A generalized stress correction scheme for the Maxwell elasto-brittle rheology: impact on the fracture angles and deformations

The Maxwell elasto-brittle (MEB) rheology uses a damage parameterization to represent the brittle fracture of sea ice without involving plastic laws to constrain the sea ice deformations. The conventional MEB damage parameterization is based on a correction of super-critical stresses that binds the simulated stress to the yield criterion but leads to a growth of errors in the stress field. A generalized damage parameterization is developed to reduce this error growth and to investigate the influence of the super-critical stress correction scheme on the simulated sea ice fractures, deformations and orientation of linear kinematic features (LKFs). A decohesive stress tensor is used to correct the super-critical stresses towards different points on the yield curve. The sensitivity of the simulated sea ice fractures and deformations to the decohesive stress tensor is investigated in uniaxial compression experiments. Results show that the decohesive stress tensor influences the growth of residual errors associated with the correction of super-critical stresses, the orientation of the lines of fracture and the short-term deformation associated with the damage, but it does not influence the long-term post-fracture sea ice deformations. We show that when ice fractures, divergence first occurs while the elastic response is dominant, and convergence develops post-fracture in the long term when the viscous response dominates – contrary to laboratory experiments of granular flow and satellite imagery in the Arctic. The post-fracture deformations are shown to be dissociated from the fracture process itself, an important difference with classical viscous plastic (VP) models in which large deformations are governed by associative plastic laws. Using the generalized damage parameterization together with a stress correction path normal to the yield curve reduces the growth of errors sufficiently for the production of longer-term simulations, with the added benefit of bringing the simulated LKF intersection half-angles closer to observations (from 40–50 to 35–45∘, compared to 15–25∘ in observations).

Subsurface stresses in an elliptical Hertzian contact

The traditional solution for the stresses below an elliptical Hertzian contact expresses the results in terms of incomplete Legendre elliptic integrals, so are necessarily based on the length of the semi-major axis a and the axis ratio k. The result is to produce completely different equations for the stresses in the x and y directions; and although these equations are now well-known, their derivation from the fundamental, symmetric, integrals is far from simple. When instead Carlson elliptic integrals are used, they immediately match the fundamental integrals, allowing the equations for the stresses to treat the two semi-axes equally, and so providing a single equation where two were needed before. The numerical evaluation of the Carlson integrals is simple and rapid, so the result is that more convenient answers are obtained more conveniently. A bonus is that the temptation to record the depth of the critical stresses as a fraction of the length of the semi-major axis is removed. Thomas and Hoersch’s method of finding all the stresses along the axis of symmetry has been extended to determine the full set of stresses in a principal plane. The stress patterns are displayed, and a comparison between the answers for the planes of the major and minor semiaxes is made. The results are unchanged from those found from equations given by Sackfield and Hills, but not previously evaluated. The present equations are simpler, not only in the simpler elliptic integrals, but also for the “tail” of elementary functions.

An Experimental Study on the Creep Characteristics of Sandstone in the Interval of Different Critical Stresses

Creep tests on brittle sandstone specimens were performed to investigate the time-dependent characteristics in the interval of different critical stresses. The results showed that failure will not occur when the loaded stress σ1 is less than the critical stress of dilation σcd, while all specimens were destroyed when σ1 is larger than σcd. In addition, the value of σcd was very close to the long-term strength obtained by the method of the isochronous stress-strain curve. Therefore, σcd can be regarded as the long-term strength of the sandstone specimens. When σ1 is larger than σcd, the time required for the failure of specimen tf decreases with the increase of σ1; the creep rate dε/dt increases with time t, and the specimen will be destroyed when it reaches a maximum value (dε/dt)max. Both relationships tf and σ1 and (dε/dt)max and σ1 can be described by the exponential function. Then, a nonlinear damage creep model considering the deformation damage and strength damage in the interval of different critical stresses was established, which can describe the whole creep process and predict the failure time of sandstone specimens.

Optimum Design of Reinforced Cylindrical Shells Under Combined Axial Compression and Internal Pressure

This paper discusses the use of the random search method for the optimal design of single-layered rib-reinforced cylindrical shells under combined axial compression and internal pressure with account taken of the elastic-plastic material behavior. The optimality criterion is the minimum shell volume. The search area for the optimal solution in the space of the parameters being optimized is limited by the strength and stability conditions of the shell. When assessing stability, the discrete rib arrangement is taken into account. In addition to the strength and stability conditions of the shell, the feasible space is subjected to the imposition of constraints on the geometric dimensions of the structural elements being optimized. The difficulty in formulating a mathematical programming problem is that the critical stresses arising in optimally-compressed rib-reinforced cylindrical shells are a function of not only the skin and reinforcement parameters, but also the number of half-waves in the circumferential and meridional directions that are formed due to buckling. In turn, the number of these half-waves depends on the variable shell parameters. Consequently, the search area becomes non-stationary, and when formulating a mathematical programming problem, it is necessary to provide for the need to minimize the critical stress function with respect to the integer wave formation parameters at each search procedure step. In this regard, a method is proposed for solving the problem of optimally designing rib-reinforced shells, using a random search algorithm whose learning is carried out not only depending on the objective function increment, but also on the increment of critical stresses at each extremum search step. The aim of this paper is to demonstrate a technique for optimizing this kind of shells, in which a special search-system learning algorithm is used, which consists in the fact that two problems of mathematical programming are simultaneously solved: that of minimizing the weight objective function and that of minimizing the critical stresses of shell buckling. The proposed technique is illustrated with a numerical example.

MODELING THE INFLUENCE OF METAL PHASE IN DIAMOND GRAINS ON SELF-SHARPENING OF GRINDING WHEELS ON CERAMIC BONDS

The article presents the results of theoretical studies using finite element modeling, which made it possible to determine the rational characteristics of diamond wheels based on ceramic and polymer bonds. The effect of the parameters of the diamond-bearing layer on the change in its stress-strain state in the process of microcutting of hard alloys and superhard materials has been studied. It is established that the determining factor in the occurrence of critical stresses during grinding is the temperature in the cutting area, the increase of which in the presence of metal phase inclusions in diamond grains with high values of thermal expansion coefficient can lead to destructive stresses in grains and, consequently, their premature destruction. It is advisable to use diamond grains with a minimum content of metal phase and the use in the manufacture of synthetic diamonds solvent metals with a low value of this coefficient, which will significantly increase the use of potentially high resource diamond grains.

Constraining maximum event magnitude during injection-triggered seismicity

Understanding mechanisms controlling fluid injection-triggered seismicity is key in defining strategies to ameliorate it. Recent triggered events (e.g. Pohang, Mw 5.5) have exceeded predictions of average energy release by a factor of >1000x, necessitating robust methodologies to both define critical antecedent conditions and to thereby constrain anticipated event size. We define maximum event magnitudes resulting from triggering as a function of pre-existing critical stresses and fluid injection volume. Fluid injection experiments on prestressed laboratory faults confirm these estimates of triggered moment magnitudes for varied boundary conditions and injection rates. In addition, observed ratios of shear slip to dilation rates on individual faults signal triggering and may serve as a measurable proxy for impending rupture. This new framework provides a robust method of constraining maximum event size for preloaded faults and unifies prior laboratory and field observations that span sixteen decades in injection volume and four decades in length scale.

Распределение напряжений при статическом растяжении цилиндрических образцов из мелко- и крупнозернистого алюминиевого сплава 6101

Проблема расчета прочности и долговечности различных конструкций из металлов является одной из важнейших в современном мире. Для ее решения необходимо понимание определенных механических критериев материала, таких как прочность, пластичность и др. [1, 2]. В данной работе приводятся данные расчета и указан характер распределения критических напряжений, которые определяют зарождение пор внутри материала, в данном случае в Al-6101, при статическом нагружении. Зарождение и слияние пор представляют собой первую стадию разрушения материала. При наличии данных о критических напряжениях материала можно спрогнозировать его дальнейшее разрушение [3, 4]. Calculation of strength and durability of various metal structures presents one of the most significant tasks in the contemporary world. To achieve it, the different mechanical criteria of the material, such as strength, ductility, etc. [1, 2] should be known. The calculation data and t distribution pattern of critical stresses that define formation of pores in the material (in our case, Al-6101) under static loading are presented in this article. The first phase of material fracture is the pore formation and merging. Therefore, its subsequent fracture can be estimated using the data on the critical stresses of the material [3, 4].