Abstract
A technique is presented which allows separation of the principal plastic strains within an enclave at a crack tip in relatively thin plates. For plates with a number of crack lengths, several degrees of tensile loading are applied to five ductile materials with widely varying mechanical properties. Principal plastic strain distributions, plastic distortional strain energy density and total plastic energy are determined within the resulting plastic encalves. It is shown that the degree of loading and strain hardening greatly affect the principal plastic strain and energy density distributions and that this is reflected in the amount of strain energy that can be plastically absorbed at a crack tip.
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Abbreviations
- a :
-
half crack length
- ΔA :
-
incremental area within enclave
- ɛ1,ɛ2,ɛ3 :
-
principal plastic strains
- δ:
-
relative retardation of 2.27×10−5 in. corresponding to first fringe order
- E :
-
tensile modulus of elasticity
- F :
-
loading factor defined in eq (7)
- γoct :
-
octahedral shear strain
- k :
-
strain optical coefficient
- n :
-
strain-hardening exponent
- r, θ:
-
polar coordinates
- r max :
-
distance from crack tip along maximum extension of enclave
- r p :
-
arbitrary value to define elastic-plastic boundary
- r p(θ):
-
shape of enclave
- r p′ :
-
maximum extension of enclave measured at ɛ1=2000 μin./in
- r θ=0o :
-
distance from crack tip along line of crack extension
- σ0 :
-
applied stress, gross section
- σ ys :
-
uniaxial yield stress
- t :
-
plate thickness
- t c :
-
thickness of photoelastic coating
- τoct :
-
octahedral shear stress
- U p :
-
plastic strain energy in one enclave
- ω:
-
plate width
- W d :
-
plastic distortional strain energy density
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Part II of this paper will be published in the December 1964 issue of
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Gerberich, W.W. Plastic strains and energy density in cracked plates. Experimental Mechanics 4, 335–344 (1964). https://doi.org/10.1007/BF02323544
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DOI: https://doi.org/10.1007/BF02323544