Internal Fractures in Spheres Due to Stress Wave Focusing
01 Jan 1977-International Journal of Solids and Structures (Pergamon)-Vol. 13, Iss: 11, pp 1007-1017
TL;DR: In this article, the locations and times of occurrence of internal fractures in Perspex spheres subjected to localized explosive loading are investigated, and an analysis of stress wave reflection from free boundaries based on the method of geometrical acoustics is found to give predictions which are in good agreement with results obtained from high speed photographs.
About: This article is published in International Journal of Solids and Structures.The article was published on 1977-01-01 and is currently open access. It has received 10 citations till now. The article focuses on the topics: Reflection (physics) & Geometrical acoustics.
Summary (2 min read)
Jump to: [Introduction] – [Composition of geopolymer mortar] – [Experimental program] – [Standard tests.] – [Numerical program] – [Comparison of results] and [Final remarks]
Introduction
- The digital revolution has led to rapid development of various generative modeling tools in the last decade that introduced the concepts of parametric architecture and digital fabrication.
- The interrelation between architectural design, structural design and manufacturing has been a key to be overcome for the application of these technological innovations point.
- This new class of generative programs allows users to implement their own algorithms through an open code.
- The Figure 2 shows some examples of discrete surfaces used for the geometrical definition of the structural elements supporting the glass skin facade of buildings.
- Figures 3 and 4 present the projects consist of hollow elements of high geometric complexity, produced with geopolymer mortar.
Composition of geopolymer mortar
- The geopolymers are binder materials that can be obtained by alkaline activation of natural or industrial products, including dejects and solid waste containing aluminosilicate in an amorphous state.
- The geopolymerization, a term created by Joseph Davidovits [3] , is related to the alkaline activation at low temperatures and free handling.
- Potassium silicate has a silica modulus of 3.26 and with the addition of potassium hydroxide this ratio drops to 1.65, increasing the reactivity of the solution without compromising the free handling of personal protective equipment.
- To calculate the quantities of starting materials, in addition to the technical data of products manufactured, X-ray Fluorescence analysis was realized to quantify the oxides present in an amorphous state.
- The mix order, begins with the homogenization of metakaolin and sand (dry part) followed by the addition of the activator solution using a mechanical mixer.
Experimental program
- Two sets of experiments were performed to characterize the mechanical properties of geopolymer mortar required in the mathematical representation in finite element models.
- The first includes testing for obtaining elastic properties and stress limits of the material by means of standardized specimens.
- The second set involves a nonstandard pull-out and push-out tests of the metallic body and bending tests of geopolymer plates reinforced with carbon fiber fabrics.
Standard tests.
- The specimens were densified in vibrating table for expelling the gas phase, and demolded in 24 hours and cured, wrapped in PVC film, in a room temperature at 25 o C and relative humidity at 60% until the date of the tests.
- The tests described below were carried out at 7 days of age and results are the average values obtained from three specimens.
- The compressive strength prescribed in Brazilian standard NBR 7215:1996 [4] , were obtained from the molding of cylindrical specimens, three for each specified date, 50 mm diameter by 100 mm high.
- Cylindrical and conical metallic body, also known as Two configurations were tested.
Numerical program
- The numerical program was developed in ATENA Computer Program for Nonlinear Finite Element Analysis of Reinforced Concrete Structures, version 5.02 [10] .
- For the carbon fiber was assumed perfect elastic-plastic behavior for tension-only.
- For interface geopolymer mortar/metallic body was used the Mohr -Coulomb Criterion delimiting the boundary between the laws of bond/slip to shear stress and bond/detachment to normal stresses.
- Figure 16 summarizes the behavior of materials of the model of finite elements and the properties obtained in the experimental program.
- Five finite element models were developed to predict the peak-load of the plate for two loading conditions and three reinforcement configurations.
Comparison of results
- Figures 18-22 show the results of numerical and experimental programs for the five analyzed cases.
- It makes no sense to adjust this value exactly as tests show variations of the order of 20% of this load.
- First, concerning the case of traction punching (Fig. 18 and Fig. 19 ), the defined plate stiffness in a finite element model represent faithfully the behavior observed in the tests.
- Beyond this point, there is a relative displacement of the metallic body for loss of adhesion at the interface with the geopolymer plate.
- This behavior was not reproduced in a finite element model because there is no practical interest.
Final remarks
- The use of geopolymer mortar promotes energy efficiency of constructions reflected in significant gains in the environmental field.
- The use of geopolymer mortar brings numerous advantages in the production of precast and exhibit excellent performance as protective materials against fire and high temperatures in buildings in fire conditions.
- At present, the search for unique architectural concepts and the use of new materials emphasize the importance of experimental and numerical evaluations for the safety of the structures.
- The nonlinear mathematical models allow clearly describe the failure mechanisms of structural elements reinforced with composite systems with high-strength fibers.
- The use of these resources leads to decision-assertive decision on the use of reinforcement to increase the bearing capacity and ductility of structural elements.
Did you find this useful? Give us your feedback
Citations
More filters
TL;DR: In this paper, the authors reviewed recent extensions of the analytical methods for the problem of thermal stress-focusing in spheres and cylindrical rods, and the major accomplishment of this study is in gaining a better understanding of the thermal stress focusing effect in solid spheres and cylinders.
Abstract: Stress waves that develop following the rapid uniform heating of linear-elastic spheres and long cylindrical rods display a stress-focusing effect as they proceed radially toward the center in these geometries. The stress-focusing effect is the phenomenon that, under a rapid uniform heating, stress waves reflected from the free surface of the spheric or the cylindrical rod result in very high stresses at the center even though the initial thermal stress might be relatively small. This phenomenon may be observed in the solid spheres subjected to the spherical symmetric heating and in the cylindrical rods subjected to the cylindrical symmetric heating. This type of heating may be caused by the absorption of infrared rays radiation or electromagnetic radiant energy. This article reviews recent extensions of the analytical methods for the problem of thermal shock in spheres and cylindrical rods, especially for the problem of the thermal stress-focusing effect in spheres and cylindrical rods. First, considering the problem of thermal shock in a hollow sphere subjected to the rapid uniform heating, if the ratio of the outer radius to the inner radius of the sphere increases, the peak tangential stress at the internal surface becomes higher and higher. In the limit case, for a solid sphere, it might be possible to observe the stress-focusing effect. Next, as for the analysis of a cylindrical rod due to the rapid uniform heating, stress waves also show the stress-focusing effect. Hence, the major accomplishment of this study is in gaining a better understanding of the thermal stress-focusing effect in solid spheres and cylindrical rods.
14 citations
TL;DR: In this paper, the final crack and fracture damage found in hemispherically-ended "Perspex" (PMMA) rods loaded explosively by electrical detonators at their hemispherical end is described.
Abstract: The final crack and fracture damage found in hemispherically-ended ‘Perspex’ (PMMA) rods loaded explosively by electrical detonators at their hemispherical end is described. The mechanisms of the formation of the major features are also considered.
5 citations
01 Jan 1981
TL;DR: In this paper, internal fractures in spherical, paraboloidal, hyperboloidal and elliptical solids subjected to concentrated surface explosive loading are investigated and the initiation and growth of the internal fractures are associated with the focusing effect of P and S wave fronts reflected from the curved boundaries.
Abstract: Internal fractures in spherical, paraboloidal, hyperboloidal and elliptical solids subjected to concentrated surface explosive loading are investigated. The initiation and growth of the internal fractures are associated with the focusing effect of P and S wave fronts reflected from the curved boundaries. High speed photography on perspex specimen is used for the verification of predictions of simple methods of geometrical optics and propagation of discontinuities. The speed with which these internal fractures grow are found to depend upon the geometry of the surface of the solid.
2 citations
TL;DR: In this article, an attempt has been made to explain the form and the location of the spalls in terms of stress wave optics considering first and second reflections of the incident waves at the spherical boundary and the energy distribution of incident waves when reflected from this boundary.
2 citations
TL;DR: In this paper, it was shown that phase transformation of rutile into denser orthorhombic modification occurs in TiO2, and the content of phases with higher oxygen amount increases in Cu2O and CoO.
Abstract: Powders TiO2, CuO, Cu2O, and CoO mixed with inert filler are subjected to shock waves in cylindrical preservation devices. The shock waves are generated by the explosion of TG40 charge at a detonation speed of 7.8 km/sec and detonation wave pressure of 28 GPa. It is established that shock-wave processing of oxide powders leads to changes in particle-size distribution since coarse and medium particles are crushed, coherent scattering regions become smaller, and concentration of phase distortions increases. Phase transformation of rutile into denser orthorhombic modification occurs in TiO2, and the content of phases with higher oxygen amount increases in Cu2O and CoO.
1 citations
Cites background from "Internal Fractures in Spheres Due t..."
...According to [8, 9 ], shock waves are reflected from the free surface of particles in spherical bodies and they disintegrated at places where these waves are located....
[...]
References
More filters
31 citations
TL;DR: In this article, the propagation of an initially sharp plane pressure pulse through a linear elastic composite medium is analyzed and the reflection and transmission coefficients can be determined for the stress gradient and the higher order derivatives at an arbitrary interface.
Abstract: : The propagation of an initially sharp plane pressure pulse through a linear elastic composite medium is analysed. Wave front and ray theory analogous to geometrical optics is shown to determine the change in shape of the leading wave front and also the stresses immediately behind it. For certain circumstances the stress amplitudes on this front, or the corresponding tensile stresses on its reflection at the free back surface of a slab, may be critical in design. Examples are presented of an initially sharp plane pressure pulse transmitted through an elastic circular cylinder and an elastic spherical inclusion. The method can be applied to more general composite configurations, and can be extended to determine the stress gradient behind the front. For the latter, general formulae are derived by which the reflection and transmission coefficients can be determined for the stress gradient and the higher order derivatives at an arbitrary interface.
19 citations
TL;DR: In this paper, the separation at the interface of a circular inclusion embedded in a matrix of lower characteristics impedance and subjected to incident compressive waves is investigated, both experimentally and analytically.
Abstract: : Separation at the interface of a circular inclusion embedded in a matrix of lower characteristics impedance and subjected to incident compressive waves is investigated, both experimentally and analytically. In the experiment, the compressive waves were generated by small explosive charges. The qualitative analytical treatment is based on the methods of propagating stress discontinuities. It is shown that a compressive stress wave is converteed into a tensile wave after a refraction and a reflection inside the inclusion. The results of this paper apply to the behavior of fiber-reinforced composites under dynamic loading conditions. (Author, modified-PL).
16 citations
TL;DR: In this article, the internal fracturing of a Perspex sphere due to a localised explosive loading on its surface has been investigated both analytically and experimentally, and the locations and times of occurrence of the fractures are predictable from an analysis of stress wave reflection from the free surface based on the methods of geometrical acoustics.
15 citations
TL;DR: In this article, the results of an experimental study of the fracture of solid spheres and circular disks due to the explosion of a detonator on the surface are presented and a simple analysis is developed which reasonably explains the nature of the characteristic fracture patterns encountered.
14 citations