13th International Conference on Fracture June 16–21, 2013, Beijing, China 1 Scatter of measured KIC related to the scatters of local parameters Xf, σf and εpc Jian Hong Chen* and Rui Cao Department of Material Science and Engineering and State Key laboratory of Non-ferrous Metals of Lanzhou University of Technology, Lanzhou, China * Corresponding author: zchen@lut.cn Abstract 42 values of KIC measured at -100 oC are related to the measured values of local fracture stress σf and the fracture distance Xf by the formula: KIC= β-(N+1)/2Xf 1/2[σf (1+N)/2N/ σ y (1-N)/2N]. The scatters of KIC caused by σf or Xf are assessed separately at constant values of Xf or σf. It is found that at a constant Xf the scatter of KIC induced by the scatter of σf accounts for only 20% of the total scatter, while at a nearly constant σf the scatter of KIC caused by the scatter of Xf can reach almost 100% of the total scatter of KIC. It means that the effect of the scatter of Xf on the scatter of KIC is much larger than that of σf. This idea is opposite to the assumption widely accepted in local approach that the distribution of various sizes of the carbide particles which present various values of σf is the main event in the statistical calculation. Instead, the random distribution of (Xf) of weakest particles with the lowest values of σf should be considered as the determining factor in statistical assessment for the cleavage fracture. Keywords Scatter of KIC, Local fracture stress σf., Fracture distance Xf, Fracture strain εpc 1. Introduction The relationships between global toughness, such as the critical stress intensity factor KIC and the critical values of parameters specified in the micromechanism of cleavage fracture, such as local fracture stress σf , fracture distance Xf and fracture strain εpc, are of great significance. These relationships offer the bases for establishing the statistical model (such as the local approach) which uses the micro-parameters to predict the global failure probability. For pre-cracked specimens of a normalized C-Mn steel the relations between the global toughness measured in cleavage-fractured specimens and the critical values of local parameters εpc, σf and Xf had been discussed in a previous paper[1], where the discussion started from the Eq. (1) [2] ( ) ( ) ( ) [ ] N N y N N f K N IC X K 1 /2 1 /2 1 /2 1/2 / − + − + = σ σ β , (1) β is the amplitude of HRR crack tip stress singularity [3,4] Here this equation is modified to Eq. (2) by substituting Xf for Xk. ( ) ( ) ( ) [ ] N N y N N f f N IC X K 1 /2 1 /2 1 /2 1/2 / − + − + = σ σ β , (2) In Eq. (1) Xk is the ‘characteristic distance’ [5], In Eq. (2) Xf is the fracture distance i.e. the measured distance from the cleavage initiation site to the blunted precrack tip. In Eq. (2) the factor ( ) ( ) [ ] N N y N N f f F X 1 /2 1 /2 1/2 / − + = σ σ , (3) correlates the global fracture toughness KIC to the local parameters σf and Xf. In following, the relations will be analyzed using the data of Table 1 which were measured in 42 specimens at -100oC. The C-Mn steel specimens were normalized, austenized at 900oC for 2 hours then air cooled. The uniform microstructure is composed of the ferrite grains of 9.3μm in average size and 22μm for the largest grains and the pearlite colonies around 3.2μm in the average size and 20μm for the largest.
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