Global Stress State Research Articles

Time-varying elastic wave mode conversion in vibrating elastic beams with subwavelength nonlinearity

Introduction of time-varying properties in a background medium can enable unconventional wave behavior. Furthermore, it is well-known that subjecting nonlinear materials to time-varying stress can be used for material characterization [Appl. Phys. Lett. 94, 011905 (2009)]. We propose a technique called Dynamic Asymmetric Transmission Measurement (DATM) that combines structural dynamic (SD) and ultrasonic (US) testing modalities in an elastic waveguide to detect and characterize changes in the global stress state of a structure that result in local time-varying stress conditions due to local nonlinearity. Asymmetric geometric features in beams and plates, paired with time-varying stress conditions, result in asymmetric mode conversion of guided US waves that depend on large-scale structural dynamics. The DATM technique is explored through finite element modeling, semi-analytical methods, and experiments and discussed in a structural health monitoring context. We also discuss the use of dynamic structures with engineered defects to introduce time-varying stress conditions for the purpose of manipulating elastic waves. [Sandia National Laboratories is a multimission laboratory managed and operated by the National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.]

Local impact resistance of curved sandwich panels with coaxial and concentric honeycombs

The local impact resistance of honeycomb sandwich panels with curved and flat geometries differs due to the global stress state. In this study, curved sandwich panels with coaxial and concentric honeycombs are designed and their resistance is investigated against local impact. The numerical model is calibrated with the air cannon test results and then used to compare the performance of structures that are sandwiched by different honeycombs. The comparable study shows that the impact resistance of flat sandwich structures outperforms that of curved ones at a low impact velocity, and a small radius of curvature should be avoided when considering an enhancement of the impact resistance by curvature design. In addition, under the high-velocity impact, sandwich panels with concentric honeycombs show an improved impact resistance as compared to those with coaxial honeycombs. However, the influence of honeycomb configurations on the impact resistance is reduced as the radius of curvature increases. Using the equivalent analysis, the equivalent face sheet thickness and equivalent impact velocity of curved sandwich structures with different radii of curvature, which are compared to the flat structures that are subjected to typical impact loads, are achieved.

Global Frictional Equilibrium via Stochastic, Local Coulomb Frictional Slips

AbstractBased on the assumption that fault slip dominates in the stress relaxation in the brittle crust, Coulomb theory allows for the crustal stress estimation with an empirical frictional coefficient. However, natural variability of fault friction and slip uncertainty exist in the Earth's crust. To address the extent to which heterogeneous frictional slips influence crustal stress and its evolution, we establish a quasi‐static, 2D model to represent the fractured crustal rock mass. The model consists of randomly oriented fractures with heterogeneous distribution of frictional coefficients. The global mechanical response is quantitatively related to the cascades of local frictional slips under specific boundary conditions. The temporal evolution of stress is explicitly modeled by an iterative process where a simple slip law is assumed for critical fractures. We particularly illustrate the stress evolution in a normal faulting stress regime, considering different distributions of frictional coefficients. All cases indicate that the decrease in differential stress manifests as a self‐organized process, eventually leading to the frictional equilibrium of the fractured rock mass. The final stress state upon equilibrium jointly depends on the orientation and frictional coefficient of all fractures therein. The model informs that the global stress state of a stochastic system can depart substantially from a deterministic estimation via an empirical frictional coefficient. This model quantitatively corroborates and extends the notion of frictional equilibrium, and reveals far more profound influence of system heterogeneity on the local and global stress evolution.

Effect of Twin Schmid Factor on the Tension Twinning Activities in a Highly Textured Mg-3Al-1Zn

We investigated the effect of twin Schmid factor on the tension twinning of individual grains in deformed textured Mg-3Al-1Zn samples. The samples were deformed to ~3% strain (normal-direction compression and tension, rolling-direction compression and tension, and 45 o compression). Statistical analyses on the electron backscatter diffraction results revealed tension twinning generally obeys the Schmid law for individual grains, regardless of whether the global stress state favors tension twinning or not. The strong dependence of tension twinning on Schmid factor is in contrast to the reported weak correlation of dislocations and Schmid factor in the same material system. Such observations are anticipated to advance the understanding of the Schmid factor effect on the deformation behavior of polycrystalline Mg alloys.

The Effect of Fiber Waviness on the Residual Stress State and Its Prediction by the Hole Drilling Method in Fiber Metal Laminates: A Global-Local Finite Element Analysis

In this paper, fiber waviness, as one of the most frequently occurring defects in fiber reinforced composites, is numerically investigated with regard to the formation of residual stresses in fiber metal laminates. Furthermore, the prediction of the residual stress state in the thickness direction by means of the simulated hole drilling method is studied. To this regard, a global-local finite element analysis based on the submodel technique is presented. The submodel technique essentially consists of two governing steps: In the first step, a global model is first utilized to calculate and analyze the residual stress distribution and deformation in the intrinsically joined hybrid structure. Effective cure-dependent thermo–elastic properties predicted by a numerical homogenization procedure were used to simulate the curing-process and analyze the residual stresses state. However, the dimension of the intrinsically manufactured hybrid plate is large compared to the diameter of the drilled hole (2 mm), so that a local model is necessary, which provides only a geometric partial portion of the global model. The local model takes the global stress state into account and is subsequently used to simulate the incremental hole drilling method with a refined mesh discretization. The production-related fiber waviness is modeled by an element-wise orientation approximating a sinus function. In order to validate the global-local modeling approach, a comparison between numerical results and experimental data from literature is presented. The comparison between global residual stress state (global model) and the simulated hole drilling method (local model) is used to assess the applicability and reliability of the hole drilling method in case of fiber waviness. It is found that an in-plane fiber waviness leads to a rather low variance of residual stresses over thickness. In case of an out-of-plane fiber waviness, oscillating residual stress fields occur over the entire thickness along the fiber direction. Moreover, the current limits of the incremental hole drilling method could be pointed out by the presented investigations. It is seen that the simulated results of the incremental hole drilling method are sensitive to waviness, even if the amplitude-wavelength-ratio is small. Without further adjustment of the calibration coefficients the oscillating stress and strain fields lead, in particular fiber waviness in thickness direction, to unreliable predictions. For the experimental application it can be concluded that the specimens have to be carefully examined with regard to fiber waviness.

Identification of stress state dependent fracture micromechanisms in DP600 through representative volume element modeling

The stress state dependent fracture behavior of DP600 was investigated using a representative volume element (RVE) based finite element model. To simulate fracture at the microscale, fracture models for ferrite and martensite were incorporated into the RVE, which was loaded under seven stress states. To compare the simulated damage accumulation and eventual failure in the RVE with experimentally measured continuum-based strain to failure, five RVE-level failure criteria are presented, and their ability to predict the continuum-level stress state dependent fracture strain of the material is discussed. The microstructural heterogeneity resulted in heterogeneous strain fields, and played a dominant role in the stress state dependent fracture behavior of materials. The simulations showed that in DP600, microcracks initiate from martensite regardless of the global stress state, whereas the propagation of cracks or initiation of new cracks depends on stress state.

On the effect of strain and triaxiality on void evolution in a heterogeneous microstructure – A statistical and single void study of damage in DP800 steel

In order to improve the understanding of damage evolution in mechanically heterogeneous microstructures, like the ones of dual-phase steels, the influence of the applied stress state is a key element. In this work, we studied the influence of the globally applied stress state on the evolution of damage in such a microstructure. Classical damage models allow predictions of damage during deformation based on considerations of the material as an isotropic continuum. Here, we investigate their validity in a dual phase microstructure that is locally dominated by its microstructural morphological complexity based on a statistical ensemble of thousands of individual voids formed under different stress states. For this purpose, we combined a calibrated material model incorporating damage formation to assess the local stress state in samples with different notch geometries and high-resolution electron microscopy of large areas using a deep learning-based automated micrograph analysis to detect and classify microstructural voids according to their source of origin. This allowed us to obtain both the continuum stress state during deformation and statistically relevant data of individual void formation. We found that the applied plastic strain is the major influence on the overall number, and therefore the nucleation of new voids, while triaxiality correlates with the median void size, supporting its proposed influence on void growth. In contrast, coalescence of voids leading to failure appears related to local instabilities in the form of shear band formation and is therefore only indirectly determined by the global stress state in that it determines the global distribution, density and size of voids.

Stress concentration factors of shear connection by composite dowels with MCL shape

In this paper, the authors present studies leading to the evaluation of the elastic resistance of the steel part of a continuous shear connection named MCL dowel. The MCL dowel is now the most commonly used shape of continuous connector, chosen among many others for its combination of good fatigue, elastic, and ultimate resistances. A method for the calculation of stress in the steel dowel is described in the paper. It is based on mathematical derivations followed by FE analysis. It is assumed that the steel connector is stressed as a result of a global stress state at the dowel root (being a part of the entire beam) and of a local effects of longitudinal shearing between the steel and concrete parts. Results of the mathematical derivations are confirmed experimentally. Full-scale tests of beam elements were performed with measures of strain in many points of selected connectors. A comparison of strains derived from the proposed design methodology and measured during the experimental tests is shown and discussed. The results herein presented are fundamental research which were one of backgrounds for fatigue limit states of composite dowels for purposes of implementation of composite dowels to the second version of Eurocode 1994-2.

Numerical determination of the mechanical stiffness of a force measurement device based on capacitive probes: Application to roller bearings

Abstract Bearings allow external loadings to be transferred from one raceway to the other through rolling elements, which induces strains in the bearing constituents. In order to measure the radial component of these forces, the fixed ring is inserted within a housing equipped with capacitive probes able to measure displacements with very high sensitivity. This work mainly focuses on determining the optimal housing shape using FE simulations and their influence on the global stress state undergone by the structure. Finally, an averaged global stiffness is computed, allowing proper calculation of the contact forces involved in the bearing. Highlights The principle of capacitive measurement is explained. We model the upper half of the bearing placed in a housing in which grooves for the capacitive probes have been machined. Numerical results in terms of stress field due to probe housings presence and fillets on this housing are explained. FE simulations allow computation of local mechanical stiffness and transmitted radial forces. Very good agreement is obtained between recomputed roller-wise radial force and that directly extracted from the FE results.

Development of a widely applicable gradientless shape optimization based bone adaptation model for comparative parametric studies

Many gradientless optimization based methods have been developed to predict mechanically-driven strength adaptations of bone and to improve the failure resistance of inert mechanical components. However, because the gradientless optimization methods commonly used in these applications typically do not result in a unique solution, few are capable of providing quantitative comparisons of the effects of different boundary conditions on the resulting shape and strength changes of the objects studied. Driven by relative measures of the current local stress state, global stress state, and variation of the local stress state over the design region, a condition-independent, system-independent shape/strength adaptation model was developed that can be applicable to a system with a large number of design variables. Using a local extrema independent quantitative measure of the progression of the design region to a more uniform stress state, a consistent comparison point was defined that can be used regardless of the system studied, the boundary conditions applied, or the initial amount of stress variation. The implementation of the developed model demonstrated its effectiveness in the repeatable prediction of shape and strength changes over multiple orders of magnitude differences in boundary values with no changes to the modeling parameters or stopping criteria. The developed gradientless optimization based shape adaptation technique can be a useful tool in the comparison of the effects of various loading conditions on the strength changes in bones and in the creation of exercise regimens to strengthen fracture prone regions.

Comparison of the deformation behaviour of commercially pure titanium and Ti–5Al–2.5Sn(wt.%) at 296 and 728 K

The tension and tensile-creep deformation behaviours of a fully-α phase commercially pure (CP) Ti and a near-α Ti–5Al–2.5Sn(wt.%) alloy deformed in situ inside a scanning electron microscope were compared. Tensile tests were performed at 296 and 728 K, while tensile-creep tests were performed at 728 K. The yield stress of CP Ti decreased dramatically with increasing temperature. In contrast, temperature had much smaller effect on the yield stress of Ti–5Al–2.5Sn(wt.%). Electron backscattered diffraction was performed both before and after the deformation, and slip trace analysis was used to determine the active slip and twinning systems, as well as the associated global stress state Schmid factors. In tension tests of CP Ti, prismatic slip was the most likely slip system to be activated when the Schmid factor exceeded 0.4. Prismatic slip was observed over the largest Schmid factor range, indicating that the local stress tensor varies significantly from the global stress state of uniaxial tension. The basal slip activity in Ti–5Al–2.5Sn(wt.%) was observed in a larger faction of grains than in CP Ti. Pyramidal ⟨c + a⟩ slip was more prevalent in CP Ti. Although twinning was an active deformation mode in tension tests of the CP Ti, it was rare in Ti–5Al–2.5Sn(wt.%). During creep, dislocation slip was the primary apparent deformation mechanism in CP Ti, while evidence for dislocation slip was much less apparent in Ti–5Al–2.5Sn(wt.%), where grain boundary sliding was dominant. A robust statistical analysis was carried out to assess the significance of the comparative activity of the different slip systems under the variety of experimental conditions examined.

Computational determination of inner stresses in rock masses

PurposeThis paper aims to present a computational approach which – setting off from measures obtained by using an overdrilling method – determines, automatically and accurately, stress changes undergone in terrain as a consequence of human activity.Design/methodology/approachThe method presented uses the data from three boreholes and the elasticity theory to represent a numerical system whose resolution allows determining the stress state in a particular point. Since the system obtained is over‐dimensioned, the Levenberg‐Marquardt minimization method has been used in order to minimize errors. This paper details the analysis carried out in order to develop the computational method.FindingsThis paper provides the algorithm for determining inner stresses in a particular point of a rock mass. Besides, a method to verify obtained results is presented, including its computational encoding in C#. Furthermore, the developed methods have been integrated in a computer tool which presents the results in a graphic environment.Research limitations/implicationsThe algorithms presented are applicable when using an overdrilling method to measure stresses.Practical implicationsA reliable determination of global stress state demands the use of any method that is numerically difficult to use. Thus, in practice, it is of great importance to dispose of some reliable automatic tool to calculate stress state.Originality/valueAccuracy in the results obtained with the tool, together with the simplicity of its interface, involves a certain advantage regarding the use of a general‐scope commercial tool, since it allows – without being necessary to be an expert user – quickly obtaining results within the analysed working area.

Micromechanical Modeling of Grain Boundary Resistance to Cleavage Fracture Propagation

A micromechanical model representing two adjacent grains is developed. Rapid crack propagation from one grain into another driven by a constant global stress state is simulated. The normal of the crack face in the grain where the micro-crack initiates coincides with the principle loading direction. In the adjacent grain, the propagation direction changes and separation occurs in a mixed way, involving both normal and shear separation. The largest grain size that can arrest a rapidly propagating micro-crack is defined as the critical grain size. The effects of the global stress state and temperature on the critical grain size is examined. The influence of the mismatch in lattice orientation between two neighboring grains is qualitatively described. The influence of temperature is modeled by a temperature dependent viscoplastic response.

鳥形山地域の広域的応力状態の推定

A scheme to estimate the global stress state from the local stress state evaluated by the field stress measurement is proposed. In the scheme it is assumed that the global stress is expressed by the superposition of the stress induced by the gravity and that by the horizontal movement of the upper crust. The local stress state in the rock mass under the pit of Torigata-yama open cut mine, located in Shikoku Island, Japan, was measured by the Conical-Ended Borehole Technique. The local stress distribution in Mt. Torigata region was evaluated by the 3-dim. FE-analysis and the global strain and stress states were estimated by the proposed scheme. From the comparison between the local stress states measured and calculated, it is made clear that , in Mt. Torigata region, the stress state induced by the horizontal movement of the upper crust is nearly uni-axial compression and the direction of the maximum compression is ranging from N24E to N27E Furthermore, it is pointed out that the distribution of horizontal stresses are strongly affected by the Poisson's ratio of rock mass and that the high horizontal stress is acting at the floor of excavation of the mine.

Comparison of cross-weld creep testing and service welds

Creep testing of cross-weld specimens is often used to predict weld performance. The global stress state in a cross-weld creep test is substantially different to that occurring in service welds. Using finite element analysis (FEA), the results of cross-weld creep testing were compared with a number of service weld situations. This work was compared to previous published data. Modelling suggested that the results of cross-weld creep testing are not indicative of expected weld performance in service welds.

Model for predicting thermal stresses in thin polycrystalline films

This paper reports the development of a numerical model to analyze thermal stresses induced in thin polycrystalline films deposited on thick substrates. The model accounts for viscoplastic deformations due to crystallographic slip in each grain of the polycrystal. The microstructural processes, which constrain dislocation slip due to the substrate, surface layer, and grain boundaries as well as due to hardening on the slip systems themselves, are considered and incorporated into the model. Using this model, the predicted stress-temperature curves for aluminium films with a natural oxide layer are in good agreement with the measured curves, especially for thicker films. It was found that the predictions of stress-temperature curves for 〈111〉 fiber textured films are not substantially affected by reasonable deviations from a perfect fiber texture. Therefore, one can globally model the deformation of a 〈111〉 textured polycrystalline film by assuming it to be a single crystal provided the film is in a state of equal biaxial strain. However, it is also shown that for an equal biaxial thermal strain, the local stress state at the grain level is more complicated due to the effect of the orientation of the individual grains, although the global stress state will be equal biaxial for a 〈111〉 textured film. In fact, very high local stress gradients might have to be accommodated.

The global distribution of giant radiating dike swarms on Venus: Implications for the global stress state

Magellan radar data of Venus reveal 163 large radial lineament systems composed of graben, fissure, and fracture elements. On the basis of their structure, plan view geometry, and volcanic associations, at least 72% are interpreted to have formed primarily through subsurface dike swarm emplacement, the remainder through uplift or a combination of these two mechanisms. The population of swarms is used to determine regional and global stress orientation. The stress configuration recorded from 330–210°E (Aphrodite Terra) is best explained by isostatic compensation of existing long wavelength topography or coupling between mantle flow and the lithosphere. The rest are correlated with concentrations of rifting and volcanism in the Beta‐Atla‐Themis region. The global stress field on Venus is different than that of Earth, where plate boundary forces dominate.

Micromechanical Model of Composite Materials Subjected to Ball Indentation

Recent results on continuous ball indentation tests of unidirectional com posite materials have demonstrated that this technique is sensitive to fiber/matrix interfa cial quality. In order to quantitatively determine the micro-parameters of interest such as interfacial shear strength, by a meso-test such as this one a micromechanical formulation is necessary. In this article, we present an approximate micromechanical model to predict local stress states and local strength parameters from experimentally determined data. This macro/micro analysis utilizes an existing elasticity solution to develop the global stress state for the ball indentation problem of an infinite transversely isotropic half space. These stresses are then used to pose the traction boundary conditions on a fiber-matrix element. With the use of trigonometric approximations, which yield a more tractable solu tion, and the equilibrium equations, which provide stress relations, the stress variations in the fiber and matrix are predicted. The analytical model suggests that certain regions of the composite are subjected to high stresses as a result of the indentation process. These regions are a zone of large compressive stress directly under the ball near the surface and a high shear stress region near the outer edge of the ball deep inside the material. The micromechanics model is utilized in conjunction with ball indentation test results to gener ate quantitative values for the fiber/matrix interfacial shear strength. Computed interfacial shear stress (ISS) values for AU-4/Epon 828 MPDa are compared to other test meth odologies presently being employed by the scientific community to measure this value.

A fracture mechanical treatment of free edge stress singularities applied to a brazed ceramic/metal compound

The theoretical fracture mechanical treatment of craek problems in regular stress fields is extended to account for singular stresses as occur in bi-material systems whenever a discontinuity in material properties and geometry exists. The singular stress fields are derived for arbitrary material combination and geometry and the global stress state as occurs in a real compound is obtained by Finite Element (FE) calculations. Then especially the mode I stress intensity factors are calculated for semi-elliptical surface cracks in the ceramic component of a brazed ceramic/metal joint. Critical crack sizes are determined for failure analysis of the compound.

Effects of profile, roughness and friction on contacting bodies in compression

Numerical simulation of bodies compressed together along an interface reveals a significant effect of profile shape on the resulting stress state, interface tractions and the plasticity index. Although friction plays an active role (particularly for material combinations of mismatched stiffness) in the development of slip and shear tractions, it only weakly affects the global stress state. The effect of the roughness of a particular profile is one of degree, but it is critical to the onset of plastic action. Some interesting differences are also found if the interface is near a free edge. Although the problem is idealized, it is demonstrated that numerical simulation offers a powerful tool for detailed analysis.