Nonlinear Fracture Research Articles

Effect of moisture on the nonlinear viscoelastic fracture behavior of polymer nanocompsites: a finite deformation phase-field model

The mechanisms underlying damage in high-performance polymer nanocomposites are remarkably affected by hygrothermal conditions. In this study, we develop a phase-field formulation to investigate the influence of hygrothermal conditions on the nonlinear viscoelastic fracture behavior of epoxy resins and their nanocomposites at finite deformation. For this, the Helmholtz free energy, capturing the effect of temperature and moisture and nanoparticle contents, is defined based on an additive decomposition of the energy into an equilibrium, a non-equilibrium, and a volumetric contribution with different definitions under tensile and compressive loading. The coupled displacement phase-field problem is solved using a quasi-Newton monolithic algorithm and a staggered solution scheme. Numerical examples show that the monolithic algorithm is more efficient. Simulations are performed to investigate the effect of temperature, deformation rate, and moisture content on the force–displacement response of boehmite nanoparticle/epoxy samples in benchmark numerical problems. Comparing numerical predictions and experimental data for compact-tension tests shows good agreement at different nanoparticle contents. Also, the model’s capability to predict fracture patterns is evaluated using simulations of single-edge notched nanocomposite plates under tensile and shear loading.

A computational investigation of applicability of nonlinear fracture mechanics in nano-scale fracture of graphene

One of the main concerns for large-scale applications of graphene is unwanted fracture due to its low fracture toughness, close to that of an ideally brittle solid. However, graphene fracture properties and criteria have not been fully understood yet and the related understanding at the continuum-mechanics level is mostly limited to the linear elastic fracture mechanics (LEFM) investigations. In this paper, the applicability of nonlinear fracture mechanics (NLFM) to describe the fracture behavior of graphene is investigated through modeling the graphene sheets, including a center crack along the armchair and zigzag directions under mode I and mode II loading. A hyperelastic high-order continuum description is developed to be used in the nonlinear finite element simulations at the continuum level, by expanding the elastic strain energy in terms of the Lagrangian strains up to the seventh-order terms. The proposed continuum model is parameterized using the molecular dynamics (MD) simulation results to accurately reproduce the nonlinear mechanical behavior of graphene in uniaxial strain, equi-biaxial strain, and simple shear deformations. Finally, the applicability of NLFM, compared to LEFM, is investigated for graphene fracture through the continuum mechanics and MD fracture simulations. © 2001 Elsevier Science. All rights reserved

Fracture characterisation of bone-cement bonded joints under mode I loading

Over the years, many techniques have been developed for the stabilisation of bone fractures. The study of the adhesion of bone-to-bone cement is an important step towards the development of new immobilization systems. Although bone cement has been used for more than fifty years, very few studies have been performed regarding the evaluation of fracture properties. In this work, numerical and experimental investigations were conducted to evaluate the strain energy release rate under mode I loading in a bone-cement bonded joint, using the Double Cantilever Beam (DCB) test. Cohesive zone laws were also measured combining the finite element method with non-linear elastic fracture mechanics. This has been made in a cortical bone bonded joint with polymethylmethacrylate (PMMA). Consistent results have been obtained regarding fracture toughness in a widely used bone-to-bone cement joint in many biomedical applications.

The Role of Retinal Plasticity in the Formation of Irreversible Retinal Deformations in Age-Related Macular Degeneration

Purpose To construct a realistic physical model of viscoelastic retinal stretching and, on its basis, derive a universal quantitative criterion of irreversible retinal deformations during age-related macular degeneration. Methods In this work, standard methods of nonlinear fracture mechanics of ductile and viscoelastic materials were applied to study the evolution of retinal deformation progress in patients with neovascular age-related macular degeneration in the area of large druses or subretinal or sub-retinal pigment epithelium fluid accumulation. A two-dimensional rhombic model of viscoelastic Kelvin-Feucht primitives was used to reconstruct the parameters included in the approximation of the creep strain growth rate. A clinical case of a patient with age-related macular degeneration and retinal pigment epithelium detachment in the macula was taken as a basis for theoretical research. The patient underwent retinal optical coherent tomography on DRI Swept-Source OCT. Results A closed realistic theoretical model of retinal stretching in the projection of retinal pigment epithelium elevation due to its detachment or drusen based on a two-dimensional rhombic Kelvin-Feucht primitives model was constructed. The calculation of stress in the retinal tissue with consistent consideration of creep effects was performed. Conclusions The time of critical retinal loading – a new quantitative criterion for the irreversibility of retinal stretching in age-related macular degeneration is proposed. This criterion allows the prediction of the functional outcome of antiangiogenic therapy in patients with age-related macular degeneration with identical initial retinal morphometric parameters.

Research on fracture toughness and strength of thin-walled Ti–B25 pipes using small notched beams

One of the most essential processing procedures for thin-walled titanium pipe is hot extrusion. The non-uniform distribution of microstructure along the wall thickness and pipe axis of thin-walled pipes produced with this technology, on the other hand, would affect the non-uniformity of mechanical characteristics. Although it is generally difficult to process specimens that meet the linear elastic fracture mechanics (LEFM) conditions for this thin-walled titanium alloy Ti–B25 pipe, a simple method for non-linear elastic fracture of material was used to test the yield strength σY and fracture toughness KIC of this thin-walled titanium alloy Ti–B25 pipe in this paper. Three-point bending (3-p-b) was used to test the single edge notched beam (SENB) specimens. The fracture surface of each specimen was examined using a scanning electron microscope (SEM). The discrepancy of yield strength values measured by 3-p-b test and tensile test is 0.6% when the fictitious crack zone △afic equals 2.5 mm, and the fracture toughness KIC of the Ti–B25 pipe is determined to be 83.28 MPa m0.5. This method is a simple and practical way to evaluate the fracture toughness of thin-walled pipe, and it can be used to ensure the safe design and application of titanium alloy pipe.

Improved peridynamics approach for the progressive fracture of marine concrete

Crack initiation and propagation in marine concrete play a significant role in the security and durability of concrete in ocean construction. Peridynamics (PD), which reformulates classical continuum mechanics in terms of spatial integral equations instead of partial differential equations, has been used successfully to match the fracture patterns observed in experiments. However, the classical bond-based peridynamics (BPD) describe brittle fracture instead of quasi-brittle fracture; this includes the failure of quasi-brittle solid marine concrete. Further, the models have significant surface effects, and the effect of the internal length on nonlocal long-range forces is not reflected. The current work proposes an improved BPD approach to overcome the three drawbacks of fracture analyses of marine concrete. A novel kernel function is incorporated, an effective PD surface effect correction method is used, and the BPD bond stiffness at the boundary is modified. Then, the constitutive force function of the BPD is established based on the linear and nonlinear mechanical behaviours of the progressive fracture of ocean concrete materials, and a corresponding failure criterion is given. The validity and accuracy of the proposed method are demonstrated via numerical analyses and experiments. The proposed method can fully capture the nonlinear deformation and progressive fracture of marine concrete.

Transient Interporosity Flow in Shale/Tight Oil Reservoirs: Model and Application.

The dual-porosity model has been used widely to describe the fracture network in well test or numerical simulation due to the high computational efficiency. The shape factor, which can be used to determine the capability of mass transfer between the matrix and fracture, is the core of the dual-porosity model. However, the conventional shape factor, which is usually obtained under pseudo-steady state assumption, has certain limitation in characterization of the mass transfer efficiency in a shale/tight reservoir. In this study, a new transient interporosity flow model has been established by considering the influence of nonlinear flow, stress sensitivity, and fracture pressure depletion. To solve this new model, a finite difference and Newton iteration method was applied. According to the Duhamel principle, the solution for time-dependent fracture pressure boundary condition has been obtained. The solution has been verified by using the fine-grid finite element method. Then, the influence of nonlinear flow, stress sensitivity, and fracture pressure depletion on shape factor and interporosity flow rate has been studied. The study results show that constant shape factors are not suitable for unconventional reservoirs, and the interporosity flow in the shale/tight reservoir is controlled by multiple factors. The new model can be used in test interpretation and numerical simulation, and also provides a new approach for the optimization of the perforation cluster number.

Coupled peridynamic model for geometrically nonlinear deformation and fracture analysis of slender beam structures

AbstractSlender beam structures can experience large displacements, large rotations and fractures, even if the structures are only subjected to small loads. A coupling model of peridynamics (PD) and classical continuum mechanics (CCM) for beam fracture analysis in geometrically nonlinear deformations is developed in this study. Firstly, the formulations of virtually nonlinear strain energy density of each incremental step are obtained by using the updated Lagrangian (UL) formulation and von Karman beam theory, then the nonlinear PD beam parameters are established on the geometrically nonlinear micro‐beam bonds via the principle of virtual work and homogenization. Secondly, the coupling model of PD and CCM for geometrically nonlinear beams is proposed, for which the morphing method is applied to create a balance between the stiffness of geometrically nonlinear CCM beam model and the weighted coefficients of geometrically nonlinear PD beam model. Thirdly, a new fracture criterion for PD beam models considering the effect of geometrical nonlinearity is adopted. Finally, the large deformation and fracture analysis of straight beam, spiral slender beam and complex frame subjected to different loading conditions illustrate the validity and accuracy of the proposed PD‐CCM coupling model.

Assessment of failure probabilities and the allowable size of defects in structural elements using the criteria of fracture mechanics

The possibility of assessing the safe size of the defects of metal continuity using risk criteria are considered. Such defects occur at all stages of the life cycle of structures. Assessment of their hazard and determination of their allowable size becomes important when the defects can lead to brittle or quasi-brittle fracture. In this case, models of linear and nonlinear fracture mechanics are used. In these models, defects are considered as internal elliptical or surface semi-elliptical cracks. The stochastic variety of shapes, sizes, locations, and orientations of defects has a significant effect on the destruction mechanisms. In this regard, the relevant probabilistic problem of assessing the permissible size of defects according to the criteria of the risk of destruction comes to the fore. We consider a general approach to assessing hazard of defects by risk criteria. Two settings of the probabilistic problem of risk assessment based on of one- and two-parameter fracture criteria are presented. The risk function in the form of the probability of fracture according to a given criterion is used as the main calculated characteristic. The expression of the risk function based on one-parameter criteria of fracture mechanics is presented. The main attention is paid to the probabilistic model based on the two-parameter fracture criterion by E. M. Morozov. This criterion provides ample opportunities for analyzing fracture mechanisms with a change in the size of defects. An expression for the risk function based on the family of two-dimensional probability distributions of Lu – Bhattacharya of the Weibull type is obtained. It is shown that the correlations of the fracture mechanisms can significantly affect the values of the fracture probabilities, and, consequently, the allowable size of defects.

Assessing the Secondary Stress in a Pipe System With Circumferential Surface Crack Using Finite Element Modeling

Abstract In flaw evaluation criteria, the design limits for the secondary stresses are frequently different than the primary stresses. The evaluation procedure for primary stresses is load-controlled based which is independent of pipe deformation. The evaluation procedures for secondary stresses are displacement controlled which are dependent on pipe deformation. Certain stress components such as thermal expansion, thermal stripping, welding residual stress, misalignment/cold-springing, dynamic anchor motion are historically considered secondary stresses and their design limits are based on elastic stress analysis. In reality, there can be much more rotation/displacement of the pipe with nonlinear fracture behavior due to nonlinear material behavior and plasticity at the crack plane providing extra margins on the elastically calculated rotation values that come from uncracked-pipe design analyses. In assessing secondary stress margin, a secondary stress reduction factor is defined as the ratio of elastic-plastic moment to elastic moment. This is equivalent to another concept using a plastic reduction factor (PRF) as well as the inverse of structural (or safety) factor (SF) in ASME Section XI flaw evaluation criteria for various service levels. In this work, the secondary stress reduction factor was determined for a representative pipe system with multiple crack sizes, crack locations, and loading conditions. Nonlinear finite element (FE) analyses of a whole uncracked-pipe system were performed using abaqus® under various loading combinations to determine the critical locations for cracks in the pipe system. Next, FE analyses of the cracked-pipe system were carried out using cracked-pipe element—a methodology developed by the authors. Cracked-pipe system analyses were conducted for two loading conditions—one producing contained plasticity or single-hinge system and the other producing larger plasticity in the pipe system. Several analyses were conducted for each loading condition with a combination of two crack sizes at two key locations. Secondary stress reduction factors were then calculated for both loading conditions in the pipe system. Finally, the margin in secondary stress was assessed for the pipe system by comparing the secondary stress reduction factors with that for straight pipe sections (determined for experimental bend tests) as well as with the recommended equivalent PRF and the equivalent ASME secondary stress correction factors.

Fracture mechanism of alumina-spinel castables containing ZrO2 by wedge splitting test and digital image correlation technique

To clarify the fracture mechanism of alumina-spinel castables, two kinds of alumina-spinel castables with or without fused zirconia-alumina (FZA) were prepared. The full-field strains and crack propagation process in the region of interest (ROI) of alumina-spinel castables were investigated by wedge splitting test (WST) and digital image correlation (DIC) technique. Fractographic methods were used to analyze the crack propagation path of the castables after the WST. The results indicated that the load-displacement curve of alumina-spinel castables containing FZA exhibits a non-linear fracture, demonstrated typical ductile fracture; while that of alumina-spinel castables without FZA is linear, showed typical brittle fracture. The characteristic length reaches to 258.9 mm in FZA containing castables, more than 4 times that of the castables without FZA. In contrast, castables containing FZA has longer and more tortuous crack propagation path, larger damage zone length, which results in the increase of the dissipated energy. Crack branching can be observed around the main crack in castables containing FZA, meaning that microcracks toughening is the main mechanism for flexibility improvement of the alumina-spinel castables containing FZA, formation of micro-cracks can be attributed to the martensitic transformation of zirconia.

Effect of entanglement on rheological and ultimate properties of inorganic HPAM gels

The influence of the entanglement on the mechanical properties of partially hydrolyzed polyacrylamide gels is investigated. In the entangled gels, a power law, relating the plateau modulus and the polymer concentration, with an exponent of 2.3 is dominant. By contrast, the exponent of the power law is determined by the crosslinking density in the unentangled gels. On basis of the in-situ gelling method, the strain hardening characteristic of partially hydrolyzed polyacrylamide gels was observed. The strain hardening behavior is found to be controllable by the component of gels, but is insensitive to the frequency. In general, gels with higher polymer concentration exhibit a weaker tendency of stiffening and tend to fracture at lower strain. However, concentration dependence of the non-linear rheology and fracture properties is discontinuous around the entanglement concentration. The underlying mechanism is assumed to be relevant with the conversion of the crosslinking type, which is promoted from inter-crosslinking to intra-crosslinking due to entanglements. As a result, the fracture stress experiences a significant reduction as the polymer concentration exceeds the entanglements concentration. This article points out the significance of entanglements on the fracture toughness of polymer gels, and we hope it would provide suggestions for further studies.

Experimental study and numerical modeling of ENF scheme: Comparison of different beam approaches

In the present paper five beam models are presented to reproduce the experimental response of the End Notch Flexure (ENF) test. In particular, a specific ENF scheme is considered; it is made of two symmetric laminates partially bonded by a adhesive layer, whose thickness is not negligible. The failure occurs at the interface between one laminate and the adhesive, leading to an unsymmetrical failure; moreover, because of the presence of the adhesive layer, the two arms representing the initial defect of the ENF are not in contact. The experimental setup is described and five beam models are introduced to simulate the nonlinear response of the ENF scheme, characterized by an increasing improved kinematics. Failure is studied considering both linear and nonlinear elastic fracture mechanics, introducing in the latter case a very simple cohesive interface model. Solutions obtained by the five beam models are compared with the ones recovered with finite element (FE) analyzes and with the results of the experimental tests, remarking the reliability, the simplicity and the computational efficiency of the beam schemes. It is found that the improved kinematics and the cohesive fracture evolution play an important role in accurately reproducing the response of the ENF scheme.

Investigation of notch effects on load-bearing capacity of AA7075-AA7075 friction-stir welded joints under mixed mode I/II loading

In this research, mixed mode I/II fracture of AA7075-AA7075 friction-stir welded (FSWed) joints weakened by V-notches is studied. This study consists of two parts: experimental and theoretical. In the experimental part, the load-bearing capacity (LBC) of rectangular specimens made of welded AA7075-T6 aluminum alloy containing a central V-shaped notch under mixed mode I/II loading is measured. Due to the elastic–plastic behavior of the specimens and noticeable deformations at the notch neighborhood, prediction of fracture of the specimens under test using nonlinear fracture mechanics criteria is complex and time consuming. As a result, in the theoretical part, using the Equivalent Material Concept (EMC) in combination with two brittle fracture models (mean stress, MS, criterion and maximum tangential stress, MTS, criterion), the LBC of the samples tested is estimated. By comparing the experimental results with the theoretical ones, it is clear that both theoretical criteria used in combination with EMC are well able to predict the LBC of the notched specimens. Also, based on the fracture tests performed and the analysis of the samples in a commercial finite element software, it is observed that the size of the plastic zone in the vicinity of notch increases with increasing the share of mode II, i.e. from pure mode I to pure mode II. Observed is also that the enlargement of the plastic zone increases the LBC of the samples.

三次元直交織構造を考慮したセラミックス基複合材料の損傷モデリング

Ceramic matrix composites (CMCs) are expected to be applied to high-temperature parts of jet engines because they are lighter and have higher heat resistance than Ni-based alloys which have been conventionally applied to turbines. One of the challenges in applying CMCs to engine parts is the difficulty of design due to the difference in material strength due to the microstructure composed of fiber bundles and matrix. The two types of microstructure models were prepared. The one is "unit cell model" which is a simplified shape model with a rectangular three-dimensional orthogonal weave structure. The other one is "CT model" which is a complex detailed shape model created by image recognition technology based on image data acquired by X-ray Computed Tomography (CT). Structural analyses of these models were conducted using a damage model based on continuum damage mechanics including a nonlocal damage theory proposed by the authors. It was confirmed that the fracture strength varies depending on the microstructures which are narrow area of yarns and void in matrix. On the other hand, it was unclear how the parameters related to the damage model affected the material behavior. Thus, the effect of damage model on material behavior was investigated by changing the parameters in this study. As a result, it was found that there was an appropriate parameter for nonlocal damage theory to avoid the mesh dependence of nonlinear behavior and fracture strength.

Paths of the semi-elliptical inclined surface cracks under complex low-cycle loading

The results of calculated–experimental and numerical studies of the relative strain intensity factors in the case of semi-elliptical inclined surface cracks in the of 12Kh18N10T austenite stainless steels. Strain-based fracture criterion was applied for obtaining the refined comprehensive estimation of basic provisions of non-linear fracture mechanics and general methodology of design for strength and damage tolerance of metallic components of critical equipment used in nuclear, thermal and space power engineering. The design and experimental kinetic and static dependences between fracture characteristics for developing inclined surface semi-elliptic low-cycle cracks have been obtained using strain-based criterion, analytical and numerical methods.

Proposal of analysis method of global-local finite element method for finite strain elastic-plastic fracture mechanics analysis

The purpose of this study is to make it possible to perform a large number of paratric analyzes on the position and shape of cracks under finite elasto-plastic deformation. In this report, we propose a one-way coupled analysis method using displacement interpolation between a global finite element method analysis model created without assuming cracks and a local finite element method analysis model assuming cracks. The proposed method is based on the superconvergent patch recovery, and uses the least-squares method to apply the nodal displacements of the global finite element model to the nodes of the local finite element model as displacement boundary conditions. In addition, we will create an merged finite element method analysis model assuming a crack directly in the global finite element method analysis model and identify the application conditions that can be applied to the problem without loss of accuracy through relative comparison by J-integral calculation at the crack tip which is nonlinear fracture mechanics parameter.

Fracture testing of adhesive joints in mixed-mode I+III

The Mixed-Mode Controlled Double Cantilever Beam (MC-DCB) test has been developed to test samples under mixed-mode loading in a combination of mode I and mode III. The mixed-mode ratio is defined based on J-integral and the principle of superimposition holds even in the case of nonlinear fracture behavior. This mixed-mode ratio is externally controlled to be constant during the entire test duration by realizing the MC-DCB test setup as a dual-actuator test in a biaxial testing machine.In this work, test results at constant mode-mixity on two different kinds of adhesive joints are presented: elastic-plastic adhesive joints made of SikaPower®-498 and rather brittle adhesive joints made of Henkel Teroson® EP4510GB. These recently achieved test results give more detailed information on the fracture behavior of the particular adhesive joints. With regard to cohesive zone modelling of possible joint failure, the traction-separation behavior at the initial crack tip has been evaluated by considering the crack-tip opening displacement, which has been measured by digital image correlation in the experiments.

The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

Abstract This study applies the Boundary Element Method (BEM) for the fracture failure modelling of three-dimensional concrete structures subjected to concentrated boundary conditions. The non-requirement of domain mesh by the BEM enables high accuracy in the domain fields assessment in addition to less complex remeshing procedures during crack propagation. However, concentrated boundary conditions often occur in fracture mechanics. The Lagrangian version of the BEM enforces such boundary conditions approximately by small length elements, which lead to numerical instabilities or even inaccurate problem representation. This study proposes a formulation for representing properly concentrated boundary conditions within the Lagrangian BEM framework. Nonlinear fracture mechanics describes the material failure processes herein. The classical cohesive crack approach governs the nonlinear energy dissipation processes, in which constant and tangent operators solve the resulting nonlinear system. Three applications demonstrate the accuracy of the proposed formulation, in which the BEM responses are compared against numerical and experimental results available in the literature.

Fully coupled thermo-hydro-mechanical approach to model fracture response to injection process in enhanced geothermal systems using displacement discontinuity and finite element method

Assessing, predicting, and controlling injection-induced seismicity is a major challenge for developing enhanced geothermal systems (EGS) due to the complexity of coupled thermo-hydro-mechanical (THM) processes. This study aimed to develop a fully coupled numerical model to assess the complex behavior of a low permeable matrix-fracture during non-isothermal single-phase fluid injection process. A thermo-poroelastic displacement discontinuity (DD) method combining with different forms of finite element method are implemented to encapsulate the fractured medium response and transport processes, respectively. The nonlinear characteristics of normal (changing the joint to hydraulic fracture status) and shear (changing the stick to slip fracture status) fracture deformation are taken into account through fracture constitutive relations. Developed numerical approach was applied to simulate cool water injection into fracture/matrix systems, analyzing the role of coupled processes on spatiotemporal variation of matrix-fracture stresses, temperature and pore pressure and assessing induced seismicity (slippage) and permeability alteration. Numerical simulations demonstrate a fully coupled relation between matrix dilation, shrinkage, and non-linear fracture deformation. The redistribution of dynamic and kinematic parameters along with non-linear fracture deformation showed that although the poroelastic effects are dominant in the early stages, thermoelastic effects dominate in the long-term injection stages. • A fully-coupled Thermo-Hydro-Mechanical approach was developed to model injection process in EGS. • Displacement discontinuity and finite element methods were combined to encapsulate fracture deformation and transport processes, respectively. • Fracture constitutive laws were implemented to model non-linear crack deformation. • Poroelastic effects are dominant in the early stages, and thermoelastic effects dominate in the long-term injection stages.