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.
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.
This research introduces a novel mixed-mode discrete crack formulation to simulate crack growth in concrete using position-based High Aspect Ratio (HAR) finite elements. The approach is based on the discrete crack methodology known as Mesh Fragmentation Technique (MFT) and uses HAR interface elements to model cracks through a proposed mixed-mode continuous damage model. In this study, a recently extended version of MFT is employed, which is position-based and accounts for large displacements and rotations. The framework addresses mixed-mode crack behavior through a novel damage model that incorporates both shear and tensile displacements to compute the scalar damage variable. The study includes validation examples that confirm the accuracy of the formulation, along with comparisons between numerical results and experimental data for load-bearing capacity and crack propagation trajectories. Additionally, an example under large displacements is presented to demonstrate the applicability of the proposed framework in geometric nonlinear problems. The results demonstrate that the formulation accurately represents mixed-mode crack growth in concrete.
In this work, plane strain finite element simulations are conducted to analyze the growth of a circular void ahead of a notch tip in a shape memory alloy subjected to combined modes I and II loading, under small-scale yielding and transformation conditions. This study is motivated by a recent experimental investigation which showed predominantly dimple fracture occurring near a crack tip in a NiTi shape memory alloy as the mode II component is increased. An isotropic constitutive model that captures the coupled nature of superelasticity and plasticity is employed in the present simulations. The material is taken to be initially in the austenite phase above the austenite finish temperature. Also, computations are performed for a reference elastic-plastic material having austenite properties to understand the role of phase transformation on near-tip void growth and coalescence. It is found that the energy release rate at coalescence of the void and the notch, Jc, decreases with enhancement in mode II component for both materials, which corroborates with experimental observations. It is traced to faster strain localization mediated by intense shearing in the ligament bridging the notch tip and the void. Furthermore, phase transformation plays a benevolent role by impeding plastic strain development in the ligament resulting in 30 to 35% higher Jc compared to the reference elastic-plastic material, irrespective of mode mixity. It also leads to slower void growth especially at later stages of loading. A systematic analysis of inelastic strain, martensite volume fraction and hydrostatic stress/triaxiality prevailing in the ligament and in the region around the void is conducted to clearly understand the above trends.
This study examines the propagation of a pre-existing fluid-driven fracture in a permeable rock. Incompressible laminar Newtonian fluid drives the fracture which experiences fluid loss through the fracture interface into the surrounding rock matrix. Because the Carter’s model derived from Darcy law has its many flaws, a new model for the fluid loss relating the leak-off depth to the net fluid pressure in the fracture is employed in this work. The elasticity of the rock is modelled using the Khristianovic-Geertsma-de Klerk (KGD) model. Starting out with lubrication equations, a system of partial integro-differential equations relating the width of the fracture to the net pressure and the leak-off depth is derived. Similarity solutions derived for the fracture half-width, net pressure, and depth of leak-off are used to reduce the system of partial integro-differential equations to a system of ordinary integro-differential equations. Numerical results are obtained for the fracture length, fracture half-width, leak-off depth and the net fluid pressure.
We investigate whether signatures of the underlying microstructure can be revealed through a post mortem statistical characterization of the fracture profile. To this end, we use the phase field model of fracture within a Finite Element framework to generate cracks that are resolved at the dominant microstructural length scale and run at least 100 times longer. The synthetic microstructures through which the crack propagates are carefully designed to provide some control over the eventual crack path. In each case, the fracture specimen is loaded in remote Mode-I. Cracks that are designed to be perfectly intergranular or propagate through a field of random toughness variations, lead to fracture profiles that are invariably flat at large scales. However, when profiled at the level of the dominant microstructural length scale, the same profiles appear to be self-affine and anti-persistent. On the other hand, in microstructures with randomly distributed defects that force the crack to follow a path largely dictated by the distribution of defects, the fracture profile is self-affine and persistent over a larger range of length scales. Thus, large scale persistence of the fracture profile in brittle fracture seems to be a sure indicator of the presence of random, ‘crack attracting’ defects like voids. In case of anti-persistent profiles, the microstructure is harder to discern. We show that even in these cases, the distribution of slopes of the crack segments, which in turn are connected to the local Mode-II perturbations encountered by the propagating crack tip, can provide some useful information about the nature of the underlying microstructure.
We investigate how the removal of a single bond affects the fracture behavior of triangular spring networks, whereby we systematically vary the position of the removed bond. Our simulations show that removing the bond has two contrasting effects on the fracture energy for initiation of crack propagation and on the fracture energy for failure of the entire network. A single missing bond can either lower or raise the initiation fracture energy, depending on its placement relative to the crack tip. In contrast, the failure fracture energy is always equal to or greater than that of a perfect network. For most initial placements of the missing bond, the crack path remains straight, and the increased failure fracture energy results from arrest at the point of maximum local fracture resistance. When the crack deviates from a straight path, we observe an even higher fracture energy, which we attribute primarily to crack bridging. This additional toughening mechanism becomes active only at low failure strains of the springs; at higher failure strains, the crack path tends to remain straight. Altogether, our results demonstrate that even a single bond removal can significantly enhance toughness, offering fundamental insights into the role of defects in polymer networks and informing the design of tough architected materials.
The reliability and structural integrity of the components get reduced when cracks grow during their service. This becomes even more critical when casting defects, such as macropores, are present in the component. This work investigates the crack trajectory in the presence of selected hole configurations by integrating phase field modelling with photoelasticity, serving as a precursor for modelling macroporosity. By lowering the computational burden typically associated with phase field modelling, photoelasticity has helped to arrive at a simple and consistent PFM approach capturing complex crack trajectories, validated experimentally for a wide configuration of holes with repeatability. Numerically simulated isochromatics are used to corroborate the findings from the phase field simulations and experiments.
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