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An analysis of the forces and bending moments generated during the notched beam impact test

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Abstract

An analysis is presented which predicts the hammer force and specimen bending moment-time responses during impact from the dynamics of the system and the fracture characteristics of the material. The theoretical predictions are compared to available experimental observations and good agreement is obtained for brittle materials.

Résumé

L'analyse qui est présentée permet de prédire, à partir de la dynamique du système et des caractéristiques de rupture du matériau, l'évolution dans le temps de la force du mouton et du moment de flexion dans l'éprouvette.

On compare ces predictions théoriques avec les observations recueillies au, cours d'essais, et l'ón conclut à un accord satisfaisant dans le cas des matériaux fragiles.

Zusammenfassung

Es wurde eine Analyse präsentiert, die die Hamerkraft and die Reaktion des Moments der Modelbiegung während des Aufschlages von der Dynamik des Systems and den Bruchmerkmalen des Materials bestimmte. Theoretische Vorausbestimmungen wurden mit vorhandenen experimentellen Beobachtungen verglichen and gute Übereinstimmung wurde für brüchige Materiale erhalten.

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Abbreviations

a :

Notch depth

A g :

Cross sectional area of gross section

A :

Beam cross sectional area

B 1 :

Portion of the boundary over which displacements are prescribed

B 2 :

Portion of the boundary over which tractions are prescribed bBeam thickness

d :

Unbroken ligament depth

E :

Young's modulus

F:

Hammer force

Fi:

Body force vector

fi:

\([t * F_l ] + \rho [t\dot u_i (0,x) + u_l (0,x)]\)

G:

Shear modulus

G I :

Mode I fracture toughness

h :

Beam half height

H :

Heaviside unit step function

I :

Cross sectional moment of inertia about the c.g.

I g :

Moment of inertia of the gross section

k 2 :

Constant in the Hertz theory of contact forces

k 4 :

Constant in the assumed linear contact theory LBeam length

M :

Beading moment

m 1 :

Hammer mass

m 2 :

Anvil mass

p :

Applied load per unit length on the top surface of the beam; also the Laplace transform parameter

R :

Bounded region of Euclidean 3-space

T :

Prescribed surface traction on B 2

û i :

Prescribed displacement vector on B 1

u i :

Displacement vector

u y :

Beam deflection referred to the embedded coordinates x i

V:

Shear force

V i :

Hammer velocity referred to the fixed coordinates X i

V 2 :

Rigid body beam velocity referred to the fixed coordinates X i

V 01 V 02 :

Initial hammer or rigid body beam velocity

References

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Authors and Affiliations

  1. Metallurgy Division, U. S. Naval Research Laboratory, 20390, Washington, D.C.

    Gerald E. Nash

Authors
  1. Gerald E. Nash
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Nash, G.E. An analysis of the forces and bending moments generated during the notched beam impact test. Int J Fract 5, 269–286 (1969). https://doi.org/10.1007/BF00190957

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  • DOI: https://doi.org/10.1007/BF00190957

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