Crack Tip Stress Field Research Articles

Finite deformation near a crack tip terminated at an interface between two neo-Hookean sheets

A crack terminating at an arbitrary angle to the interface between two neo-Hookean sheets is investigated under plane stress conditions using finite deformation theory. The asymptotic crack-tip deformation and stress fields are analyzed as a function of the ratio of the moduli and the angle of the crack relative to the interface. Full-field numerical calculations and experimental studies validate the analytical results. A stretch-based crack growth criterion is developed using crack-tip field solutions. Such criterion can predict the delay of crack growth through the bi-material interface observed in experiments and can be extended to any heterogeneity and material.

Investigation of the effect of the blast waves on the opposite propagating crack

The stress waves have a significant effect on crack propagation during blasting. In this paper, a microsecond controlled blasting case involved with the interactions between blast waves and an opposite propagating crack is studied using dynamic photoelasticity method. The results show that the stress waves influence the local stress field of dynamic crack tip , and alter the crack propagation behavior. Moreover, during crack-wave interactions, both the singular stresses and the nonsingular stresses around the crack tip changed apparently. With the incidence of dilatational wave , the non-singular stresses σ ox and σ oy around the tip of opposite propagating crack increase remarkably, inducing an increase in the crack extension resistance, and decreasing both the crack velocity and the dynamic stress intensity factor K I d . Whereas, when the shear wave impinges onto the opposite propagating crack, the crack tends to increase the crack velocity. In addition, the fractal dimension of the crack velocity decreases during the incidence of dilatational wave, and increases when the shear wave impinges upon the opposite propagating crack.

Effect of creep-fatigue loading condition on crack tip fields of grade 91 steel at crack initiation and growth

In this paper, the effect of creep-fatigue loading condition on crack tip deformation and stress fields of Grade 91 steel at 600 °C at crack initiation and growth is studied. By using finite element debond analysis method, creep-fatigue crack growth tests using C(T) specimens under various load ratios and hold times are simulated, and the effect of creep-fatigue load ratio and hold time on the crack opening profile, equivalent stress, crack-opening stress and triaxiality at crack initiation and growth is presented. It is found that the crack tip deformation and stress fields under tension–compression creep-fatigue loading are overall different from those under tension-tension creep-fatigue and pure creep loading, due to re-sharpening of the crack tip.

Effect of plastic deformation on the elastic stress field near a crack tip under small-scale yielding conditions: An extended Irwin's model

The effective stress intensity factor derived from Irwin’s model is greater than the linear elastic counterpart. This is in contradiction to the shielding effect of crack-tip plastic zone. Besides, the classic Irwin’s model underestimates the size of the crack-tip plastic zone compared with Dugdale’s model and FE analysis. In this paper, an extended Irwin’s model for elastic perfectly-plastic material under small-scale yielding conditions is developed through imposing static equivalence between the plasticity-affected stress field and linear elastic stress field in the plasticity-affected zone. The extended Irwin’s model is capable of quantifying the effect of the crack-tip plastic zone on the crack-tip elastic stress field. It reduces to the classic Irwin’s model in the limiting case. This new version of Irwin’s model provides new insights in elucidating the effect of the crack-tip plastic zone on fracture behavior.

A unified description of mechanical and actuation fatigue crack growth in shape memory alloys

The damage tolerance approaches to fatigue rely on fracture mechanics concepts to explicitly account for the fatigue crack growth process. These approaches typically adopt the Paris equation, which relates the crack growth per cycle to the range of variation of the stress intensity factor, ΔK, during cyclic loading by means of experimentally calibrated parameters. Conditions on the validity of a single parameter description of the near crack tip stress and strain fields restrict the applicability of ΔK to fatigue crack growth resistance in Shape Memory Alloys (SMAs) under general thermomechanical loading paths. These conditions are substantially relaxed for the cyclic ΔJ–integral approach, which can achieve similitude over a wider range of loading conditions and geometric configurations. Thus, ΔJ qualifies as a potential unified descriptor of thermomechanical fatigue crack growth resistance in SMAs, an assertion, which is tested in this work for data from both purely mechanical and actuation fatigue crack growth experiments of a high temperature SMA, Ni50.3Ti29.7Hf20. In the latter, compact tension specimens are subjected to thermal cycling under constant load between an upper and a lower cycle temperature that allows for the stable phase to alternate in each cycle. It is shown here that a Paris-type power-law crack growth expression based on the ΔJ-integral can fit fatigue crack growth rate data from both types of experiments with a single set of parameters. This new analysis method for both actuation and mechanical fatigue crack growth rates provides a unified description for fatigue crack growth in SMAs and can allow estimating actuation fatigue crack growth rates, laborious and challenging to measure, from easier to detect mechanical fatigue crack growth rates.

Extracting fracture mechanics parameters (higher-order coefficients of Williams series expansion) from FEM analysis and digital photoelasticity method

The paper describes new algorithms and procedures proposed for determining fracture mechanics parameters from finite element analysis using the over deterministic method. The multi-parameter crack tip stress field description is used. The algorithms and procedures based on multi-parameter stress field representations in series form are shown to be a powerful tool for reliable and accurate parameter determination. The technique is aimed at the determination of coefficients of the Williams series expansion from finite element analysis and is based on the over deterministic approach. The methodology is illustrated and applied to several cases of cracked specimens. Examples are presented for crack-tip fields recorded using digital photoelasticity. The results of finite element analysis are compared with the digital photoelasticity experiments. The results are in good agreement. The principal stresses obtained from finite element method are in good agreement with the isochromatic fringe patterns obtained by the photoelasticity method. Explanation has been made for giving guidance to a user on how best to approach implementation of the method from a practical standpoint.

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.

On the crack-tip stress field due to the presence of isotropic dilatational inclusion: theoretical and numerical analysis

In this paper, the stress field at the crack-tip of a semi-infinite crack interacting with an isotropic dilatational inclusion is studied. The fundamental solution for a semi-infinite crack interacting with an eigenstrained point is presented first. By employing it as Green’s function, a crack enclosed by a homogenous inclusion is formulated and its Kolosov–Muskhelishvili complex potentials are obtained. Then the approximate solutions for the full-field stress in the vicinity of the crack-tip are derived. Finally, numerical method is performed, which not only reveals the distribution of the stress field, but also validates the theoretical analysis. As expected, theoretical and numerical results show that the presence of dilatational inclusion will produce a significant shielding effect on crack-tip. Importantly, it is found that a stress jump occurs at the interface between inclusion and matrix, which may unexpectedly trigger a micro-damage prior to the semi-infinite crack-tip. This mechanism is capable of leading to the crack growth fundamentally, when it is exposed to an oxidizing or corrosive environment.

Estimation of the creep crack-tip stress field considering the effect of threshold stress

Because of the presence of second-phase particles or nanoscale particles, a term of threshold stress incorporated into the power-law creep model of some materials, such as magnesium, aluminum, and chromium alloys. The estimation of the creep crack-tip stress field for these materials is notably important to facilitate their exploitation in high-temperature structures. In the present work, a two-term asymptotic expansion of the stress field is developed to predict the creep crack-tip stress field for power-law creep materials with threshold stress. The finite element method is used to verify the accuracy of the two-term asymptotic expansion of the stress field. The simulation results reveal that the two-term asymptotic expansion of the stress field is accurate enough as an engineering method in estimating the creep crack-tip stress field. In addition, the existing estimation method of the time-dependent C-integral of C(t) can be directly implemented in power-law creep materials with threshold stress.

On the Topology Update of the Numerical Manifold Method for Multiple Crack Propagation

Crack initiation and propagation are the two key issues of concern in the geotechnical engineering. In this study, the numerical manifold method (NMM) is applied to simulate crack propagation and the topology update of the NMM for multiple crack propagation is studied. The crack-tip asymptotic interpolation function is incorporated into the NMM to increase the accuracy of the crack-tip stress field. In addition, the Mohr-Coulomb criterion with tensile cut off is adopted to be the crack propagation criterion to judge the direction of crack initiation and propagation. Then a crack tip searching method is developed to automatically update the position of the crack tips. The inapplicability of the original loop search method in the NMM is also illustrated and a novel loop search method based on manifold elements is developed for physical loop updating. Moreover, methods for the manifold element updating and physical cover updating are provided. Based on the above study, the developed numerical method is capable to simulate multiple crack propagation. At last, typical rock rupture problems are numerically simulated to manifest the effectiveness of the developed numerical method.

Experimental study on mode-I and mixed-mode crack propagation under tangentially incident P waves, S waves and reflected waves in blasts

A dynamic crack subjected to tangentially incident P and S waves, as well as reflected waves, was studied by caustics method in a PMMA plate under two explosions of 20 mg and 60 mg lead azide. Periodic P and S waves are visualized as fringes with different densities, which is verified by calculations of arriving time and different caustics patterns in the crack tip. Distorted and classical caustics patterns occur under P and S waves, respectively, indicating that crack-tip K-dominated stress field is destroyed by P waves, while it is less disrupted by S waves. Hence, modified caustics interpretation previously proposed by authors and classical one are employed to reproduce experimental caustics patterns under P and S waves, respectively, to obtain crack-tip positions, crack velocity, KI and KII. Results show that P-wave compression loading plays a dominant role to arrest the crack, despite temporary crack re-initiation by P-wave tension loading, and that S waves temporarily accelerate the crack with alternate positive and negative KII, indicating periodic shear stress is not a sustainable driving force for crack propagation. Reflected waves cause mixed-mode crack propagation with periodic crack deflections, in which peaks of KI correspond to peaks of crack velocity and flat crack path, however peaks of KII correspond to crack slowdowns and crack deflections. Finally, this paper emphasizes a comprehensive analysis including crack path, cack-tip positions, crack velocity, caustics shape, KI and KII is required for evaluating mixed-mode crack propagation in blasts.

Flaw Resistance and Mode - I Fracture Energy Redistribution in Bamboo - A Correlation

Bamboo is a unidirectional fibre-reinforced composite with radially graded and almost transversely isotropic elastic properties. The cracks originated in bamboo under bending due to wind loads propagate along the fibre direction. This process is controlled by interlaminar fracture toughness. In order to observe the spatial distribution of the fracture toughness in bamboo, energy release rate is theoretically deduced from the general equations for crack-tip stress fields in anisotropic bodies. The analysis shows that the fracture toughness has graded distribution and the trend is opposite to that of axial modulus. To verify this, the energy release rate (or fracture toughness) is experimentally calculated for double cantilever beam specimens (with a crack placed in different fibre density region) in mode-I i.e. crack opening mode. It is observed that the crack propagation parallel to fibres (splitting) develops easily and the energy release rate decreases with increased density of fibre bundles. The observed trend closely corroborates the results from theoretical analysis. From the results of real-time wind load simulations (reported elsewhere) on tapered bamboo-like structure it is concluded that with the help of radially graded fracture toughness bamboo converts flaws of all orientations into splitting mode.

Fatigue damage growth and fatigue life of unidirectional composites

A micromechanical model is developed for the prediction of the growth rate of fatigue damage zones in unidirectional fibre composites subjected to cyclic tension-tension loading. The fatigue damage occurs by progressive fibre breaks caused by the debond crack tip stress fields of fibres that have broken in earlier load cycles. The debond crack tips are taken to advance along the broken fibres due to a cyclic slip-induced decrease in the frictional sliding shear stress acting along the debonded parts of the fibres that undergo repeated forward and reverse slip. The fatigue life is calculated as the number of load cycles for damage zones to reach a critical size where rapid composite failure can occur by longitudinal splitting cracks connecting damage zones within the specimen. A parameter study is performed to explore how the damage growth rate and fatigue life depend on microscale parameters (mechanical properties of fibre, matrix and fibre/matrix interface).

Automatic Crack Tip Meshing Approach for Constraint-Based Fracture Mechanics Application

Finite element analysis is a popular method used to characterize crack tip stress and strain fields in fracture mechanics problems. In a constraint-based elastic-plastic fracture mechanics, the crack tip stress and strains are essentially dependent on the accurate crack tip finite element configuration. Typical finite element software does not provide control of node and elemental numbering order and sequence which caused difficulty to examine different crack configuration state of stress–strain using automated post-processing codes. A method to automate the creation of finite element mesh of arbitrary lengths and shapes of standard and nonstandard fracture mechanics geometries using a geometric progression technique is described. A list of equations was proposed to develop nodal and elemental model data that represented a defined region of a cracked geometry. Assembly of the regions produced a finite element mesh representing a fracture mechanics cracked geometry which can be incorporated into a typical finite element program. The approach can eliminate the modeling processes of finite element of cracked specimens and offers the ability to control the nodal and elemental numbering system to allow systematic stress and strain elucidation for large degrees of freedom mesh and history-dependent incremental plasticity crack tip analysis. The approach used to develop the finite element mesh was discussed, and examples of the finite element mesh generated by the approach were compared to established two-parameter elastic-plastic fracture mechanics results. Finally, the algorithm codes used to develop the cracked models are supplied as supplementary files to interested users.

Photoelastic evaluation of stress fields and coefficients of multi-parameter asymptotic expansion of the crack-tip stress field

In this work, digital photoelasticity method is appliedfor estimation of the crack tip fracture mechanics parameters for a plate with double edge notches and different crack configurations.The digital image processing tool for experimental data obtained from the photoelasticity experiments is developedand utilized. The digital image processing tool is based on the Ramesh approach but allows us to scan the image in any direction and to analyse the image after any number of logical operations. In the digital image processing fringe analysis, the optical data contained in the transmission photoelasticisochromatics were converted into text file and then the points of isochromatic fringes with minimum light intensity were used for evaluating fracture mechanics parameters. The multi-parameter stress field approximation is used. The mixed mode fracture parameters, especially stress intensity factors (SIF) are estimated for specimen configurations like double edge notches and inclined center crack using the proposed algorithm based on the classical over-deterministic method. The effects of higher-order terms in the Williams expansion were analysed for different cracked specimens. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.

EXTRACTION OF FRACTURE MECHANICS PARAMETERS FROM FEM ANALYSIS: ALGORITHMS AND PROCEDURES

The paper describes new algorithms and procedures proposed for determining fracture mechanicsparameters from finite element analysis using the over deterministic method. The multi-parameter cracktip stress field description is used. The algorithms and procedures based on multi-parameter stress fieldrepresentations in series form are shown to be a powerful tool for reliable and accurate parameterdetermination. The technique is aimed at the determination of coefficients of the Williams series expansionfrom finite element analysis and is based on the over deterministic approach. The methodology is illustratedand applied to several cases of cracked specimens. Examples are presented for crack-tip fields recorded usingdigital photoelasticity. The results of finite element analysis are compared with the digital photoelasticityexperiments. The results are in good agreement. The principal stresses obtained from finite element methodare in good agreement with the isochromatic fringe patterns obtained by the photoelasticity method.Explanation has been made for giving guidance to a user on how best to approach implementation of themethod from a practical standpoint.

Determination of SIFs and T-stress using an over-deterministic method based on stress fields: Static and dynamic

An over-deterministic method based on crack-tip stress fields is proposed for evaluating stress intensity factors (SIFs) and T-stress at crack tip for mode I, mode II or mixed-mode I/II cracks under static or dynamic loading. In this method, the coordinates and stresses of the nodes around the crack tip, obtained from finite element method (FEM) or extended finite element method (XFEM), are brought into the expansion of Williams’ stress series when the cracked body is subjected to static or dynamic loading. Then, a set of over-deterministic equations can be obtained, and the optimal solution of SIFs as well as T-stress can be achieved by solving these equations using the least square method. Various cracked bodies are employed to verify the accuracy of the proposed method, and the effects of the number of terms in Williams’ series expansion, the number and location of the nodes selected around the crack tip, and the mesh around the crack tip on SIFs and T-stress are detailed discussed. Results show that the proposed method is quite simple and convenient to obtain SIFs and T-stress under static or dynamic loading, with being in good agreement with the solutions from previous works. Satisfactory results can be achieved only if the coordinates and stresses of the nodes around the crack tip are accurate enough. In addition, it can be found that the proposed method can also be used to calculate higher-order coefficients of Williams’ series expansion.

Fatigue Crack Growth in Plastically Compressible Solids: Role of Negative Stress Ratio, Plastic Compressibility and Strain Softening

The effect of cyclic loading on fatigue crack growth in plastically compressible solids is investigated at negative stress ratio under plane strain and small scale yielding conditions. The material is characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The plastic crack growth, crack tip opening displacement (CTOD) and near crack tip stress fields are presented using finite element method. Material hardening/ softening has a major relevance on crack growth, CTOD and the evolution of stress distribution. It is revealed here that the negative stress ratio can significantly influence the loading conditions at the crack tip and thereby increase the crack growth for tension–compression loading for hardening material whereas the fatigue crack growth of plastically compressible hardening-softening-hardening material is only slightly affected by the negative stress ratio albeit it is accepted in literature that compressive loads contribute to fatigue crack growth significantly. In the present studies, the CTOD variation with applied load and the near stress distribution are also very unusual in nature.

Fabrication and characterization of aluminum - magnetic shape memory alloy composites

Smart composites, manufactured with embedded functional materials, hold the potential for a new type of structural health monitoring systems. The work herein focuses on how embedding Ni 43 Co 7 Mn 39 Sn 11 metamagnetic shape memory alloy (MMSMA) sensory particles into pure aluminum matrix modifies the chemical constitution and mechanical properties of both materials. Martensitically transforming particles in pure Al or Al alloys can interact with crack tip stress fields and undergo stress-induced martensitic transformation. This process emits acoustic signals and changes the magnetic state of the particles, which can then be exploited using acoustic monitors and/or magnetic sensors to determine the crack locations. Fabrication of these composites consisted of consolidation of homogeneously mixed powder precursors containing 10 vol% of Ni 43 Co 7 Mn 39 Sn 11 MMSMA particles. Elemental composition, hardness, and elastic modulus of the embedded particles and resulting diffusion region between the particles and the matrix were determined using wavelength dispersive spectrometry and instrumented nanoindentation. Elastic constants of the sintered bulk composites were also experimentally determined using resonant ultrasonic spectroscopy (RUS). Compositional analysis revealed that the diffusion region contained a diverse group of intermetallics. Nanoindentation results demonstrated that the diffusion region exhibits a high hardness value of 10.0 ± 0.3 GPa and an elastic modulus of 163 ± 5 GPa, as compared to the embedded particles having a hardness of 4.5 ± 0.4 GPa, and elastic modulus of 127 ± 6 GPa. Poisson's ratio and the stiffness tensor components (C 11 , C 12 , and C 44 ) were found to be 0.34, 214 GPa, 111 GPa, and 52 GPa, respectively, through RUS. The important material properties determined in the present study, especially the interface properties, can be used to model the composite system to optimize the particle size, distribution, and the size of the interfaces for desired bulk mechanical properties and damage sensing ability.

Deformation inhomogeneity at the crack tip of polycrystalline copper

Molecular dynamics simulation is conducted on single crystal and polycrystalline copper. Two different crack tip orientations (001) [-110] and (001) [010] are selected for copper single crystal. For copper single crystal with crack tip orientation of (001) [010], stress is concentrated at the crack tip, and cleavage crack propagation happens due to lack of dislocation activity at the crack tip. For copper single crystal with crack tip orientation of (001) [-110], continuous emission of dislocations from crack tip results crack tip blunting and reduction of stress concentration as well. Homogeneous crack tip stress and strain fields are evident for copper single crystals, however, stress and strain fields slightly alter with the generation of dislocations and defects. Crack tip stress and strain distribution are inhomogeneous from the beginning of the deformation for polycrystalline copper. Higher stress concentration at the grain boundary than crack tip results in nucleation of initial dislocations from the grain boundary during plastic deformation.