K.N. Solanki

FINITE ELEMENT ANALYSIS OF PLASTICITY-INDUCED FATIGUE CRACK CLOSURE: AN OVERVIEW

Abstract Finite element analysis is perhaps the most commonly used numerical method to model plasticity-induced fatigue crack closure. The state-of-the-art is reviewed and a comprehensive overview is presented, summarizing issues which must be considered and emphasizing potential difficulties. These include mesh refinement level, crack advancement schemes, crack shape evolution, geometry effects, and crack opening value assessment techniques.

Finite element modeling of plasticity-induced crack closure with emphasis on geometry and mesh refinement effects

Abstract Two-dimensional, elastic–perfectly plastic finite element analyses of middle-crack tension (MT) and compact tension (CT) geometries were conducted to study fatigue crack closure and to calculate the crack-opening values under plane-strain and plane-stress conditions. The behaviors of the CT and MT geometries were compared. The loading was selected to give the same maximum stress intensity factor in both geometries, and thus approximately similar initial forward plastic zone sizes. Mesh refinement studies were performed on both geometries with various element types. For the CT geometry, negligible crack-opening loads under plane-strain conditions were observed. In contrast, for the MT specimen, the plane-strain crack-opening stresses were found to be significantly larger. This difference was shown to be a consequence of in-plane constraint. Under plane-stress conditions, it was found that the in-plane constraint has negligible effect, such that the opening values are approximately the same for both the CT and MT specimens.

Numerical simulations of multiple vehicle crashes and multidisciplinary crashworthiness optimization

Abstract In this study, a full-scale finite element vehicle model of a 1996 Dodge Neon is used in simulating two types of vehicle crashes, offset-frontal and side impacts. Based on an analysis of the vehicles internal energy absorption under both impacts, twenty-one components are selected and represented by thirteen design variables for the multidisciplinary optimization including the weight, intrusion distance, and energy absorptions. The second-order polynomials are used in creating the metamodels for the objective and constraint functions. The optimization results show that the weight can be significantly reduced while decreasing the intrusion distance and keeping the original level of energy absorption. With the successfully implemented optimization scheme, a set of non-dominated (tradeoff) solutions is obtained and the final design can be selected based on the designers preference. A simulation of 100 ms offset-frontal impact using LS-DYNA MPP v970 takes approximately 17 hours with 36 processors on an IBM Linux Cluster with Intel Pentium III 1.266 GHz processors and 607.5 GB RAM. A simulation of 100 ms side impact takes approximately 29 hours with the same condition as that of the offset-frontal simulation.

Grain Boundary Segregation of Interstitial and Substitutional Impurity Atoms in Alpha-Iron

The macroscopic behavior of polycrystalline materials is influenced by the local variation of properties caused by the presence of impurities and defects. The effect of these impurities at the atomic scale can either embrittle or strengthen grain boundaries (GBs) within. Thus, it is imperative to understand the energetics associated with segregation to design materials with desirable properties. In this study, molecular statics simulations were employed to analyze the energetics associated with the segregation of various elements (helium, hydrogen, carbon, phosphorous, and vanadium) to four 〈100〉 (Σ5 and Σ13 GBs) and six 〈110〉 (Σ3, Σ9, and Σ11 GBs) symmetric tilt grain boundaries in α-Fe. This knowledge is important for designing stable interfaces in harsh environments. Simulation results show that the local atomic arrangements within the GB region and the resulting structural units have a significant influence on the magnitude of binding energies of the impurity (interstitial and substitutional) atoms. These data also suggest that the site-to-site variation of energies within a boundary is substantial. Comparing the binding energies of all 10 boundaries shows that the Σ3(112) boundary possesses a much smaller binding energy for all interstitial and substitutional impurity atoms among the boundaries examined in this study. Additionally, based on the Rice–Wang model, our total energy calculations show that V has a significant beneficial effect on the Fe grain boundary cohesion, while P has a detrimental effect on grain boundary cohesion, much weaker than H and He. This is significant for applications where extreme environmental damage generates lattice defects and grain boundaries act as sinks for both interstitial and substitutional impurity atoms. This methodology provides us with a tool to effectively identify the local as well as the global segregation behavior that can influence the GB cohesion.

A new methodology for computing crack opening values from finite element analyses

Abstract Finite element analyses are frequently used to model growing fatigue cracks and the associated plasticity-induced crack closure. A new methodology is presented to calculate crack opening values in planar geometries using the crack surface nodal force distribution under minimum loading as determined from finite element analyses. The calculated crack opening values are compared with values obtained using finite element analysis and more conventional crack opening assessment methodologies, which focus on a single node near the crack tip. The new method eliminates the need to arbitrarily select a single node when defining the opening load or stress.

Improving the accuracy of vehicle crashworthiness response predictions using an ensemble of metamodels

Due to the scale and computational complexity of current simulation codes for vehicle crashworthiness analysis, metamodels have become indispensable tools for exploring and understanding the design space. Traditional application of metamodelling techniques is based on constructing multiple types of metamodels based on a common data set, selecting the most accurate one and discarding the rest. However, this practice does not take full advantage of the resources devoted for constructing different metamodels. This drawback can be overcome by combining individual metamodels in the form of an ensemble. Two case studies with a high-fidelity finite element vehicle model subject to offset-frontal and side impact conditions are presented for demonstration. The prediction accuracies of the individual metamodels and the ensemble of metamodels are compared, and it is found for all the crash responses of interest that the ensemble of metamodels outperforms all individual metamodels. It is also found that as the number of metamodels included in the ensemble increases, the prediction accuracy of the ensemble of metamodels increases.

Quantifying the energetics and length scales of carbon segregation to α-Fe symmetric tilt grain boundaries using atomistic simulations

Segregation of impurities to grain boundaries (GBs) plays an important role in both the stability and macroscopic behavior of polycrystalline materials. The research objective in this work is to better characterize the energetics and length scales involved with the process of solute and impurity segregation to GBs. Molecular statics simulations are used to calculate the segregation energies for carbon within multiple substitutional and interstitial GB sites over a database of 125 symmetric tilt GBs in Fe. The simulation results show that there are two energetically favorable GB segregation processes: (1) an octahedral C atom in the lattice segregating to an interstitial GB site and (2) an octahedral C atom and a vacancy in the lattice segregating to a grain boundary substitutional site. In both cases, lower segregation energies than appear in the bulk lattice were calculated. Moreover, based on segregation energies approaching bulk values, the length scale of interaction is larger for interstitial C than for substitutional C in the GB (?5?? compared to ?3?? from center of the GB). A subsequent data reduction and statistical representation of this dataset provides critical information about the mean segregation energy and the associated energy distributions for carbon atoms as a function of distance from the grain boundary, which quantitatively informs higher scale models with energetics and length scales necessary for capturing the segregation behavior of alloying elements and impurities in Fe. The significance of this research is the development of a methodology capable of ascertaining segregation energies over a wide range of GB character (typical of that observed in polycrystalline materials), which herein has been applied to carbon segregation to substitutional and interstitial sites in a specific class of GBs in ?-Fe.

Extreme creep resistance in a microstructurally stable nanocrystalline alloy

Nanocrystalline metals, with a mean grain size of less than 100 nanometres, have greater room-temperature strength than their coarse-grained equivalents, in part owing to a large reduction in grain size. However, this high strength generally comes with substantial losses in other mechanical properties, such as creep resistance, which limits their practical utility; for example, creep rates in nanocrystalline copper are about four orders of magnitude higher than those in typical coarse-grained copper. The degradation of creep resistance in nanocrystalline materials is in part due to an increase in the volume fraction of grain boundaries, which lack long-range crystalline order and lead to processes such as diffusional creep, sliding and rotation. Here we show that nanocrystalline copper–tantalum alloys possess an unprecedented combination of properties: high strength combined with extremely high-temperature creep resistance, while maintaining mechanical and thermal stability. Precursory work on this family of immiscible alloys has previously highlighted their thermo-mechanical stability and strength, which has motivated their study under more extreme conditions, such as creep. We find a steady-state creep rate of less than 10−6 per second—six to eight orders of magnitude lower than most nanocrystalline metals—at various temperatures between 0.5 and 0.64 times the melting temperature of the matrix (1,356 kelvin) under an applied stress ranging from 0.85 per cent to 1.2 per cent of the shear modulus. The unusual combination of properties in our nanocrystalline alloy is achieved via a processing route that creates distinct nanoclusters of atoms that pin grain boundaries within the alloy. This pinning improves the kinetic stability of the grains by increasing the energy barrier for grain-boundary sliding and rotation and by inhibiting grain coarsening, under extremely long-term creep conditions. Our processing approach should enable the development of microstructurally stable structural alloys with high strength and creep resistance for various high-temperature applications, including in the aerospace, naval, civilian infrastructure and energy sectors.

Binding energetics of substitutional and interstitial helium and di-helium defects with grain boundary structure in α-Fe

The formation/binding energetics and length scales associated with the interaction between He atoms and grain boundaries in BCC α-Fe were explored. Ten different low Σ grain boundaries from the ⟨100⟩ and ⟨110⟩ symmetric tilt grain boundary systems were used. In this work, we then calculated formation/binding energies for 1–2 He atoms in the substitutional and interstitial sites (HeV, He2V, HeInt, He2Int) at all potential grain boundary sites within 15 A of the boundary (52 826 simulations total). The present results provide detailed information about the interaction energies and length scales of 1–2 He atoms with grain boundaries for the structures examined. A number of interesting new findings emerge from the present study. For instance, the Σ3(112) twin boundary in BCC Fe possesses a much smaller binding energy than other boundaries, which corresponds in long time dynamics simulations to the ability of an interstitial He defect to break away from the boundary in simulations on the order of nanoseconds. ...

Atomic scale investigation of grain boundary structure role on intergranular deformation in aluminium

The role that grain boundary (GB) structure plays on the directional asymmetry of an intergranular crack (i.e. cleavage behaviour is favoured along one direction, while ductile behaviour along the other direction of the interface) was investigated using atomistic simulations for aluminium 〈1 1 0〉 symmetric tilt GBs. Middle-tension (M(T)) and Mode-I crack propagation specimens were used to evaluate the predictive capability of the Rice criterion. The stress–strain response of the GBs for the M(T) specimens highlighted the importance of the GB structure. The observed crack tip behaviour for certain GBs (Σ9 (2 2 1), Σ11 (3 3 2) and Σ33 (4 4 1)) with the M(T) specimen displayed an absence of directional asymmetry which is in disagreement with the Rice criterion. Moreover, in these GBs with the M(T) specimen, the dislocation emission from a GB source at a finite distance ahead of the crack tip was observed rather than from the crack tip, as suggested by the Rice criterion. In an attempt to understand discrepancy between the theoretical predictions and atomistic observations, the effect of boundary conditions (M(T), Mode-I and the edge crack) on the crack tip events was examined and it was concluded that the incipient plastic events observed were strongly influenced by the boundary conditions (i.e. activation of dislocation sources along the GB, in contrast to dislocation nucleation directly from the crack tip). In summary, these findings provide new insights into crack growth behaviour along GB interfaces and provide a physical basis for examining the role of the GB character on incipient event ahead of a crack tip and interface properties, as an input to higher scale models.