International Journal of Fracture最新文献

This study introduces a theoretical and numerical model for the spontaneous nucleation and propagation of distributed brittle fractures in initially intact materials. The formulation adopts a kinematic description of nested discontinuities characterized by a micromechanical interface law accounting for cohesion, unilateral contact and friction. The model allows for a unified treatment of the mixed-mode frictional fracture. The implementation of the model into a finite element framework is validated against benchmark tests, exhibiting independence of the discretization. The solution of selected quasi-static boundary value problems demonstrates the predictive capabilities of the framework in capturing key features observed in laboratory tests and in field problems involving confined quasi-brittle materials.

In the present work, macro-mechanical modelling of reinforced concrete structures under corrosion is performed. A traction based damage model is adopted. A discrete crack approach is used to model the fracture behaviour of concrete. The bond-slip relation between reinforcement steel and concrete is continuously evolving under corrosion, as a function of corrosion level and stress state. This is a non trivial issue, which is dealt with taking into account a total approach. Other corrosion aspects considered in this work are the reduction of the sane cross section of the reinforcement steel as well as spalling of the concrete cover. Bending tests are performed to evaluate the influence of corrosion at structural level, namely the increase of deformation as well as the decrease of the strength of the structure, leading to premature failure. Furthermore, stirrup confinement, in association with spalling, and slippage of the anchorage zone are analyzed.

In recent years, there has been growing interest in using acoustic emission (AE) time series data to develop fracture precursors for predicting imminent failure in cementitious materials. In this context, natural time (NT) analysis used in seismology has proven to be a useful tool, offering insights into the critical stage, namely the region of criticality, that precedes the mainshock event. Therefore, in the present study, the occurrence of impending macroscopic fracture in cementitious composites is predicted using the NT analysis of acoustic emission. To achieve this, the parameters of natural time, namely the variance, (kappa _{1}), the change in entropy, (Delta S), and the complexity measure, (Lambda _{i}), were utilized as precursors. Furthermore, the Tsallis q-index, obtained from the non-extensive statistical mechanics framework, was used in conjunction with the NT parameters. It was observed that the NT parameters, (kappa _{1}) reached a critical value of 0.07, (Delta S) attained a global minimum, and (Lambda _i) exhibited an abrupt increase before the mainshock event, similar to that observed in seismicity prior to major earthquakes. Furthermore, a sudden drop in Tsallis q-index was observed before the mainshock event. In addition, the behavior of the cementitious composite material closely resembled that of the Olami–Feder–Christensen earthquake model, as evidenced by the significant increase in cumulative AE energy observed after the region of criticality. Therefore, (kappa _{1}), (Delta S), and (Lambda _i) in combination with the q-index could be utilized as precursors for detecting impending macroscopic fracture in cementitious composites.

Fracture mechanics, originating from Griffith’s pioneering theory, has evolved into a foundational framework for understanding and predicting material failure across scales. Over the past century, it has expanded from linear elasticity to encompass nonlinear, dynamic, and stochastic behaviors—capturing fracture, fatigue, rupture, damage, and fragmentation in materials ranging from metals and ceramics to polymers, composites, soft matter, and biological tissues. Despite these advances, the field is far from complete. As modern materials and structures operate under unprecedented extremes of size, rate, and environment, classical assumptions—continuum validity, small-scale yielding, and singular field dominance—are increasingly challenged.

This Perspective identifies 25 outstanding issues that delineate the current and emerging frontiers of fracture mechanics. Organized across three interrelated domains—theoretical foundations, material behavior, and engineering applications—these issues span the limits of continuum theory, attainable fracture toughness, multiscale crack coalescence, fracture under extreme environments, and the integration of artificial intelligence for data-driven modeling. Collectively, they highlight a paradigm shift toward multiscale, multiphysics, and information-rich approaches that bridge atomistic processes and macroscopic failure. Far from a mature or closed discipline, fracture mechanics remains an evolving science—one that will continue to play a central role in designing materials and structures with unprecedented strength, toughness, and resilience in the century ahead.

In this work, a new damage model for cohesive fracture is presented. The concept of damage driving mechanism is introduced, from which the damage evolution law is derived. Special attention is paid to non pure mode-I and mode-II fracture modes, such as mixed-mode fracture and mode-II fracture under compression. Conversely to the previous traction-based damage model (Alfaiate et al. 2023), where the damage variables are derived from uniaxial tensile and shear relationships, the damage variables are now obtained explicitly from reference traction-jump displacement relationships, leading to an integration of fracture mechanics concepts with a damage mechanics approach. In this way, it is possible to explicitly control the dissipation of energy. The model is aimed at the simulation of the behaviour of reinforced concrete structures under corrosion. Corrosion affects i) cracking, which is modelled with a discrete crack approach, ii) bond-slip degradation between steel and concrete, iii) the reduction of the sane cross section of the reinforcement steel and iv) spalling of the concrete cover. In this work some illustrative examples of the performance of the model are shown. In part II, examples of reinforced concrete structures with and without corrosion are presented.

Laser powder bed fusion (LPBF) imposes steep thermal gradients, resulting in distortion and the formation of significant residual stresses, which often precipitate in-situ cracking at support interfaces and sharp geometric features. To isolate their influence on structural integrity, we combined fracture mechanics testing with residual stress evaluation on as-built compact tension specimens printed in two orthogonal orientations. The experimentally measured apparent stress-intensity factor was deconvolved into mechanical and residual-stress components, yielding a residual-stress-free fracture toughness (({K}_{ICeff})). Apparent fracture toughness (({K}_{IC})) ranged from 25 to 35 MPa m^1/2, whereas ({K}_{ICeff}) increased to 45–52 MPa m^1/2. Residual stresses, therefore, depress the material’s residual-stress-free resistance by up to ~ 50% and accentuate orientation-dependent anisotropy. The framework presented offers a route for quantifying process-induced toughness degradation in LPBF alloys.

Due to their microstructural inhomogeneity, predicting damage and fracture mechanisms in polycrystalline materials at the micron scale remains challenging. Therefore, accounting for microstructural features involved in damaging processes is of paramount importance in addressing this critical problem. This study proposes a novel cohesive phase-field approach to seamlessly simulate intergranular and transgranular failure within a realistic polycrystalline microstructure, capable of accounting for grain boundary cohesive properties. It relies on complete control of local material properties within the considered solid domain while exploiting the flexibility of the cohesive phase-field formulation. To exploit the model’s capabilities, an image segmentation technique was developed, enabling realistic microstructure modelling. This technique serves as input for Finite Element-based simulations in an open-source FEniCS library integrated into GPFniCS, a code previously proposed by the authors. Two case studies demonstrate the model’s capabilities: a one-dimensional problem with a cohesive interface and a two-dimensional cantilever bending scenario in polycrystalline material. The proposed approach is also validated with the commercial cohesive zone method (CZM). The proposed model opens new avenues for designing and optimising polycrystalline materials with unprecedented fracture toughness, while also revealing the failure mechanisms at this critical scale in currently available materials.

Graphical abstract

This work focuses on the relationships between microstructure and cleavage fracture of a high strength, medium carbon, low alloy steel. The local approach to brittle fracture was applied to both a tempered martensitic microstructure and a mixed tempered martensite + upper bainite microstructure. Three tempering levels were considered to vary the carbide size distribution. Tensile tests were carried out at −196 °C on smooth and notched tensile specimens, followed by fracture surface investigations and finite element analysis.

In tempered martensite microstructures, both from actual cleavage initiation sites as well as from Smith’s model predictions, the fracture mechanism and the cleavage fracture stress were driven by the size of coarser M₃C carbides (namely, the 2% coarser particles). The presence and spatial distribution of upper bainite packets in the tempered martensite matrix governed cleavage fracture initiation of the mixed microstructures, leading to lower and more scattered values of the cleavage fracture stress.

This study presents a phase-field modeling framework that combines an interfacial phase-field approach with adaptive mesh refinement to simulate thermomechanically-induced fractures in layered rocks. Meanwhile, this study implements the interfacial phase-field method in COMSOL. The interfacial phase-field method captures smooth transitions in material properties across bedding planes, avoiding explicit interface modeling while accurately representing mechanical and thermal responses near these interfaces. To reduce the computational cost typical of phase-field fracture simulations, an adaptive mesh refinement strategy is employed using the COMSOL API. The mesh refinement is dynamically guided by the phase-field variable within COMSOL’s Application Builder, enabling focused refinement around evolving cracks while maintaining coarser meshes elsewhere. The coupled four-field system (temperature, displacement, phase-field, and interfacial phase-field) is solved through segregated solution steps (staggered solution scheme). Compared with uniform mesh refinement, the adaptive approach significantly reduces computational demands without sacrificing accuracy in predicting crack paths and fracture morphologies. Validation through multiple numerical examples under quasi-static thermomechanical loading demonstrates the framework’s capability to capture complex fracture processes influenced by thermal effects and bedding-plane heterogeneity. This approach offers a robust and efficient tool for modeling fractures in layered rocks, with practical implications for geothermal energy extraction, nuclear waste disposal, and deep underground engineering.