Fully plastic crack-tip fields for plane strain shallow-cracked specimens under pure bending

1996 ◽  
Vol 78 (1) ◽  
pp. 21-34 ◽  
Author(s):  
Yun-Jae Kim ◽  
Guoyu Lin ◽  
Alfred Cornec ◽  
Karl-Heinz Schwalbe
Keyword(s):  
Plane Strain ◽  
Crack Tip ◽  
Pure Bending ◽  
Crack Tip Fields ◽  
Cracked Specimens

Plane-Strain Crack-Tip Fields for Pressure-Sensitive Dilatant Materials

1990 ◽  
Vol 57 (1) ◽  
pp. 40-49 ◽  
Author(s):  
F. Z. Li ◽  
J. Pan
Keyword(s):  
Plane Strain ◽  
Effective Stress ◽  
Hydrostatic Stress ◽  
Yield Criterion ◽  
Crack Tip ◽  
Flow Rule ◽  
Pressure Sensitivity ◽  
Crack Tip Fields ◽  
Pressure Sensitive ◽  
Plane Strain Crack

Plane-strain crack-tip stress and strain fields are presented for materials exhibiting pressure-sensitive yielding and plastic volumetric deformation. The yield criterion is described by a linear combination of the effective stress and the hydrostatic stress, and the plastic dilatancy is introduced by the normality flow rule. The material hardening is assumed to follow a power-law relation. For small pressure sensitivity, the plane-strain mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, 1968a, b; Rice and Rosengren, 1968). The angular distributions of the fields depend on the material-hardening exponent and the pressure-sensitivity parameter. The low-hardening solutions for different degrees of pressure sensitivity are found to agree remarkably with the corresponding perfectly-plastic solutions. An important aspect of the effects of pressure-sensitive yielding and plastic dilatancy on the crack-tip fields is the lowering of the hydrostatic stress and the effective stress directly ahead of the crack tip, which may contribute to the experimentally-observed enhancement of fracture toughness in some ceramic and polymeric composite materials.

The Higher Order Crack Tip Fields for Arbitrary FGM Composite Functions

2011 ◽  
Vol 19 (4-5) ◽  
pp. 401-404
Author(s):  
Dai Yao ◽  
Zhang Lei ◽  
Liu Jun-feng ◽  
Zhong Xiao
Keyword(s):  
Crack Tip ◽  
Higher Order ◽  
Composite Functions ◽  
Crack Tip Fields

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.

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