Estimation of Stress and Strain at the Notch Root in the Elastic-plastic Range using the J-integral

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An elastic-plastic analysis of notched plates was made. The J-integral of the notched plates was computed, and the relations between the value of J-integral and the stress and strain at the notch root were discussed. It was found that a master-curve representation of the stress σ or the strain ε at the notch root was possible on a σ/σ_Y (or ε/ε_Y)-J/J_<yield> diagram( σ_Y : yield stress, ε_Y : yield strain, J_<yield> : the J-integral value at which notch root yielding starts). The J-integral was found to be approximately given as J=J_<linear> ( = elastic J-integral) when P/P_<GY>≦1,regardless of the stress condition, the elastic stress concentration factor K_t and the strain hardening characteristics of the material (P : the applied load, P_<GY> : the gross yield load of the respective notched plate) By combining these two findings, a simple method was proposed to estimate the stress and strain at the notch root in the elastic-plastic range up to gross yielding.
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