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Crack-opening angle and dissipation-rate analysis of R-curves for side-grooved pieces of HY130 steel in bending

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Abstract

The behaviour of side-grooved deep-notch three-point bend test pieces of 20 mm thick HY130 steel has been studied for large amounts of crack growth in three different widths. Growth occurs at limit load and the conventional R-curves follow the pattern that wider pieces give lower R-curves. Analysis of this behaviour is made in terms of the crack-tip opening angle, (CTOA) and the energy dissipation rate, dW dis/Bda, or D, from which a particular R-curve, J dis, can be formed. After an initial transient regime of about 2 mm growth, a steady-state region develops in terms of both CTOA and D. The steady state CTOA reduces with increase of initial width. The energy rate, D, is split into areal and volumetric components, γ and ρ, and, with neglect of the elastic components, ρ is related to the steady-state CTOA. The cumulative dissipation defined by J dis is compared to several conventional R-curves. It is concluded that the interpretation of steady-state crack growth in deep-notch three-point bend pieces can be expressed in terms of either CTOA or D, but that transference of data even from one size of a side-grooved piece to another, let alone to another configuration, cannot yet be made except on a lower bound basis.

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Abbreviations

a :

initial crack length

b :

size of ligament, (W a)

B :

thickness

G :

energy release rate in lefm

J i :

J-integral measure of toughness at initiation

J o, JU, Jm, Jj+1, Jdis :

particular forms of J used for R-curves, as defined in the text

L :

the ratio of actual to nominal load due to plastic constraint on a notched section

q :

displacement

Q :

load

r :

the fraction of b that defines the apparent centre of rotation in a bend-test piece

s :

shear-lip size (the same in thickness and axial directions for a 45° lip)

S :

span

U :

work done

w :

internal energy

W :

width

η:

geometric factor used in evaluating J

γ, τ, ρ:

specific intensities of energy dissipation rate (defined in the text)

σFl :

flow stress for general plasticity

c:

current value after some crack growth

dis:

dissipation, including both plastic and fracture components

el:

elastic (linear)

o:

original value before crack growth

pl:

plastic

app:

apparent

tot:

the total or combined elastic and plastic terms

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Author notes

  1. Z. F. Li

    Present address: Engineering Division, Qindao Institute of Architecture, Qindao, People’s Republic of China

Authors and Affiliations

  1. Mechanical Engineering Department, Imperial College, London, UK

    Z. F. Li & C. E. Turner

Authors
  1. Z. F. Li
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  2. C. E. Turner
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Li, Z.F., Turner, C.E. Crack-opening angle and dissipation-rate analysis of R-curves for side-grooved pieces of HY130 steel in bending. JOURNAL OF MATERIAL SCIENCE 28, 5922–5930 (1993). https://doi.org/10.1007/BF00365202

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  • DOI: https://doi.org/10.1007/BF00365202

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