Fracture Control
2.2 Effect on Stress State
Traditionally when evaluating a material’s fracture toughness through notched specimens, the fracture area is homogeneous and the through-thickness stress state is continuous. However, when separations occur on the fracture surface, the main fracture plane becomes divided into multiple, disconnected fracture planes and the through-thickness stress state is disrupted. This is what complicates the analysis of fracture toughness in notched specimens having separations.
Below the notch tip in a notched specimen, a high value of stress triaxiality exists. Stress triaxiality is defined as the ratio of hydrostatic stress to the equivalent von Mises stress. Stress triaxiality is well-known to locally reduce the ductility of structural materials. This can be accomplished in two ways.
First, stress triaxiality can prevent plastic deformation while the level of stress increases until a failure stress is reached and a cleavage fracture results. The other mechanisms is by encouraging void growth in the material. Preexisting inclusions in the material (e.g., non-metallic inclusions), generate microvoids that enlarge because of plastic straining until the voids coalescence and the material ruptures. Triaxiality stress states are greatly influenced by the material’s initial geometry and any changes that occur during deformation.
Effect on Stress State 75
Fig. 2.11: Stress components on fracture plane of notched specimen.
A notched specimen is exposed to three, orthogonal stress during deformation.
Figure2.11shows the three stress states along the x-, y-, and z-direction. These stress states also result in shear stresses τx y, τxz, and τyz. When concerned with the crack divider type separation, the stress along the through-thickness direction, σzz, is very important.
The stress state ahead of the fracture front has a great influence on the fracture energy and toughness of the material. Studies have shown that reducing the triaxiality stress, the material toughness can increase [And05;Kno73].
Reducing the triaxiality stress state can be accomplished by minimizing the through-thickness stress. It is for this reason that separations reduce the DBTT of Charpy specimens. With every new separation, the through-thickness stress is further reduced until reaching the plane stress condition, where σzz 0 [MM07]. With a low through-thickness stress the specimen is less likely to fail by cleavage fracture. The downside is that as the specimen is divided into thinner specimens, the Charpy USE reduced [Mor75]. Figure2.12shows the
Fig. 2.12: Effect of separation of through-thickness stress [Yan+08b].
change in σzz as a function of the through-thickness location for a specimen with and without a separation.
Separations in line pipe steels are generally reported to only occur at test temperatures above the DBTT [Bou83]. Separations are in a contest with cleavage fracture on the main fracture plane. If the critical stress for a separation is not met before the critical stress for cleavage fracture, the separation will not form and the specimen will fail in a brittle manner.
Mintz and Morrison [MM07], building on the work of Bourell [Bou83], attempted to create a model to predict when separations will occur with respect to the stress state and test temperature in a Charpy specimen from an X65 line pipe steel. Mintz and Morrison observed that when the temperature was below −80◦C, separations did not form as cleavage fracture dominated
Effect on Stress State 77
Fig. 2.13: Schematic showing how separations form over certain temperature ranges.
The yield stress σ∗Ywas adjusted for the strain rate of the Charpy test. Arrows show the transition of curve A to curve B once separations are possible [MM07].
the main fracture plane. Also, when the temperature was significantly high (>20◦C), separations once again did not form. Between these temperatures, separations were observed.
Both Bourell and Mintz and Morrison based their model on studies showing that the triaxial stress state adjacent to a Charpy notch loaded in a plane strain condition increases the longitudinal tensile stress at yield by as much as 2.18 times [GH56; TM67; WP66]. In other words, the stress along the x-axis in Figure 2.11 can be expressed as 2.18σY. The same studies found that the through-thickness stress along the z-axis is less than the σx value, having a relationship to the yield stress 1.68σY. Therefore, they considered two curves—one describing the longitudinal stress (σxx) and one describing the through-thickness stress (σzz). They plotted these curves over a range of temperatures shown in Figure2.13. In this figure, curve A, B, and C correspond to the σxx, biaxial stress, and σzz, respectively. The curves accounted for the
high strain rate of the Charpy test by modifying the yield strength.
Curves D and F represent the fracture stress vs temperature relationship for the main fracture plane and separation fracture plane, respectively. Therefore, the curves consider the fracture stress for brittle initiation along the fracture plane to be independent of temperature [BB78], while the fracture stress for separation formation is dependent on temperature.
The four critial temperatures T1, T2, T3, and T4are summarized as follows:
(T1) For steels not exhibiting separations, this temperature marks the point where the fracture mode will change from ductile to brittle.
(T2) This signifies the point where the main fracture plane and separation plane stress intersect, so if separations exists, they are expected to occur above this temperature, but below this temperature cleavage on the main fracture plane will dominate.
(T3) At this temperature, the splits will no longer appear in the sample.
(T4) This temperature represents the point where tensile triaxiality is com-pletely removed for brittle fracture.
If separations are present, the temperature at which brittle failure occurs along the main fracture plane will be reduced. Between T2and T1the main fracture mode should be ductile, which was confirmed by experiments.
Modified Charpy Specimens Evaluating the Effect of Separations 79