There has been some uncertainty in the field of fracture mechanics as to whether shifts in the ductile-to-brittle transition with specimen size are caused by statistical sampling effects or constraint effects. Fracture toughness data for three carbon-manganese steels were analyzed to examine the effectiveness of each model in predicting the results of different sized specimens. The data set used in this investigation contains nearly 500 crack tip opening displacement (CTOD) values for various geometries of single edge notched bend (SENB) specimens with thicknesses ranging from 10 to 100 mm. A limited amount of data for single edged notched (SENT) specimens and side grooved SENB specimens was also included.
It was found that the mechanism which accounts for size effects most effectively depends on the amount of plastic flow prior to fracture. Under conditions of small scale yielding, high constraint is maintained in both small and large specimens. In this region the Landes and Shaffer statistical sampling model appears to work well for explaining the higher average toughness of small specimens. However, when the ligament yields prior to fracture, the shifts in transition observed with specimen size cannot be explained by statistical sampling effects alone.
The temperature at which net section yielding first occurs tends to shift upward as (1) the specimen thickness increases, (2) the ligament length is decreased (in a bend specimen), or (3) the mode of loading is changed from tension to bending. When the ligament yields, the plastic deformation relaxes the crack tip constraint and the brittle-to-ductile transition becomes steep. The relaxation of crack tip constraint occurs more rapidly and at lower temperatures in smaller specimens. This gives rise to a steeper transition curve and a shift in transition temperature which cannot be accounted for by statistical effects. Thus as the critical CTOD increases the relative contribution of statistical sampling on size effects decreases and constraint effects tend to dominate.