Static Crack Propagation Research Articles

Peridynamic fracture analysis of film–substrate systems

When subjected to mechanical, thermal, or other loads, film–substrate systems may undergo complex cracking behaviors, which encompass film and substrate cracking, interfacial debonding, and their combinations, exhibiting rich fracture patterns, such as three-dimensional helical cracks. Identifying the mechanisms underlying these fracture phenomena may lead to more advanced strategies for technologically significant applications. In this paper, we develop an interfacial cohesive peridynamic method for fracture analysis of multiple-phase materials. Particularly, we focus on the modeling of coupled film cracking and interfacial debonding in film–substrate systems. By introducing cohesive interfacial bonds to describe the mechanical properties of the interfaces and adopting a displacement-based cohesive failure criterion, the model is able to predict the critical condition and path of interfacial crack propagation. The robustness of the interfacial cohesive peridynamic method is validated through a series of representative examples. We also demonstrate its efficacy in simulating three-dimensional cracks and identify the essential role of the interfacial energy release rate in controlling the cracking mode transition from a restricted pattern to a helical pattern. The numerical predictions of cracking paths and stress distributions agree well with the previous experimental results. This study provides a valuable tool for analyzing different cracking patterns in film–substrate systems and composite materials.

Steady-state crack propagation during DCB test with viscoelastic-viscoplastic interface – Correlation between rheological behavior and effect of crack propagation rate

Adhesively bonded joints are known to suffer from creep and relaxation phenomena due to the viscous nature of the adhesive. These effects are detrimental to the durability of structural joints as they can lead to progressive and slow crack propagation rate phenomena and possible delayed failure. Master curve approaches are often used to assess the durability of structural assemblies, but the physical justification for such approaches requires additional investigation to more accurately assess the coupling between structural effects and the possible complex long-term rheological behaviour of the adhesive layer. Following similar approaches developed to study the steady-state crack propagation regime in bulk materials, an Eulerian description of crack propagation along a viscous adhesive layer during a double cantilever beam test is implemented. Taking into account viscoelastic-viscoplastic and various hardening rules, some master curves can be obtained describing the evolution of the crack propagation rate as a function of the stationary loading conditions. With such a model, the role of adhesive layer behaviour and joint geometry on crack propagation conditions can be discussed, as well as the applicability of such a master curve approach.

Fatigue crack growth properties of PMMA material used in underwater transparent structures

ABSTRACT Polymethyl methacrylate (PMMA) is an ideal material used in underwater transparent structures such as submersible windows and the fully-transparent pressure chamber of the sightseeing submersibles. The failure of PMMA structures usually come from small crack-like defects. In this paper, the fatigue crack growth experiments were carried out on PMMA materials with different thicknesses (B = 3, 6, 12 mm) and stress ratios (R = 0.1, 0.3) as well as plane strain fracture toughness test for unstable crack propagation conditions. Thickness effect and dwell time effect are experimentally investigated in addition to load ratio effect. The applicability of an improved crack growth rate model on PMMA material is validated by test results. The application of this model for prediction of crack growth rates can greatly save experimental time under different working conditions and can be applied in fatigue assessment of full-transparent structures under random loading.

Optimization of damage repair with piezoelectric actuators using the Taguchi method

Over the last two decades, piezoelectric actuators have emerged as a promising solution for structural repair. In this work, initially the stress intensity factor (SIF) estimation using the finite element (FE) approach at crack tips in aluminium 2024-T3 plates. Based on Taguchi’s L9 orthogonal array the FE simulation has been conducted. Later, this study uses the optimization method via the design of experiments to systematically evaluate the effect of various dimensions and material qualities, especially under the conditions of Mode-I crack propagation. It also investigated the complex interaction of factors impacting adhesive bonds, piezoelectric actuators, and aluminium plates, The study not only analyses the parameter relationships but also examines their controls, identifying those best aligned with primary objectives. This sensitivity enhances the piezoelectric actuator's efficacy and quality. The research determines an optimal parameter combination, developing active repair performance and establishing an essential SIF benchmark. This research explores the complex world of piezoelectric actuator-assisted repairs, providing a road map for better structural rehabilitation.

Resistance of Heterogeneous Metal Compositions to Fracture under Dynamic and Cyclic Loads

This paper presents the results of experimental data analysis, which indicate an increased resistance of heterogeneous multilayer clad composites to dynamic loading destruction compared with homogeneous materials. The reason for this is the crack retardation caused by lamination at the boundary of the layers. The destruction of heterogeneous compact composite samples by cyclic off-center stretching also occurs with crack retardation, with the fractogram clearly demonstrating the transverse tightening of the sample section. We argue that crack nucleation plays a decisive role in the process of dynamic destruction of heterogeneous composites obtained by both multilayer cladding and explosion welding. This study presents generalized calculated data confirming the influence of the sign and magnitude of residual stresses (the appearance of a stress discontinuity) on the conditions of fatigue surface crack nucleation and propagation. Unlike homogeneous materials obtained by casting, forging (rolling), or cladding, which are characterized by a linear dependence of the crack propagation velocity on the dynamic stress intensity coefficient, for multilayer composites consisting of strong and viscous layers, a sharp crack deceleration is observed. This is due to the transition of the crack boundary between the strong and viscous layers. This paper presents studies of the corresponding properties of adjacent layers on the integral characteristics of the deposited composite.

Phase-field analysis of the effects of particle size, diffusivities, and mechanical properties on the cracking of silicon nanoparticle

In this study, a multiphysics model that reproduces the cracking of Si nanoparticle for a battery application was demonstrated. Two types of cracks appear on Si nanoparticle during lithiation. An essential condition for surface crack (SC) nucleation and propagation is a fast charging rate to form a high concentration gradient of lithium ions near the surface. A slower charging rate induces internal cracks (ICs) radiating from the center of the particle. The critical charging rates, at which SC or IC occurs, decrease rapidly with increasing particle radius. This indicates the difficulty of cracking of small nanoparticles, which is in a good agreement with the previous experimental results. Multiple cracks can appear in the particle, especially when the diffusivity is high. These cracks can be combined during the charging process, leading to the fracture or isolation of the particles. Additionally, two different peak stresses and Young's moduli from the literature were used considering their effects on the cracking of Si nanoparticle films. We believe our results provide a guideline for the fabrication and operation of Si nanoparticle-based anodes for lithium ion batteries.

Influence of accelerated corrosion on Al/steel RSW joints by in situ compression tests

The present work investigates the correlations between galvanic corrosion, intermetallic compound (IMC) formation, and the input of welding energy with respect to the initiation and propagation of micro-cracks in micropillars of resistant spot welding (RSW) joints between aluminum (Al) and steel. The present results indicate that, in the high welding energy region, Al was corroded first after 26 cycles of corrosion, and Al5Fe2 IMC was corroded after 72 cycles of corrosion due to its high corrosion potential predicted by the calculations based on density functional theory (DFT) in terms of the Nernst equation. In comparison with the high welding energy region, less corrosion was observed in the middle welding energy region due to the thinner Al5Fe2 IMC layer, a lower amount of Al13Fe4 IMC in the Al matrix, and lower residual stress. Mechanical properties at different locations after various corrosion conditions were obtained using in situ compression tests, including the stress-strain responses and the strain rate sensitivity. The micropillars from the high welding energy region have a higher average yielding stress due to the thicker IMC layer than those from the middle welding energy region. The yielding stress decreases gradually with increasing corrosion cycles. Three conditions for crack initiation and propagation have been identified: firstly, for pillars from the high welding energy region before corrosion or the middle welding energy region (before or under the minimal corrosion conditions), the cracks initiate within the IMC layer; secondly, for pillars from the high welding energy region after 26 cycles of corrosion (under the moderate corrosion condition), cracks propagate at the Al/IMC interface; finally, for pillars from the high welding energy region after 72 cycles of corrosion (under the severe corrosion condition), the cracks initiate at the IMC/steel interface.

Influence of adhesive rheological behavior on stable mode II crack propagation in bonded interface subjected to shear loading condition

Bonded joints exhibit high mechanical performances but also suffer from poor durability in humid and/or hot environmental conditions. Indeed, delayed failures can be observed under stationary loading conditions due to chemical aggression but also due to creep failure. Despite bonded joints are generally loaded in shear, discussion on crack initiation and propagation condition under mode II stationary loading condition are lacking. Then, a semi-analytical model is proposed here to determine response of a End loaded Split (ELS) like test specimen considering viscoelastic-viscoplastic interface behavior, stationary loading condition and steady-state crack propagation regime. From these simulations, the evolution of crack propagation rate as a function of macroscopic loading intensity is obtained. The intrinsic nature of such “master curves” is finally discussed.

On crack propagation in weak geomaterials: Revisiting the superdislocation model in the context of hydraulic fracture

In this paper the problem of hydraulic fracture in elasto-plastic pressure sensitive material is analyzed. The superdislocation model is used to approximate the plastic deformations in the crack tip area. This model is employed to derive a new crack propagation condition based on the concept of effective fracture toughness. A parametric analysis supported by FEM simulations is conducted to verify the underlying assumptions of the superdislocation model and the resulting crack propagation condition. The results, obtained with the new crack propagation condition for the HF problem, are compared with those produced by a commercial geomechanical FEM package Elfen. The comparison proves the validity of the new crack propagation condition and the proposed modeling approach.

Influence of the interfacial transition zone between a steel inclusion and cement-based composite on the fracture response of a bent specimen

The influence of the interfacial transition zone (ITZ) between a steel inclusion and fine-grained cement-based composite on fracture behaviour of the specimen with the inclusion is investigated. Three-point bending fracture tests were conducted and the mechanical fracture properties of the composite were evaluated based on the results of the tests. The numerical analysis of the fracture test was performed and related to the experimental data obtained during crack propagation, and the microstructure of fracture surfaces. The crack propagation conditions were assessed based on the criterion of the average value of tangential stress calculated over certain distance in dependence on the polar angle (GMTS criterion). We concluded that the fracture toughness of the interface KIc, ITZ is equal to 33 % of the fracture toughness of matrix KIc, MTX. The poor fracture properties of ITZ are responsible for the reduction of load-bearing capacity of whole specimen with inclusion in comparison to the sample without the inclusion.

Study on root strain concentration of girth weld joint with variable wall thickness for X80 pipe

In this study, considering the particularity of variable wall thickness joints, a strain concentration characterization method for variable wall thickness joint is proposed. The finite element simulation method is used to establish a finite element model consistent with the physical joint, and calculate the root strain concentration under different misalignment, different weld strength matching, different pipes strength collocation and different heat affected zone (HAZ) softening conditions. Based on the aforementioned analysis, it is found that the misalignment, the weld strength matching, the pipes strength configuration and HAZ softening all affect the strain concentration at the root of the joint. In particular, the misalignment is easy to cause geometric structure mutation of root, which is the main factor leading to strain concentration for root of weld. The larger misalignment, the lower strength matching of the weld, and the higher pipes strength can increase the strain concentration at the root. However, a large root strain concentration can induce strain aging embrittlement or coupling with welding defects to cause material damage, providing conditions for root crack initiation and propagation.

Analiza udarne žilavosti i kritičnog faktora intenziteta napona KIc kod feritno-austenitnih zavarenih spojeva različitim unosom toplote

Introduction/purpose: Constructions always have several critical points that can be sources of possible defects. All these critical places must be taken into account in safety assessment where the most unfavorable exploitation factors are considered and the local safety of a joint is assessed. Today, joints of various compositions are becoming more frequent in metal constructions. Due to the requirements of economy and ecology, welded joints of microalloyed ferritic steels with high-alloyed austenitic steels are increasingly encountered during the construction of power plants, chemical facilities, etc. Tests of such welded joints have been performed on tanks for oil derivatives, where parts of the tank shell are made of microalloyed ferritic steel and the roof structure is made of high-alloyed austenitic steel. Methods: In the paper, an experimental analysis of crack propagation in an austenitic-ferritic welded joint was performed. The welding was performed by the MIG welding process with two different heat inputs, and the same filler material MIG 18/8/6 was used. Two types of welded plates were tested. the characteristics of the base, filler and auxiliary materials and welding 16 technologies are given. Notched test specimens with an initiated crack-type fracture were made in order to determine the impact properties and fracture mechanics parameters. The results: The research carried out within this study aimed to compare the obtained results of the impact toughness and fracture toughness at flat deformation in a ferrite-austenitic welded joint. An evaluation of the results obtained during the testing of the experimental plates welded with different amounts of heat input is also given. Conclusion: These test results established the dependence of the geometry of a propagating crack and the stress conditions for further crack propagation. It is possible to determine the values of the parameters that describe the behavior of the material, both in linear-elastic and in elastoplastic fracture mechanics.

Occurrence condition for steady crack propagation in quasi-brittle fracture and its application in determining initial fracture toughness

Crack propagation is commonly assumed to be a parallel motion called the steady state in quasi-brittle materials. The steady crack propagation can be used to determine softening traction-separation relation because one-to-one correspondence exists between the crack growth resistance and the softening traction-separation relation. However, the steady-state crack propagation that all quantities like crack opening displacement and cohesive stress keep invariable may not occur due to the limitation of the fracture process zone (FPZ). For quasi-brittle fracture, it is essential to define when the steady crack propagation occurs for ensuring the applicability to determine the softening traction-separation relation based on steady crack propagation. In this study, numerical test results of three specimen geometries, seven specimen sizes and three softening traction-separation relations are employed to analyze the steady crack propagation. Through comparison between crack growth resistance based on steady-state assumption and equivalent LEFM R-curve, a pseudo-steady state regime that is very similar to the steady crack propagation is found. At the pseudo-steady state, the relationship between the softening traction-separation relation and the crack growth resistance under steady crack growth is still applicable. The occurrence condition for the pseudo-steady crack propagation is deduced. It is found that for most laboratory specimens, the critical situation (load reaches its maximum value) can be seen as a pseudo-steady state with an error of <20%. By choosing the softening traction-separation relation based on the pseudo-steady assumption, the initial fracture toughness can be determined. The errors of the initial fracture toughness determined by this method can be approximately estimated based on the range of lFPZ/(D-ac).

Evaluating the Time-Varying Mesh Stiffness of Planetary Gear Set With Gear Crack Considering the Friction Force Under Mixed Elastohydrodynamic Lubrication Condition

Abstract The mesh stiffness calculation of the planetary gear system with gear crack is investigated, and gear crack is modeled into end-face and addendum extended crack. Furthermore, the mesh stiffnesses are calculated under the effect of friction force obtained under the mixed elastohydrodynamic lubrication (EHL) condition. The nonuniformly distributed gear cracks on external and internal gear pairs are comprehensively modeled and analyzed, which is rarely investigated in previous studies. Moreover, the influence of crack propagation conditions on the meshing stiffness of the planetary gear system is analyzed. The obtained results show that the mesh stiffnesses experience abrupt variation in the pitch area during meshing, the extent of change is determined by the amplitude of the friction coefficient; in addition, gear crack position and extent could cause mesh stiffness reduction at varying levels at different stages of gear meshing.

A control method for hydraulic fracturing of the hard roof with long and short boreholes

During the mining of the working face, the hard roof can lead to a series of problems, such as air leakage in goafs, gas emission and concentration, casualties, and damages to buildings and ecological environment. The treatment of the hard roof has always been a difficult problem in major coal-producing countries. Although many scholars have conducted some theoretical research and field practice in this field in recent years, the aforementioned safety problems still occur frequently. In order to understand the mechanism of crack propagation caused by hydraulic fracturing of the roof, based on the theoretical analysis of linear elastic fracture mechanics and coal rock mechanics, the shear fracture criterion was determined for the formation of horizontal fractures in the natural cracks. The anisotropy of the crack tip, the adhesion forces in the coal and rock fracture surface and the conditions for hydraulic-induced crack propagation were also considered. The formation of cracks involves a vertical main crack and multiple extended-airfoil branch cracks which interconnect transversely and longitudinally. Under the effect of hydrodynamic water wetting and hydraulic fracturing, the stress of coal and mass changed. Meanwhile, the mechanical parameeters, such as compression, tensile strength and elasticity modulus and etc., were weakened, thus achieving the goal of structural transformation and slight weakening of coal and rock mass. According to the bidirectional stress of coal and rock mass, the maximum principal compressive stress of crack opening was calculated, and the propagation mechanism of hydraulic fracturing cracks in the hard roof was obtained. The hydraulic fracturing technology for controlling the hard roof was illustrated and has been applied in No. 2 Well of Sihe Coal Mine for many years. The research results could provide reference for the control of the hard roof in other similar mines.

The micromechanics‐based rate‐dependent constitutive model of flawed rocks at intermediate strain rate

AbstractIn the previous works conducted by Zhou and Yang, the deformation induced by wing crack coalescence was not investigated. In this paper, a novel micromechanics‐based rate‐dependent constitutive model is proposed to investigate the effect of wing crack coalescence on the mechanical properties of rocks at intermediate strain rate. The rate‐dependent damage mechanism is revealed using the frictional sliding crack model. Wing crack interaction is defined using pseudo‐traction method as well as the dynamic stress intensity factors. Strain energy density factor approach is applied to determine the critical condition of wing crack initiation, propagation, and coalescence. The strain softening behaviors of flawed rocks is studied by using thermodynamic theory.

Theoretical Analysis of Critical Conditions for Crack Formation and Propagation, and Optimal Operation of SOECs

A theoretical analysis on crack formation and propagation was performed based on the coupling between the electrochemical process, classical elasticity, and fracture mechanics. The chemical potential of oxygen, thus oxygen partial pressure, at the oxygen electrode-electrolyte interface () was investigated as a function of transport properties, electrolyte thickness and operating conditions (e.g., steam concentration, constant current, and constant voltage). Our analysis shows that: a lower ionic area specific resistance (ASR), and a higher electronic ASR () of the oxygen electrode/electrolyte interface are in favor of suppressing crack formation. The thus local pO2, are sensitive towards the operating parameters under galvanostatic or potentiostatic electrolysis. Constant current density electrolysis provides better robustness, especially at a high current density with a high steam content. While constant voltage electrolysis leads to greater variations of Constant current electrolysis, however, is not suitable for an unstable oxygen electrode because can reach a very high value with a gradually increased A crack may only occur under certain conditions when

A phase field model for high-speed impact based on the updated Lagrangian formulation

High-speed impact problems usually undergo a form of highly localized plastic deformation under high strain rate with intense shock waves. In this paper, we present a coupled phase field model to simulate fracture in these situations. Our model considers the dynamic finite deformation with both strain hardening and strain rate hardening by the Johnson–Cook plasticity model. In particular, the formulation is posed in an updated Lagrangian framework and the constitutive update is realized with a return-mapping algorithm. Considering the tension–compression asymmetry, a new history variable is developed to enforce the irreversibility condition of crack propagation. The effectiveness of the proposed method is validated with a numerical example of 45 steel impact experiment along with two numerical simulations of split Hopkinson bar experiments on concrete and aluminum alloy specimens, where strong shock waves are generated. Besides, the effect of a few parameters is studied, namely, the regularization length parameter, the energy release rate, the initial impact velocity, and parameters of the Johnson–Cook model. These show the correct trend in terms of the time and extent of crack propagation.

A simplified modelling of hydraulic fractures in elasto-plastic materials

In this paper the problem of a plane strain hydraulic fracture propagating in an elasto-plastic material is analyzed. A new stress redistribution model for the proximity of the fracture tip is formulated and a resulting plasticity-dependent crack propagation condition is introduced. A modified variant of the KGD problem that accounts for the plastic deformations in the near-tip zone only is proposed. It is demonstrated that this model can be a credible substitute for the full elasto-plastic hydraulic fracture problem in the case of moderate plastic deformation. The crack-tip shielding effect introduced by the plastic deformation is quantified.

Research on crack propagation law of rotating bending fatigue cropping process based on cusp catastrophe theory

A large number of experimental results show that in variable load low-stress fatigue cropping there are two forms of fatigue crack propagation, stable crack propagation and sudden-jump crack propagation, but sudden-jump crack propagation seriously affects cropping section quality. In this paper, the process of crack propagation under cropping is analyzed, and the condition of alternate stable-jump crack propagation under circumferential rotating bending fatigue loading is proposed from the fracture mechanism. Based on the energy method, the cusp-catastrophe model potential function of cropping process is constructed, and with XFEM (extended finite element) and total potential energy catastrophe theory, the multiple catastrophe positions in the cropping process are obtained. The results of the AE (acoustic emission) measurement experiment in cropping confirm the phenomenon of multiple catastrophe in the process of fatigue crack propagation. The loading curve based on catastrophe theory is obtained by fatigue strength theory. Compared with current common loading curves, the obvious sudden-jump crack propagation phenomenon is eliminated basically, no obvious catastrophe trace is observed in the propagation area, and the fracture area is reduced by 54.65%, which significantly improves the quality of cropping section.