Dynamic Fracture Process in Beams

1975 ◽  
Vol 42 (2) ◽  
pp. 435-439 ◽  
Author(s):  
J. D. Colton ◽  
G. Herrmann
Keyword(s):  
Dynamic Fracture ◽  
High Speed ◽  
Beam Theory ◽  
Bending Moment ◽  
Strain Gages ◽  
Second Stage ◽  
Deformation And Fracture ◽  
Initial Fracture ◽  
Beam Thickness ◽  
Stage Process

The relief waves created by the dynamic fracture of a brittle beam were determined. An experiment was conducted on an effectively infinite beam loaded over a finite area with sheet explosive. The time sequence of deformation and fracture was determined by terminal observation, high-speed framing camera photographs, and strain gages. Beam response was also predicted analytically by numerically integrating the characteristic equations of Timoshenko beam theory. Comparison of calculated and measured strains showed that the effect of an initial fracture in a beam at a location of pure bending can be approximated by a two-stage process that specifies how the bending moment at the fracture point is reduced to zero after fracture. In the first stage, the crack propagates to the neutral axis, and the stress distribution remains unchanged. In the second stage, the crack propagates through the remainder of the beam thickness while the stress continuously redistributes itself.

Dynamic Fracture of a Beam or Plate in Plane Bending

1976 ◽  
Vol 43 (1) ◽  
pp. 112-116 ◽  
Author(s):  
L. B. Freund ◽  
G. Herrmann
Keyword(s):  
Crack Length ◽  
Dynamic Fracture ◽  
Crack Tip ◽  
Bending Moment ◽  
Fracture Initiation ◽  
Fracture Plane ◽  
Multiple Reflections ◽  
Pure Bending ◽  
Strain Fracture ◽  
Beam Thickness

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam across a cross section. An analysis is presented by means of which the crack length and bending moment at the fracturing section are determined as functions of time after fracture initiation. The main assumption on which the analysis rests is that, due to multiple reflections of stress waves across the thickness of the beam, the stress distribution on the prospective fracture plane ahead of the crack may be adequately approximated by the static distribution appropriate for the instantaneous crack length and net section bending moment. The results of numerical calculations are shown in graphs of crack length, crack tip speed, and fracturing section bending moment versus time. It is found that the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then rapidly decelerates in the final stage of the process. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.

Multiple Fracture of Beams Under Localized Impulsive Loading

1977 ◽  
Vol 44 (2) ◽  
pp. 259-263 ◽  
Author(s):  
J. D. Colton
Keyword(s):  
High Speed ◽  
Beam Theory ◽  
Impulsive Loading ◽  
Time Sequence ◽  
Bending Stress ◽  
Multiple Fracture ◽  
Fracture Patterns ◽  
Deformation And Fracture ◽  
Impulsive Loads ◽  
Framing Camera

The fracture patterns produced by localized impulsive loading on brittle beams and their dependence on the intensity and length of the load have been determined. Experiments were performed on effectively infinite beams loaded over a finite length with sheet explosive. The mechanisms, location, and time sequence of deformation and fracture were determined by posttest observation and by high-speed framing camera photographs. It was found experimentally that all fractures were initiated by bending stress and that the localized impulsive loading produced three different fracture patterns. The beam response was also predicted analytically by numerically integrating the characteristic equations of Timoshenko beam theory. It was found analytically that, depending on load length and intensity, a total of four fracture patterns, including the three observed experimentally, can be produced by localized impulsive loads.

Effect of Axial Force on Dynamic Fracture of a Beam or Plate in Pure Bending

1977 ◽  
Vol 44 (4) ◽  
pp. 647-651 ◽  
Author(s):  
H. Adeli ◽  
G. Herrmann ◽  
L. B. Freund
Keyword(s):  
Experimental Data ◽  
Dynamic Fracture ◽  
Axial Force ◽  
Fracture Process ◽  
Bending Moment ◽  
Critical Value ◽  
Pure Bending ◽  
Strain Fracture ◽  
Beam Thickness ◽  
Tip Velocity

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam. As an extension of previous work, a dynamically induced axial force which is generated during the fracture process is included in the analysis. Thus an improved formulation is presented by means of which the crack length, crack tip velocity, bending moment, and axial force at the fracturing section are determined as functions of time after crack initiation. It is found that the effect of the axial force becomes significant after the crack travels about one third of the beam thickness, and better agreement with experimental data is achieved. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.

Multiple Fracture of Plates Under Localized Impulsive Loading

1976 ◽  
Vol 43 (1) ◽  
pp. 33-38 ◽  
Author(s):  
J. D. Colton
Keyword(s):  
High Speed ◽  
Plate Theory ◽  
Impulsive Loading ◽  
Mindlin Plate ◽  
Strain Gages ◽  
Fracture Patterns ◽  
Deformation And Fracture ◽  
Impulsive Loads ◽  
Mindlin Plate Theory ◽  
Framing Camera

An investigation was performed to determine the fracture patterns produced by localized impulsive loading on brittle plates and their dependence on the intensity and area of the load. Experiments were performed on effectively infinite plates loaded over a finite area with sheet explosive. The mechanisms, location, and time sequence of deformation and fracture were determined by terminal observation, high-speed framing camera photographs, and strain gages. It was found that all fractures were initiated by bending stress; two different fracture patterns in plates were produced experimentally. The plate response was also predicted analytically by numerically integrating the characteristic equations of Mindlin plate theory. It was found analytically that, depending on loading intensity and duration, a total of five fracture patterns in plates, including both those observed experimentally, can be produced by localized impulsive loads.

Deflection analysis of the airship structure based on the tapered inflatable beam

2019 ◽  
Vol 91 (4) ◽  
pp. 601-606
Author(s):  
Zheng Chen ◽  
Haitao Zhao ◽  
Xiaowang Li ◽  
Ji’an Chen
Keyword(s):  
High Speed ◽  
Beam Theory ◽  
Bending Moment ◽  
Research Area ◽  
Engineering Practice ◽  
Content Type ◽  
Shell Elements ◽  
Beam Elements ◽  
Deflection Analysis ◽  
The One

Purpose The purpose of this paper is to analyse the deflection of the flexible airship structure in a new way which can decrease the calculation amount and improve the calculation speed. Design/methodology/approach Infinitesimal method and tapered inflatable beam theory are combined to study the mechanics characteristics of the airship. Firstly, infinitesimal method is introduced into the airship structure analysis. The airship structure can be divided into several tapered inflatable beam elements. Then, tapered inflatable beam theory is improved and a developed model of the tapered inflatable beam under bending moment is presented. Besides, it is proved that deflection caused by pure load and pure moment can be linearly superimposed. Finally, the deflection of the airship structure is studied by means of tapered inflatable beam theory. Findings This paper improved the tapered inflatable beam theory. Besides, the proposed method for deflection analysis of the flexible airship in this paper can reach the same accuracy with traditional finite element method (FEM). However, the number of beam elements is much less than the one of FEM shell elements, which will decrease the calculation amount much and improve the calculation speed. Practical implications The flexible airship is a new and developing research area in engineering practice. The proposed method in this paper provides one precise and high-speed way to analyse the deformation of the airship. Originality/value The paper draws its value from the contributions to development of inflatable structure and the flexible airship mechanics research.

Finite Element Modeling of Self-Loosening of Bolted Joints

2004 ◽  
Author(s):  
Ming Zhang ◽  
Yanyao Jiang ◽  
Chu-Hwa Lee
Keyword(s):  
Finite Element ◽  
Contact Pressure ◽  
Bending Moment ◽  
Shear Loading ◽  
Transverse Load ◽  
Fe Model ◽  
Bolted Joint ◽  
Cyclic Bending ◽  
Second Stage ◽  
Cyclic Bending Moment

A three-dimensional finite element (FE) model with the consideration of the helix angle of the threads was developed to simulate the second stage self-loosening of a bolted joint. The second stage self-loosening refers to the graduate reduction in clamping force due to the back-off of the nut. The simulations were conducted for two plates jointed by a bolt and a nut and the joint was subjected to transverse or shear loading. An M12×1.75 bolt was used. The application of the preload was simulated by using an orthogonal temperature expansion method. FE simulations were conducted for several loading conditions with different preloads and relative displacements between the two clamped plates. It was found that due to the application of the cyclic transverse load, micro-slip occurred between the contacting surfaces of the engaged threads of the bolt and the nut. In addition, a cyclic bending moment was introduced on the bolted joint. The cyclic bending moment resulted in an oscillation of the contact pressure on the contacting surfaces of the engaged threads. The micro-slip between the engaged threads and the variation of the contact pressure were identified to be the major mechanisms responsible for the self-loosening of a bolted joint. Simplified finite element models were developed that confirmed the mechanisms discovered. The major self-loosening behavior of a bolted joint can be properly reproduced with the FE model developed. The results obtained agree quantitatively with the experimental observations.

A Short Fatigue Crack Growth Law for 1Cr18Ni9Ti Weld Metal

2006 ◽  
Vol 324-325 ◽  
pp. 571-578 ◽  
Author(s):  
Yong Xiang Zhao ◽  
Bing Yang ◽  
Wei Hua Zhang
Keyword(s):  
High Speed ◽  
Compression Tests ◽  
Temporal And Spatial Distribution ◽  
Primary Stage ◽  
Second Stage ◽  
Final Failure ◽  
Brewing Process ◽  
Ae Signal ◽  
Failure Location ◽  
Low Amplitude

A series of uniaxial-compression tests were conducted on some representative brittle rock specimens, such as granite, marble and dolerite. A multi-channel, high-speed AE signal acquiring and analyzing system was employed to acquire and record the characteristics of AE events and demonstrate the temporal and spatial distribution of these events during the rupture-brewing process. The test result showed that in the primary stage, many low amplitude AE events were developed rapidly and distributed randomly throughout the entire specimens. In the second stage, the number of AE increased much slower than that in the first stage, while the amplitude of most AE events became greater. Contrarily to the primary stage, AE events clustered in the middle area of the specimen and distributed vertically conformed to the orientation of compression. The most distinct characteristic of this stage was a vacant gap formed approximately in the central part of the specimen. In the last stage, the number of AE events increased sharply and their magnitude increased accordingly. The final failure location coincidently inhabited the aforementioned gap. The main conclusion is that most macrocracks are developed from the surrounding microcracks existed earlier and their positions occupy the earlier formed gaps, and the AE activity usually becomes quite acute before the main rupture occurs.

scholarly journals Monitoring and Modeling Railway Structures on High-Speed Lines with Asphalt Concrete Underlay: A Study on the Bretagne–Pays de la Loire Line

2020 ◽  
Vol 2674 (12) ◽  
pp. 600-607
Author(s):  
Diana Khairallah ◽  
Olivier Chupin ◽  
Juliette Blanc ◽  
Pierre Hornych ◽  
Jean-Michel Piau ◽  
...  
Keyword(s):  
Asphalt Concrete ◽  
High Speed ◽  
Large Scale ◽  
Strain Gages ◽  
Railway Transportation ◽  
Dynamic Stresses ◽  
High Speed Railway ◽  
High Frequencies ◽  
High Acceleration ◽  
High Speed Trains

The design and durability of high-speed railway lines is a major challenge in the field of railway transportation. In France, 40 years of feedback on the field behavior of ballasted tracks led to improvements in the design rules. However, the settlement and wear of ballast, caused by dynamic stresses at high frequencies, remains a major problem on high-speed tracks leading to high maintenance costs. Studies have shown that this settlement is linked to the high acceleration produced in the ballast layer by high-speed trains traveling on the track, disrupting the granular assembly. The “Bretagne–Pays de la Loire” high-speed line (BPL HSL), with its varied subgrade conditions, represents the first large-scale application of asphalt concrete (GB) as the ballast sublayer. This line includes 77 km of conventional track with a granular sublayer of unbound granular material (UGM) and 105 km of track with an asphalt concrete sublayer under the ballast. During construction, instruments such as accelerometers, anchored deflection sensors, and strain gages, among others, were installed on four sections of the track. This paper examines the instrumentation as well as the acquisition system installed on the track. The data processing is explained first, followed by a presentation of the ViscoRail software, developed for modeling railway tracks. The bituminous section’s behavior and response is modeled using a multilayer dynamic response model, implemented in the ViscoRail software. A good match between experimental and calculated results is highlighted.

Explosively Driven Expansion and Fragmentation Behavior for Cylinders, Spheres and Rings of 304 Stainless Steel

2010 ◽  
Vol 638-642 ◽  
pp. 1035-1040 ◽  
Author(s):  
Tetsuyuki Hiroe ◽  
Kazuhito Fujiwara ◽  
Hidehiro Hata ◽  
Mitsuru Yamauchi ◽  
Kiyotaka Tsutsumi ◽  
...  
Keyword(s):  
Stainless Steel ◽  
High Speed ◽  
Fracture Behavior ◽  
Copper Wire ◽  
304 Stainless Steel ◽  
Fragmentation Model ◽  
Fragmentation Behavior ◽  
Deformation And Fracture ◽  
Test Parameters ◽  
Fine Copper

Explosive loading techniques are applied to expand tubular cylinders, spherical shells and rings of 304 stainless steel to fragmentation, and the effects of wall thicknesses, explosive driver diameters and the constant proportionality of the in-plane biaxial stretching rates are investigated on the deformation and fracture behavior of three basic structures experimentally and numerically. In the cylinder tests, the driver is a column of high explosive PETN, inserted coaxially into the bore of a cylinder and initiated by exploding a fine wire bundle at the column axis using a discharge current from a high-voltage capacitor bank. In case of the ring tests, ring specimens are placed onto a single cylinder filled with the PETN as a expansion driver, and for sphere tests, specimens filled with the PETN are also initiated by exploding a fine copper wire line with small length located at the central point. Two types of experiments are conducted for every specimen and test condition. The first type uses high speed cameras to observe the deformation and crack generation of expanding specimens showing the final maximum in-plane stretching rate of above , and the second uses soft capturing system recovering typically most fragments successfully. The fragments are measured and investigated using a fragmentation model. The effects of test parameters on the deformation and fracture behavior for three types of structures are discussed in need of modified fragmentation model for shell structural elements.

scholarly journals A new methodology for polyvalent intravenous immunoglobulin solution production with a two-stage process of viral inactivation

2010 ◽  
Vol 46 (4) ◽  
pp. 777-783
Author(s):  
Antônio Edson de Souza Lucena ◽  
Divaldo de Almeida Sampaio ◽  
Ednaldo Rosas da Silva ◽  
Virgínia Florêncio de Paiva ◽  
Ana Cláudia Santiago ◽  
...  
Keyword(s):  
Intravenous Immunoglobulin ◽  
Immunoglobulin G ◽  
Cation Exchanger ◽  
Product Analysis ◽  
Viral Inactivation ◽  
Two Stage ◽  
Second Stage ◽  
Neutralizing Capacity ◽  
Stage Process ◽  
Sodium Caprylate

Highly purified intravenous immunoglobulin G concentrate (IV IgG) was produced with the use of polyethylene glycol associated to a single-stage precipitation by ethanol, instead of the classic Cohn-Oncley process, which employs cold alcohol as the precipitating agent, in a three-stage process. Precipitation of crude fraction containing more than 95% of immunoglobulin G was performed by liquid chromatography with a cation exchanger, CM-Sepharose, as a stationary phase. During the process, the product was subjected to two-stage viral inactivation. The first stage was performed by the action of sodium caprylate, 30 mM at pH 5.1+/- 0.1, and the second stage was performed by the action of a solvent-detergent mixture. The finished product was formulated at 5% with 10% sucralose as the stabilizing agent. The process yields 3.3g of IgG/liter of plasma. The finished product analysis showed an anti-complementary activity lower than 1CH50. Polymer and aggregate percent levels were lower than 3% in the five batches studied. The analysis of neutralizing capacity showed the presence of antibacterial and antiviral antibodies in at least three times higher concentrations than the levels found in source plasma. The finished product fulfilled all purity requirements stated in the 4th edition of the European pharmacopeia.

Sign in / Sign up

Export Citation Format

Share Document