International Journal of Fracture最新文献

It is well recognized in the literature that the fracture process of thin metal sheets involves three energy dissipation mechanisms i.e., plasticity, necking and surface separation. However, the complex stress state in thin structures hinders the experimental assessment of these quantities and, consequently, the failure modelling. This work evaluates the contribution of these mechanisms to the ductile damage of a thin advanced high strength steel sheet under different stress triaxiality ranges. The essential work of fracture test was carried out on a set of different notch geometry specimens that cover a wide range of stress states. The experimental trend of these specimens was simulated in ABAQUS/Explicit using a VUSDFLD subroutine. Bai and Wierzbicki uncoupled fracture model, which is a function of fracture plastic strain to stress triaxiality (η) and normalized Lode angle ((overline{theta })), was selected as damage initiation criterion. A quantitative relationship of the fracture energy (G₀) as a function of (η) was proposed in this work and implemented in the model as a damage evolution law. The model captures well the experimental response and the influence of (η) on the softening behavior of the material. It was found that the sensitivity of G₀ to η is significant between 0.7 and 1.5. Above this rage, it seems that (η) has no influence on G₀. The model showed also the relationship between the two local damage parameters (G₀) and the necking (G_n) with respect to the stress state. G₀ represents less than 10% of the total work of fracture, while the largest contribution comes from (G_n).

This work introduces a novel approach for characterizing the residual load bearing capacity of fractured components based on the Phase Field fracture model. The underlying idea involves exploiting this well-established framework for fracturing materials and applying it to mechanically loaded domains in which fracture has already occurred. Hence, the continuous phase field here portrays the smeared representation of known crack patterns, based on which the unilateral contact interactions between the crack lips are enforced through a suitable strain energy decomposition. This allows for a theoretically robust and implicit treatment of the originally discontinuous problem while remaining in a continuum framework. As such, the proposed approach avoids the numerically challenging definition and management of conventional contact pairs, thus proving to be especially promising for its application to domains with multiple fragments. Besides presenting the theoretical foundation and algorithmic convenience of the approach, its accuracy and representativeness are proven against theoretical predictions and numerical results from Finite Element models featuring conventional contact interactions.

The material mismatch between the dissimilarly oriented plies within laminated structures induces localised singular interlaminar stresses at free edges, under various loading conditions such as mechanical, moisture, or thermal. These interlaminar stresses lead to premature interlaminar cracking. This study introduces the application of Finite Fracture Mechanics (FFM) for predicting free edge delamination in angle-ply laminates under uniform thermal loading. The current framework assumes nucleation of semi-elliptically shaped crack at the dissimilar interface, resulting in a 3D FFM criterion. For a given material intrinsic properties, e.g. interlaminar fracture toughness and strength, calculation of quantities such as interlaminar stresses and incremental energy release rates are required. These quantities, necessary for the evaluation of the FFM criterion, are determined semi-analytically through expressions derived from dimensional analysis and finite element models. Dimensional analysis facilitates the finding of these quantities only once using non-dimensionalised functions. The resulting non-dimensionalised functions for stresses and energy release rates are not a function of thermal load and ply thickness. This eliminates the requirement to re-solve the underlying boundary value problem for varying loads and ply thicknesses. The accuracy of finite element models is confirmed against results from models available in literature and dimensional analysis is validated against numerical solutions. The 3D FFM system is solved by assuming a homothetic crack extension and is implemented as a standard constrained nonlinear optimisation problem. In addition to the 3D FFM, another model based on the Theory of Critical Distances (TCD) is employed for validation purposes. The predictions from both the 3D FFM and TCD are compared to those from models available in the literature.

The resistance to volumetric deformations displayed by polymer networks is largely due to secondary and tertiary interactions between neighboring polymer chains. These interactions are both entropic and enthalpic in nature but are fundamentally different from the entropic forces that resist shearing in these networks. In this paper, we introduce a new depiction of elastomers as a crosslinked Van der Waals fluid. Starting from first principles, we develop constitutive equations that are implemented in a continuum model as well as a discrete network model. Our models predict that the failure of polymer networks may be driven by an instability in the underlying polymer bulk ‘fluid’ or by the breaking of polymer chains, depending on the loading path taken. The results of this study indicate that material failure in elastomers exposed to a purely triaxial state, such as in a poker chip experiment, may be driven by an entirely different mode of instability than those deformed in pure shear, such as in a uniaxial tension experiment.

A novel computational framework integrating the phase field approach with the solid shell formulation at finite deformation is proposed to model the anisotropic fracture of silicon solar cells in the thin-walled photovoltaic laminates. To alleviate the locking effects, both the enhanced assumed strain and assumed natural strain methods are incorporated in the solid shell element formulation. Aiming at tackling the poor convergence performance of standard Newton schemes, the efficient and robust quasi-Newton scheme is adopted for the solution of phase field modeling with enhanced shell formulation in a monolithic manner. Due to fracture anisotropy of the brittle silicon solar cells, the second-order structural tensor that is defined by the normal of preferential crack plane is introduced into the crack energy density function in the phase field modeling. On the other hand, to efficiently predict the crack growth of silicon solar cells, a global–local approach in the 3D setting proposed in the previous work is adopted here for the fracture modeling. In this approach, both mechanical deformation and phase field fracture are accounted for at the local model, while only mechanical deformation is addressed at the global level. At each time step, the solution of the global model is used to drive the local model, which corresponds to the one-way coupling in line with experimental evidence that the silicon cell cracking has negligible influence on the stiffness of photovoltaic modules. The capability of the modeling framework is demonstrated through numerical simulation of silicon solar cell cracking in the photovoltaic modules when subjected to different loading cases.

Soft adhesion has been rapidly studied and developed for various applications in recent years. Compared to existing toughening mechanisms based on the adherend or adhesive materials themselves, building architectures or patterns in soft adhesion offers an attractive way of enhancing adhesion without modifying the intrinsic material properties. However, despite the recent progress in soft architected adhesion, the fundamental interplay between the geometry and material properties remains largely unexplored. This results in questions about the geometric conditions for effective toughening and the roles of intrinsic material parameters in governing these conditions. Here we explore the geometry-elasticity interplay in toughening a soft architected bilayer with one-dimensional rectangular interfacial pillars. Using finite element simulations on 90-degree peel, we investigate effects of the adherend modulus, pillar aspect ratio, and interfacial contact ratio on the peel strength. We show that compared to a uniform interface, soft interfacial pillars (shear modulus ~ 0.6 MPa) with a high aspect ratio (> 4) can enhance the peel strength to more than 4 times, while stiff pillars (shear modulus ~ 1.5 MPa) only provide a limited enhancement (up to 1.5 times). Such enhancement is further amplified by increasing the interfacial contact ratio, where the best enhancement occurs when pillars are closely packed like a cross-cut surface (100% in contact yet architected). We develop a theory and scaling for the effective adhesion toughness and identify the fractoadhesive length of architected adhesion. We show that the fractoadhesive length provides a lower bound of the architecture feature size for effective toughening, while a large stretch at debonding in pillars further amplifies the toughening. Using an Ashby plot of the relevant architecture feature size and the fractoadhesive length in various architected adhesion systems, we conclude that macroscale architectures are necessary for effective toughening of soft adhesion with large fractoadhesive lengths.

CT-based finite element analysis (FEA) of human bones helps estimate fracture risk in clinical practice by linking bone ash density ((rho _{ash})) to mechanical parameters. However, phase field models for fracture prediction require the heterogeneous fracture toughness (G_{Ic}), which can be derived from the critical stress intensity factor (K_{Ic}), determined through various experimental methods. Due to a lack of standards for determining cortical bone’s (K_{Ic}), an experimental campaign is presented using 53 cortical specimens from two fresh frozen femurs to investigate whether a correlation exists between (K_{Ic}) and (rho _{ash}). We investigated various experimental techniques for correlating (K_{Ic}) with (rho _{ash}). We conducted FEAs employing the phase field method (PFM) to determine the most suitable correlation among the five possible ones stemming from the experimental methods. The ASTM standard using displacement at force application point was found to be the recommended experimental method for the estimation of (K_{Ic}) perpendicular to osteons’ direction

The corresponding statistical critical energy release rate bounds were determined:

with a standard deviation (SD= 0.30) representing a 95.4% confidence interval. The average (G_{Ic}) resulted in good correlations between the predicted fracture force by PFM-FEA of four representative specimens and experimental fracture forces. The proposed correlations will be used in CT-based PFM FEA to estimate the risk of hip and humeral fractures.

This article introduces a novel method for investigating crack propagation in porous quasi-brittle structures. The method combines isogeometric analysis (IGA) with higher-order phase-field theory. IGA is particularly useful for representing complex geometries through high-order Non-Uniform Rational B-Spline (NURBS)-based elements. It gives it an advantage over conventional methods that rely on enriched nodes. The phase-field approach uses a scalar field to implicitly define the trajectory of cracks, eliminating the need to predefine an initial crack location. The study was conducted on a porous plate model with multiple perforations. The porosity level significantly affects the structural integrity of the domain under consideration. The degradation functions that characterize material softening concerning porosity are obtained through careful examination. These degradation functions are further implemented into numerical problems to observe the effect of porosity on crack initiation and propagation behavior. The results have demonstrated the proposed approach’s efficiency and accuracy in analyzing porous concrete’s failure behavior. The analysis results contribute to advancing our understanding of crack propagation and showcase the efficacy of the presented methodological framework in enhancing predictive capabilities in structural mechanics.

Many engineering structures are subjected to variable amplitude loading. A number of studies investigate the effects of post overload, even-though it is crucial to describe what occurs during the overloading. The aim of this paper is to provide effective independent descriptors based on purely kinematic measurements for the analysis of overloading. Fatigue tests were conducted on a SENT specimen. Investigating crack propagation was through direct measurements using Digital Image Correlation and Linear Elastic Fracture Mechanics via Williams’ series expansion. The higher terms in Williams’ series expansion, referred to as crack features were analyzed in cycles with and without overload. In a case without overload, all features exhibit a proportional regime. Singular value decomposition (SVD) analysis confirms that a single feature is adequate to characterize the mechanism. In a cycle with overload, the regime changes during the overloading phase, making it a signature of this phase. In this case, the SVD analysis reveals that two descriptors are needed for these cycles. A subsequent analysis allows the definition of two physically interpretable features. This work presents a robust method to identify, based on kinematic measurements and SVD analysis, independent descriptors for the processes that occur during a cycle with overload.

Unraveling the material behavior at the microscale is one of the challenges of this century, demanding progress in experimental and computational strategies. Among the latter, two approaches are commonly applied for predicting crack nucleation. The Coupled Criterion (CC) and the Phase Field (PF) model, both depending on a material length parameter. In brittle materials at the macroscale, this parameter is significantly smaller than the specimen size. However, when the scale decreases, this material length might approach the structural dimensions. In this context, a comprehensive comparison between the two models is conducted, changing the ratio between the material length parameter and the dimensions of the specimen. Results indicate that when this ratio is sufficiently small predictions from both models coincide, otherwise both the CC and the PF model predict different results. Despite their differences, an agreement with experiments reported in the literature have been observed.