Brittle Fracture and Fracture Mechanics
Introduction
Steels used for construction of components and equipment are ductile but not immune to fracture failures. Small tensile specimens of these materials stretch plastically by a large amount before breaking. Yet large components fabricated from these same materials sometimes fracture without much plasticity at nominal stresses below the yield stress. Such fractures are caused by cracks or crack-like defects.
Large components can harbor cracks or defects which tend to grow under regular service loads. Sometimes the initial flaw size and the amount of growth are so small that the crack remains harmless. However, small flaws that grow slowly and progressively can become serious problems. Eventually, the crack reaches a critical size. At this stage, the crack can penetrate through the cross section of a component in a fraction of a second. It should be understood that the conventional tensile properties of yield strength, tensile strength and elongation have virtually no bearing on the vulnerability of a material to crack extension and fracture.
Brittle Fracture of Normally Ductile Materials
The field of fracture mechanics is that methodology that quantifies the relationships among flaw size, stress and material toughness so that the severity of flaws can be assessed in equipment and structures on a fitness-for-service basis. The field of fracture mechanics can be divided into several categories, based on a materials toughness, and include: (1) linear elastic fracture mechanics (LEFM), (2) elastic plastic fracture mechanics (EPFM) and, (3) plastic fracture mechanics (PFM). With low toughness materials that exhibit brittle fracture such as those represented by the 1/4-pitch RGV pinions, LEFM methodologies typically apply.
Brittle fracture is fracture that involves little or no plastic deformation. It is usually associated with flaws or defects in the material where bulk stresses concentrate. A stress intensity is associated with flaws or geometric notches (Figure 1) and a stress concentration factor can be assigned to the flaw or notch based on its geometry, location and orientation. The more acute the flaw or notch, the greater the stress intensity (Figure 2).
The stress intensity factor is described by KI. The fracture resistance of a material can be expressed by the material's fracture toughness, denoted as KIc, the stress intensity factor. Fracture occurs when the stress intensity KI = KIc.
In its simplest form the stress intensity KI is given by the expression KI = 1.77 x Ó x a1/2 where Ó is the acting stress and "a" is the size of an existing flaw. Based on the equation, it becomes apparent that the stress intensity increases with an increase in stress Ó and in the flaw size "a".
The relationship between stress and stress intensity is a linear one (Figure 3) where the relationship between crack size and stress intensity is not (Figure 4).
For a brittle fracture to occur in a normally ductile material, the following factors must be present simultaneously:
1. A stress concentrator must be present. This can be a weld defect, a fatigue crack, or a geometric notch such as a sharp corner, thread, hole, etc. The stress concentrator must be large enough and sharp enough to be a "critical flaw" in terms of fracture mechanics.
2. A tensile stress must be present. The tensile stress must be of a magnitude high enough to provide microscopic plastic deformation at the tip of the stress concentration. The tensile stress need not be an applied stress on the structure, but may be a residual stress inside the structure, i.e., from welding or uneven cooling, etc.
3. The temperature must be relatively low for the steel concerned. The lower the temperature for a given steel, the greater the possibility that brittle fracture will occur. For some steels the ductile/brittle transition temperature may be above room temperature.
Characteristics of Brittle Fracture
A fracture is "brittle" when it is associated with very little plastic deformation. Such fractures can take place in otherwise ductile materials if they contain cracks. Brittle fractures have certain characteristics that permit them to be identified:
1. There is no gross permanent or plastic deformation of the metal in the region of brittle fracture.
2. The surface of a brittle fracture is perpendicular to the principle tensile stress.
3. Characteristic markings on the fracture surface frequently point back to the location from which the fracture originated. These markings are sometimes referred to as "chevron" or "herringbone" marks.
Figure 5 shows the relationship between toughness and fracture. Components A, B, and C are made out of three different materials, with A exhibiting low toughness, B intermediate toughness and C high toughness. The three materials contain the same crack size, are of equal yield stress and are loaded to the same stress. At a certain stress fracture occurs in Component A. The fracture is associated with little plastic deformation; therefore, it is a brittle fracture. It took place at a nominal stress substantially below yield. Due to their higher toughness, Components B and C are not yet ready to fail. The stress can be raised causing an increase of the plastic zone until the entire uncracked ligament is plastic. Component B fails at this point because plastic deformation is confined to the ligament, while the nominal stress is still below yield. Fracture of Component C requires a still higher stress at which eventually gross yielding will occur. The fracture is ductile because it is associated with gross plasticity and stresses above yield.