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Photoelasto-plastic studies on brittle fracture of high-polymer solids

A simple photoelasto-plastic method for the determination of stress-concentration factors in plane-elasticity problems is suggested on the basis of experimental results

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Abstract

The mechanism of brittle fracture of high-polymer solids is experimentally investigated under one-or two-dimensional stress states by a new photoelastoplastic method suggested by the author. The application of the photoelasto-plastic method on the brittle-fracture problem is based on the principle that breaking stress can be computed in brittle fracture by the measurement of the fringe orderN B of isochromatic lines at fracture point.

Bending under three-point and four-point loads, and the plane problems, some having stress concentration and others being under contacting load, are examined by using rigid polyester cast resin containing styrol as a model specimen; and, in conclusion, the brittle fracture of high-polymer solids under one- or two-dimensional stress states is decided by the constant tensile stress, whose magnitude depends only upon the material used as a model specimen, and is larger than its ultimate tensile strength.

Many kinds of factors in fracture are defined, and stress-concentration factors in fracture are compared with stress-concentration factors in elasticity. A new photoelasto-plastic simple method for the determination of stress-concentration factors in elasticity is suggested by utilization of the experimental results on this brittle fracture of high-polymer solids and is examined on the perforated plane problem having finite width under tension in comparison with theoretical analysis and the experimental results by other measuring methods.

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Abbreviations

σ t :

tensile stress, Kg/mm2

ε t :

tensile strain, %

N :

fringe order of isochromatic line, F.O.

λ:

wave length of monochromatic, circularly polarized light, Å

α:

photoelastic sensitivity, F.O./Kg/mm

N B :

fracture fringe order at fracture point in test specimen, F.O.

t :

thickness of plate test specimen, mm

(σ1 - σ2):

difference of principal stresses, Kg/mm2

\({\bar \sigma }\) :

effective stress, Kg/mm2

\(\bar \varepsilon\) :

effective strain, %

M B :

breaking bending moment, Kg/mm

b σBN :

extreme fiber stress at fracture measured by photoelasto-plastic method, Kg/mm2

b σB cal :

extreme fiber stress at fracture computed from breaking bending moment, Kg/mm2

σT :

ultimate tensile strength of test specimen, Kg/mm2

σC :

ultimate compressive strength of test specimen, Kg/mm2

c :

distance between two supports for a beam in three-point bending, mm

σA, σE :

stress at pointsA andE, respectively, of perforated-plate specimen, Kg/mm2

l :

initial length of specimen, mm

w :

initial width of specimen, mm

d :

initial diameter of circular hole in perforated-plate specimen, mm

σ c ′, ε c ′:

apparent compressive stress and strain for perforated-plate specimen, computed on the basis of the cross-sectional area without a hole, Kg/mm2, %

P :

applied load, Kg

c σm :

mean compressive stress in plate specimen in the cross section without a hole, Kg/mm2

c σBM :

mean compressive stress in plate specimen in the cross section without a hole at fracture, Kg/mm2

c σBN :

fracture stress at fracture point of plate specimen under compressive load, measured by photoelasto-plastic method, Kg/mm2

k A ,k E :

analytical value of stress-concentration factor in elasticity at pointsA andE, respectively, for perforated specimen under uniform tension, computed on the basis of mean stress in the cross section with a hole

k A′ ,k E′ :

analytical value of stress-concentration factor in elasticity at pointsA andE, respectively, for perforated specimen under uniform tension, computed on the basis of mean stress in the cross section without a hole

N max :

maximum fringe order of isochromatic lines, F.O.

d P :

diameter of circular, load-carrying pin, mm

t σBN :

fracture stress at fracture point of plate specimen under tensile load, measured by photoelasto-plastic method, Kg/mm2

t σBM :

mean tensile stress in plate specimen in the cross section without a hole, at fracture, Kg/mm2

P B :

breaking load, Kg

t P B :

breaking tensile load, Kg

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  1. Division of Engineering, Brown Univ., Providence, R. I.

    Katsuhiko Ito (Research Associate)

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Ito, K. Photoelasto-plastic studies on brittle fracture of high-polymer solids. Experimental Mechanics 1, 159–168 (1961). https://doi.org/10.1007/BF02327587

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