New theory for. Mode I crack-tip dislocation emission

A material is intrinsically ductile under Mode I loading when the critical stress intensity K-Ie for dislocation emission is lower than the critical stress intensity K-Ic for cleavage. K-Ie is usually evaluated using the approximate Rice theory, which predicts a dependence on the elastic constants and the unstable stacking fault energy gamma(usf) for slip along the plane of dislocation emission. Here, atomistic simulations across a wide range of fcc metals show that K-Ie is systematically larger (10-30%) than predicted. However, the critical (crack tip) shear displacement is up to 40% smaller than predicted. The discrepancy arises because Mode I emission is accompanied by the formation of a surface step that is not considered in the Rice theory. A new theory for Mode I emission is presented based on the ideas that (i) the stress resisting step formation at the crack tip creates lattice trapping against dislocation emission such that (ii) emission is due to a mechanical instability at the crack tip. The new theory is formulated using a Peierls-type model, naturally includes the energy to form the step, and reduces to the Rice theory (no trapping) when the step energy is small. The new theory predicts a higher K-Ie at a smaller critical shear displacement, rationalizing deviations of simulations from the Rice theory. Specific predictions of K-Ie for the simulated materials, usually requiring use of the measured critical crack tip shear displacement due to complex material non-linearity, show very good agreement with simulations. An analytic model involving only gamma(usf), the surface energy gamma(s), and anisotropic elastic constants is shown to be quite accurate, serves as a replacement for the analytical Rice theory, and is used to understand differences between Rice theory and simulation in recent literature. The new theory highlights the role of surface steps created by dislocation emission in Mode I, which has implications not only for intrinsic ductility but also for crack tip twinning and fracture due to chemical interactions at the crack tip. (C) 2017 Elsevier Ltd. All rights reserved.

Mixed-Mode Static and Fatigue Failure Criteria for Adhesively-Bonded FRP Joints

Moslem Shahverdi

Fiber-reinforced polymer (FRP) composites are increasingly used in many load-bearing structures. Joints are the most critical structural elements as they often become the weak links in engineering structures. Bonding and bolting are two of the main joining techniques used for composite elements but, although bolted and bonded joints have their advantages and disadvantages, adhesively-bonded joints are often preferred. This is thanks to their better performance in terms of cost-effective structures with uniformly distributed stresses without the need for cutting fastener holes that result in high stress concentrations in the FRP adherends at the edges of the holes. In addition, due to the absence of stress concentrations, adhesively-bonded joints exhibit better fatigue behavior. However, the efficient and reliable use of adhesively-bonded joints requires a thorough understanding of their failure mechanisms under mixed-mode quasi-static and fatigue loading conditions. In real structural applications, failure of adhesively-bonded joints occurs due to crack initiation and propagation under varying mixed-mode ratios. Since it is difficult to describe this progressive fracture in a structural joint, fracture joints with constant mode-mixity ratios are used to determine the strain energy release rates for crack initiation and propagation. Subsequently, mixed-mode failure criteria based on the determined strain energy release rates can be established and used to model/predict the fatigue and fracture behaviors of structural joints. The main objectives of this thesis were to understand the fracture and fatigue behaviors of adhesively-bonded FRP fracture joints under Mode I, Mode II, and mixed-Mode I/II loading conditions and, consequently, develop mixed-mode static and fatigue failure criteria applicable to structural joints. To fulfill these objectives a combined experimental-analytical-numerical study was undertaken. Double cantilever beam (DCB-Mode I), end-load split (ELS-Mode II), and mixed-mode bending (MMB-Mode I/II) specimens were examined under quasi-static and constant amplitude fatigue loading. Analytical approaches were used to determine the strain energy release rates under quasi-static and fatigue loading, whereas phenomenological models were developed to characterize the fatigue and fracture behaviors of the joints. A new approach designated the “extended global method” was established and applied for the analysis of the quasi-static and fatigue experimental data and the fracture mode partitioning in the mixed-mode experiments. In parallel, non-linear finite element models were developed to simulate the quasi-static fracture behavior and investigate the effects of both the existing asymmetry and the observed fiber bridging on the fracture behavior of the examined joints. The bridging zone was modeled by zero-thickness cohesive elements. An exponential traction-separation description of the cohesive zone model was shown to appropriately model the fiber bridging and calculate its contribution to the fracture energy under quasi-static loading. The FE models were successfully employed for the separation of the fracture parameters, i.e. strain energy released at the crack tip (Gtip) and the amount of energy released along the crack-bridging zone (Gbr), in the quasi-static mixed-mode failure criterion for crack propagation. In addition to the studies on the quasi-static fracture behavior of the joints, a new phenomenological fatigue crack growth formulation for the modeling and prediction of Rratio effects on the Mode I fatigue behavior of adhesively-bonded joints was also derived. The model was used for prediction of the fatigue behavior of the examined joints under different R-ratios. The results proved that the model could accurately simulate the fatigue behavior of the examined joints and was also capable of predicting behavior exhibited under unseen loading conditions, i.e. the R-ratios used for estimating the model parameters were different from those used for validating its prediction capability. The experimental results and numerical analyses combined with the phenomenological models were used to establish mixed-mode static and fatigue failure criteria for crack initiation and crack propagation for the adhesively-bonded joints. The derived mixed-mode failure criteria can be used for simulating/predicting the crack initiation and progressive crack propagation in structural joints comprising the same adhesive and adherends.

EPFL2013

Atomistic study of hydrogen embrittlement of grain boundaries in nickel: I. Fracture

William Curtin, Ali Tehranchi

Hydrogen ingress into a metal is a persistent source of embrittlement. Fracture surfaces are often intergranular, suggesting favorable cleave crack growth along grain boundaries (GBs) as one driver for embrittlement. Here, atomistic simulations are used to investigate the effects of segregated hydrogen on the behavior of cracks along various symmetric tilt grain boundaries in fcc Nickel. An atomistic potential for Ni-H is first recalibrated against new quantum level computations of the energy of H in specific sites within the Ni Sigma 5(120)< 100 > GB. The binding energy of H atoms to various atomic sites in the Ni Sigma 3(111) (twin), Ni Sigma 5(120)< 100 >, Ni Sigma 99(557)< 110 >, and Ni Sigma 9(221)< 110 > GBs, and to various surfaces created by separating these GBs into two possible fracture surfaces, are computed and used to determine equilibrium H concentrations at bulk H concentrations typical of embrittlement in Ni. Mode I fracture behavior is then studied, examining the influence of H in altering the competition between dislocation emission (crack blunting; "ductile" behavior) and cleavage fracture ("brittle" behavior) for intergranular cracks. Simulation results are compared with theoretical predictions (Griffith theory for cleavage; Rice theory for emission) using the computed surface energies. The deformation behavior at the GBs is, however, generally complex and not as simple as cleavage or emission at a sharp crack tip, which is not unexpected due to the complexity of the GB structures. In cases predicted to emit dislocations from the crack tip, the presence of H atoms reduces the critical load for emission of the dislocations and no cleavage is found. In the cases predicted to cleave, the presence of H atoms reduces the cleavage stress intensity and makes cleavage easier, including Ni Sigma 9(221)< 110 > which emits dislocations in the absence of H. Aside from the one unusual Ni Sigma 9(221)< 110 > case, no tendency is found for H to cause a ductile-to-brittle transformation for cracks along GBs in Ni, either according to theory or simulation for initial equilibrium H segregation and with no, or limited, H diffusion near the newly-created fracture surfaces. The Ni Sigma 3(111) twin boundary does not absorb H at all, suggesting that embrittlement is more difficult in materials with higher fraction of such twin boundaries, as found experimentally. Experimental observations of cleavage-like failure are thus presumably caused by mechanisms involving H diffusion or dynamic crack growth. (C) 2017 Elsevier Ltd. All rights reserved.

Elsevier2017

Atomistic modeling of fracture

Predrag Andric, William Curtin

Atomistic modeling of fracture is intended to illuminate the complex response of atoms in the very high stressed region just ahead of a sharp crack. Accurate modeling of the atomic scale fracture is crucial for describing the intrinsic nature of a material (intrinsic ductility/brittleness), chemical effects in the crack-tip vicinity, the crack interaction with different defects in solids such as grain boundaries, solutes, precipitates, dislocations, voids, etc. Here, different methods for atomistic modeling of fracture are compared in their ability to obtain quantitatively useful results that are in agreement with the basic principles of linear elastic fracture mechanics (LEFM). We demonstrate that the complicated atomic crack-tip behavior is precisely described in simulations of semi-infinite cracks, where the loading is uniquely controlled by the applied stress intensity factor K. Such 'K-test' simulations are shown to be equally applicable in crystalline and amorphous materials, and to be suitable for quantitative evaluation of various critical stress intensity factors, the overall material fracture toughness, and quantitative comparison with theories. We further demonstrate that the simulation of a nanoscale center-crack tension (CCT) specimen often leads to the results that do not satisfy the conditions for application of LEFM. The simulated intrinsic fracture toughness, one of the basic material properties, using CCT test geometry is shown to be dependent on the crack size and far-field loading. In general, this study resolves quantitative differences between several methods for atomistic modeling of fracture and recommends that application of simulations based on nanoscale finite size cracks not be pursued.