The objective of this paper is to develop further a framework for computationally modeling microstructurally small fatigue crack growth in AA 7075-T651 (Bozek et al 2008 Modelling Simul. Mater. Sci. 16 065007). The focus is on the nucleation event, when a crack extends from within a secondphase particle into a surrounding grain, since this has been observed to be an initiating mechanism for fatigue crack growth in this alloy. It is hypothesized that nucleation can be predicted by computing a non-local nucleation metric near the crack front. The hypothesis is tested by employing a combination of experimentation and finite element modeling in which various slip-based and energy-based nucleation metrics are tested for validity, where each metric is derived from a continuum crystal plasticity formulation. To investigate each metric, a non-local procedure is developed for the calculation of nucleation metrics in the neighborhood of a crack front. Initially, an idealized baseline model consisting of a single grain containing a semi-ellipsoidal surface particle is studied to investigate the dependence of each nucleation metric on lattice orientation, number of load cycles and non-local regularization method. This is followed by a comparison of experimental observations and computational results for microstructural models constructed by replicating the observed microstructural geometry near second-phase particles in fatigue specimens. It
Microstructurally small fatigue crack (MSFC) formation includes stages of incubation, nucleation and microstructurally small propagation. In AA 7075-T651, the fracture of Al 7 Cu 2 Fe constituent particles is the major incubation source. In experiments, it has been observed that only a small percentage of these Fe-bearing particles crack in a highly stressed volume. The work presented here addresses the identification of the particles prone to cracking and the prediction of particle cracking frequency, given a distribution of particles and crystallographic texture in such a volume. Three-dimensional elasto-viscoplastic finite element analyses are performed to develop a response surface for the tensile stress in the particle as a function of the strain level surrounding the particle, parent grain orientation and particle aspect ratio. A technique for estimating particle strength from fracture toughness, particle size and intrinsic flaw size is developed. Particle cracking is then determined by comparing particle stress and strength. The frequency of particle cracking is then predicted from sampling measured distributions of grain orientation, particle aspect ratio and size. Good agreement is found between the predicted frequency of particle cracking and two preliminary validation experiments. An estimate of particle cracking frequency is important for simulating the next
It has been observed during fatigue cracking of AA 7075-T651 that a small percentage of Al 7 Cu 2 Fe particles crack during manufacturing or very early in their life. Some of the cracked particles eventually nucleate cracks into the surrounding microstructure, and among these the number of cycles required for nucleation varies widely. It is important to comprehend the mechanics underpinning the observed variation so that the subsequent propagation stage can be accurately modeled. To this end, finite element models of replicated grain and particle geometry are used to compute mechanical fields near monitored cracked particles using an elastic-viscoplastic crystal plasticity model that captures the effect of the orientation of the grains near each monitored particle. Nonlocal, slip-based metrics are used to study the localization and cyclic accumulation of slip near the cracked particles providing mechanics-based insight into the actuation of the nucleation event. A high slip localization and cyclic accumulation rate are found to be a necessary, but not sufficient, condition for nucleation from cracked particles. A sufficient local driving stress must also be present, which is strongly dependent on the local microstructure and accumulated slip. Furthermore, the simulation results elucidate a quantitative relationship between the slip accumulated during fatigue loading and a consequential reduction of the critical local driving stress for nucleation, providing a physical basis for the fatigue damage concept. The
Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in understanding intergranular fracture in polycrystals. First, 3D grain boundary geometries comprise a five-dimensional space. Second, the energy and peak stress of grain boundaries have singularities for all commensurate grain boundaries, especially those with short repeat distances. Thirdly, fracture nucleation and growth depend not only upon the properties of grain boundaries, but also in crucial ways on edges, corners and triple junctions of even greater geometrical complexity. To address the first two challenges, we explore the physical underpinnings for creating functional forms to capture the hierarchical commensurability structure in the grain boundary properties. To address the last challenge, we demonstrate a method for atomistically extracting the fracture properties of geometrically complex local regions on the fly from within a finite element simulation.
The fatigue resistance of metallic structures is inherently random due to environmental and boundary conditions, and microstructural geometry, including discontinuities, and material properties. A new methodology for fatigue life prediction is under development to account for these sources of randomness. One essential aspect of the methodology is the ability to perform truly multiscale simulations: simulations that directly link the boundary conditions on the structural length scale to the damage mechanisms of the microstructural length scale. This presentation compares and contrasts two multiscale methods suitable for fatigue life prediction. The first is a brute force method employing the widely-used multipoint constraint technique which couples a finite element model of the microstructure within the finite element model of the structural component. The second is a more subtle, modified multi-grid method which alternates analyses between the two finite element models while representing the evolving microstructural damage. Examples and comparisons are made for several geometries and preliminary validation is achieved with comparison to experimental tests conducted by the Northrop Grumman Corporation on a wing-panel structural geometry.
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