture resistance curves thus obtained remain similar at different locations along the crack front and comparable with the fracture resistance measured using a standard side-grooved compact tension specimen at a finite crack extension.

Fatigue performance of tubular X-joints: Numerical investigation

The cyclic actions due to waves, currents and winds on offshore platforms frequently cause fatigue cracks at hot-spot locations. The remaining fatigue life of such connections depends significantly on the fatigue driving force often measured by the stress-intensity factors. This study examines the fatigue performance of tubular joints fabricated using a new type of enhanced partial joint penetration weld details under constant-amplitude brace in-plane bending actions. The numerical study ascertains the crack propagation angle, the crack-front profile and the interaction between adjacent cracks on the stress-intensity factors.

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.

Crankshaft failure analysis of a motor vehicle

A case study of a crankshaft catastrophic failure of a motor vehicle and its failure analysis is presented. The crankshaft suffered a mechanical seizure on the crankpin no. 2 after 3years in service. It was repaired and after 30,000km the vehicle had a damage again, with a catastrophic failure on the same crankpin. A transversal macrograph of the crankpin revealed that the crankpin was rectified and filled with a metal alloy for the same nominal diameter. Two fatigue cracks growing to the center of the crankpin where the final fracture occurred. The symmetric semi-elliptical crack front profile confirms the effect of a pure mode I under alternating bending. The catastrophic failure was a consequence of the inadequate repairing by a non-authorized manufacturer.

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.

Crack front penetration in transgranular cleavage cracking in an iron-silicon alloy

Based on the analysis of the crack trapping effect of cleavage ridges and penetration of crack front segments in an iron-silicon alloy, the distance between break-through points along a high-angle grain boundary is investigated. If the break-through points are close to each other, the crack trapping effect is dominant; otherwise, the grain boundary separation in break-through windows governs the front transmission process. The relationship between the overall grain boundary fracture resistance and the break-through-point distance is quite complex. The minimum grain boundary resistance is achieved when the break-through points are about 2–3 µm apart, which is also influenced by the grain boundary shear strength, the crystallographic toughness and orientation, as well as the crack front profile.