The resistance to fracture of a material is known as its fracture toughness.
Fracture toughness generally depends on temperature, environment, loading rate,
the composition of the material and its microstructure, together with geometric
Fracture toughness is a critical input parameter for fracture-mechanics based
fitness-for-service assessments, an indication of the amount of stress required
to propagate a preexisting flaw. It is a very important material property since
the occurrence of flaws is not completely avoidable in the processing,
fabrication, or service of a material/component.
Flaws may appear as cracks, voids, metallurgical inclusions, weld defects,
design discontinuities, or some combination thereof. Since engineers can never
be totally sure that a material is flaw free, it is common practice to assume
that a flaw of some chosen size will be present in some number of components and
use the linear elastic fracture mechanics (LEFM) approach to design critical
components. This approach uses the flaw size and features, component geometry,
loading conditions and the material property called fracture toughness to
evaluate the ability of a component containing a flaw to resist fracture.
A parameter called the stress-intensity factor (K) is used to determine the
fracture toughness of most materials. A Roman numeral subscript indicates the
mode of fracture and the three modes of fracture are illustrated in Fig.1. Mode
I fracture is the condition in which the crack plane is normal to the direction
of largest tensile loading. This is the most commonly encountered mode and,
therefore, for the remainder of the material we will consider KI.
The stress intensity factor is a function of loading, crack size, and structural
geometry. The stress intensity factor may be represented by the following
KI is the fracture toughness in
σ is the applied stress in MPa or psi
a is the crack length in meters or inches
(β) is a crack length and component geometry factor that is different for each specimen and is dimensionless.
Figure 1: Modes of fracture
Specimens having standard proportions but different absolute size produce different values for KI. This results because the stress states adjacent to the flaw changes with the specimen thickness (B) until the thickness exceeds some critical dimension (Fig.2). Once the thickness exceeds the critical dimension, the value of KI becomes relatively constant and this value, KIC , is a true material property which is called the plane-strain fracture toughness.
The relationship between stress intensity, KI, and fracture toughness, KIC, is similar to the relationship between stress and tensile stress. The stress intensity, KI, represents the level of “stress” at the tip of the crack and the fracture toughness, KIC, is the highest value of stress intensity that a material under very specific (plane-strain) conditions that a material can withstand without fracture. As the stress intensity factor reaches the KIC value, unstable fracture occurs. As with a material’s other mechanical properties, KIC is commonly reported in reference books and other sources.
Plane-Strain and Plane-Stress
When a material with a crack is loaded in tension, the materials develop plastic strains as the yield stress is exceeded in the region near the crack tip. Material within the crack tip stress field, situated close to a free surface, can deform laterally (in the z-direction of the image) because there can be no stresses normal to the free surface.
The state of stress tends to biaxial and the material fractures in a characteristic ductile manner, with a 45° shear lip being formed at each free surface. This condition is called "plane-stress" and it occurs in relatively thin bodies where the stress through the thickness cannot vary appreciably due to the thin section.
Figure 2: Relationship between KC and specimen thickness
However, material away from the free surfaces of a relatively thick component is not free to deform laterally as it is constrained by the surrounding material. The stress state under these conditions tends to triaxial and there is zero strain perpendicular to both the stress axis and the direction of crack propagation when a material is loaded in tension. This condition is called “plane-strain” and is found in thick plates.
Under plane-strain conditions, materials behave essentially elastic until the fracture stress is reached and then rapid fracture occurs. Since little or no plastic deformation is noted, this mode fracture is termed brittle fracture.
When performing a fracture toughness test, the most common test specimen configurations are the single edge notch bend (SENB or three-point bend), and the compact tension (CT) specimens. From the above discussion, it is clear that an accurate determination of the plane-strain fracture toughness requires a specimen whose thickness exceeds some critical thickness (B). Testing has shown that plane-strain conditions generally prevail when:
B is the minimum thickness that produces a condition where plastic strain energy at the crack tip in minimal
KIC is the fracture toughness of the material
σy is the yield stress of material
When a material of unknown fracture toughness is tested, a specimen of full material section thickness is tested or the specimen is sized based on a prediction of the fracture toughness. If the fracture toughness value resulting from the test does not satisfy the requirement of the above equation, the test must be repeated using a thicker specimen. In addition to this thickness calculation, test specifications have several other requirements that must be met (such as the size of the shear lips) before a test can be said to have resulted in a KIC value.