Simulating intergranular hydrogen enhanced decohesion in aluminium using density functional theory

Materials modelling at the atomistic scale provides a useful way of investigating the widely debated fundamental mechanisms of hydrogen embrittlement in materials like aluminium alloys. Density functional theory based tensile tests of grain boundaries (GBs) can be used to understand the hydrogen enhanced decohesion mechanism (HEDE). The cohesive zone model was employed to understand intergranular fracture from energies obtained in electronic structure calculations at small separation increments during ab initio tensile tests of an aluminium Σ11 GB supercell with variable coverages of H. The standard rigid grain shift test and a quasistatic sequential test, which aims to be faster and more realistic than the rigid grain shift method, were implemented. Both methods demonstrated the effects of H on the cohesive strength of the interface. The sequential method showed discrete structural changes during decohesion, along with significant deformation in general compared to the standard rigid approach. H was found to considerably weaken the GB, where increasing H content led to enhanced embrittlement such that, for the highest coverages of H, GB strength was reduced to approximately 20% of the strength of a pure Al GB - it is proposed that these results simulate HEDE. The possibility of finding H coverages required to induce this effect in real alloy systems is discussed in context by using calculations of the heat of segregation of H.

Bond parameters for peeling and debonding in thin plated RC beams subjected to mixed mode loading – Framework

Studies have primarily focussed on predicting mode-II debonding failure; whereas, in real-case-scenario, flexurally strengthened reinforced concrete (RC) beams observe premature failure mechanisms under mixed-mode loading conditions engaging geometrical and material variations. Peeling is a consequence of flexural crack as debonding is of interfacial shear crack. Under bending, peeling failure is considerably catastrophic over debonding due to the nature of crack formation; therefore, this needs to be distinguished in predictive analysis. In this paper, a new numerical modeling methodology is approached using eXtended finite element method (xFEM) for flexural cracks and Cohesive Zone Model (CZM) for shear cracks without predefining crack locations. The parameters of the constitutive models are identified through comparing finite element results with the experimental data. These parameters are related to key material properties. Based on proposed framework, the models provide a good estimation of plate strain distribution, cracks and failure type, in terms of mode and load of failure. Bilinear bond-slip curve is a closer match over exponential crack evolution at interface.

Inter-Element Crack Propagation with High-Order Stress Equilibrium Element

The present contribution proposes a formulation based on the use of hybrid equilibrium elements (HEEs), for the analysis of inter-element delamination and fracture propagation problems. HEEs are defined in terms of quadratic stress fields, which strongly verify both the homogeneous and inter-element equilibrium equations and they are employed with interfaces, initially exhibiting rigid behavior, embedded at the elements’ sides. The interface model is formulated in terms of the same degrees of freedom of the HEE, without any additional burden. The cohesive zone model (CZM) of the extrinsic interface is rigorously developed in the damage mechanics framework, with perfect adhesion at the pre-failure condition and with linear softening at the post-failure regime. After a brief review, the formulation is computationally tested by simulating the behavior of a double-cantilever-beam with diagonal loads; the obtained numerical results confirm the accuracy and potential of the method.

Study on Crack Development of Concrete Lining with Insufficient Lining Thickness Based on CZM Method

The most common structural defect of a tunnel in the operation period is the cracking of concrete lining. The insufficient thickness of tunnel lining is one of the main reasons for its cracking. This study studied the cracking behavior of standard concrete specimens and the failure behavior of tunnel structures caused by insufficient lining thickness using Cohesive Zone Model (CZM). Firstly, zero-thickness cohesive elements were globally inserted between solid elements of the standard concrete specimen model, and the crack development process of different concrete grades was compared. On this basis, a three-dimensional numerical model of the tunnel in the operation period was established. The mechanism and characteristics of crack propagation under different lining thicknesses were discussed. In addition, the statistics of cracks were made to discuss the development rules of lining cracks quantitatively. The results show that the CZM can reasonably simulate the fracture behavior of concrete. With the increase in concrete strength grade, the number of cohesive damaged elements and crack area increases. The insufficient lining thickness changes the lining stress distribution characteristics, reduces the lining structure’s overall safety, and leads to the cracking of the diseased area more easily. When surrounding rock does not contact the insufficient lining thickness, its influence on the structure is more evident than when surrounding rock fills the entire lining thickness. The number of cohesive damaged elements and the size of the crack area increases significantly.

The Impacts of Increased Ductility in Organic-Rich Shale on Fracture Network Growth by Hydraulic Fracturing

The difficulty of hydraulic fracturing in organic-rich shale caused by the increased ductility has not been well interpreted quantitatively, although it is well perceived that the increased shale ductility can impede the propagation of hydraulic fractures and enhance the healing of created fractures upon injection shutdown. This study aims to quantitatively study the impacts of increased ductility on the stimulated reservoir volume (SRV) using an advanced XFEM-based simulator. To achieve this goal, a modified cohesive zone model has been integrated into an in-house fully coupled poroelastic XFEM framework. The study continues by extending the functionality of the numerical framework to simulating multiple interacting fractures. The utilization of the object-oriented programming paradigm in the development of the framework makes it an easy extension to include the multi-fracture network by creating more instances of crack segments. A main hydraulic fracture with an arbitrary number of intersected branches can thus be modeled. A series of parametric studies will be conducted to investigate the impacts of increased ductility on the induced SRV by varying four involved material parameters individually. The modified cohesive zone model, which is essentially a traction-separation law (TSL), is characterized by four parameters: the initial tensile strength Tini, ultimate tensile strength Tkrg, the critical separation Dc, and the final crack separation Dmax. It can flexibly model different crack opening scenarios and simulate more realistically the increased shale ductility. The fully coupled poroelastic XFEM framework has been comprehensively verified against the latest semi-analytical solutions on the four well-known propagation regimes. The numerical results show that the shape of TSL does affect the main hydraulic fracture growth as well as the evolvement of the fracture network, given the same cohesive crack energy and tensile strength. It infers that ductility is not only controlled by cohesive crack energy and tensile strength, which further indicates the necessity of the newly proposed cohesive zone model. The magnitude of the initial tensile strength, controlling when the cohesive crack starts propagating, is found to have the greatest impacts on the fracture length, and SRV, among all four TSL parameters. The novelty of this study is two-fold. First, the newly modified cohesive zone model can more realistically represent the increased shale ductility. Second, the advanced XFEM framework that enables the simulation of a fracture network can study the impacts of increased ductility on the whole SRV but not a single crack.

Modelling the nucleation and propagation of cracks at twin boundaries

Fracture arising from cracks nucleating and propagating along twin boundaries is commonly observed in metals that exhibit twinning as a plastic deformation mechanism. This phenomenon affects the failure of macroscopic mechanical components, but it is not fully understood. We present simulations in which a continuum model for discrete twins and a cohesive zone model are coupled to aid the understanding of fracture at twin boundaries. The interaction between different twin systems is modelled using a local term that depends on the continuum twin variables. Simulations reveal that the resolved shear stress necessary for an incident twin to propagate through a barrier twin can be up to eight times the resolved shear stress for twin nucleation. Interface elements are used at the interfaces between all bulk elements to simulate arbitrary intragranular cracks. An algorithm to detect twin interfaces is developed and their strength has been calibrated to give good agreement with the experimentally observed fracture path. The elasto-plastic deformation induced by discrete twins is modelled using the crystal plasticity finite element method and the stress induced by twin tips is captured. The tensile stress caused by the tip of an incident twin on a barrier twin is sufficient to nucleate a crack. A typical staircase fracture path, with cracks propagating along the twin interfaces, is reproduced only if the strength of the twin interfaces is decreased to about one-third of the strength of the bulk material. This model can be used to help understand fracture caused by the activation of multiple twin systems in different materials.