MODELING OF SCHEMES OF CRACK DEVELOPMENT IN SHAPE SHELLS BASED ON TRAJECTORIES OF THE LARGEST TENSION STRESS

В статье для пологой оболочки, загруженной равномерно распределенной нагрузкой, со схемой опирания на шарнирные опоры получено аналитическое решение. Нагрузка и неизвестные функции прогиба и напряжений представлены с помощью двойных тригонометрических рядов. Выполнены расчеты напряженно-деформированного состояния, определены усилия и перемещения. Дана оценка точности суммирования рядов по перемещениям и усилиям. В окрестности точек нижней, срединной и верхней поверхностей оболочки вычислены нормальные и касательные напряжения, а также главные напряжения и главные площадки. Показана картина двухосного напряженного состояния и на ее основе построены графики траекторий наибольших растягивающих напряжений. Графики траекторий на нижней поверхности оболочки сопоставлены с экспериментальными схемами развития трещин. По траекториям наибольших растягивающих напряжений, построенных в точках нижней поверхности, делается прогноз о месте, направлении и последовательности появления трещин в оболочке. An analytical solution is obtained in the article for a shallow shell loaded with a uniformly distributed load, with a scheme of bearing on hinged supports. Load and unknown deflection and stress functions are represented using double trigonometric series. Calculations of the stress-strain state were performed, forces and displacements were determined. An assessment of the accuracy of summation of the series of displacements and efforts is given. In the vicinity of the points of the lower, middle and upper surfaces of the shell, normal and shear stresses, as well as principal stresses and principal areas, are calculated. The picture of the biaxial stress state is shown and on its basis, the graphs of the trajectories of the highest tensile stresses are constructed. The trajectory plots on the lower surface of the shell are compared with the experimental crack propagation schemes. The trajectories of the highest tensile stresses plotted at the points of the lower surface are used to predict the location, direction, and sequence of cracks in the shell.

Design and Analysis of a Bulge Test Device

The aim of this work is to present the methodological process to design a device capable of performing Bulge tests. This kind of device allows obtaining more information about the plastic behavior of a material than the one provided by a traditional tensile test. The engineering specifications of the device were evaluated through the QFD methodology. Then, a basic design of the device was performed based on available analytical models such as thick-walled pressure vessel theory, annular plate theory, and a basic plasticity model for the biaxial stress state. Later, a detailed design of the device was proposed, which was evaluated by means of a 3D model of finite elements and a linearstatic analysis for the main components. Finally, a 2D axisymmetric model and a dynamic non-linear analysis were performed to validate the proposed design. The main novelty of the work consists of articulating the methodology of the mechanical design process and the conception, design, and validation of a Bulge device while solving the deficiencies found in the literature regarding the design and validation processes of this type of devices.

Effect of Multi-Axial Stress State on the Deformation Path in Tube Flaring Process By Necking Instability Criteria

Various parts for automotive, appliance and oil industry are pro- duced from tubes that are assembled and welded. For gaining the best weight savings, durability and cost reasons (energy saving, production cost, etc) the formability of the tubular materials is very important. The overall success of deformation process heavily depends on the incoming tubular material proper- ties. In this work, formability of tubular steels is experimentally characterized and with the development of a numerical model the effect of biaxial stress state has been investigated. An experimental method has been developed to characterize the importance of multi-axial stress state on the formability of tubes. This requires the deformation in form of flaring of the tubular samples through a conical die. Damage strains are determined with the help of Hill-Swift Sheet Metal Forming Criteria and a plot of main strains occurring during the tube flaring test, after variation of the die-angle and friction coefficient has been resulted. Experimental results were then entered into the damage models of finite element program DEFORMTM-PC PRO and used to calibrate the damage model for formability so that a sizable variation of range of multiaxial state of stress could be produced. The results showed that with increasing the stress multiaxiality of tubular steels, the damage strain was reduced. This indicates that the proposed method could be used of benefit in quality control in the production of tubes specially in the monitoring and controlling of tubes production such as tube rolling, welding and annealing.

DEVELOPMENT OF TESTING METHODS FOR BRICK AND MASONRY SAMPLES, CONSIDERING THE BIAXIAL STRESS STATE

The article contains a brief description about the addition of the test program of the walls from masonry and the processing of results of experimental studies. It'll make the processing of the results so much easier and improve their accuracy.

Об особенностях использования явления акустоупругости при контроле напряженного состояния анизотропного материала технических объектов при отрицательных температурах

The paper considers the features of using the modern method of acoustoelasticity for monitoring the uniaxial and biaxial stress state of acoustically anisotropic structural materials as part of technical objects operated in Arctic conditions. The features of using the method of acoustoelasticity for materials with different values of acoustoelastic coefficients, acoustic anisotropy and temperature dependence coefficients of acoustic parameters that appear in the calculation algorithms are analyzed. It has been established that the existing approaches to taking into account temperature effects in acoustoelastic calculations in a number of important cases lead to noticeable errors in determining mechanical stresses in the material of critical technical objects. In this case, taking into account the temperature corrections in a number of cases is necessary for both biaxial (planar) and uniaxial stress states. The presence of anisotropy of thermoacoustic coefficients of transverse waves for materials with anisotropy is shown experimentally. Refined calculation formulas are proposed for determining the uniaxial and biaxial stress state of an anisotropic material, taking into account the anisotropy of the thermoacoustic coefficients of transverse waves.

Mykhailo Dendiuk, Lyubomir Flud, Nazar Semenyshyn Software implementation of the construction of curves short-term strength of wood with biaxial stress state

This paper is devoted to implementing the algorithm for constructing short-term strength curves of wood with biaxial stress states in the radial-tangential plane of structural symmetry. To implement this algorithm was developed software based on the Qt cross-platform toolkit, which allows to build and analyze short-term strength curves in the cross section of wood. The created program has a possibility to choose one of three failure criteria, a kind of wood, temperature and humidity distribution of lumber. The C++ program code is designed so that you can easily add another type of wood as well as a failure criterion. To display the curves, you can select table or graph mode. Graphs can be fixed on a graphics widget, and new ones can be added to compare to previous ones. Based on the analysis of the constructed curves, the ultimate stress state of the material in partial cases is established. In conclusion about expedient using some criteria to describe the strength characteristics of wood with strong and weak asymmetry of strength limits.

An approximate analytical model for modification of size effect law for open-hole composite structure under biaxial load

Nominal strength prediction remains the main challenge in the field of design and manufacturing of composite laminates. An approximate model to study the stress distribution around a circular hole in composite laminates is derived in this study. This model is constructed using well-known cohesive zone models and mainly depends on the un-notch strength and in-plane fracture toughness. The model attempts to modify and extend the specimen size effect curves, extracted using two-parameter cohesive laws (linear, exponential, and constant), into a biaxial stress state. It successfully predicts the damage initiation, propagation, and fracture of multidirectional composite laminates. Moreover, the stress concentration factor for a composite plate under varying biaxiality is calculated.