Crack Tip Strain Fields Research Articles

Quantifying fatigue overload retardation mechanisms by energy dispersive X-ray diffraction

The fatigue crack retardation mechanisms operating after an overload event are investigated for a bainitic steel using high spatial resolution energy dispersive synchrotron X-ray diffraction. The elastic crack-tip strain fields are mapped at mid-thickness of compact tension samples at R-ratios of 0.1 and 0.4. The same overload stress intensity factor (KOL = 60 MPa m1/2) is applied in each case with the cracks then propagating under the same applied stress intensity range, ΔKapp = 27 MPa m1/2. The competing retardation mechanisms are directly quantified and separated, with the associated fatigue crack growth (FCG) rates then being predicted according to a 2-parameter Walker-type assessment and validated against those measured. The stress intensity factor associated with the overload residual stress field is calculated using a weight function approach. For R=0.1, shielding from residual stress controls retardation when crack growth through the overload plastic zone, rpOL, is small (specifically <0.6rpOL). For more extensive crack growth, discontinuous crack closure controls the retardation behaviour, with significant load transfer across opposing crack faces being observed at minimum load (for R=0.1). These crack face tractions are associated with the plastic asperity created during overload. The traction forces holding the crack faces open at minimum load are, for the first time, used to directly quantify the associated stress intensity factor, Kmintract as a function of crack growth. While no crack shielding is expected, nor observed, for R=0.4, the variation in FCG rate after overload is explained by changes in effective R-ratio.

Fatigue crack tip strain evolution and crack growth prediction under single overload in laser melting deposited Ti-6.5Al-3.5Mo-1.5Zr-0.3Si titanium alloy

This paper focuses on the fatigue crack tip strain evolution in laser melting deposited Ti-6.5Al-3.5Mo-1.5Zr-0.3Si titanium alloy under constant amplitude loading plus single overload (OL). The digital image correlation (DIC) technique was used to capture and evaluate the crack tip strain fields and crack closure variation; the results showed that the strains near the crack tip become larger and the crack opening load increases after the application of the OL. The size of the retardation distance is consistent with the analysis results of the crack tip strain fields. The crack closure model based on the DIC analysis results can provide good predictions of the crack growth life for both the low and high overload ratios.

Effect of microstructure on fatigue crack tip field of laser melting deposited Ti–5Al–5Mo–5V–1Cr–1Fe titanium alloy

In this paper, experimental and simulated investigations were carried out to understand the effect of microstructure on the fatigue crack tip strain field of laser melting deposited Ti–5Al–5Mo–5V–1Cr–1Fe titanium alloy. The mechanical properties of the laser melting deposited material corresponding to different microstructure zones were measured by digital image correlation method under in-situ static stretching, and the results indicate that the direction of primary α lamellas has great influence on the mechanical property of each grain. The crack tip strain fields considering the influence of material microstructure under constant amplitude conditions were measured, and the strain field of plastic zone has significant difference. Crystal plasticity finite element simulation of the static tensile and crack tip field considering the microstructure effect had been conducted and compare with experiment results. The simulation results are in good agreement with the test results in both the static tension strain field and crack tip strain field.

Stress Intensity Factor calculation from displacement fields

In the last two decades, visual image techniques such as Digital Image Correlation (DIC) enabled to experimentally determine the crack tip displacement and strain fields at small scales. The displacements are tracked during loading, and parameters as the Stress Intensity Factor (SIF), opening and closing loads, T-stress can be readily measured. In particular, the SIFs and the T-stress can be obtained by fitting the analytical equation of the Williamstype expansion with the experimentally-determined displacement fields. The results in terms of fracture mechanics parameters strictly depend on the dimension of the area considered around the crack tip in conjunction with the crack length, the maximum SIF (and thus the plastic tip radius), and the number of terms to be considered in the Williams-type expansion. This work focuses in understanding the accuracy of the SIF calculation based on these factors. The study is based on Finite Element Analysis simulations where purely elastic material behavior is considered. The accuracy of the estimation of the SIF is investigated and a guide-line is provided to properly set the DIC measurements. The analysis is then experimentally validated for crack closure measurements adopting the SENT specimen geometry.

Digital Image Correlation for Crack Tip Strain Field inside Grain and across Grain Boundary

Digital Image Correlation for Crack Tip Strain Field inside Grain and across Grain Boundary

Validation of a cyclic plasticity computational method using fatigue full‐field deformation measurements

AbstractThe evolution of crack tip displacement and strain fields during uniaxial, room temperature, low‐cycle fatigue experiments of Nickel superalloy compact tension specimens was measured by a digital image correlation approach and was further used to validate a cyclic plasticity model and corresponding deformation calculations made by a finite elements methodology. The experimental results provided data trends for the opening displacements and near crack tip strains as function of cycles. A finite element model was developed to capture test conditions for a measured crack size. The model captures crack tip plasticity by using a constitutive model calibrated against stress‐strain measurements performed on a round bar. Similar quantities were extracted from the model predictions to compare with the digital image correlation measurements for model validation purposes. This type of direct comparison demonstrated that the computational model was capable to adequately capture the crack opening displacements at various stages of the specimen's fatigue life, providing in this way a tool for quantitative cyclic plasticity model validation. In addition, this integrated experimental‐computational approach provides a framework to accelerate our understanding related to interactions of fatigue test data and models, as well as ways to inform one another.

Predicting fracture energies and crack-tip fields of soft tough materials

Soft materials including elastomers and gels are pervasive in biological systems and technological applications. Whereas it is known that intrinsic fracture energies of soft materials are relatively low, how the intrinsic fracture energy cooperates with mechanical dissipation in process zone to give high fracture toughness of soft materials is not well understood. In addition, it is still challenging to predict fracture energies and crack-tip strain fields of soft tough materials. Here, we report a scaling theory that accounts for synergistic effects of intrinsic fracture energies and dissipation on the toughening of soft materials. We then develop a coupled cohesive-zone and Mullins-effect model capable of quantitatively predicting fracture energies of soft tough materials and strain fields around crack tips in soft materials under large deformation. The theory and model are quantitatively validated by experiments on fracture of soft tough materials under large deformations. We further provide a general toughening diagram that can guide the design of new soft tough materials.

2D mapping of plane stress crack-tip fields following an overload

The evolution of crack-tip strain fields in a thin (plane stress) compact tension sample following an overload (OL) event has been studied using two different experimental techniques. Surface behaviour has been characterised by Digital Image Correlation (DIC), while the bulk behaviour has been characterised by means of synchrotron X-ray diffraction (XRD). The combination of both surface and bulk information allowed us to visualise the through-thickness evolution of the strain fields before the OL event, during the overload event, just after OL and at various stages after it. Unlike previous work, complete 2D maps of strains around the crack-tip were acquired at 60?m spatial resolution by XRD. The DIC shows less crack opening after overload and the XRD a lower crack-tip peak stress after OL until the crack has grown past the compressive crack-tip residual stress introduced by the overload after which the behaviour returned to that for the baseline fatigue response. While the peak crack-tip stress is supressed by the compressive residual stress, the crack-tip stress field changes over each cycle are nevertheless the same for all Kmax cycles except at OL.

In Situ Experimental Study of Near-Tip Strain Evolution of Fatigue Cracks

Near crack tip strain fields in a stationary and a growing fatigue crack have been studied in situ using the Digital Image Correlation (DIC) technique in a compact tension specimen of stainless steel 316 L under tension-tension cyclic loading. The evolution of near-tip strains normal to the crack plane was monitored at selected locations ahead of the crack tip in consecutive cycles during fatigue crack growth experiments. A stationary crack was examined first to provide a baseline reference whilst the evolution of the strain field ahead of a growing crack was monitored in situ at peak loads during fatigue cycling. The results show that strain accumulation with loading cycle occurred at all tracked locations in both cases, and it is particularly evident close to the crack tip. Moreover, a higher strain accumulation rate was found near the growing crack tip than that near the stationary crack tip. The results on near-tip strain evolution were collected for the first time in situ during the fatigue crack growth experiments, which may hopefully inform a physical-based modelling strategy of fatigue crack growth.

Plastic pre-compression and creep damage effects on the fracture toughness behaviour of Type 316H stainless steel

The influence of inelastic damage in the form of plastic pre-strain and creep damage, on fracture toughness of Type 316H stainless steel has been examined. Creep damage has been introduced into the 8% pre-compressed material by interrupting creep crack growth tests. Comparisons have been made between the fracture toughness test results from the as-received, pre-compressed and creep damaged materials. Furthermore, the effects of creep crack discontinuities on the crack tip strain fields have been examined by digital image correlation measurements. Inelastic damage was found to reduce the fracture toughness of the material, with creep damage having more severe effects than pre-strain.

Measuring overload effects during fatigue crack growth in bainitic steel by synchrotron X-ray diffraction

In this work we present the results of in situ synchrotron X-ray diffraction measurements of fatigue crack-tip strain fields following a 100% overload (OL) under plane strain conditions. The study is made on a bainitic steel with a high toughness and fine microstructure. This allowed a very high (60μm) spatial resolution to be achieved so that fine-scale changes occurring around the crack-tip were captured along the crack plane at the mid-thickness of the specimen. We have followed the crack as it grew through the plastic/residually stressed zone associated with the OL crack location. We observed two effects; one when the enhanced plastic zone is ahead of the crack and one after it has been passed. Regarding the former it was found that the compressive stress at the crack-tip initially falls sharply, presumably due to the increased plastic stretch caused by the OL. This is associated with a concomitant fall in peak tensile stress at Kmax, the elastic excursion between Kmin and Kmax remaining essentially unchanged from before OL. Subsequently discontinuous closure as seen previously for plane stress caused by crack face contact at the OL location limits the elastic strain range experienced by the crack tip and thereby retards crack growth.

Investigation of Crack Tip Stress and Strain Fields at Crack Initiation of A106 Gr. B Carbon Steels under High Strain Rates

This paper analyzes crack tip stress and strain fields at crack initiation under high strain rates. In the range of high strain rates, the mechanical behavior of a material is characterized by an increased in strain rate sensitivity. However, due to geometry and constraint of various test specimen, it is difficult to quantify strain rate on the at constant test speed. To quantify the strain rate, we simulate crack tip stress and strain fields using three-dimensional finite element model. Our analysis models are fracture toughness (CT) specimen and full scale circumferential cracked pipe component. Dynamic material properties used in the finite element analysis are based on Pipe Fracture Encyclopedia. Pipe Fracture Encyclopedia provides strain rate dependent tensile test, fracture toughness test and full-scale four point bending test. All experiments were tested at 288°C and test specimens were extracted from A106 Gr, B carbon steel pipes. Three different strain rate tensile test (4 x 10-4/s, 3.4/s and 11.6/s) are fitted using Johnson-Cook model. Our results show that, applied strain rate and strain rate at characteristic length have similar values as in the CT specimen simulation result. Similar outcomes were shown in the pipe simulation result.

Crack-Tip Strain Field Mapping and the Toughness of Metallic Glasses

We have used high-energy x-ray scattering to map the strain fields around crack tips in fracture specimens of a bulk metallic glass under load at room temperature and below. From the measured strain fields we can calculate the components of the stress tensor as a function of position and determine the size and shape of the plastic process zone around the crack tip. Specimens tested at room temperature develop substantial plastic zones and achieve high stress intensities () prior to fracture. Specimens tested at cryogenic temperatures fail at reduced but still substantial stress intensities () and show only limited evidence of crack-tip plasticity. We propose that the difference in behavior is associated with changes in the flow stress and elastic constants, which influence the number density of shear bands in the plastic zone and thus the strain required to initiate fracture on an individual band. A secondary effect is a change in the triaxial state of stress around the crack tip due to the temperature dependence of Poisson's ratio. It is likely that this ability to map elastic strains on the microscale will be useful in other contexts, although interpreting shifts in the position of the scattering peaks in amorphous materials in terms of elastic strains must be done with caution.

The Research on Oblique Crack Tip Deformation Field of Airship Envelope Composites Based on the Digital Speckle Correlation Method

The tearing mechanical properties and the deformation field distribution of 45 degree oblique direction of the crack tip was studied on the stratospheric airship envelope reinforced by plain woven Kevlar-fiber composite. Here, the material samples were prefabricated with the initial length of 20mm unilateral incision, and the digital speckle correlation experimental method was used to obtain the perpendicular crack tip displacement and strain fields with artificial spots under mono-axial tear test. The results show the deformation field changes with the characteristic of discrete step and the strain concentration phenomenon, and the strain concentration zone expands as increasing tensile load. The warp and weft step maximum displacement reaches 6.00mm and 1.7mm, and deformation in every step exhibits a diminishing step law, the warp deformation in the rear area of the crack tip are evenly, while the shear and weft strain volatile in a wide range

Analysis of the Stress and Strain Field of a Thin-Walled Pipeline with Penetrated Crack Using Numerical Simulation

The model of a thin-walled pipeline with penetration crack was built using the software of ANSYS; the model was meshed with shell elements and the singular point was set. As per the results of stress analysis, using the general post processor of ANSYS, the stress intensity factor was calculated based on the plane displacement extrapolation method and the result was compared with that calculated according to the theoretical formula. The characteristic dimension of the crack-tip plastic zone was calculated according to the numerical simulation and theoretical formula respectively. Results showed that the method for building the thin-walled pipeline model with penetration crack and analysis provided in this paper could accurately describe the crack-tip stress and strain field and thus widely be used for the failure analysis of pressure pipelines.

Study of overload effects in bainitic steel by synchrotron X-ray diffraction

This work presents an in-situ characterisation of crack-tip strain fields following an overload by means of synchrotron X-ray diffraction. The study is made on very fine grained bainitic steel, thus allowing a very high resolution so that small changes occurring around the crack-tip were captured along the crack plane atthe mid-thickness of the specimen. We have followed the crack as it grew through the overload location. Oncethe crack-tip has progressed past the overload event there is strong evidence that the crack faces contact in theregion of the overload event (though not in the immediate vicinity of the current locations of the crack tip) atKmin even when the crack has travelled 1mm beyond the overload location. It was also found that at Kmax thepeak tensile strain ahead of the crack-tip decreases soon after the overload is applied and then graduallyrecovers as the crack grows past the compressive region created by the overload.

Micromechanical modeling of R-curve behaviors in human cortical bone

The risk of bone fracture increases with age because of a variety of factors that include, among others, decreasing bone quantity and quality due to increasing porosity and crack density with age. Experimental evidence has indicated that changes in bone microstructure and trace mineralization with age can result in different crack-tip strain field and fracture response, leading to different fracture mechanisms and R-curve behaviors. In this paper, a micromechanical modeling approach is developed to predict the R-curve response of bone tissue by delineating fracture mechanisms that lead to microdamage and ligament bridging by incorporating the influence of increasing porosity and crack density with age. The effects of age on fracture of human femur cortical bone due to porosity (bone quantity) and bone quality (crack density) with age are then examined via the micromechanical model.

Crack–grain boundary interactions in zinc bicrystals

In polycrystalline materials that fail by transgranular cleavage, it is known that crystallographic misorientation of preferred fracture planes across grain boundaries can provide crack growth resistance; despite this, the micromechanisms associated with crack transmission across grain boundaries and their role in determining the overall fracture resistance are not well understood. Recent studies on diverse structural materials such as steels, aluminum alloys and intermetallics have shown a correlation between fracture resistance and the twist component of grain misorientation. However, the lack of control over the degree and type of misorientation in experimental studies, combined with a dearth of analytical and computational investigations that fully account for the three-dimensional nature of the problem, have precluded a systematic analysis of this phenomenon. In this study, this phenomenon was investigated through in situ crack propagation experiments across grain boundaries of controlled twist misorientation in zinc bicrystals. Extrinsic toughening mechanisms that activate upon crack stagnation at the grain boundary deter further crack propagation. The mechanical response and crack growth behavior were observed to be dependent on the twist angle, and several accommodation mechanisms such as twinning, strain localization and slip band blocking contribute to fracture resistance by competing with crack propagation. Three-dimensional finite element analyses incorporating crystal plasticity were performed on a stagnant crack at the grain boundary that provide insight into crack-tip stress and strain fields in the second grain. These analyses qualitatively capture the overall trends in mechanical response as well as strain localization around stagnant crack-tips.

Crack observation methods, their application and simulation of curved fatigue crack growth

Abstract The observation of cracks with curved crack path has to be done optically. It is shown that a modified commercial flat bed scanner and a combination of a high-resolution scanner camera system with 10,000 × 10,000 pixels with a telecentric lens are appropriate for high-resolution (up to 8 μm/pixel) optical recording of multiple crack ends on sample areas up to 210 mm × 290 mm. The high-resolution photographs are suitable for determination of crack lengths. It is also possible to observe crack paths or geometrical crack tip parameters and strain fields by image correlation. The method is used to determine static crack resistance and cyclic crack growth curves on center crack tension and biaxial cruciform samples. Furthermore, the paper presents an improved finite element technique for the simulation of curved fatigue crack growth in a multiple arbitrarily pre-cracked isotropic sheet under biaxial plane stress loading applying a predictor–corrector procedure in combination with the modified virtual crack closure integral (MVCCI) method including the consideration of the plastic limit loads. For this, the program PCCS-2D was extended to analyse the crack growth and the plastic limit load for each crack propagation step in a fully automatic simulation. The proposed solution algorithm provides a powerful tool for flaw assessment with the failure assessment diagram procedure in combination with a numerical crack path simulation. Finally, the simulation is verified experimentally.

Wood transverse fracture analysis at the mesoscopic scale

The present study is an analysis of wood fracture behavior at the mesoscopic scale (i.e. the scale of growth ring). Radial TR crack growth mechanisms are complex and involve several events such as secondary cracks creation while cracks extend from one growth ring to another. Crack tip strain field of radial TR crack is measured by digital image correlation in order to better understand these phenomena. A numerical model for wood fracture has been conducted and a transverse model of spruce wood has been implemented. The simulation is realized by Material Point Method, a meshless method that discretizes material bodies into a collection of material points or particles. This promising tool improves the understanding of transverse fracture in spruce wood and can easily be used in further studies.