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.

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.

Effect of Shear and Rotary Inertia on Dynamic Fracture of a Beam or Plate in Pure Bending

1982 ◽  
Vol 49 (4) ◽  
pp. 773-778 ◽  
Author(s):  
C. Levy ◽  
G. Herrmann
Keyword(s):  
Dynamic Fracture ◽  
Axial Force ◽  
Opposite Effect ◽  
Bending Moment ◽  
Rotary Inertia ◽  
Pure Bending ◽  
Strain Fracture ◽  
The Moment ◽  
Tip Velocity ◽  
Total Fracture

The dynamic fracture response of a long beam of brittle material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased quasi-statically to a critical value, a crack will propagate from the tensile side of the beam. As an extension of previous work, the effect of shear and of rotary inertia on the moment and induced axial load at the fracturing section is included in the present analysis. Thus an improved formulation is presented by means of which the crack length, crack-tip velocity, bending moment, and axial force at the fracture section are determined as functions of time after crack initiation. It is found that the rotary effect diminishes the axial force effect and retards total fracture time whereas the shear has an opposite effect. Thus by combining the two effects (to simulate to first order the Timoshenko beam) overall fracture is retarded and better agreement with experimental data is achieved. The results also apply for plane-strain fracture of a plate in pure bending provided the value of the elastic modulus is appropriately modified.

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.

An Experimental Measurement of Toughness Locus for a Ductile Material

2005 ◽  
Vol 297-300 ◽  
pp. 2410-2415 ◽  
Author(s):  
Dong Hak Kim ◽  
Jeong Hyun Lee ◽  
Ho Dong Kim ◽  
Ki Ju Kang
Keyword(s):  
Crack Length ◽  
Nuclear Power ◽  
Power Plants ◽  
Test Procedure ◽  
Stress Triaxiality ◽  
Crack Tip ◽  
Potential Drop ◽  
Image Correlation ◽  
Ductile Material ◽  
Main Steam

A toughness locus Jc-Q for a ductile steel, SA106 Grade C used in the main steam piping of nuclear power plants, has been experimentally evaluated. Along with the standard fracture test procedure for J-R curve, Q as the second parameter governing stress triaxiality nearby the crack tip is measured from the displacements nearby the side necking which occurs near the crack tip on the lateral surface of a fracture specimen. The displacements nearby the side necking are measured from the digital images taken during the fracture experiment based on Stereoscopic Digital Photography (SDP) and high resolution Digital Image Correlation (DIC) software. The crack length is monitored by Direct Current Potential Drop (DCPD) method and the J-R curve is determined according to ASTM standard E1737-96. The effects of crack length, specimen geometry and thickness of specimen are studied, which are included in the toughness locus Jc-Q.

J-Integral Analysis of Surface Cracks in Round Bars under Bending Moments

2011 ◽  
Vol 52-54 ◽  
pp. 43-48 ◽  
Author(s):  
Al Emran Ismail ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Mariyam Jameelah Ghazali ◽  
Ruslizam Daud
Keyword(s):  
Finite Element ◽  
Crack Depth ◽  
Crack Tip ◽  
Bending Moment ◽  
Limit Load ◽  
Fe Model ◽  
Surface Cracks ◽  
Element Analysis ◽  
Reference Stress ◽  
Proposed Model

This paper presents a non-linear numerical investigation of surface cracks in round bars under bending moment by using ANSYS finite element analysis (FEA). Due to the symmetrical analysis, only quarter finite element (FE) model was constructed and special attention was given at the crack tip of the cracks. The surface cracks were characterized by the dimensionless crack aspect ratio, a/b = 0.6, 0.8, 1.0 and 1.2, while the dimensionless relative crack depth, a/D = 0.1, 0.2 and 0.3. The square-root singularity of stresses and strains was modeled by shifting the mid-point nodes to the quarter-point locations close to the crack tip. The proposed model was validated with the existing model before any further analysis. The elastic-plastic analysis under remotely applied bending moment was assumed to follow the Ramberg-Osgood relation with n = 5 and 10. J values were determined for all positions along the crack front and then, the limit load was predicted using the J values obtained from FEA through the reference stress method.

Crack tip plasticity in dynamic fracture

1987 ◽  
Vol 48 (11) ◽  
pp. 985-1005 ◽  
Author(s):  
P.A. Mataga ◽  
L.B. Freund ◽  
J.W. Hutchinson
Keyword(s):  
Dynamic Fracture ◽  
Crack Tip ◽  
Crack Tip Plasticity

Dynamic fracture initiation behavior of an HY-100 steel

1993 ◽  
Vol 24 (4) ◽  
Author(s):  
Sunghak Lee ◽  
Je Won Rhyu ◽  
Kyung-Mox Cho ◽  
Jacques Duffy
Keyword(s):  
Dynamic Fracture ◽  
Fracture Initiation
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