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

C. Levy; G. Herrmann

doi:10.1115/1.3162549

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

Journal of Applied Mechanics ◽

10.1115/1.3424151 ◽

1977 ◽

Vol 44 (4) ◽

pp. 647-651 ◽

Cited By ~ 10

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.

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

Journal of Applied Mechanics ◽

10.1115/1.3162616 ◽

1982 ◽

Vol 49 (4) ◽

pp. 773-778 ◽

Cited By ~ 4

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.

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Dynamic Fracture of a Beam or Plate in Plane Bending

Journal of Applied Mechanics ◽

10.1115/1.3423760 ◽

1976 ◽

Vol 43 (1) ◽

pp. 112-116 ◽

Cited By ~ 79

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.

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Bending With Axial Force of Curved Bars in Plasticity

Journal of Applied Mechanics ◽

10.1115/1.4010506 ◽

1952 ◽

Vol 19 (3) ◽

pp. 327-330

Author(s):

Aris Phillips

Keyword(s):

Axial Force ◽

Strain Distribution ◽

Axial Load ◽

Bending Moment ◽

High Accuracy ◽

Pure Bending ◽

Stress Strain

Abstract The problem of symmetrical pure bending with axial force of a curved bar in plasticity is considered. A method is given for finding the axial load and bending moment which produce a given strain distribution. This method is based upon approximating the stress-strain curves by means of broken lines. By increasing the number of sides of these broken lines it is possible to solve our problem with as high accuracy as is desired.

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