Mixed-mode Crack Propagation Research Articles

Mixed-mode thermo-mechanical fracture: An adaptive multi-patch isogeometric phase-field cohesive zone model

This work presents an adaptive phase-field cohesive zone model (PF-CZM) for simulating mixed-mode crack nucleation and growth in isotropic rock-like materials subjected to thermo-mechanical interactions. The proposed approach combines an adaptive multi-patch isogeometric analysis (MP-IGA) and length-scale insensitive PF-CZM. The formulation captures the distinct critical energy release rates for Mode-I and Mode-II fractures, which is crucial for predicting mixed-mode thermo-mechanical fracture behavior in isotropic rock-like materials. The PF-CZM governing equations are solved with isogeometric analysis based on locally refined non-uniform rational B-splines (LR NURBS), and the complex structural geometry is exactly described with multiple LR NURBS patches. The field variables, such as displacement, phase-field, and temperature at the interface of adjacent patches, are coupled using Nitsche’s method. To enhance the computational efficiency while maintaining accuracy, a refinement-correction adaptive scheme combined with the structured mesh refinement strategy is developed. The proposed framework is validated against recent numerical and experimental results in the literature, particularly in the context of capturing complex behavior of mixed-mode crack propagation in isotropic rock-like materials subjected to thermo-mechanical loading.

Experimental and virtual testing of mode II and mixed mode crack propagation under dynamic loading

Under static loading, measuring experimentally the mode II and mixed mode fracture toughness of composite materials and adhesive joints is well standardised. However, under dynamic loading, no standard procedure has been defined yet. Therefore, this paper proposes an experimental methodology to measure the mode II and mixed mode interlaminar fracture toughness of composite materials and adhesive joints. The methodology is based on a modified split Hopkinson compression bar. Two different data reduction schemes are explored and compared, one based on measuring the crack length, and another based on measuring the force from the strains in the transmitted bar. The two data reduction methods provided considerably different results. By using the method based on measuring the force, the mode II and mixed mode fracture toughness for both interlaminar and adhesive joints decreased for higher strain rates, while the opposite was found with the other approach. The method based on the crack length measurement was deemed to be unreliable due to the difficulties in measuring it.

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.

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Investigation of the effect of loading angle on mixed-mode fatigue crack propagation of AA2024-T351 friction stir welded joint

Investigation of the effect of loading angle on mixed-mode fatigue crack propagation of AA2024-T351 friction stir welded joint

Mixed-Mode Crack Propagation in Presence of Vein Fracture in Shale Sample in SCB Test

Mixed-mode fracture toughness refers to the ability of a material to withstand loads and expand under multiple modes of loading. It is usually tested by a semi-circular bend (SCB) to investigate the shale fracture toughness under combined modes of loading, such as tension and shear. When shale samples contain vein fractures, the dimensionless parameters Y1 and Y2 used in the SCB test method can be affected. The finite element method (FEM) was used to conduct a study investigating the impact of the natural fracture angle on the dimensionless parameters Y1 and Y2. The research findings indicate that as the vein fracture angle increases, Y1 and Y2 gradually increase. A construction was made to simulate the propagation path of a mixed-mode crack and compare it under various experimental conditions, utilizing the cohesive zone method (CZM). The results indicate that as the thickness of the vein fracture increases, the propagation path of the fracture becomes more tortuous. When the fracture encounters a vein with lower fracture strength, it will extend the vein fracture propagation. On the other hand, when the fracture encounters a vein with higher fracture strength, it will cross the vein fracture. This research considers the magnitude of the dimensionless stress intensity factor under different vein angles, simulating the crack propagation for varying vein widths and strengths.

Mixed mode brittle fracture of stereolithographic 3D-printed parts

Technical advances in additive manufacturing (AM), also known as three-dimensional (3D) printing, have led to applications of this technology in creation of end-use items. Consequently, performance and the mechanical strength of AMed parts have become of significant importance. In this research, fracture behavior and crack propagation of AMed cracked plates are investigated. To this aim, the stereolithography (SLA) technique is used to fabricate square plate specimens with a hole in the center and radial cracks that started at the perimeter of the central hole. Here, full range of mixed-mode fracture (from pure mode I to pure mode II) are obtained by altering the angle between the crack and the applied load. We used the finite element method to determine stress intensity factors. This study deals with a series of experiments on 3D-printed cracked plates to study mixed-mode fracture and crack propagation in brittle fracture of SLA 3D-printed components. Additionally, the digital image correlation technique was used to determine strain field on the surface of the specimens. As SLA is one of the most commonly used concepts in polymer 3D printing and has garnered significant attention for fabrication of complex structural elements, the outcomes of this study are useful for next developments and innovative designs of 3D-printed polymeric components.

A novel multiscale model for mixed-mode fatigue crack growth in laminated composites

A multiscale model is developed to predict mixed-mode fatigue crack growth (FCG) behavior in laminated composites by considering the micromechanical effects of fiber bridging. The proposed model consists of a micromechanical part dedicated to the fiber bridging mechanism near the crack tip, a macroscopic FCG model based on the maximum principal strain criterion, and an effective crack tip processing zone (i.e., an equivalent critical distance) connecting the two parts of the model. The core novelty of the presented model is to connect two scales (micro and meso) through a measurable physical quantity – called equivalent critical distance – accounting for various micromechanical as well as macroscopic phenomena occurring at both scales. The suggested model is validated against FCG test data available in the literature for laminated glass fiber composites under mode I, mode II, and mixed mode I/II conditions. It is found that the proposed framework is superior to its conventional (pure macroscopic) version, which eliminates fiber bridging effects, in the prediction of the cyclic mixed-mode crack propagation behavior in laminated composites. The multiscale nature of the proposed FCG model offers less complexity than fully micromechanical approaches while providing higher accuracy as compared to pure macroscopic models that ignore micromechanical phenomena occurring at the fiber scale.

A phase-field model for mixed-mode elastoplastic fatigue crack

One of the most common damage modes of aero-engine hot-end components is crack. Because of the complicated geometry and harsh working environment, the crack is typically in a mixed-mode and under elastoplastic conditions. The phase-field fracture method is a numerical simulation method that has recently attracted extensive attention. However, attention toward material damage and crack initiation before the crack emerges is lacking to solve the problem of elastoplastic mixed-mode fatigue crack propagation. In this study, an enhanced phase-field fracture method addresses this issue and predicts the propagation behavior of the elastoplastic mixed-mode fatigue crack. The effect of some parameters of this model is analyzed. This achievement is a significant contribution to the safety of aircraft engines and a novel method that can be further improved to solve problems in the future.

Phase field study of the thermo-electro-mechanical fracture behavior of flexoelectric solids

Piezoelectrics working in a temperature varying environment are prone to thermo-electro-mechanical fracture due to their brittle nature. In the meantime, flexoelectricity can greatly influence the fracture behavior of piezoelectrics since large strain gradients exist near the crack tip. In this paper, a novel phase field model is developed to investigate the thermo-electro-mechanical fracture behavior of piezoelectrics with consideration of the flexoelectric effect. In the proposed phase field model, the crack surfaces are assumed to be thermally adiabatic and electrically impermeable. The damage driving force is derived from the Clausius-Duhem inequality where the mechanical part is regarded as the driving force for the crack evolution. The mechanical driving force is decomposed to properly characterize the mixed mode crack propagation behavior. The governing equations of the four-field-problem are derived from the variational principle and solved numerically with the mixed finite element method. The fracture behavior of the flexoelectric solid under combined thermal, electrical and mechanical loads is then investigated by phase field modelling. The numerical results indicate that the proposed phase field model can well characterize the multi-physical effects and predict complex crack propagation trajectories in flexoelectric solids. Besides the mechanical and electrical loads, the thermal effect, the flexoelectric effect and the temperature dependence of the flexoelectric coefficients can all have significant influences on the thermo-electro-mechanical fracture behavior of flexoelectric solids. The present phase field model can thus act as a promising numerical tool to predict the reliability of flexoelectric components working in a temperature varying environment.

Jk-integral applied to mixed-mode fatigue crack propagation and life prediction in metal welding interface

In this paper, an innovative fatigue crack propagation model of metal welding interface is investigated based on the concept of Jk-integral (k = 1, 2) in elastic–plastic material, including the prediction of crack propagation path and life. In order to validate the effectiveness of the present fatigue model, the experiments of mixed-mode interface fatigue cracks are carried out on compact tensile shear specimens of N36 zirconium alloy using DIC methods. The results demonstrate that the fatigue crack only propagates along the interface under mode I loading where the relationship between the crack growth rate da/dN and ΔJ1 (the J1-integral range per loading cycle) is logarithmic linear. As for mode I/II mixed-mode loading, interface cracks start to propagate along the interface when J1 reaches Jint-C (the interface fracture toughness). When Jtotal (the vector sum of J1 and J2) reaches Jsub-C (the substrate fracture toughness), the crack deflects to the substrate in the Jtotal direction. In this case, da/dN shows a two-stage logarithmic linear relation with ΔJtotal (the Jtotal-integral range per loading cycle) under mixed-mode loading, and the critical Jtotal at the beginning of crack deflection is approximately matching the specific value. The theoretical deflection angle (i.e. the Jtotal direction) calculated from the corresponding J1 and J2 at the beginning of crack deflection is wellconsistentwiththe actual deflection angle observed in experiments. Moreover, the model can clearly describe the two-stage process from the crack propagation along the interface to the crack deflection to the substrate under mixed-mode loading. It is concluded that the proposed fatigue model based on Jk-integral can accurately predict the fatigue crack propagation path and lifetime of metal welding interface.

A Numerical Study of Crack Mixed Mode Model in Concrete Material Subjected to Cyclic Loading

In quasi-brittle materials such as concrete, numerical methods are frequently used to simulate the crack propagation for monotonic loading. However, further research and action are required to better understand the fracture properties under cyclic loading. For this purpose, in this study, we present numerical simulations of mixed-mode crack propagation in concrete using the scaled boundary finite element method (SBFEM). The crack propagation is developed based on a cohesive crack approach combined with the thermodynamic framework of a constitutive concrete model. For validation, two benchmark crack-mode examples are modelled under monotonic and cyclic loading conditions. The numerical results are compared against the results from available publications. Our approach revealed good consistency compared to the test measurements from the literature. The damage accumulation parameter was the most influential variable on the load-displacement results. The proposed method can provide a further investigation of crack growth propagation and damage accumulation for cyclic loading within the SBFEM framework.

Multi-scale modelling of fatigue crack propagation due to liquid droplet impingement

We develop a sequential multi-scaling framework for studying the problem of fatigue crack propagation due to liquid droplet impingement. The scope is limited to a hypothetical material and a hypothetical liquid. The multi-scaling is achieved by handshaking the atomistic scale molecular dynamics (MD) simulations with the continuum scale smoothed particle hydrodynamics (SPH). The handshaking, in turn, is performed by evaluating the material, the fracture and the loading properties from MD simulations, and using them as inputs in the continuum scale SPH model. Due to the qualitative agreement of the pressure developed in the fluid and the substrate between the MD simulations and already published results, the liquid droplet impact in SPH is simulated through appropriate surface stresses. Further, we incorporate the pseudo-spring approach within the SPH model to develop a methodology for studying mixed-mode fatigue crack propagation. Our methodology provides good agreement with the existing literature for several cases. Lastly, we calculate the fatigue life of an edge-cracked specimen due to liquid droplet impingement.

Mixed-mode fatigue crack propagation simulation by means of [formula omitted] and walker models of the structural steel S355

In this paper, a numerical simulation method of mixed-mode fatigue crack propagation was explored using the extended finite element method (XFEM) and the Virtual Crack Closure Technique (VCCT). Both 2D and 3D numerical models were selected to simulate the fatigue crack propagation of steel specimens. Two coefficients were proposed to calculate the equivalent energy release rate (Geq) for a better simulation of the mixed-mode fatigue crack propagation of S355 steel. The Walker equation and the calculation formula of Geq were realized by a user-defined subroutine. A set of optimal correction coefficients of mode II energy release rate (GII) and mode III energy release rate (GIII) were quantitatively comparing the simulation results and test data. The results will contribute to fatigue crack propagation prediction of steel structures in the civil engineering field.

Forward and backward mixed-mode crack estimation using artificial neural network

PurposeIn this manuscript, the authors aimed to demonstrate the influences of influential parameters in mixed-mode crack propagation phenomenon. The authors attempted to cover almost all surrounding issues of this subject as the authors know simulating of propagating cracks as internal strong discontinuity is a complicated issue.Design/methodology/approachIn this manuscript, the authors demonstrated the influences of influential parameters in mixed-mode crack propagation phenomenon. The authors attempted to cover almost all surrounding issues of this subject as the authors know simulating of propagating cracks as internal strong discontinuity is a complicated issue. Furthermore, three different scenarios for crack growth are considered. In reality, edge-cracked plate, center-cracked plate and cracked plate in the presence of void and inclusion are studied. In fact, by designing suitable artificial neural network's (ANN) architectures all the three aforementioned conditions are trained and estimated through those architectures with very good agreement with input data. Also by conducting a series of sensitivity analysis, the most affecting factors in mixed-mode crack propagation in different situations are demonstrated. The obtained results are very interesting and useful for other researchers and also the authors hope the results would be cited by researchers.FindingsThe influential parameters on mixed-mode crack propagation were found in this paper.Originality/valueThe computer code using MATLAB was prepared to study the mixed-mode crack paths. Also using ANNs toolbox, the crack path estimation was investigated.

Bifurcation and propagation of mixed mode fatigue crack in steel plates repaired with prestressed CFRP laminates

The mixed-mode crack propagation model was proposed to predict crack growth trajectory of a central cracked tensile steel plate with prestressed carbon fiber-reinforced polymer (CFRP) reinforcement through verification of previous experiments. A sensitivity analysis of different parameters including CFRP fiber orientation, initial crack geometry, and prestress level was conducted to investigate CFRP repairing efficiency by using a combination of the programs FRANC3D and ABAQUS. The results show that the applied loading direction primarily governs the bifurcation angle of crack propagation. Increasing prestress level of CFRP along the applied loading direction can achieve ten-fold repairing efficiency of damaged steel structures.

Effects of biaxial residual stress components on mixed-mode fatigue crack propagation behavior in friction stir welded 7075-T6 aluminium alloy panel

Residual stress in friction stir weld (FSW) joint significantly affects fatigue performance. It can often combine critically with the applied load cause premature fatigue failure. Research on the residual stress effects on fatigue behavior is required to assess the damage tolerance issues in FSW joints. In this study, the effect of biaxial residual stress components (longitudinal residual stress and transverse residual stress) on mixed-mode crack propagation behavior in FSWed 7075-T6 fuselage panel was studied. Residual stress profiles across the welded plate were measured by X-ray diffraction technique. Fatigue crack propagation for mode mixity angles of 30°, 45° and 60° were carried out. The stress intensity factors (SIFs) at the crack tip were evaluated by finite element method and used to study the effect of biaxial residual stress and the individual component on mixed-mode crack behaviors. The results show that the variation of crack path is strongly linked with the residual stress component as well as the initial oblique crack angle. SIF components are affected by the individual residual stress component. Both two components are required to study the mixed-mode crack propagation in FSWs.

An eXtended Finite Element Method implementation in COMSOL Multiphysics: Solid Mechanics

This paper presents the implementation of the eXtended Finite Element Method (XFEM) in the general-purpose commercial software COMSOL Multiphysics for the first time. An enrichment strategy is proposed, consistent with the structure of the software. To this end, for each set of enrichment functions, an additional Solid Mechanics module is incorporated into the numerical framework, coupled with compatible modifications to the internal variables. The Linear Elastic Fracture Mechanics (LEFM) is exclusively adopted for the crack analysis. The model pre-processing, level set update, stress intensity factor calculation and crack propagation analysis are conducted by employing COMSOL’s built-in features in conjunction with external MATLAB functions through COMSOL LiveLink. All implementational aspects and suggested remedies for the treatment of enriched elements, framework setup, evaluation of stress intensity factors, and numerical integration are described in detail. The accuracy and robustness of the proposed method are examined by several numerical examples, including mixed-mode crack propagation in 2D domains as well as stationary planar fractures in 3D settings. The results represent excellent agreement with available analytical, numerical and experimental observations in the literature.

Numerical prediction based on XFEM for mixed-mode crack growth path and fatigue life under cyclic overload

The numerical prediction based on the extended finite element method (XFEM) is carried out in this paper, where the mixed-mode crack propagation process is simulated accurately and the fatigue life considering the cyclic overload effect is calculated conveniently by using the proposed novel method. In this method, a simple crack surface updating strategy that can simulate the through-thickness crack in a three-dimensional structure is proposed, and it replaces the complex level set updating algorithm. Meanwhile, the cycle-by-cycle method for overload fatigue life is also proposed. The prediction is implemented based on the ABAQUS software by Python codes and the corresponding functional modules are developed. Compared with the built-in crack propagation modules of XFEM in ABAQUS, the method in this paper contains the complete crack tip enhancement functions and presents strong robustness in computational convergence and excellent calculation efficiency. The accuracy in calculating stress intensity factors (SIFs) and predicting mixed-mode crack growth paths is verified through examples. In addition, the fatigue life under cyclic overload is also predicted accurately by the developed modules. The effects from different parameters of load spectrum with overload are obtained according to the numerical results. Moreover, combined with the shell-to-solid coupling method, the large and complex practical engineering structure is simulated and analyzed in detail.

Effects of residual stress induced by laser shock peening on mixed-mode crack propagation behavior in 7075-T6 aluminum alloy panel

The effects of residual stress on mixed-mode crack propagation behavior of 7075-T6 aluminum alloy panel subject to multiple laser shock peening (LSP) impacts were investigated. Residual stress was obtained by an efficient LSP simulation termed continuous explicit-dynamic impact strategy. A numerical method, combining finite element (FE) method and residual stress intensity factor (SIF) analysis, was used to predict the mixed-mode (I/II) crack propagation in peened compact tension shear (CTS) sample. The effects of residual stress on the mixed-mode crack behaviors in different coverage areas were analyzed. It was found that the LSP-induced residual stress can change the crack path. Compressive residual stresses increase the effective crack length, and delay the crack propagation. The increased LSP coverage area and the decreased distance from the treated area to the crack tip are beneficial to the fatigue performance. The obvious crack turning point near the peened area is related to the significant change of mode II SIF components (KIIload and KIIres). The proposed numerical method provides a new idea for the damage tolerance analysis with respect to the applications of LSP technology in aircraft structures.