In discussing the fatigue crack propagation, the stress state and the structure of the material ahead of the crack tip will attract the interest of many researchers. In the present paper, as the first step to evaluate the strength of material at crack tip, the tensile deformation of low carbon steel has been examined by the X-ray micro beam technique and the micro Vickers hardness. The tensile true stress and the natural strain are correlated with the excess dislocation density obtained from the X-ray micro beam observation and micro Vickers hardness. The results obtained are summarized as follows;
(1) The excess dislocation density Dm
is proportional to the natural strain ε during the deformation from Lüders elongation to about 10% strain, as
When ε exceeds 10%, Dm
does not increase so much as expected by the above equation.
(2) The true stress σ is related to Dm
in the manner expressed by the equation during the strain ranging from Lüders elongation to about 20% strain,
where the first term of the right hand side of the equation is considered to be the frictional stress of this material.
(3) On the other hand, the frictional stress is found to be derived from the true stress-strain curve by taking the value of stress at zero, the strain obtained by extrapolating the linear work hardening portion just after Lüders elongation of the true stress-strain curve.
(4) Micro Vickers hardness HV
is related to the natural srain ranging from Lüers elongation to about 10% strain, as
It is worthy of note that the hardness 86 of annealed material is nearly equal to the value 84 which is given by substituting ε=0 into the equation.
(5) The following linear relation is established between HV
and the true stress σ during the strain ranging from Lüders elongation to about 20% strain.
When the hardness of annealed material is substituted into the equation, the corresponding stress of 11kg/mm2
is obtained which is the same value as the frictional stress given in item (2). This suggests that the initial locking of dislocations in annealed material used in this study which causes yield drop in the stress-strain curve has no influence on micro Vickers hardness.
The above mentioned relations will be successfully applied to the investigation on the strength of materials, particularly the strength of small area in specimens such as crack tip of fatigued specimens.