Resolved Normal Stresses Research Articles

A microdamage model for FCC single crystals considering a mixed failure mechanism of slip and cleavage

In this study, a microdamage model is newly proposed to predict the failure process of FCC single crystals. Two micro damage mechanisms, slip and cleavage, are both involved in the model. A microscopic damage variable is first defined at the slip plane scale, and a damage coupled crystal plasticity constitutive equation in a co-rotational tensor framework is then established. A damage driving force consisting of generalized energies related to the resolved shear stress and the positive resolved normal stress is proposed to reflect the mixed failure mechanism of FCC single crystals induced by slip and cleavage. The damage evolution equation is then derived in the framework of thermodynamics. An explicit algorithm for the damage coupled crystal plasticity finite element method is given. The proposed microdamage model is utilized to predict the slip-dominant fracture behavior of a single crystal copper and the cleavage-dominant fracture behavior of a nickel-based single crystal alloy. The damage evolution process of slip planes is given and the influence mechanism is revealed. The calculated results agree well with the experimental data, which verifies the good capability of the proposed model in describing and predicting the multi failure processes of FCC metals. Finally, a 2D fracture simulation of a single crystal notched specimen under shear loading is conducted, and the effect of damage parameters on the fracture modes is also discussed.

Development of a microstructural cohesive zone model for intergranular hydrogen environmentally assisted cracking

During the initial stages of hydrogen environmentally assisted cracking (HEAC), including crack incubation, initiation and microstructurally short cracking, the geometrical configuration of the microstructure greatly influences the crack growth behaviour. Therefore, there is a big incentive to generate a model which can replicate intergranular HEAC at a microstructural scale. This report provides a general framework to implement a microstructural intergranular HEAC model by using a cohesive zone approach in Abaqus. The parameters of the phenomenological model were fitted by using in-situ synchrotron tomography observations of crack initiation and propagation during HEAC of AA7449-T7651. After fitting the parameters, the real HEAC behaviour of the aluminium alloy 7449-T7651 has been replicated accurately. Several characteristic HEAC features were achieved, including crack segmentation, preferential cracking along grain boundaries with a high resolved normal stress and cracks slowing down at grain boundary triple junctions. Comparisons with experimental observations show the suitability of this approach for the prognosis of crack initiation and propagation at a microstructural scale under HEAC conditions.

An analysis of the factors that control fault zone architecture and the importance of fault orientation relative to regional stress

AbstractThe moment magnitude 7.2 El Mayor–Cucapah (EMC) earthquake of 2010 in northern Baja California, Mexico produced a cascading rupture that propagated through a geometrically diverse network of intersecting faults. These faults have been exhumed from depths of 6–10 km since the late Miocene based on low-temperature thermochronology, synkinematic alteration, and deformational fabrics. Coseismic slip of 1–6 m of the EMC event was accommodated by fault zones that displayed the full spectrum of architectural styles, from simple narrow fault zones (< 100 m in width) that have a single high-strain core, to complex wide fault zones (> 100 m in width) that have multiple anastomosing high-strain cores. As fault zone complexity and width increase the full spectrum of observed widths (20–200 m), coseismic slip becomes more broadly distributed on a greater number of scarps that form wider arrays. Thus, the infinitesimal slip of the surface rupture of a single earthquake strongly replicates many of the fabric elements that were developed during the long-term history of slip on the faults at deeper levels of the seismogenic crust. We find that factors such as protolith, normal stress, and displacement, which control gouge production in laboratory experiments, also affect the architectural complexity of natural faults. Fault zones developed in phyllosilicate-rich metasedimentary gneiss are generally wider and more complex than those developed in quartzo-feldspathic granitoid rocks. We hypothesize that the overall weakness and low strength contrast of faults developed in phyllosilicate rich host rocks leads to strain hardening and formation of broad, multi-stranded fault zones. Fault orientation also strongly affects fault zone complexity, which we find to increase with decreasing fault dip. We attribute this to the higher resolved normal stresses on gently dipping faults assuming a uniform stress field compatible with this extensional tectonic setting. The conditions that permit slip on misoriented surfaces with high normal stress should also produce failure of more optimally oriented slip systems in the fault zone, promoting complex branching and development of multiple high-strain cores. Overall, we find that fault zone architecture need not be strongly affected by differences in the amount of cumulative slip and instead is more strongly controlled by protolith and relative normal stress.

Analysis of shear fatigue properties of iron single crystals regarding possible effects of the resolved normal stresses on the slip planes

Crystal orientation effects on the shear fatigue limits of iron single-crystals were investigated by considering the influence of normal stress of the slip plane on the critical resolved shear stress (CRSS). The shear fatigue limit with the (123) plane in the shear loading position was experimentally confirmed to exceed that with shear loading on the (110) plane. On the contrary, the shear yield stress of the (123) plane, evaluated by monotonic shear tests, was lower than that of the (110) plane. To solve this seeming contradiction, it was postulated that body-centred cubic crystals possessed 24 slip systems and that the CRSS was sensitive to the resolved normal stress (RNS) on the slip plane. That is, it was assumed that the CRSS decreased under the tensile RNS according to its magnitude, but increased under the compressive RNS. The mathematical model of the CRSS dependence on the RNS was simply introduced to the work-hardening law proposed by Peirce et al. allowing formulation of the algebraic equations yielding the crystalline slip rates. This crystal plasticity model was applied to analyse monotonic shear and shear fatigue tests. By considering the effect of the RNS sensitivity, the shear yield stress with the (123) plane in the shear loading position was calculated to be lower than that with the (110) plane, showing agreement with the experimental results of the monotonic shear tests. Furthermore, in the application of cyclic shear loads corresponding to the fatigue limits, it was confirmed that the plastic strain range of the primary slip plane converged to similar values despite the differences in the crystal orientations of the shear plane and the normal stresses to it. These results imply that the present method allows the prediction of fatigue limits under different crystal orientations and loading conditions.

Strength and deformation of shocked diamond single crystals: Orientation dependence

Understanding and quantifying the strength or elastic limit of diamond single crystals is of considerable scientific and technological importance, and has been a subject of long standing theoretical and experimental interest. To examine the effect of crystalline anisotropy on strength and deformation of shocked diamond single crystals, plate impact experiments were conducted to measure wave profiles at various elastic impact stresses up to \ensuremath{\sim}120 GPa along [110] and [111] crystal orientations. Using laser interferometry, particle velocity histories and shock velocities in the diamond samples were measured and were compared with similar measurements published previously for shock compression along the [100] direction. Wave profiles for all three orientations showed large elastic wave amplitudes followed by time-dependent inelastic deformation. From the measured wave profiles, the elastic limits were determined under well characterized uniaxial strain loading conditions. The measured elastic wave amplitudes for the [110] and [111] orientations were lower for higher elastic impact stress (stress attained for an elastic diamond response), consistent with the result reported previously for [100] diamond. The maximum resolved shear stress (MRSS) on the {111}⟨110⟩ slip systems was determined for each orientation, revealing significant orientation dependence. The MRSS values for the [100] and [110] orientations (\ensuremath{\sim}33 GPa) are 25%--30% of theoretical estimates; the MRSS value for the [111] orientation is significantly lower (\ensuremath{\sim}23 GPa). Our results demonstrate that the MRSS depends strongly on the stress component normal to the {111} planes or the resolved normal stress (RNS), suggesting that the RNS plays a key role in inhibiting the onset of inelastic deformation. Lower elastic wave amplitudes at higher peak stress and the effect of the RNS are inconsistent with typical dislocation slip mechanisms of inelastic deformation, suggesting instead an inelastic response characteristic of shocked brittle solids. The present results show that the elastic limit (or material strength) of diamond single crystals cannot be described using traditional isotropic approaches, and typical plasticity models cannot be used to describe the inelastic deformation of diamond. Analysis of the measured wave profiles beyond the elastic limit, including characterization of the peak state, requires numerical simulations that incorporate a time-dependent, anisotropic, inelastic deformation response. Development of such a material description for diamond is an important need.

Influence of single crystal orientation on homogeneous dislocation nucleation under uniaxial loading

Atomistic simulations are used to investigate how the stress required for homogeneous nucleation of partial dislocations in single crystal copper under uniaxial loading changes as a function of crystallographic orientation. Molecular dynamics is employed based on an embedded-atom method potential for Cu at 10 and 300 K. Results indicate that non-Schmid parameters are important for describing the calculated dislocation nucleation behavior for single crystal orientations under tension and compression. A continuum relationship is presented that incorporates Schmid and non-Schmid terms to correlate the nucleation stress over all tensile axis orientations within the stereographic triangle. Simulations investigating the temperature dependence of homogeneous dislocation nucleation yield activation volumes of ≈ 0.5 – 2 b 3 and activation energies of ≈ 0.30 eV . For uniaxial compression, full dislocation loop nucleation is observed, in contrast to uniaxial tension. One of the main differences between uniaxial tension and compression is how the applied stress is resolved normal to the slip plane on which dislocations nucleate—in tension, this normal stress is tensile, and in compression, it is compressive. Last, the tension–compression asymmetry is examined as a function of loading axis orientation. Orientations with a high resolved stress normal to the slip plane on which dislocations nucleate have a larger tension–compression asymmetry with respect to dislocation nucleation than those orientations with a low resolved normal stress. The significance of this research is that the resolved stress normal to the slip plane on which dislocations nucleate plays an important role in partial (and full) dislocation loop nucleation in FCC Cu single crystals.

Paleostress inversion of fault-slip data using the shear stress solution of Means (1989)

Means (1989) presented a graphical solution for shear and normal stress orientations on any generally oriented plane. This solution can be used to solve for paleostress orientations for a population of faults where slip direction and slip sense are known. A grid-search method is used which tests a range of stress orientations and stress ratios, attempting to find the tensor which minimizes the angle between measured and predicted slip directions, minimizes resolved normal stresses and maximizes resolved shear stresses. Comparison with previously published tensor-search algorithms indicates that computation speed is increased with no loss of accuracy. Test analysis of data from the Yuli aftershock sequence indicates that this method produces results similar to previously published solutions. Analysis of geologic faults from the Piedmont of South Carolina indicates a pre-Jurassic period of normal faulting and extensional deformation dominated by a northwest trending σ 3 .