Crack Tip Region Research Articles

Thermo-mechanical coupling analysis of edge-cracked rubber specimen focusing on the crack tip: Experimental observation and numerical simulation

The fatigue performance of rubber composite cannot be ignored in the field of engineering. Fatigue crack growth rate (FCGR) test by using a planar tensile specimen with a crack or cracks is often used for rubber fatigue characterization. Thermo-mechanical coupling characteristics of rubber composite under dynamic loading are significant and need to be considered. In our work, an interesting experimental phenomenon was observed during rubber FCGR test. The temperature around crack tip region is the highest at the beginning, and then the high temperature region shifts from the crack tip to the central region of the planar tensile specimen, and finally a steady-state temperature distribution is achieved. To explain such observation, a thermo-mechanical coupling method based on finite element analysis (FEA) for the edge-cracked rubber specimen was established. The simulation result was consistent with the experimental observation, and can explain the heat build-up phenomenon of the edge-cracked rubber well.

Methodology to evaluate stress corrosion cracking in ethanol environments, applied to circumferential welds on API 5 L steel pipelines

This work presents an experimental methodology developed to perform fatigue crack growth (FCG) and slow strain rate (SSR) tests in ethanol environments aiming to evaluate stress corrosion cracking (SCC) susceptibility of circumferential welds on steel pipelines. FCG and SSR specimens were machined from a welded pipe and the notches were properly designed to promote crack propagation in the different regions of the weld. Tests were carried out keeping the crack-tip region fully immersed in an ethanol solution, which was fueled by a circulation system to ensure replenishment and aeration throughout the test. When applied to a welded API X70 steel pipe, this experimental methodology proved to be an efficient and simple method to achieve relevant and important informations on environmentally assisted crack growth and SCC susceptibility. The method developed here is inserted in the aspects as follows:•Perform tests in slow strain rate and cyclic bend loading in circulating ethanol, to promote the fracture in the different regions of a circumferential weld joint of a steel pipe.•Investigate sensitivity to stress corrosion cracking (SCC) of these different weld regions in ethanolic environment.•This method presents constructive details of a suitable apparatus which the experiments can be easily replicated.

Unnotched fatigue of Inconel 718 produced by laser beam-powder bed fusion at 25 and 600°C

Porosity—and hence poor fatigue performance—is a major concern for additively manufactured (AM) alloys using powders as the raw materials. Since the microstructures in these alloys are also often unique, a detailed understanding of the interactions between the fatigue cracks emanating from the pores and the microstructural features is necessary for the successful deployment of the AM alloys in industry. Keeping this in view, the microstructures and mechanical properties of the as-built Inconel 718 alloy, produced using laser beam powder bed fusion (LB-PBF) process, were investigated at room temperature (RT) and 600 °C. Emphasis was on the high cycle fatigue behavior evaluated using the rotating bend fatigue tests, and the role of the lack of fusion pores (LOFs) on the fatigue resistance. The experimental results show that the unnotched fatigue strength (σf) at 600 °C is 23% lower than that at RT. This was due to the lower work hardening rate at 600 °C, which facilitates easy crack initiation at LOFs that both favorably located and oriented. For stress amplitudes (σa) higher than σf, however, dynamic recrystallization at the crack tip regions of the specimens fatigue tested at 600 °C retards the short fatigue cracks (SFCs) and leads to a substantially higher fatigue life as compared to that at RT. Postmortem analyses were for understanding the initiation and growth mechanisms of SFCs and the roles of plasticity/oxidation induced crack closure on them. It shows that the LB-PBF induced microstructural characteristics such as solidification cells with high dislocation density are effective in resisting the growth of SFCs at 600 °C, as compared to RT. These results further highlight the roles of the unique microstructural aspects of additively manufactured alloys on the fatigue resistance, especially at high temperatures.

Analysis of stress fields at the crack tip and fracture resistance parameters under conditions of gradient plasticity

This paper presents a numerical analysis based on previously obtained experimental data on crack growth for P2M and 34X steels, aluminum 7050 and titanium alloy Ti-6Al-4V compact samples (CTS) with a one-sided lateral incision, within the framework of the conventional theory of strain gradient plasticity (CMSG), based on the Taylor dislocation model. In this study, the initial points of the curved crack trajectory were considered for two classical states: plane strain and plane stress with normal separation and pure shear. The constitutional equations of material behavior for CMSGP theories were introduced into the finite element computational complex and new fields of stress-strain state parameters for the conditions of strain gradient plasticity were obtained. The results of FE calculations show a significant increase in the magnitude of the true stress fields at the crack tip, taking into account the plastic deformation gradients and the internal characteristic length of the material. The numerical results also show that the singularity in the crack tip region is different for the model of gradient plasticity of deformations and depends on the mode I/II. An important conclusion regarding the numerical results regarding the parameters of the material's fracture resistance is that the new plastic stress intensity coefficients for gradient plasticity differ for plane strain and plane stress, and also show significant sensitivity to the plastic properties of the material and to the scale parameter of the intrinsic material length, which is attractive from the point of view of practical application and further fundamental research.

Stage-II fatigue crack growth model from 3D dislocation dynamics simulations

ABSTRACT Stage-II fatigue crack propagation in FCC metals is investigated using 3D discrete dislocation dynamics (DD) simulations. The calculations show that dislocation/grain–boundary interaction affects slip dispersion everywhere in the grain, including in the crack tip region. The results are analysed and drawn in the form of simple, quantitative mathematical expressions, depending on a set of physical variables. This approach helps in developing a comprehensive crack propagation model, where the crack growth rate da/dN depends on both the crack tip opening displacements and the tip-related nucleation of nano-cavities. It is shown that the modelled crack response is compatible with the well-known Paris expression, which we further interpreted as a ratio between the energy stored in the tip region over the energy spent extending the crack surfaces. The model validity is finally evaluated by a comparison with relevant experimental evidence.

In situ observation of fracture in homogeneous and functionally graded 6061Al/SiCp composites

In the present work, 6061Al/SiCp homogeneous composites and 6061Al/SiCp functionally graded materials were prepared by vacuum hot pressing sintering. Fracture behaviors of composites were studied through three-point bending tests and fracture toughness tests with in situ observation. Results show that SiC content in the composite has a great influence on bending strength and fracture toughness. Bending strength and fracture toughness of functionally graded materials are the results of the strength, plasticity, and interlayer synergy. The fracture mechanism of composites is the initiation and growth of microcracks. A large number of microcracks initiate in matrix of the crack tip region and connect with each other to make the main crack propagate.

Interaction of shear waves with semi-infinite moving crack inside of a orthotropic media

The present work investigates the motion of a semi-infinite moving crack inside a semi-infinite half-space of orthotropic medium subjected to anti-plane shear wave. The crack is located at a finite depth from the surface of semi-infinite orthotropic medium. Our aim is to examine how such anisotropy and geometric parameters can be adjusted to reduce the magnitude of stress intensity factor (SIF) to control the crack propagation near the crack tip region. As mathematical tools, Fourier transformation and inverse Fourier transformation techniques are employed to convert the governing mixed boundary value problem to the well-known Weiner-Hopf equation with suitable boundary conditions. Some physical quantities such as SIF at the crack tip and crack opening displacement (COD) around the crack tip have been derived. Graphical exhibition has been carried out to show the impact of relevant parameters such as crack velocity, layer depth from the surface to crack and orthotropic material properties on SIF and COD. The numerical results show that SIF decay with crack depth from the layer. It is also observed that SIF decreases with an increase in crack velocity and finally tends to zero as crack velocity approches near SH-wave velocity. Also, the value of COD decays as we move along the damage near the crack tip along negative x-axis and finally tends to zero at the crack tip. This behavior of COD is consistent with the physical nature of the semi-infinite crack of the problem. The results are validated for isotropic material with some reported work and are well in agreement. The study of these physical quantities (SIF, COD) ensures the arrest of onset of crack expansion by monitoring geometric parameters and wave velocity to avoid fracture.

Tiny yet tough: Maximizing the toughness of fiber-reinforced soft composites in the absence of a fiber-fracture mechanism

Tiny yet tough: Maximizing the toughness of fiber-reinforced soft composites in the absence of a fiber-fracture mechanism

A phase field model for fracture based on the strain gradient elasticity theory with hybrid formulation

In this paper, a novel phase field (PF) model for fracture is developed in the framework of strain gradient elasticity. The strain energy decomposition methods initially proposed for linear elastic fracture problems are extended to the gradient elasticity situation. The PF model is numerically implemented through Abaqus subroutine UEL (user defined element) with nine-node quatrilateral C1-continous element. The finite element implementation is validated by studying the stress field near the static crack tip. When the length-scale parameter of the gradient elasticity is zero, the stress field is consistent with the analytical solution predicted by linear elastic fracture mechanics (LEFM). For non-zero length-scale parameters, the Cauchy stress at the crack tip is found to be non-singular and the numerical results exhibit less mesh sensitivity in the crack tip region compared with the linear elastic case. After that, four different strain energy decomposition methods (Method I-IV) are compared and discussed by studying Mode I fracture behavior under tensile load. It is found that Method I can properly characterize the toughening effect of gradient elasticity. Based on Method I, the influences of the fracture length-scale parameter lc and the strain gradient length-scale parameter l on the characteristics of the smeared crack model and the load–displacement curves are systematically discussed. The specimen size effect of Mode I crack propagation is also investigated. It is found that the length-scale parameter l has a larger influence on the load–displacement curve as the specimen size decreases. Finally, crack propagation behavior in pure shear test, three point bending test and tensile test of a notched plate with hole is investigated. It is demonstrated that the proposed PF model can well predict the curvilinear crack propagation path and properly characterize the effect of gradient elasticity. Thus, the PF model developed in this paper can be applied to study complex fracture behaviors in the framework of gradient elasticity, where the effect of internal structure on the mechanical responses become significant.

Essential work of fracture of soft elastomers

Stress concentration occurs at the crack tip of a notched sample when loaded. The crack tip region has been recognized of consisting of two regions: the inner (or end) region, which is also called the fracture process zone, and the surrounding outer region where inelastic deformation occurs. The size of these regions is strongly related to the fatigue threshold and the toughness of the material, and has been extensively studied both experimentally and numerically. Here, we study the crack tip fields of highly stretchable elastomers by adopting the concept of essential work of fracture. In the experiments, double deep edge notched tension (DENT) specimens are loaded to rupture, during which the loading curves are recorded. By changing the ligament length, two length scales around the crack tip are identified: one is the size of the fracture process zone, and the other is that of the inelastic zone. Their experimental measurements are comparable with the fractocohesive length and fracto-dissipative length of the materials, respectively. Moreover, we find that the essential work of fracture weof a highly stretchable elastomer, obtained by extrapolating the specific work of fracture wf to zero ligament length, resembles the fatigue thresholdTth obtained by a separate fatigue test. Furthermore, we compare the fatigue threshold with those predicted by Lake-Thomas model and Wells model. The present work links the essential work of fracture to the fatigue threshold, and elucidates the physics embedded in the crack tip fields of highly stretchable materials.

Analysis of crack on the labyrinth part of the gas turbine engine

The main objective of this study is to analyze the crack developed in the Labyrinth seal of a gas turbine engine and to determine the number of cycles required for the crack to grow to various lengths. Here, ANSYS Mechanical APDL is the tool to carry out the crack analysis. The crack is modelled and analyzed according to the principles of Linear Elastic Fracture Mechanics (LEFM) theory by Griffith and Paris law because of the negligible plasticity found at the crack tip. Here, the model is analyzed with and without the crack for the temperature and stress profile. The stress intensity factor is obtained using the ANSYS software. The information is derived from the graph of crack propagation rate as a function of stress intensity factor of Haynes 25 material which was used to analytically determine the number of cycles the labyrinth seal could sustain. The maximum and minimum temperatures were 1132 °C and 250 °C over a span of 10 mm length, which was the region of interest. The maximum thermal stress generated was around 1430 MPa at crack tip region for full crack model. The stress intensity factor was obtained was found to be 18.7 MPa√mm. The crack propagation rate was calculated analytically over a range of 2–4 mm with an increment of 0.5 mm. The number of cycles required for the crack to propagate over the successive 0.5 mm intervals was 97, 82, 71 and 63 cycles respectively.

A sideface traction approach for cohesive and frictional crack growth problems using SBFEM

This study develops a new procedure for solving cohesive and frictional crack growth problems in quasi-brittle materials such as concrete using the scaled boundary finite element method (SBFEM). In this procedure, the cohesive and contact tractions near the crack-tip region are modelled as linearised​ tractions on the ‘sidefaces’ of the cracked subdomains. The tractions away from the crack-tip region are implemented by utilising zero-thickness interface elements. A novel scheme is proposed to estimate the linearised sideface tractions in the cracked subdomain. The scheme utilises stress intensity factors (SIFs) iteratively within the load-step such that the crack-tip singularities vanish when the equilibrium position is reached. This leads to the stress fields in the crack-tip region being accurately captured without mesh refinement. A stress-based criterion is used to determine the crack propagation condition and direction, which requires minimal computational effort as the stresses in the crack-tip region are directly extracted from the semi-analytical formulation of SBFEM. The proposed method is versatile as it can solve both the cohesive and frictional crack growth problems. The efficacy of the method is shown through benchmark examples and practical applications.

The Analysis of a Cracked Material under Combined Unsymmetric Thermal Flux and Symmetric Linear Mechanical Loading

An improved partially permeable crack model is put forward to deal with the problem of a single crack embedded in an orthotropic or isotropic material under combined unsymmetric thermal flux and symmetric linear mechanical loading. With the application of the Fourier transform technique (FTT), the thermoelastic field is given in a closed form. Numerical results show combined unsymmetric linear thermal flux, symmetric linear mechanical loading, and dimensionless thermal conductivity, and the coefficient has influences on fracture parameters. For the improved partially permeable crack, the mode II stress intensity factor and the energy release rate might be zero or positive under combined unsymmetric thermal flux and symmetric linear mechanical loading. Therefore, closure of the crack tip region need not be considered under combined unsymmetric thermal flux and symmetric linear mechanical loading when making use of fracture parameters as a criterion.

Single edge crack effect on mechanical property of polyimide flexible composite envelope

The existence of cracks has a great influence on the life span of the envelope material of aerostats, especially for stratospheric airships that operate in harsh environments. Understanding the relationship between fracture mechanism and composite structure of envelope materials is of great significance to the design and development of envelope materials. To explore the fracture mechanism of envelope material, a novel polyimide (PI) envelope was developed by lamination method. Then, the fracture behavior and mechanism of PI envelope with single edge crack was studied and analyzed in detail by means of experimental method and theoretical model analysis. It was found that the crack orientation has no significant effect on the fracture strength of PI envelope, while the increase of crack length will increase the strength loss rate and decrease the crack sensitivity. These phenomena suggest that the fracture strength loss of envelope is mainly determined by the number of cut-off longitudinal yarns. And the stress transfer effect of coating and transverse yarns which causes stress concentration in the crack tip region is another important factor affecting the fracture strength of PI envelope. Besides, the interfacial properties between coating and fibers as well as the size effect of coating also play an important role in the fracture property of PI envelope. Finally, stress intensity factor theory and critical stress field theory were chosen to study the fracture behavior of PI envelope. The calculation results indicated that critical stress field theory can better predict the fracture strength of PI envelope.

Stress field solution to anisotropic plate with mode II crack based on pan-complex function

The crack-tip stress problem to the anisotropic materials was mainly discussed under the shear loading model. For the sake of solving the stress boundary problem, the pan-complex function method was achieved in the first place. The elastic theory of composite materials has been clearly reviewed in order to determine the material physical parameters. Equilibrium equations and deformable compatibility condition were introduced on the basis of plane elastic mechanics. The key to the settlement of the boundary question must lie in solving the partial derivative equation and the axial transformation of the pan-complex variables. The reasonable stress functions were chosen in order to meet the needs of shear loading states. The pan-complex function and the polar coordinate replace approach are utilized with the aim of solving the stress boundary problems for the anisotropic plate. The formulas of the stress components near the crack-tip region were finally determined by the real functions. The method in this article may be much important to the fracture analysis of composite materials.

FATIGUE CRACK GROWTH BEHAVIOR OF CARBON BLACK–REINFORCED NATURAL RUBBER

ABSTRACTFatigue crack growth behavior of carbon black–reinforced natural rubber is investigated. Rubber compounds of Shore A = 70 are prepared by varying the formulation loadings of a wide range of carbon black types based on their structure and surface area properties. The resulting fatigue crack growth behavior shows significant variation in β exponent values, depending on the properties of the carbon black. These variations are rationalized by considering the strain amplification of natural rubber by carbon black aggregates in the region of compound directly ahead of the crack tip. An assumption is made that little networking of the carbon black aggregates exists in this region of very high strain and that hydrodynamic calculations that consider occluded rubber can therefore provide realistic values for strain amplification. A reasonable scaling of power law crack growth parameters to calculated strain amplification factors is found, with the exponent, β, decreasing with increasing strain amplification. The implication here is that enhanced strain amplification promotes the formation of strain-induced crystallites in the crack tip region. Performance tradeoffs resulting from the crossover of crack growth data sets dependent on the carbon black type are discussed. Of practical significance is the fact that the strain amplification factors can be calculated directly from knowledge of carbon black type and loading in rubber formulations.

Water promotes the formation of fibril bridging in antler bone illuminated by in situ AFM testing

Water, as one of the main components of bone, has a significant impact on the mechanical properties of bone. However, the micro-/nanoscale toughening mechanism induced by water in bone remains at only the theoretical level with static observations, and further research is still needed. In this study, a new in situ mechanical test combined with atomic force microscopy (AFM) was used to track the micro-/nanocrack propagation of hydrated and dehydrated antler bones in situ to explore the influence of water on the micro-/nanomechanical behavior of bone. In hydrated bone, observations of the crack tip region revealed major uncracked ligament bridging, and the conversion of mineralized collagen fibrils (MCFs) from bridging to breaking is clearly seen in real time. In dehydrated bone, multiple uncracked ligament bridges can be observed, but they are quickly broken by cracks, and the MCFs tend to break directly instead of forming fibril bridges. These experimental results indicate that the hydrated interface promotes slippage between collagen and the mineral phase and slippage between MCFs, while the dehydrated interface causes MCFs to fracture directly under lower strain. The platform we built provides new insights for studying the mechanism of toughening of the components in bones.

Effect of aggregate gradation on crack propagation in asphalt mixtures at low temperatures based on the Eshelby equivalent inclusion theory

This paper presents a study to evaluate the mixed-mode crack propagation behavior of several typical asphalt mixtures at low temperatures. Based on the Eshelby equivalent inclusion theory and Griffith micro-fracture theory, the basis for determining the I-II mix mode fracture types during crack propagation was established. A random particle-based growth algorithm was adopted to develop a heterogeneous DEM model for three typical asphalt mixtures: open-graded structure (OGFC-13), gap-graded structure (SMA-13), and dense-graded structure (AC-13) mixtures, and a virtual indirect tensile test was conducted. The characteristics of the development of I-II mix mode fractures for three asphalt mixtures at low temperatures were analyzed in four aspects: changes in the number of micro-cracks, proportions of crack types, energy release rates, and force chain diagrams of crack tip stress fields. The results indicate that: (1) From the perspective of the changes in the number of cracks, the dense-graded asphalt mixture has the largest number of micro-cracks, and the proportion of mode I cracks that are mainly due to tension is dominant, while the proportion of mode II cracks that are mainly due to shear is insignificant; (2) The crack energy release rate G(t) in the time-domain increases as the rate of internal energy consumption increases, along with a reduction in the energy storage rate, as the spatial distribution of aggregates change in the open-graded, gap-graded, and dense-graded asphalt mixtures. From an energy standpoint, it was found that more energy is required when the dense-graded asphalt mixture is fractured; (3) In terms of the stress field distributions in the crack tip regions, compared with the open-graded and gap-graded asphalt mixtures, the interior of a dense-graded asphalt mixture is less likely to develop stress concentrations, which is beneficial in suppressing the occurrence of a shear stress field, thereby reducing the occurrence of mode II low-temperature cracks. The results of this research provide theoretical support for the anti-cracking design of asphalt mixtures based on meso-characteristics.

Oscillatory and tip-splitting instabilities in 2D dynamic fracture: The roles of intrinsic material length and time scales

Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length scales — a nonlinear elastic length scale ℓ and a dissipation length scale ξ — that do not exist in Linear Elastic Fracture Mechanics (LEFM), the classical theory of cracks. In particular, it has been shown that at a propagation velocity v of about 90% of the shear wave-speed, cracks in 2D brittle materials undergo an oscillatory instability whose wavelength varies linearly with ℓ, and at larger loading levels (corresponding to yet higher propagation velocities), a tip-splitting instability emerges, both in agreements with experiments. In this paper, using phase-field models of brittle fracture, we demonstrate the following properties of the oscillatory instability: (i) It exists also in the absence of near-tip elastic nonlinearity, i.e. in the limit ℓ→0, with a wavelength determined by the dissipation length scale ξ. This result shows that the instability crucially depends on the existence of an intrinsic length scale associated with the breakdown of linear elasticity near crack tips, independently of whether the latter is related to nonlinear elasticity or to dissipation. (ii) It is a supercritical Hopf bifurcation, featuring a vanishing oscillations amplitude at onset. (iii) It is largely independent of the phenomenological forms of the degradation functions assumed in the phase-field framework to describe the cohesive zone, and of the velocity-dependence of the fracture energy Γ(v) that is controlled by the dissipation time scale in the Ginzburg–Landau-type evolution equation for the phase-field. These results substantiate the universal nature of the oscillatory instability in 2D. In addition, we provide evidence indicating that the tip-splitting instability is controlled by the limiting rate of elastic energy transport inside the crack tip region. The latter is sensitive to the wave-speed inside the dissipation zone, which can be systematically varied within the phase-field approach. Finally, we describe in detail the numerical implementation scheme of the employed phase-field fracture approach, allowing its application in a broad range of materials failure problems.

Study on prediction method of crack propagation in absorber weld by experiment and simulation

As an important equipment for purifying crude oil and natural gas in energy industry, absorber is subjected to harsh working environment of high stress and severe corrosion. Especially, weld is the weak region of the absorber, which faces significant risk of crack propagation due to residual stress caused by the welding process, working pressure and temperature. Meanwhile, crack propagation in absorbers with high pressure, high temperature and toxic media can often cause disastrous consequences. Therefore, to solve this problem, a systematic method considering welding, heat treatment and working process is presented in this paper to predict crack propagation completely in the weld. In the case, based on actual conditions, a finite element model (FEM) of welding process considering transient heat transfer and heat radiation for residual stress field analysis is established to obtain the far-field stress for cracks. Then, the detailed analysis of stress field and stress intensity factor (KI) under the obtained far-field stress at the crack tip is carried out through the method of integrating the strain energy density (SED) in the crack tip region. Finally, experiments of fracture toughness (KIC) of undamaged weld specimens and post-corrosion weld samples are carried out to compare with KI obtained by FEM and evaluate the safety of existing cracks. The method presented in this paper is a complete system that can provide a universal technological basis for crack propagation prediction and safety assessment of pressure vessel.