Complete Stress Tensors Research Articles

End-to-end deep learning method to predict complete strain and stress tensors for complex hierarchical composite microstructures

Due to the high demand for materials with superior mechanical properties and diverse functions, designing composite materials is an integral part in materials development. However, due to the heterogeneity and complexity of composites, measurements of properties and designs of optimal structures are often experimentally or computationally intractable. Here we report complete strain and stress tensors predictions given input composite geometries, based on a deep learning approach. The model not only predicts all strain and stress tensor components accurately, but also observes rigorous continuum mechanical principles. Furthermore, through tuning data statistics, the model performance is enhanced even with a small amount of data in terms of handling material microstructures with varying constituent ratios and hierarchical geometries. The method vastly improves the efficiency of predicting comprehensive mechanical behaviors of composite materials and provides a powerful tool for design problems such as multifunctional composites design and hierarchical structures optimization.

In Situ Stress Determination for Liquefied Petroleum Gas Storage Caverns by Hydraulic Tests on Pre-existing Fractures

The hydraulic fracturing (HF) technique has been widely used for measuring in situ stresses of intact rocks in the mining and petroleum industry, etc., due to its simple operation and no theoretical limit of testing depth. However, when there are pre-existing fractures in rock masses, the ‘hydraulic tests on pre-existing fractures’ (HTPF) is usually preferred (Cornet and Valette 1984). The HTPF is a generalization of classical hydraulic fracturing (Cornet et al. 1997), and aims to measure the normal stress supported by the pre-existing fracture plane. Different from HF, the HTPF is independent of pore pressure effects and does not require any material property determination. In order to determine a complete stress tensor, however, the HTPF requires testing more than eight fractures with at least six different orientations, due to the need of correction for uncertainties (Cornet et al. 1997). Furthermore, when test intervals are distant from one another by more than 50 m, stress gradients must be considered and additional tests are required. With the HTPF technique, the stress tensor is evaluated so as to best fit the normal stress measurements obtained for all the tested fractures. This requires a parameterization of in situ stress field and the definition of a misfit function (Haimson and Cornet 2003). Cornet and Valette (1984), Cornet (1993) and Cornet et al. (1997, 2003) made a detailed discussion of the inversion method for the regional stress field, and obtained complete stress tensors using the least-squares algorithm, the Monte-Carlo method and the genetic algorithm, respectively. Nevertheless, it should be noted that, during the search for the best solution for the stress field, the assumption of linear variations of the stresses with depth from the ground to the bottom along the borehole axis is not always appropriate, especially for cases where geological conditions are complex. As an alternative, an assumption of linear variation of the stresses with depth limited in the zone of interest may be more reasonable. In the past several decades, underground liquefied petroleum gas (LPG) storage facilities have been extensively constructed in many countries in response to the rapidly increasing demand for energy consumption and additional stockpiles. However, the commercialized underground storage of liquefied natural gas (LNG) in unlined rock caverns was progressing slowly. A major difficulty in LNG underground storage is the prevention of leakage of liquid and gas from the containment system to the rock mass caused by tensile failures due to shrinkage of the rock mass around the caverns. Park et al. (2007, 2010) developed a new concept for storing LNG in a lined rock cavern, to provide a safe and economical solution. The concept consisted of protecting the host rock against the extremely low temperature and providing a liquid-tight and gas-tight liner. They demonstrated its technical feasibility by examining the overall performance of a pilot underground liquefied nitrogen storage cavern in Daejeon, Korea. In addition to the tightness of underground caverns, the stability of caverns and the hydrogeological Y. Liu (&) H. Li J. Li B. Liu X. Xia State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, Hubei, People’s Republic of China e-mail: yqliu@whrsm.ac.cn

Change of stress magnitudes during the polyphase tectonic history of the Cretaceous Gyeongsang basin, southeast Korea

Abstract In order to evaluate the change of stress magnitudes in the Gyeongsang basin during its tectonic history, we analyzed multiple faulting episodes in the Barremian-Aptian Hasandong Formation at the Yusu site. As elsewhere in southeast Korea, the recorded sequence consists of a succession of more than fourteen faulting episodes, and the relative chronology shows that a strike-slip faulting episode usually coexisted with a coaxial extensional episode. Likewise, seven couples of synchronous coaxial episodes recognised in the Gyeongsang basin are assigned to seven tectonic events (T_1 to T_7 events). The friction line (in the sense of Byerlee) allows us to determine the ratios between principal stress magnitudes as well as the origin of the dimensionless Mohr diagram. This line can be deduced from tension fractures on fault planes affected by friction and from the lower limit of scattered distribution of the normal stresses vs. shear stresses of faults. Dimensionless failure envelopes drawn for coaxial strike-slip and extensional episodes are adjusted to the experimental Mohr failure envelope derived from rock mechanic tests to determine the complete stress tensors. The maximum principal stress magnitudes of strike-slip episodes show a transition from 169 MPa in the Barremian-Coniacian T_1 Event through 263 MPa and 246 MPa in the T_2 and T_4 events, respectively to 235 MPa in the Quaternary T_7 Event; additional horizontal extension (ΔσT) have changed from −6 MPa in the T_1 Event through −8 MPa in the T_2 Event to −17 MPa in the T_7 Event. Because the studied site is currently exposed, the determined overburden (1.9 km) for the T_7 Event seems to be important, indicating the presumable occurrence of this event during the early Quaternary rather than at the present day.

Neutron Diffraction Analysis of Complete Residual Stress Tensors in Conventional and Rolled Gas Metal Arc Welds

Mitigation of residual stress in an arc weld by high-pressure rolling of the weld seam has been investigated using neutron diffraction. Rolling was found to greatly improve the residual stress distribution, causing significant compressive stresses at the weld line. A novel aspect of the data presented is that at each measurement location, normal strains in nine separate directions were evaluated, enabling calculation of the complete strain and stress tensors. It is thus confirmed that the principal stress directions generally lay close to the specimen coordinate axes (i.e. that they are well-aligned with the direction of welding and rolling), and that rolling does not cause any significant additional residual stresses which could have detrimental effects. Methods of uncertainty estimation and the applications of full-tensor residual stress measurements are also discussed.

Strain and stress tensors of rolled uranium plate by Rietveld refinement of TOF neutron-diffraction data

We report the complete macroscopic average strain and stress tensors for a cold-rolled uranium plate, based on the neutron TOF measurements. Both tensors were determined by the least-squares refinement of the interplanar spacings of 19 Bragg reflections. Based on the pole figures, as determined by GSAS, a triclinic sample symmetry of the uranium plate was assumed. Strain and stress are tensile in both the transverse and rolling directions and very small in the normal direction (through the thickness of the plate). Shear strain and stress components are compressive and of significant magnitude.

Determining the Complete Residual Stress Tensors in SOS Hetero-Epitaxial Thin Film Systems by the Technique of X-Ray Diffraction

This paper investigates residual stress of epitaxial silicon film on SOS thin film systems. The emphasis was to develop a method to obtain accurately the complete residual stress tensors. It was found that using the multiple asymmetric X-ray diffraction method to measure strains in 13 [hkl] directions, the complete residual stress tensors can be determined reliably. The results were verified by both the Raman Backscattering and the substrate curvature methods.

The impact of various cooling environments on the distribution of macroscopic residual stresses in near-surface layers of ground steels

Grinding often plays the role of final machining, and, therefore, its parameters significantly affect the properties of the treated surface. In this study, the state of surface residual stresses (RSs) and their depth distribution into the bulk is investigated with respect to various cooling environments during grinding. In order to acquire complete stress tensors, the sample surfaces were analysed using the X-ray diffraction technique. Since ɛ φψ(sin 2 ψ) dependences in grinding direction are non-linear and exhibit psi-splitting, the method proposed by Dölle and Hauk was used to evaluate the tensors of anisotropic triaxial state of RS. The effective penetration depth of Cr Kα X-ray radiation into ferrous materials is approximately 4 μm, and, therefore, removal of surface layers is necessary in order to pinpoint the distribution of RSs beneath the surface. The process of electro-chemical polishing ensures that the impact of material removal causes minimal or negligible mechanical and thermal distortions of the investigated state of stress.

Elastic-strain tensor and inhomogeneous strain in thin films by X-ray diffraction

Elastic residual and inhomogeneous defect-related strains are very important parameters when considering thin-film and microelectronics device properties and operation. In regard to the residual strain/stress modeling, we describe a novel approach to model diffraction line shifts caused by elastic residual or applied stresses in textured polycrystals. The model yields the complete texture-weighted strain and stress tensors as a function of crystallite orientations, the so-called weighted strain orientation distribution function. In the second part, we present an extension to the phenomenological thermodynamic theory for ferroelectrics. It includes the contribution of both residual-elastic lattice-misfit strain and inhomogeneous strain caused by lattice defects. The model yields correction terms for dielectric and ferroelectric quantities in terms of both elastic misfit strain and defect-related strain that was successfully applied to the pristine, W and Mn 1% doped Ba 0.6Sr 0.4TiO 3 epitaxial thin films grown on the LaAlO 3 substrate.

Elastic strain and stress determination by Rietveld refinement: generalized treatment for textured polycrystals for all Laue classes

A novel approach to model diffraction line shifts caused by elastic residual or applied stresses in textured polycrystals is proposed. The model yields the complete strain and stress tensors as a function of crystallite orientation, as well as the average values of the macroscopic strain and stress tensors. It is particularly suitable for implementation in Rietveld refinement programs. The requirements on refinable parameters for all crystal Laue classes are given. The effects of sample symmetry are also included and the conditions for strain invariance to both the sample symmetries (texture and stress/strain) are discussed.

Overcoring measurements in the příbram mine area and their relation to the regional stress field

A set of overcoring measurements in deep mines near Přibram is re-interpreted in order to obtain information on the regional component of in situ stress. This is achieved by averaging 17 complete stress tensors measured at the deepest level of the mine, at a depth of 1240 m. The computations indicate that (1) the mean principal stresses act roughly in the horizontal and vertical directions, and (2) the maximum principal stress is horizontal, acting NW - SE, which was also confirmed by the data from all 42 sites of the mine area. The NW - SE orientation of SH is consistent with the stress pattern in Western Europe and also with borehole breakouts observed within the Bohemian Massif, but the quality of the stress indicator obtained is poor — the standard deviation of the SH direction is 26°. High variance of the directional data is discussed with respect to stress redistribution due to the mine workings and the contact separating Proterozoic sediments from the Variscan pluton.

Methods for Depth Profiling Complete Stress Tensors Using Neutron Diffraction

Neutron diffraction has proved to be a useful tool for measuring residual and applied stresses in materials. Aspects of experimental design and methods for the mapping of complete triaxial stress tensors in a large component are discussed in the context of a comprehensive set of stress measurements made within the interior of the circumferential weld on a 0.91 m diameter cylinder. The cylinder is a subscale model of the casings for the Advanced Solid Rocket Motor being designed for the space shuttle. The subscale model was fabricated in order to characterize the residual stresses created in the welding process and to determine the effect of post weld heat treatment on the residual stresses. Control of the residual stresses in this application is necessary to eliminate possible problems with stress corrosion cracking in a salt water environment. Some illustrative results are also presented.

Stress, Strain, and Symmetry of Pseudomorphically Grown Epitaxial Layers

AbstractThe complete stress and strain tensors and the point symmetry of pseudomorphically grown epitaxial layers are calculated from the epitaxial relationship and the elastic constants of the deposit material. The angle misalignment of crystallographic directions in the deposit due to the strain is also calculated and results are given for the epitaxial systems CaF2/Si(100) and CaF2/Si(111).

X-ray macrostress determination on textured material; use of the ODF for calculating the X-ray compliances

A highly textured material with a mechanical anisotropic behavior of the single crystal cannot anymore be considered as composed of quasi-randomly orientated grains. In that case the commonly used sinΨ method for residual stresses determination by X-ray diffraction does not satisfy the hypothesis assumed. The macroscopic elastic behavior cannot anymore be described by only two Radio-crystallographic Elastic Constants (REC) and the 2θvs sin2Ψ is no more linear. In order to take into account this grain distribution anisotropy in the material, a method of calculating the REC is proposed. The coefficients of the orientation distribution function, now easily available, allows a complete description of the texture and a “weighting” of the single-crystal elastic constants. The relationship between the macroscopic scale and the microscopic one is done assuming Reuss’ hypothesis. The validity of these calculations is tested by the comparison with experimental results obtained on highly textured low-carbon steel sheets for various diffracting planes, applied strengths, and texture symmetries. Complete stress tensors are determined and commented upon. Some conclusions are drawn up on the influence of the diffracting planes used (multiplicity, Г factor) and of the texture intensities.