Crack Tip Stress Intensity Factor Research Articles

A bi-criteria combined evaluation approach for reinforcement effect of gravity dam with cracks

The reinforcement measures, such as pre-stressed anchor cable and concrete anti-seepage layer covering original dam body, are often used to improve the structural stability, control the crack development and advance the carrying capacity of concrete dam engineering. This paper focuses on the reinforcement effect evaluation problem of gravity dam with cracks. Some mechanical and mathematical methods, such as the J integral and interaction integral methods in fracture mechanics, the support vector machine (SVM) method, are combined. According to the integrated criteria on crack behavior improvement and carrying capacity advancement, the implementation approach for reinforcement effect identification and long-term forecast of gravity dam with cracks is investigated. Firstly, considering the effect of reinforcement practice on structural behavior, stress field and strain field of original crack tip zone in gravity dam, the stress intensity factor (SIF) is taken to represent the combined action response of reinforcement practice and loads. To improve the computation efficiency and accuracy, which are the shortcomings existing in the conventional methods applied to the calculation of stress field with complex crack surface and crack tip, the improved J integral method is combined with the interaction integral method to calculate the SIF of crack tip in gravity dam after the reinforcement implementation. Then, the cracking safety of gravity dam is regarded as a goal, the SIF is regarded as a control index. A SVM method is proposed to determine the critical loads ensuring the cracking safety of gravity dam. An approach using two criteria on SIF and critical load is developed to implement the reinforcement effect evaluation of gravity dam with cracks. Lastly, an actual gravity dam undergoing reinforcement practice is taken as an example. The approach proposed in this paper is used to calculate the SIF of crack tip and the critical loads of cracking safety. The reinforcement effect identification and long-term forecast of gravity dam are fulfilled by analyzing the development of SIF and critical load.

Phase field analysis of crack tip parameters in ferroelectric polycrystals under large-scale switching

The determination of fracture parameters at cracks in ferroelectrics under large-scale domain switching is still a great challenge. In order to evaluate the crack-tip mechanical and electrical field intensity factors, the interaction integral (I-integral) technique is further developed to cope with the heterogeneous microstructures based on the polarization distribution and crack tip fields from phase field simulations. The enhanced I-integral exhibits several merits over previous techniques for determining the crack-tip intensity factors. First, small-scale switching assumption is unnecessary. Second, the intensity factors of different modes are decoupled. Third, it is independent of integration area size, regardless of the presence of grain boundaries and domain walls. These advantages ensure the successful application of the enhanced I-integral to study toughening effects in ferroelectric polycrystals due to large-scale domain switching. Using this approach, a tensile test of PbTiO3 ferroelectric polycrystals with an impermeable crack is simulated. Simulations show that domain switching initiates not only from the crack tip but also from the grain boundaries due to high polarization gradient and stress concentration. Large-scale switching triggered by a critical load reduces the crack-tip stress intensity factors anomalously. In comparison to single crystals, the critical load for polycrystals is lower and even vanishes due to grain orientations. The results also demonstrate that the I-integral method possesses satisfactory accuracy and good area-independence for grain boundaries and domain walls.

Determination of crack tip stress intensity factors by singular Voronoi cell finite element model

A singular Voronoi cell finite element model (SVCFEM) is proposed for estimation of the mixed-mode stress intensity factors (SIFs) of crack tip in this paper. Formulation of a singular Voronoi cell finite element is based on a modified complementary energy principle. To satisfy the stress singularity at the crack tip, we enrich stress solution in assumed stress hybrid model. In addition to polynomial and reciprocal terms, singular stress terms of Williams expansion are added for elliptical crack to capture crack-tip stress concentrations. After obtaining the stress, SIFs of model I and model II were calculated using linear least-squares method. Comparisons of SVCFEM solution with analytical solution for crack are made to demonstrate the efficiency of SVCFEM.

Higher sensitivity Digital Gradient Sensing configurations for quantitative visualization of stress gradients in transparent solids

Two modified full-field Digital Gradient Sensing (DGS) methods of higher measurement sensitivity relative to the prevailing ones are described for quantifying small angular deflections of light rays caused by stresses in transparent solids. These methods are devised by combining or altering previously proposed reflection-mode DGS (r-DGS) [1] and transmission-mode DGS (t-DGS) [2] methods. The concept involves increasing the optical path within the stressed medium by introducing an additional reflective surface behind the transparent solid, either as a separate reflector or as a rear surface reflective film deposition. The former approach is designated as t2-DGS method whose measurement sensitivity is twice that of t-DGS. The latter method results in an even higher sensitivity and is called the transmission-reflection DGS or tr-DGS method by making the back surface of a transparent planar solid reflective. The governing equations of tr-DGS are introduced first followed by a comparative demonstration of t2-DGS and tr-DGS methods by measuring the stress gradients in the crack-tip region during dynamic and static fracture experiments, respectively. Results show that tr-DGS is approx. 1.5 times more sensitive than t2-DGS, and at least three times more sensitive than t-DGS approach. Together as a family of DGS methods, these methods are used to extract the crack-tip stress intensity factors of PMMA beams under quasi-static loading conditions. The measured stress intensity factors are in good agreement with the predictions.

Strain gradient fracture in an anti-plane cracked material layer

Fracture mechanics analysis in terms of evaluating stress intensity factors of an anti-plane isotropic cracked layer is carried out using strain gradient elasticity theory. The crack plane is assumed parallel to the layer edges. Both volumetric and surface strain gradient material characteristic lengths are considered in formulations and numerical solutions. Two boundary value problems corresponding to “stress-free” and “clamped” boundaries are considered in which each solution is reduced to the dual integral equations. The Fredholm integral equation, proceeding from the dual integral equations, is numerically solved to evaluate crack tip stress intensity factor. Stress intensity factors for stress-free boundary conditions are higher with smaller height (or with a longer crack) and vice versa for clamped boundaries. Volumetric strain gradient effect reduces stress intensity factor and demonstrates strong size effect on a smaller scale. Crack stiffness becomes more pronounced with positive surface strain gradient, while negative surface gradient leads to a more complaint crack. In general, the contribution of volumetric strain gradient is shown to be more dominant than that of surface strain gradient.

Mechanical improvement of metal reinforcement rings for a finite ring-shaped superconducting bulk

As a key technique, reinforcement of type-II superconducting bulks with metal rings can efficiently improve their mechanical properties to enhance the maximum trapped field. In this paper, we study the magnetostrictive and fracture behaviors of a finite superconducting ring bulk reinforced by three typical reinforcing structures composed of metal rings during the magnetizing process by means of the minimization of magnetic energy and the finite element method. After a field-dependent critical current density is adopted, the magnetostriction, pinning-induced stress, and crack tip stress intensity factor are calculated considering the demagnetization effects. The results show that the mechanical properties of the ring bulk are strongly dependent on the reinforcing structure and the material and geometrical parameters of the metal rings. Introducing the metal ring can significantly reduce the hoop stress, and the reduction effect by internal reinforcement is much improved relative to external reinforcement. By comparison, bilateral reinforcement seems to be the best candidate structure. Only when the metal rings have particular Young’s modulus and radial thickness will they contribute to improve the mechanical properties the most. In addition, if an edge crack is pre-existing in the ring bulk, the presence of metal rings can effectively avoid crack propagation since it reduces the crack tip stress intensity factor by nearly one order of magnitude.

Locking-free triangular plate element using polynomial incompatible approximation for analysis of cracked thick–thin plates

In this paper, a simple locking-free triangular plate element, referred to here as the Mindlin triangular plate element with full integration (MTPF), is presented for the analysis of cracked thick–thin plates. The element employs a new specially designed incompatible meshless approximation, independent of the nodes and triangle shape, in order to define displacements for the purpose of avoiding the use of reduced/selected integration to make the MTPF locking-free and valid for the thin plate. The current MTPF is also extended for the analysis of cracked thick–thin plates, and the virtual crack closure technique is applied in order to compute the crack tip stress intensity factors of the cracked thick–thin plates, where the formula derivation and numerical implementation are very simple and convenient for the present MTPF. Several representative numerical examples demonstrate that the MTPF is a robust and high-performance element for cracked thick–thin plates.

Ring cracks at the surface of a half-space

This paper uses a distribution of ring dislocations to determine the crack tip stress intensity factors for a ring crack at the surface of a half-space subjected to a point force at the axis of symmetry. Three cases are considered: a short crack (relative to its radius), fully open to its root; a longer crack open at the surface but closed and slipping to the root; and a longer crack open at the surface and slipping to some self-determining point in the closing region. The stress intensity factors and points of closure and stick are determined.

A mixed cover meshless method for elasticity and fracture problems

A mixed cover meshless method (MCMM) is developed to solve elasticity and fracture problems. In this technique, an arbitrary computational geometry is discretized using regular square cells, and meshless approximation functions are separately defined at the interior and boundary square cells using the concept of independent nodal covers and overlapping nodal covers, respectively. For the fracture analysis, a set of triangular independent nodal covers around a crack tip is employed, and the virtual crack closure technique (VCCT) is used to calculate the crack-tip stress intensity factors (SIFs). The overlapping nodal covers and independent nodal covers can be freely selected and converted as required during the simulation process of crack growth, and the square cells near geometry boundaries, such as material discontinuities, crack lines, or crack tips, can be further subdivided by quadtree decomposition to perform h-adaptivity analysis and to achieve the desired solution accuracy. The MCMM gets rid of the need for generating conforming meshes in the finite element method (FEM), possesses the merits of a concise formulation of interpolation functions, simple numerical implementation and convenient simulation of crack growth along arbitrary directions, and improves the computational efficiency compared to classic meshless methods such as the element-free Galerkin method (EFGM) and the meshless method based on Shepard function and partition of unity (MSPU). Several representative elasticity and fracture examples demonstrate the convergence, accuracy, and robustness of the present method.

An I-integral method for the crack-tip intensity factor in ferromagnetic materials with domain switching

An I-integral method is developed to calculate the crack-tip stress intensity factors (SIFs) in the ferromagnetic thin plate subjected to the external loads. The value of I-integral is not affected by the integral area size, the magnetization distributions or domain walls, which shows the applicability to the large-scale domain switching. Based on the stress and magnetic field obtained from phase-field simulations, the I-integral method is successfully employed to obtain the crack-tip intensity factors and decouples different modes of the crack-tip intensity factors in ferromagnetic thin plates with an impermeable edge crack under different mechanical and/or magnetic loadings. The influence of domain switching on the SIFs is investigated for different loadings. It is found that domain switching under a constant stress loading increases the crack-tip intensity factors, whereas domain switching decreases the crack-tip intensity factors under a constant strain loading. The results indicate that the domain switching-induced shielding or anti-shielding of a crack in ferromagnetic materials with an impermeable edge crack is dependent on the loading condition.

The interaction problem of two Zener–Stroh cracks with a nearby inhomogeneity

In this paper, the interaction among two Zener–Stroh cracks (with plastic zone correction) and a nearby circular inclusion are investigated. To evaluate the plastic zone sizes at crack tips in the current physical problem is a great challenge. As the first attempt to explore the multiple defects’ interaction effect on the yielding behavior of a crack, we focused on the analysis of one target crack, while the other crack and the circular inhomogeneity are treated as influence factors. With the help of coordinate transformation and superposition procedure, the formulated singular integral equations can be solved numerically. The influence of material properties, crack–crack positions and other parameters, such as crack length and Burgers vector of the Zener–Stroh crack, on the target crack tip stress intensity factor, plastic zone size and crack tip opening displacement are examined. It is found that the effects of the aforesaid parameters on the cracks are all inter-related and dependent on each other. This observation reveals the complexity of fracture analysis and the necessity to have a deep research on interacting defects in composite materials.

High-R low growth rate fatigue crack propagation at elevated temperatures

While fatigue cracking is widely considered as the primary cracking mode under cyclic loading conditions, this is not the case for high-R (Kmin/Kmax) low growth rate fatigue crack propagation at elevated temperatures. Creep cracks can sometimes be observed in such situations when the stress intensity factor range ΔK is around the fatigue crack growth threshold stress intensity factor ΔKth. A Time Dependent Failure Assessment Diagram (TDFAD) has been adopted in this study for predicting creep cracking in high-R cyclic loading conditions at elevated temperatures. In addition, attention is also paid to oxide-induced crack closure which is greatly influential at high temperatures. Three power plant steels with different chromium contents, namely 1%Cr, 9%Cr and 18%Cr steels, have been investigated at temperatures between 550°C and 650 °C. The experiments were performed by reducing ΔK continuously to ΔKth. Good accordance has been found between fracture surface observations and the TDFAD approach predictions of creep crack initiation. Apart from creep cracking, high-R ΔKth values have also been found to be influenced by oxide-induced crack closure at elevated temperatures. The enhancement is studied through the relationship between the crack tip opening displacement and stress intensity factor.

Finite Element Analysis on the Crack Growth and Stress Intensity Factor for the Contact Fatigue

In order to simulate contact fatigue crack propagation, the ANSYS APDL and Franc3D were used. The rolling contact model was established by the ANSYS APDL, then the distribution of the contact stress field under various loads was analyzed. The contact stress value demonstrated an error within ± 6%, compared to the obtained results from the Hertz theory. The contact stress field was imported into the Franc3D with a preset radical crack, the crack tip stress intensity factor distribution was calculated and the growth path of the three-dimensional contact fatigue cracks was analyzed. The comparisons with the experimental results demonstrated that the fatigue crack profile path from the peeling position of the subcutaneous layer was consistent with the simulated path, which was in a circular arc form. The main reason for this result was the fatigue crack change from the opening type I to the sliding type II. The a-N curves of the crack growth life under various load conditions were predicted based on the Franc3D, whereas the results displayed that the crack growth life decreased as the compressive stress increased.

Mechanical analysis of asphalt stabilized permeable base to inhibit reflective cracking

Asphalt stabilized drainage base has good drainage performance, can effectively rule out the water in pavement structure, reduce the occurrence of water damage, and maintain good pavement performance. Based on the mechanical analysis of the affect of asphalt stabilized permeable base on the inhibition of reflection crack, using the finite element software to simulate the stress characteristics of the asphalt and to do the mechanical analysis of asphalt pavement cracks at the grass-roots level to the pavement after stretching process, by comparing the pavement crack tip stress intensity factor of original pavement structure and set up the ATPB layer, respectively, to study the effect of asphalt stabilized permeable base on inhibition of reflection cracking.

Axisymmetric planar cracks in finite hollow cylinders of transversely isotropic material: part I—dislocation solution for infinite cylinders

This paper presents the solution for the crack tip stress intensity factors of a system of coaxial axisymmetric planar cracks in a transversely isotropic infinite hollow cylinder. The cylinder is under uniform axial tensile loading at infinity. First, the state of stress in an infinite hollow cylinder with transversely isotropic material containing axisymmetric prismatic and radial dislocations is studied. To this end, the solutions are represented in terms of biharmonic stress functions. Next, using the distributed dislocation technique, the mixed mode crack problem is reduced to Cauchy-type singular integral equations for dislocation densities on the surfaces of the cracks. The dislocation densities are employed to determine stress intensity factors for axisymmetric interacting cracks. For validation, the problems including one single crack in an infinite hollow cylinder with a circumferential edge crack or an annular crack are reexamined.

Axisymmetric planar cracks in finite hollow cylinders of transversely isotropic material: Part II—cutting method for finite cylinders

This paper is the outcome of a companion part I paper allocated to finite hollow cylinders of transversely isotropic material. The paper provides the solution for the crack tip stress intensity factors of a system of coaxial axisymmetric planar cracks in a transversely isotropic finite hollow cylinder. The lateral surfaces of the hollow cylinder are under two inner and outer self-equilibrating distributed shear loadings. First, the stress fields due to these loadings are given for both infinite and finite cylinders. In the next step, the state of stress in an infinite hollow cylinder with transversely isotropic material containing axisymmetric prismatic and radial dislocations is extracted from part I paper. Next, using the distributed dislocation technique, the mixed mode crack problem in finite cylinder is reduced to Cauchy-type singular integral equations for dislocation densities on the surfaces of the cracks. The problem of a cracked finite hollow cylinder is treated by cutting method; i.e., the infinite cylinder is cut to a finite one by slicing it using two annular axisymmetric cracks at its ends. The cutting method is validated by comparing the state of stress of a sliced intact infinite cylinder with that of an intact finite cylinder. The paper is furnished to several examples to study the effect of crack type and location in finite cylinders on the ensuing stress intensity factors of the cracks and the interaction between the cracks.

Phase field simulations on domain switching-induced toughening in ferromagnetic materials

Abstract A real-space phase field model is employed to investigate the domain switching-induced shielding or anti-shielding of a crack in ferromagnetic materials with single and multi-domain states. Phase field simulations demonstrate that magnetization switching takes place from the crack tip due to the highly concentrated stress in a ferromagnetic thin plate with a stationary crack. Based on the stress obtained from phase field simulations, the crack-tip stress intensity factors (SIFs) are calculated by linear extrapolation in the ferromagnetic thin plate subjected to different values of mechanical loads. The calculation results indicate that domain switching decreases the crack-tip stress intensity factors, resulting in domain-switching toughening in ferromagnetic materials. Furthermore, the domain switching in the multi-domain ferromagnetic plate induces a much larger decrease of stress intensity factor than that in the single-domain one, which suggests that engineering magnetic domains leads to the design of tougher ferromagnetic materials.

Mixed-mode I/III fracture toughness of polymer matrix composites toughened with waste particles

Abstract Fracture toughness of particle-filled polymer composite beams with different particle content for varying of crack inclination angles was investigated in mode I and mode III loading conditions. The beams were tested using three-point bending test with crack inclination angles of 30°, 45°, 75°, and 90°. Sewage sludge ash (SSA), fly ash (FA), and silicon carbide (SiC) microparticles were used as toughening fillers with 5, 10, 15, and 20 wt% contents of the total weight of the polymer composites. The scanning electron microscope (SEM) micrographs showed that a good indication was observed for dispersion of FA, SSA, and SiC particles within the polymer matrix. The critical crack tip stress intensity factors K Ic (crack angle 90°) and K IIIc, and the critical strain energy release rates G Ic and G IIIc were calculated and their results were compared. The mode I and mode III fracture toughness of the particulate polyester composite were improved by addition of particulate fillers. The maximum values of fracture toughness mode I (K Ic and G Ic) and mode III (K IIIc and G IIIc) were recorded at particle content of 5 wt% polymer composites.

Three-Dimensional Elastic Analysis of Rock Excavations by Using the g2 Constant Displacement Discontinuity Method

A fast computational code is presented that is dedicated for the elastic analysis of three-dimensional excavations and cracks in rocks. The problem is solved on the boundaries that are discretized with a new triangular leaf constant displacement discontinuity element with one collocation point. The creation of the new triangular element was inspired from Mindlin's special version of grade-2 or strain-gradient elasticity theory (second gradient of displacement, g2). This element is characterized by a much better measure of the average stress at the center of gravity of the triangular element compared to that of the classical elasticity element close to regions with stress or strain gradients (e.g. notches, cracks etc). In a verification stage, the accuracy of the computational algorithm for the pressurized penny-shaped and mixed-mode elliptical crack problems that have analytical solutions is demonstrated. More specifically, it is shown that the average error of the crack tip Stress Intensity Factor predicted by the gradient modified method for nine discretizations of varying density is around 3.5% with a máximum error of 5%, while the constant displacement discontinuity element displays errors varying around 14%. Moreover, the new method preserves the simplicity and hence the high speed of the constant displacement discontinuity with only one collocation point per element, but it is far more efficient compared to it, especially close to the crack tips and corners of excavations where the displacement and stress gradients are highest.

Fatigue Life Extension by Crack Repair Using Double Stop-Hole Technique

Drilling holes in the vicinity of the crack tip turns the crack into a notch and reduces the crack tip stress intensity factor. In this paper, a new idea is used in which instead of a single hole, two symmetric and interconnected holes are drilled at the crack tip. The main concept of double stop-hole method is to reduce the stress concentration at the edge of stop-holes in the cracked structural elements. The double stop drill hole method can be used to increase the fatigue life of the cracked components. The fatigue crack growth retardation is examined using an experimental investigation coupled with a stress analysis on the efficiency of proposed double stop-holes. The distance between the hole centers is considered as the main parameter affecting the efficiency of this method. The results show that the fatigue life extension caused by the double stop-hole method is significantly more than the conventional single stop-hole method.