Crack Tip Stress Intensity Factor Research Articles

Crack propagation simulation and overload fatigue life prediction via enhanced physics-informed neural networks

The fatigue crack growth simulation and life prediction of structures are implemented in this paper based on the physics-informed neural networks (PINNs). Firstly, the enhanced PINNs are proposed by introducing the crack tip asymptotic displacement fields, so that the crack tip stress intensity factors can be calculated accurately even when the number of collocation points is small and the distribution grid is regular. The enhanced PINNs essentially transform the solution of elastic body containing crack into the optimization of minimizing the constructed loss functions, and can invert the fracture parameters. Then, an automatic crack propagation simulation method is developed based on the enhanced PINNs. The network architecture and the overall node distribution can be unchanged during the crack propagation process, and only new crack surfaces need to be processed and corresponding loss functions need to be modified. Because the nodal refinement around crack-tip is not required, this simulation method is convenient and can accurately predict the mixed-mode crack propagation path. Finally, the fatigue crack growth life algorithm considering overload is developed, where the effect of each overload can be captured by the cycle-by-cycle method. Based on this algorithm, the retardation behavior can be characterized and the fatigue life of structure under the load spectrum with periodic overloads can be accurately predicted. The sufficient examples are given to verify the feasibility and accuracy of the method proposed in this paper.

Study on Stress Intensity Factor of Girth Weld with Crack Defects

In order to study the safety performance of the girth weld with cracks in the pressure vessel in use, based on fracture mechanics, this paper adopts ABAQUS and FRANC3D joint simulation to calculate the crack tip stress intensity factor(SIF). The influence of crack location, length and depth on the stress intensity factor of crack tip is analyzed. The results show that the crack SIF at different crack locations (inner crack > buried crack > outside crack) increases with the increase of crack length and increases with the increase of crack depth.

Identifying crack tip position and stress intensity factors from displacement data

Identifying crack tip position and stress intensity factors from displacement data

Shielding effect of ring dislocation dipole on penny-shaped crack

Mechanical behavior of strongly crystalline materials can be significantly influenced by the internal dislocation structure and their iteration with micro crack-like defects. Thus, study on the crack-dislocation interaction problems can help to understand the failure mechanism of crystalline materials. Previous theoretical analysis have been mostly limited to plane problems, where the cracks are idealized as straight slit with infinite or zero out plane dimension and the dislocations slip along an inclined straight path starting from the crack tip. In this paper, we explore a new interaction mechanism under axisymmetric deformation state. An unconventional case of a penny-shaped crack interacts with a ring dislocation dipole is considered. Both the ring dislocation dipole and crack are modelled as axisymmetric edge dislocation loops. Solutions for the dislocation loops are obtained using the GKS based method. The mixed boundary value problem is converted into Abel integral equations, which can be solved analytically. Exact closed form solutions for the stress intensity factors (SIFs) in terms of elementary functions are obtained. Numerical studies are conducted to investigate the shielding effect of the ring dislocation dipole on the crack tip SIFs. Conditions for the dislocation to shield the crack are discussed. The present solutions can also be used as weight functions to study the axisymmetric interaction between penny shaped crack and other types of eigenstrain sources.

Stress intensity factor of a cracked molar restored with different materials and designs: A 3D-FEA

ObjectiveThis work used 3D finite element analysis (FEA) to analyze and directly compare the stress intensity factor (SIF) and stress distribution at the crack tip of identical cracked tooth models restored with different materials and crown parameters. MethodsA 3D model of the cracked tooth was generated. Then, we applied 25 restorative models, including three parameters (shoulder height, width, and degree of polymerization), five restorative materials (GC, IPS, LU, ZC, VE), and two combinations of types of cement (RMGIC and GIC). An occlusal load of 800N was applied to the spherical part along the longitudinal axis. The stress distribution of the preparation and the SIF of the crack tip was analyzed. ResultsThe crack tip SIF was minimal for a shoulder height offset of 0.8 mm (P = 0.032), a shoulder width of 0.6 mm (P = 0.045), a crown material of ZC (P < 2e-16), and a cement material of RMGIC (P < 0.05), respectively. In contrast, the effect of different polymerization degrees on SIF was insignificant (P = 0.95). ConclusionOur results suggest that the selection of a larger modulus of elasticity (MOE) material for the crown, the preparation of a smaller shoulder width within a safe range, a reasonable increase in the crown length, and the selection of adhesive materials with high fracture toughness are favorable methods to prevent further crack extension.

An adaptive finite element method for crack propagation based on a multifunctional super singular element

The traditional finite element method (FEM) often requires a large number of refined meshes to analyze the mechanical behavior of geometric discontinuities, its computational efficiency and convergence speed are affected. In this paper, an adaptive FEM for crack propagation based on a multifunctional super singular element (MSSE) at the crack tip is proposed for the fracture process investigation of two-dimensional (2D) materials. The adaptive FEM for crack propagation divides the crack tip neighborhood into the MSSE region, the protection element (PE) region and the background element (BE) region. The MSSE is established based on the numerical eigen-solution of the singular stress field near the crack tip, and can be used for anisotropic material and interfacial crack problems. The PE and BE regions are still discretized by the conventional finite element meshes. Since the node degrees of freedom between MSSE and conventional finite element are unified, they can be assembled directly without transition element. The MSSE can be used to solve the crack tip stress intensity factor (SIF) directly without refining the crack tip mesh. The adaptive meshing technique reduces the difficulty of remeshing during crack growth, thus facilitating the simulation of crack propagation processes. The adaptive crack propagation algorithm is used to analyze the crack propagation problems in isotropic materials, anisotropic materials and bi-materials. The calculated results demonstrate the effectiveness and universality of the crack tip MSSE. The method has potential for application in the simulation study of residual strength and fatigue fracture of complex mechanical structures.

Static and dynamic analyses of the effects of shim material stiffness on insert crack initiation and propagation

Microcracks can form on the surface or inside an insert during forming or cutting processes. These microcracks tend to expand rapidly under impact loading, eventually leading to tool fracture and failure. Fracture and breakage of inserts cause significant limitations to the improvement of processing efficiency and safe production. This study investigated the effects of shim stiffness (using Young's modulus) on the stress distribution in the insert and at the crack tip under static and dynamic (impact) loading conditions, thereby providing a theoretical basis for correctly designing and selecting inserts for indexable tools. The extended finite element method (XFEM) was used to develop a 3D simulation model for an insert–shim system. The model was used to study crack initiation and expansion in the insert for different rigid shims under static and dynamic loading. Analyses of the crack tip stress intensity factor, the maximum principal stress, the strain, and the angle and direction of crack deflection were performed. Additionally, interrupted cutting experiments were conducted with cemented-carbide tools for four rigid shim materials. It was concluded that under static loading conditions, a weakly rigid shim reduced the crack tip stress intensity factor and the maximum principal stress, thus reducing the probability of insert fracture and that the stiffness of the shim has no effect on the angle of crack deflection on the insert surface. The shim stiffness has a more obvious effect on the crack propagation length and internal propagation direction during dynamic loading, and a weakly rigid shim increases the deflection angle as the crack expands inside the insert, thereby reducing the downward fracture length.

Simple crack tip and stress intensity factor determination method for model I crack using digital image correlation

In the past three decades, quantitative characterization of cracks attracted much attention with the development of digital image correlation (DIC), especially for estimation of crack tip position (CTP) and stress intensity factor (SIF). Quantifying CTP and SIF is of great importance in the damage tolerance assessment of fracture-critical components and structures. In previous research, multivariate fitting is performed on the displacement field to determine CTP and SIF. However, high gradient deformation near the crack tip causes inaccurate results and an involving complex estimation process. In this paper, a simple method is proposed to determine the CTP and SIF based on the displacement field calculated by DIC. Instead of the full-field fitting method, two lines symmetrically distributed on both sides of the crack tip are selected to fit the CTP. Vertical displacement differences between two lines are fitted with the theoretical solutions of mode I crack. Compared with the actual position observed by the micrograph, the estimation error is less than 2 pixels (about 6 μm). Additionally, a similar method is proposed to estimate the SIF utilizing the CTP results. To avoid the bias errors caused by the plastic zone, two lines are selected in the elastic zone away from the crack tip. Vertical displacements on two lines are fitted with the theoretical solutions to obtain SIF. The fitting results of the proposed method are close to that of the full-field fitting method. Compared with the previous methods, the computation burden of the proposed method is greatly reduced while the accuracy is not affected.

Asphalt complex cracks' sensitivity to temperature and crack depth and adjustment of the composite stress intensity factor

This paper is based on the fracture mechanics K-criterion with the composite stress intensity factor solution formula. The influence of temperature and depth in developing complex crack instability and diffusion in asphalt pavements is investigated. The crack composite stress intensity factor and development pattern are analyzed. The finite element modeling analyzes the change in stress intensity factor values at different temperatures and cracks depths. The composite stress intensity factor's temperature effect factor (t*) and crack depth effect factor (d*) are derived, and the calculation formulae are optimized. The study results show that among the complex cracks in asphalt pavements, the type I crack tip stress intensity factor (KⅠ) is the most seriously affected by temperature and crack depth and is also the main controlling factor of crack development. Type II crack tip stress intensity factor (KⅡ) is not significantly influenced by temperature but tends to rise and fall as the crack depth increases. Type III crack tip stress intensity factor (KIII) is smaller than KⅠ and KⅡ. It has less influence on the development of complex cracks in asphalt pavements. t* and d* were introduced to derive the formula for the modified composite stress intensity factor (Keff*). The formula was verified to calculate the composite stress intensity factor at different temperatures and crack depths and to study the cracking pattern of asphalt pavements.

Subcritical growth of a crack interacting with the stress field of mobile solutes in an elastic solid in the presence of image effects: A kinetic Monte Carlo study

It is well known that the presence of foreign solutes could critically affect fracture properties of the solid solutions of critical importance to many technological advances. It has been shown recently that a prevalent continuum theory widely applied to such systems is inconsistent with classical elasticity which predicts that two point defects in an isotropic unbounded solid do not interact, and interact only in a finite solid through image stresses arising due to the presence of the boundaries. Previous studies have shown that the image stresses resulting from an external boundary of a finite solid also generally raise the stress intensity factors (SIFs) induced by the solutes at a crack tip. Here, we examine the possibility that the increase in the SIFs by image stress effects together with variations in the configuration of mobile solutes around a crack tip could from time to time push the crack tip SIFs beyond the critical value required for crack growth, and hence cause subcritical crack growth over time. Incorporating crack growth criterion in kinetic Monte Carlo (KMC) simulations and fully accounting for the image stress effects, we investigate this possibility by examining how temperature, solute concentration, and the difference between the loading-induced SIF and the critical SIF could affect crack growth. In agreement with an analysis based on the central limit theorem presented for the limit of high temperatures, our simulations indicate that the probability of the Griffith-Irwin criterion being met among various solute configurations generally increases with increasing solute concentration. The model shows that, within a certain range of the loading-induced SIF below the critical SIF, the crack growth rate increases with solute concentration, and this effect becomes particularly more evident at larger temperatures.

Williams Elements With Generalized Degrees of Freedom for Crack Tip SIFs Analysis Under Crack Surface Distributed Loading

Service with cracks is the normal state of engineering structures. Due to the fluid invading into the crack, the crack surface is loaded directly, which makes the crack further expand, and even affects the safety of the structure. In the analysis of fracture problems, according to the Williams element with generalized degrees of freedom (W element), the Williams series was used to establish the displacement field of the singular zone around the crack tip, and the stress intensity factors (SIFs) can be directly obtained by solving the generalized stiffness equation with high precision and high efficiency. However, the W element needs to satisfy the free boundary condition of the crack surface in the singular zone, so it is limited in the analysis of crack surface loading. Based on the SIFs reciprocity, the loading on the crack surface is equivalent to the concentrated force on the crack surface at the periphery of the equivalent singular zone, so the loading on the crack surface in the singular zone can be avoided, and the W element can be easily used for calculation. The numerical examples show that, the size of the equivalent singular zone is 1/20 of the crack length, the suggested equivalent load coefficient <i>P</i> is 2.0, and the calculation accuracy of the W element meets the error limit of 1%. The equivalent treatment method for the analysis of crack surface loading in the singular zone is reasonable and universal, and overcomes the limitation on the W element in analysis of the loading problem on crack surface.

Mathematical study of an arbitrary-oriented crack crossing the interface of bonded functionally graded strips under thermo-mechanical loading

This article intends to explore the behavior of an arbitrary oriented crack that crosses the interface of bonded finitely thick functionally graded strips under thermo-mechanical loading. The angled crack is partially insulated. Application of the superposition technique and Fourier transformation on the governing equations of heat conduction and plane elasticity help to reduce the boundary-continuity conditions to Fredholm type singular integral equations. For solving these integral equations, the jump of the temperature and displacement across the crack surface are expressed as a series of Jacobi polynomials. Employing the residue theory and Schmidt method, the expressions of stress intensity factors (SIFs) are obtained which along with the local material parametric function determine strain energy release rates (SERRs). The novelty of the article is the investigation of the impact of thermo-mechanical loading on mode I and II crack tip SIFs and SERRs to study the behavior of arbitrary oriented partially insulated crack when it crosses the interface. The results of the present study are also validated. The key feature of the article is the graphical presentations of crack tip SIFs andSERRs for different values of crack insulation parameter, crack orientation angle, strips’ thickness, and non-homogeneity parameters.

Dislocations in an arbitrary angle wedge. Part II: Cracks in the wedge

We describe a method for calculating the crack tip stress intensity factors for the problem of one or two cracks at the apex of an arbitrary angle wedge. The kernels for a dislocation in an arbitrary angle wedge described in part 1 of this paper are used extensively. Consideration is given to variations of crack length, crack angle and wedge angle.

Influences of crack-face electric boundary conditions on stress intensity factors of ferroelectric single crystals

It is a challenge to determine the crack-tip stress intensity factors (SIFs) of ferroelectrics under large-scale domain switching. An I-integral method has been previously established for an impermeable crack. In order to investigate the influences of crack-face electric boundary conditions on domain switching and the SIFs, this paper develops the I-integral for permeable and conducting cracks to extract the crack-tip SIFs of ferroelectric materials. For all crack-face electric boundary conditions, the I-integral is independent of integration area size, even though the integration area contains domain walls. The phase field model based on the time-dependent Ginzburg-Landau theory combined with the I-integral method is employed to simulate a tensile test of a cracked PbTiO3 single-crystal plate through increasing the tensile stress step by step. The simulations show that the domain evolution process can be divided into three stages by two large-scale polarization reorientations (a local switching and a global switching) for all crack-face electric boundary conditions, including impermeable, permeable and conducting cases. In each stage, almost invariable domain pattern results in a nearly linear variation of the mode-I SIF. The mode-I SIF in the impermeable case is very close or even identical to that in the permeable case but significant larger than that in the conducting case. Except the local switching away from the crack, a local or global switching generally reduces the mode-I SIF obviously. Applied an increasing electric field, the domain evolution process contains two stages separated by a global switching causing a sudden increase of the mode-I SIF for the impermeable case and a sudden fall for the permeable and conducting cases.

Asymptotic description of fretting wear and fretting fatigue for incomplete contacts

Looking at wear of incomplete contacts in partial slip we start from an asymptotic description of the contact tractions at the contact edges. We introduce distributed dislocations along the slip zone to account for the profile reduction due to wear and find the long-term time asymptote where the contact is wholly stuck. The resulting stress field is used to find the crack tip stress intensity factors for short contact edge cracks, which are useful in predicting the crack nucleation threshold.

Long-term prediction of fatigue crack growth in ballastless track of high-speed railway due to cyclic train load

This paper proposes a vehicle-ballastless track coupled model with consideration of concrete cracks in high-speed railways through finite element method. Cracked Euler beam elements are used to model the concrete slab and the supporting layer with through-transverse cracks. In addition, an iterative method is proposed to estimate the fatigue crack growth of concrete under long-term train dynamic load on the basis of the Forman model. The vehicle-ballastless track coupled model with concrete cracks is employed to obtain the crack-tip stress intensity factor (CTSIF) of concrete under the condition of initial crack depth. The CTSIF induced by a high-speed vehicle is adopted in the Forman model to calculate the crack growth rate. The crack depth is updated by the number of passing vehicles in each iteration step, which is determined by a crack growth increment threshold. The dynamic characteristics of the vehicle-ballastless track coupled system are re-calculated based on the updated crack depth. Then, the effects of the crack depth, the stiffness of CA mortar and subgrade on the CTSIF of the concrete slab and the supporting layer are investigated in detail. The fatigue crack propagation process and residual service life under different initial crack depths of the supporting layer are discussed. Some practical conclusions are drawn, which can provide some theoretical guidances for the routine maintenance of slab tracks.

Experimental Study on the Caustics of Moving Cracks and Elliptical Curvature under Impact Loading

A dynamic caustics test system was used, and different moving cracks were analysed to study the interaction between the crack growth rate, stress intensity factor, and curvature of the elliptical end of a moving crack under impact loading. Based on the linear elastic fracture mechanics theory, linearly fitting of the crack tip stress intensity factor and the elliptical curvature were employed to obtain the specific functional expressions. ABAQUS software was used to numerically simulate the moving crack fracture process passing through different elliptical curvatures. The crack tip stress intensity factor was calculated by the stress extrapolation method. The stress intensity factor obtained from the numerical calculation and the caustics test was consistent. The test and numerical simulation results showed that the direction of moving cracks entering and passing through the elliptical defects shows a certain regularity. As the ellipse curvature increased, the moving crack stress intensity factor passing through the ellipse gradually decreased, and the moving crack also passed easily through oval defects.

Stress intensity factor calibration for short cracks at the edge of semi-infinite contacts

An asymptotic representation of the sub surface stress field allows us to find crack tip stress intensity factors for cracks nucleating from the edge of incomplete contacts. For the asymptotic representation to be valid we require the cracks to be short compared to any other dimension characterising the contact. The general asymptotic formulation allows us to incorporate the results in different contact problems as long as the contact is incomplete. We show that, for the load cases considered, crack closure is not an issue as long as the mode I stress intensity factor is positive.

Analytical solutions of multiple cracks and cavities in a rectangular cross-section bar coated by a functionally graded layer under torsion

A dislocation solution to evaluate the mode III stress intensity factors (SIFs) of the crack tips, torsional rigidity and the hoop stress around the cavities in an infinite rectangular cross-section bar coated by an FG layer under torsion is developed based on the Saint–Venant theory. The solution of the rectangular cross section with the FG coating weakened by a screw dislocation under torsion was first obtained in terms of the dislocation density function. Then, the problem is transformed into a group of Cauchy integral equations in the rectangular cross-section bar with the FG coating layer via the distributed dislocation approach. The singular integral equations are reduced to a set of algebraic equations to evaluate them numerically. After solving the integral equations, the SIFs of the crack tips, the hoop stresses around the cavities and the torsional rigidity of the entire domain are found. The obtained solution is validated by performing comparison studies in multiple cases. It is shown that the interaction between the cracks, the cracks length, variation of the shear module of the FG coating layer and distance of the crack tips from stress-free surfaces can significantly affect the SIFs of crack tips and torsional rigidity of the rectangular cross-section bar coated by an FG layer.

Crack propagation analysis of 3D printed functionally graded titanium alloy components

This paper presents an approach with a modified M-integral for determining the stress intensity factors of cracked functionally graded titanium alloy (FGTA) components. A derivative term of the strain energy density with respect to the spatial coordinate is embedded in the modified M-integral to account for the effect of the varying elastic moduli of functionally graded material. The validity of the modified M-Integral is validated by comparison with the experimental results of the crack propagation of FGTA specimens that are manufactured by using three-dimensional (3D) printing. Resistance tests of the cracked FGTA specimens are simulated to investigate the effects of the controlled changes in the material properties on the residual strength and crack-tip stress intensity factor. Further simulations of the fatigue crack propagation of the cracked FGTA specimens are performed to examine the influence of the changes in the material properties on the fatigue crack propagation life and crack propagation rate. The analysis results indicate that the numerical method in this study can accurately simulate the crack propagation of FGTA specimens. At present, due to the complexity and limitations of additive manufacturing of materials with gradient variations, it is not available to manufacture fully graded components through 3D printing for experiments. Therefore, this study assumes an FGTA beam model that is a fully graded material model to examine the effect of material gradient on crack propagation.